THE MECHANICS OF MUSIC



The Mechanics of Music
Copyright © 1970,2005-2006 Jack Sirulnikoff, All rights reserved
(Note: where sounds are used, they are MIDI (.mid) files)


Introduction

This book is basically a classroom method, intended for students at the senior secondary school or junior college or university level, who have had some experience in music but little or no organized theoretical training. It is suggested that it be produced with separate teacher's manual and student's book, but that the teacher's manual should contain all the material so that it could be used for individual study. The basic aim of the course is to provide students with an insight into all the technical elements that go into the production of a musical composition. It is assumed that when the material is presented, it will be illustrated at various points by the piano, voices, and, in later sections, by autoharp and wind instruments.

Since no two classes are alike, nor indeed are all students within one class alike, the amount of time devoted to ­ any one portion of the course would be determined by the teacher, but it is suggested that all material be covered, if only in a superficial fashion. The necessity for augmenting or occasion­ally omitting the given exercises would also be determined by the needs of a particular class and teacher. The entire length of a course utilizing this text might take one or two years depending upon students' ability, size of classes, number of periods per week, etc.

Table of Contents
I. Notation: a detailed and organized description dealing with almost all notation that might be encountered anywhere by the student. It is divided into the following sections:
(a) Pitch - including the understanding of octaves, enharmonics, etc.
(b) Rhythm - including the understanding of simple and compound time.
(c) Tempo.
(d) Dynamics.
(e) Articulation - including most generally understood articulations, but not dealing with specialized forms such as string bowings.
(f) Ornaments, abbreviations, and expression marks.

II. Scales, intervals, and chords: this section deals with musical ingredients which might be used as the basis of a composition. The material is presented in as logical a sequence as possible, and it is suggested that piano and particularly voices be used to illustrate all the elements. Although all the traditional material is dealt with in this section, the approach (as it is in the whole book) is analytical and deductive and includes the possibility of invention of new scale forms, and little experiments in composition. There is a small amount of ear training included throughout the book, but this is, of course, limited, as that would constitute an entirely separate course.

III. Harmony: this section does not purport to be as thorough as the two previous parts, and, its main aim is to provide students. with an understanding of the concepts inherent in these aspects of music. There are two approaches to the harmony, and they are presented in juxtaposition and intermingled, rather than as two separate areas. One is a study of SATB writing as found in the Bach chorales, involving analysis and harmonization of chorale melodies. Diatonic triads and seventh chords in major and minor keys, chord progression, voice leading, non-chord tones, and modulation to related keys are covered. All work should be played on the piano and sung in four parts. Worked in with the study of Bach chorale harmony are exercises for selecting triads and dominant seventh chords to accompany simple tunes. The students are encouraged ­ to do this type of harmonization partly by ear and partly by logic, and to play their own work on autoharp or piano (block triads, root position, left hand).

IV. Arranging (Studies in texture): the work in harmony is later related to writing simple piano accompaniment patterns for the songs, and arranging the chorales for various combinations of wind instruments. Since the playing of wind instruments is very common in schools and colleges today, this type of workshop is very feasible.

Ranges, transposition, technical limitations, and dynamic levels within one instrument or between several instruments are dealt with, as well as combination possibilities. However, actual experimentation in sound is the essence of this study. The ensemble arrangements can then be correlated with basic training in conducting, having the students conduct their own work.

V. Melody writing (studies in form): Wherever feasible, original work by students is encouraged.

I have taught this course or portions thereof at both secondary school and Teachers College, and have found it to be very successful. Where larger numbers of students are involved there are problems which must be solved in regard to handling assignments, but there are also advantages in having a larger number of voices and instruments available.

Index

Part One
NOTATION



Figure 1

Is that music? No, it is merely musical notation. The music itself can only exist in sound. Click for computer example. (If the player control covers the graphic, it can be moved or minimized). However, musical notation is extremely important to performers and conductors. Its primary purpose is to convey as clear and complete a picture as possible of the composer's musical intentions. In recent times, some composers have taken to creating electronic music - that is, music that is produced directly on magnetic tape or on a computer hard drive, often without the use of any conventional instruments, and, therefore, without the aid of performers. Since the composer shapes the sounds in his composition directly, working in a manner similar to that of the sculptor, notation may not be necessary except as a plan for himself, or as a guide for a technician who may be required in performance. Nevertheless notation of all types of music is also very useful as a permanent record on paper for musicians who wish to preserve and study the many technical details of a musical composition.

The notation used by composers and arrangers of today tends to be more complex than it has been in the past. There are two reasons for this: (a) modern music is often very complex, and therefore requires complex notation; and, (b) the composers and arrangers desire to provide the performers with as precise and specific a guide as possible. (Interpolation regarding early notation which provided performers with only a rough guide to the music which was essentially learned by rote. Throughout the centuries the tendency has been to make the notation provide a more and more detailed guide for the performer.)

What are the various elements of music which must be clearly notated before a performer can render the music correctly in sound?
(a) PITCH - the exact sounds as produced both consecutively and simultaneously.
(b) RHYTHM - the relative duration of each pitch and the regular recurrence of each stress or ACCENT.
(c) TEMPO - the speed of the basic underlying pulse of the music.

With full knowledge of the above three ingredients, the music can be performed in a rather "raw" or unpolished manner. However, other information is necessary before a more polished, subtle, or "musical" performance can be given. What is it?

(d) DYNAMICS - the relative loudness or softness of the pitches at any given moment.
(e) ARTICULATION - the special means by which each pitch is sounded.

Beyond this, the composer can convey some idea of the emotion or mood he wishes to evoke by means of words, but there still remain the intangible elements of "style" and "feeling" which only the most sensitive and experienced interpreters can produce.

Another aspect of notation which has almost no relevance to the actual musical performance one hears, but which is very necessary and important information for the performer, is the meaning of the great variety of abbrevia­tions which are in common use, and which serve merely as shorthand or paper-saving devices.

Let us now proceed to an investigation of the manner in which the various musical elements are notated.

Index

(a) PITCH

A musical sound, or pitch, is differentiated from other sounds by the fact that it is definite and can be measured according to the number of regular vibrations it produces in the air. A relatively small number of pitches is used in conventional music. A piano has eighty-eight keys, and can therefore produce eighty-eight pitches. Very few instruments in common use can produce pitches that are not available on the piano.

The following chart of the piano keyboard indicates the range of sounds available to some other instruments in comparison to the piano. (Play the extreme notes of the ranges of the instruments referred to on the chart.(Click for example) )


Figure 2

Each of the white and black piano keys is connected by a mechanism to a small hammer which strikes metal strings in order to produce the sound. Note that the lowest sounds are produced on the longest strings and the highest sounds on the shortest strings. The longer the string, the fewer the vibrations per second, and the lower the pitch; the shorter the string, the more frequent the vibrations, and the higher the pitch. Each of the eighty-eight pitches of the piano is relatively equidistant from its neighbor, and therefore each string has to be "tuned" to the correct tension so that each pitch is exactly correct. Consequently, if we move along the piano keyboard from left to right striking all the white and black keys in order, we will cover the complete range of pitches available to practically all instruments, from the lowest to the highest. (Demonstrate by playing chromatic scale.Click for example)

Let us now examine an example of musical pitches, and see how it corresponds to the actual piano keyboard.


Figure 3

What points do you observe?

Expected answers and teacher's elaborations:
1. Highest sounds occupy the highest locations, and vice versa for the lowest.
2. NOTES - oval shaped symbols represent the pitches.
3. STAFF.- five lines, four spaces, used for positioning notes. Two staves are needed for piano music because of its wide range of sounds, but most instruments use only one.
4. LEGER LINES are required to accommodate some pitches which exceed the bounds of the staves. These should be thought of as simple extensions of the lines and spaces of the staff.
5. Notes which occur on the same lines and spaces of the different staves are actually different sounds. How are these pitches differentiated in notation?
6. By means of CLEFS. These clefs, which are located on the extreme left of the staff, give specific pitch values to the lines and spaces. is called a TREBLE clef and is called a BASS clef.
7. Some notes are preceded by symbols and . You will notice that these affect the pitch of the notes which follow. is called a FLAT; is called a SHARP. is called a NATURAL, and this symbol is used to cancel out the effect of a sharp or flat.
8. A single pitch can be notated in more than one way.
9. The note which is on the first leger line below the treble staff, and the one on the first leger line above the bass staff are actually the same pitch.

The Naming of Notes
As a convenience for verbal reference, all of our pitches have alphabetical names. The musical alphabet extends only from A to G. You may have noticed that our treble and bass clefs actually bear a faint resemblance to the letters G and F, and they consequently give the letter name which they resemble to the line which in each case; they appear to encircle. Therefore the name of the second line from the bottom on the staff containing the treble clef is called G, and the name of the fourth line from the bottom on the staff containing the bass clef is called F.

You may wonder how eighty-eight sounds can be accommodated by only seven names. Well, first of all, these seven names refer only to the fifty-two notes which can be sounded by pressing the white keys. Secondly, only seven letters are required because many notes are given the same name.

The Octave
Is there any special relationship between two notes called A, or between two E's? Yes. Although they are still two different pitches basically, two notes with the same name do have a very special close relationship. When one produces a musical sound, and then proceeds to produce another at exactly twice as many vibrations per second, one finds that the second note sounds very much like the first, but at a higher level. (Demonstrate.Click for example) This is the closest thing there is to simply repeating the same note. The distance between these two pitches is known as an OCTAVE, and both notes of the octave are given the same name.

Within the distance, or interval, of an octave we find twelve different pitches, and each of these pitches can be reproduced one or more octaves higher or lower by doubling or halving the number of vibrations for each octave change. For example, a sound which is produced by 440 vibrations per second is A, and one produced by 880 vibrations is also A. The same name would apply to pitches of 1760, 220, and 110 vibrations per second. They are all called by the same name, and are very closely related in sound, but it is important to emphasize that they are still different pitches.

Now let us return to figure 3 and try to name all the notes. Remember that the treble clef gives the name G to the second line, and the bass clef tells us that the fourth line is F. Both of these are specific pitches, not any G or F, and this is what they sound like. (Demonstrate.Click for example) With this information we can follow a very simple and logical rule for the naming of notes.

Rule:
­ From any known letter name, moving from bottom to top, and alternating lines and spaces, apply the alphabetical names from A to G to these lines and spaces in order. When you reach G, start again at A on the next line or space. This rule applies not only to the lines and spaces of the staff, but also to the leger lines and the spaces between them, and is consistent no matter what clef is used. If you wish to name notes below a known letter name, follow the same procedure but count backwards through the alphabet. Now look at figure 3 and name all the notes from left to right.
Probable answer:­- G F C A A A D B C D
This answer is only partly right. Do you remember that only the white key pitches are referred to by simple letter names? We have some notes here that are played on black keys, and you notice that these are preceded by the sharp and flat symbols ( and ). They are obviously different sounds from the white key notes located on. the same lines and spaces and therefore they must have different names. Our fifth note is on the space A, but, because it is preceded by a flat, it is called A flat. The next note is just ordinary A, and the natural sign () is used to signify that the flat no longer applies. The next note is called A sharp. Let us now name all the notes correctly.

Answer:­ G F C E Ab A A# D Bb C# Db .

Sharp, flat, and natural symbols, when used with a particular note, are called ACCIDENTALS.

The Semitone
We have already mentioned that within an octave there are twelve different pitches, each approximately equidistant from its neighbor. This, the smallest distance, or INTERVAL, possible between any two musical pitches, is known as a SEMITONE. Let us listen to the interval of a semitone as it occurs between different notes. (Demonstrate.Click for example) You will notice on the piano keyboard that although in most cases semitones occur between white and black keys, at certain points you find two adjacent white keys, and they are also a semi tone apart in sound. (Demonstrate.Click for example)

Returning to our musical example, how can we describe the difference in sound between an A and an A#, and an A and an Ab ?

Answer: ­ An A# is a semitone higher, and an Ab is a semitone lower than A.

Therefore, the effect of a is to raise any pitch by one semitone, and the effect of a is to lower a pitch by one semitone.

Enharmonics
We have noted that it is possible for one pitch to be notated in more than one way (see figure 3), and to have several names. This is a very confusing phenomenon which is nevertheless characteristic of music theory, and which occurs not only in regard to single notes, but also in connection with the naming of note combinations. For the moment, let us merely accept this phenomenon, and as we progress in our studies we will find that there is some justification for calling a pitch C# on one occasion, and calling the same pitch Db on another.

What we can do, however, is explore the variety of names possible for the twelve semitones within the octave. We know that a sharp will raise a note by one semitone, and a flat will lower a note by the same amount. We know that Ab is a semitone lower than A. However, this same pitch, Ab, is also a semitone higher than G. Therefore, it might also be called G#. By the same token, A# is a semitone above A, but if you check the piano keyboard you will find that it is also a semi tone below B, and A# could just as easily be referred to as Bb. When we refer to the different notes which represent a single Pitch, such as F#-Gb, or G#-Ab, we call these ENHARM0NIC notes. For instance, Db is the enharmonic note of C# and vice versa. Enharmonics are also possible between two adjacent white keys. The enharmonic of B# is C, and the enharmonic of Fb is E. Figure 4 is a diagram of one octave of a piano keyboard, indicating all the notations possible for each of the twelve pitches.



Figure 4

Examination of figure 4 reveals two new symbols which have not yet been introduced. They are the double sharp () and the double flat (). These symbols operate exactly as their names suggest they might - by raising or lowering a given note two semitones. Gx , for example, raises the note G two semitones, and is the enharmonic of A and Bbb. Gbb lowers the pitch of G two semi tones, and is the enharmonic of F and E#. These two symbols are much more rarely used in music than the ones previously dealt with, but there is a theoretical justification for their use, and they should be understood.

The C Clef
Various clefs are used in the notation of music, and the reasoning behind the use of any clef is the elimination, as much as possible, of the need for leger lines. The piano uses treble and bass clef, and these can accomodate all but the extremely high and low notes. Most instruments use a single clef. Bass clef is used for instruments that play mainly low pitches, and treble clef is used for those that play in a higher range. (There are exceptions to this which will be discussed in the section on arranging.) However, some instruments, because their range falls somewhat in between high and low, will have their music notated, at least part of the time, on a clef other than treble or bass. Again, this is to avoid the excessive use of leger lines.

The clef that is used to accommodate ,these middle range sounds is called the C clef, and it indicates the location of the note middle C. Middle C is the note approximately in the centre of the piano keyboard, and it is the third note of figure 3. The C clef can be placed in various locations on the staff so that middle C could fall on any line, but the two most common uses for this clef are middle C on the third line (called ALTO clef) and middle C on the fourth line (TENOR clef). The alto clef is used mainly for the viola, a middle range string instrument, and the tenor clef is usually used for the higher notes of low pitched instruments such as cello and bassoon. Figure 5 shows the placement of the single pitch, middle C, using treble, bass, alto, and tenor clefs. Note the design of the C clef, which encloses whatever line is selected as middle C.


Figure 5



EXERCISES

1. Name all the notes in the following passages, and be able to play them on the keyboard.



2. Re-write the following passage at the exact pitch using alto, tenor, and bass clefs:



3. Notate all the enharmonic possibilities of each of the following notes:



4. (a) What does the word 'interval' mean ?
(b) Name two intervals mentioned in the preceding section.

5. Define the following in your own words and notate an example of each:
(a) staff
(b) clef
(c) sharp
(d) flat
(e) double sharp
(f) double flat
(g) leger lines
(h) octave
(i) semitone
(j) enharmonic notes

Index

­

(b) RHYTHM

Rhythm is a term which is a problem to define, as it tends to have different meanings for different .people, and when used in connection with different kinds of music. For example, in connection with jazz or folk music the word "rhythm" is often used in a particular sense. This meaning is so limiting that it implies that there is some music which has no "rhythm" at all. We will not accept this definition of the word, but will define it as an element present in all music.

Rhythm, therefore, is the relative length and shortness of the individual pitches which are combined over a given period of time in a particular composition. In other words, the rhythm of a piece of music is the horizontal pattern produced by the combination of long and short sounds which is set against the up and down, or vertical, pattern of the pitches. The relative length or shortness of any sound is determined by the continuous and steady underlying pulse, or beat, of the music, which is not necessarily heard, but. which is nevertheless always present. (Elaborate on the meaning of pulse or beat - e.g. clock ticking, heart beat, etc.. In a given piece of music the beat may be different as performed by different people, but the rhythm should be identical.)

How is the rhythmic pattern notated? We have seen the oval-shaped symbols (notes) which are used to notate pitches. These same notes are also used to indicate rhythmic values by the use of certain alterations:

WHOLE NOTE, or semibreve; the longest individual note value in common use.
HALF NOTE, or minim: half the value of a  
QUARTER NOTE, or crotchet: half the value of a 
EIGHTH NOTE, or quaver: half the value of a 
SIXTEENTH NOTE, or semiquaver: half the value of a 
32nd NOTE, or demisemiquaver: half the value of a 
64th NOTE: half the value of a 
Occasionally, usually in older music, we encounter the BREVE  , which has twice the value of a  
The following chart indicates the note value relationships in another way, and describes the parts of a note.


Figure 6

Notes containing flags may be written separately or may be joined together in various groupings. Study the example below of the notation of various note values on the staff.


Figure 7

Points to note:
­ 1) Stems which go up are placed on the right side of the head, and those going down are placed on the left.
2) When note heads are above the third line the stems go down; when below the third line the stems go up; when on the third line the direction is optional. When a series of notes crosses the third line, the majority will determine the direction of the stems.
3) When notes with flags are joined, the angle of the flags follows the angle of- the note heads.
4) Leger lines are used only to the point where they are necessary.

Now that we know how to notate pitches, and have accumulated a fine collection of rhythmic values, do we finally have sufficient material with which to set down any melody? Let us sing and then study the following familiar melodies and note the points we have not yet covered.Click here for example


Figure 8

Points noted and elaboration:
­ 1) TIME SIGNATURE - signifies the METRE of the music. The metre consists of a steady throbbing pulse onto which is superimposed regular recurring accents. The most common metres in music are those which contain groupings of two, three, or four pulsations; that is, music in which every second, third, or fourth pulsation receives an additional stress or accent. Let us clap a few measures of music in three or triple metre: 

The time signature, as noted in our example, consists of two numbers, but they are not a fraction. The top number indicates the number of pulsations in each grouping, and the bottom number specifies what note value is equal to one pulsation in this music. This little rule will have to be modified later, but for the time being we will let it stand. In our example, this means that there is the value of three quarter notes in every grouping, or that the first, fourth, seventh, tenth, etc., pulsation will be stressed or accented in performance. Often the word "beat" is used as a synonym for "pulsation".

2) BAR LINES - vertical lines outlining the metre which has been specified by the time signature. One complete grouping of the metre (the space between the bar lines) is called a BAR or MEASURE. The first note immediately following a bar line is normally stressed or accented.

N.B. Although this is unrelated to rhythm, it should be noted that a bar line in notation serves the additional function of cancelling out the effect of any accidental in a previous measure.

Although every measure of music in 3/4 metre (or 3/4 time) contains the value of three quarter notes, that does not mean that there must be three quarter notes in every measure. This point should serve to clarify the difference in meaning between the word "rhythm" and the word "metre".

Clap the metre of our example:
­
Clap the rhythm of our example:
­

Definition:­ The rhythm is the pattern of long and short note values over a period of time; the metre is the under­lying regular pattern of accented and unaccented pulsations over the same period of time.

3) DOT - this is one means of increasing our store of note values. When a dot follows a note, it increases its value by one half. For example, () and (). Sometimes two dots are used after a note, and the second dot has the value of one half of the first dot, ().

() may be notated () or (). ­ The curved line joining two notes of the same pitch is called a TIE, and, when it is used, the two notes are played or sung as a single note of the combined value. This curved line is used in various ways in musical notation, so it is very important to remember that it is a tie only when it joins two notes of the same pitch.

Let us now sing, and then analyze our next example for other rhythmic features (Click here for example):­


Figure 9

Points noted and elaboration:
­ 1) New time signature - . This tells us that there are four pulsations to each measure, and that a quarter note is equal to a single pulsation. Let us clap several measures of this metre. Do not forget to accent the first of each measure.

Do you think that the second, third, and fourth beats should naturally receive exactly the same stress? The third beat seems to require a slight emphasis, and so our 4/4 metre actually works out this way:

Let us clap a few more measures of this metre.

2) Grouping of eighth notes. Eighth notes (and all other notes with flags) can be connected, and this is usually done in instrumental music. In vocal music they are separated to coincide with each syllable of the text. However, it is very important that these notes should be grouped together properly when connected. In this case they are in four groups of two so that each beat of each measure is clearly separated. (Actually this is vocal music, but the stems are joined to illustrate this point.) Eighth notes in 4/4 time may sometimes be joined in groups of four across the first and second or third and fourth beats, but not across the second and third beats. Since the second beat is weak and the third beat is fairly strong, they should be clearly separated.

3) The REST. We notice this symbol () which is a quarter rest, equal in value to a quarter note. Silences are as important as sounds in music, and therefore there is an equivalent rest value for each note value. These are illustrated on the following staff:

­


Figure 10

Note particularly the placement of whole rests and half rests.

4) The TRIPLET (). The grouping of three eighth notes in the value of one quarter note is another way of varying the rhythm of the music. You will observe that in this metre the basic beat is the quarter note which subdivides­ naturally into multiples of two. However, it is possible to subdivide it into three (or any other odd number) provided that this is clearly indicated in the notation. This rhythm ( ) is performed in the value of one quarter note and therefore each note in the triplet has slightly less value than an ordinary eighth note. The following is an example of combinations of notes of decreasing value, all equal to one quarter note:

­


Figure 11

Try clapping this rhythm, but keep the pulse steady (Click here for example):

­

It should be noted that multiples of two and three are the most commonly used and most natural subdivisions of beats and measures.

However, like the quarter note, the half note may also be subdivided in various ways. If it is subdivided into three, the following notation is used: . Try this two part rhythm exercise (Click here for example):

It is fairly difficult, so you need not worry if you cannot quite get it, but it should serve to illustrate the tremendous possibilities for rhythmic variety in music. Whereas the pitch limitations we have are dictated both by the instruments available and the human ear, the rhythmic limitations are governed only by whatever human factors might prevent their comprehension and reproduction.

5) The PAUSE or fermata (). This symbol over any note gives that note an indefinite value, and its length is left entirely up to the judgement of the performer or conductor.

6) The UP-BEAT or anacrusis. Not all music starts on the strong first beat of the measure. Sometimes there is a weak beginning, which might consist of any portion of a measure, and the feeling of metre does not really begin until we reach the first beat of the first complete measure. The note or notes which lead up to this beat are called "up-beat" or "anacrusis". When there is an up-beat at the beginning of a piece, the last measure is always incomplete, and its value plus the value of the up-beat would equal the complete measure. (You might sing the example again, or other examples, to notice the effect of an up-beat on the feeling of the music.)

7)  is new in appearance, but it should be readily understood.

Let us now sing this next familiar tune (Click here for example):


Figure 12

­

New points for discussion:
­ 1 ) 6/8 time. What should this time signature mean'? (Six beats to a measure, and an eighth note equals one beat.) Let us sing this again; and this time clap the   beat as you sing. Does this feel natural? (No. ) Let us sing this again; and now clap the beat as you naturally feel it. (The result should be a clap on the first and fourth   of every measure.) We find that, instead of six, there are only two beats in every measure. What note value equals one beat? ( ). So we find here an example of a time signature that does not follow our original rule for interpreting time signatures. A more accurate way of notating the metre might be ( ).

2) Subdivision of the beat. How can the beat be equally divided in 6/8 time? (In three's or multiples of three.) So we find that the beat here naturally divides into three eighth notes, whereas in 4/4 time we found that when we wanted to subdivide the beat into three, it was unnatural to the metre and had to be marked specially as a triplet. Conversely, if we wished to subdivide the beat in 6/8 time into two or multiples thereof, we should have to mark it specially as a duplet () or a quadruplet (), etc.. We find, therefore, that we have essentially two basic kinds of metre:
­ a) That in which the beat subdivides naturally into multiples of two - SIMPLE TIME.
b) That in which the beat subdivides naturally into multiples of three - COMPOUND TIME.

Perhaps a comparison of the following examples will emphasize the difference between simple and compound time.


Figure 13

What points do you notice? The note values are identical, but they are grouped differently. The eighth notes are grouped so that the beats in each measure are clearly separated. Even though the note values are the same, what will be the difference in performance? The number of beats in each measure, the natural accents, and the comparative duration of each beat will be different. However, the difference in sound between the two examples will be very subtle. (Click here for the 3/4 example)(Click here for the 6/8 example)

Let us try to clap each of these examples, maintaining equal duration for the note values in both examples, but emphasizing the difference between the two metres. (This is rather difficult to achieve perfectly without the aid of a metronome. For example, if you clap the 3/4 example at a speed of   = 60, then the   in the 6/8 example should equal mm 40. If the   = 90, then make the  =60.)

This subtle difference in the effect of these two examples reveals to us the fact that each of these two metres belongs to a different basic category. In 3/4 time, there are three beats in each measure, the beat is equal to one quarter note and subdivides naturally into multiples of two. In 6/8 time, there are two beats in the measure, the beat is equal to a dotted quarter note and subdivides naturally into multiples of three.

Rule:­ Any metre in which the beat subdivides into multiples of two is called SIMPLE time. Any metre in which the beat subdivides into multiples of three is called COMPOUND time. Note that in compound time the beat ­ ­ is always represented by a dotted note.

Notes with flags are usually grouped or joined together to coincide with the beat, and therefore eighth notes in simple time will usually be grouped in two's, etc., and eighth notes in compound time will be grouped in three's,   etc..

Let us now draw up a chart which will organize for us fully all metres (time signatures). The two basic categories are simple and compound. Within each of these categories we shall have secondary categories specifying the number of beats in the measure. If there are two beats in the measure the music is in DUPLE time, three beats will be TRIPLE time, and four will be QUADRUPLE time. These are the most common and natural metres, but music based on odd metres containing five and seven beats is certainly not unknown, and is actually quite prevalent in modern music. Th se metres, however, can simply be considered combinations of duple and triple or triple and quadruple metre. This will depend entirely on the composer's intention, for he may actually want his music to have a quintuple or septuple feeling with the first beat accented and the remainder unaccented, for example,   etc..

Here is the chart of the more common time signatures:­


Figure 14

3/4 and 3/8 are somewhat ambiguous, since much music in these metres is taken at a speed which, in effect, represents one compound beat to a measure. Note the optional, and commonly used, ways of writing 4/4 and 2/2. The top number of any metre usually provides the quickest clue to its category.

Further points on grouping and rhythmic notation:
­ 1) The main objective in the grouping of eighth notes (or other notes with flags) is to make the music as clear as possible to the performer.
2) As a general rule, separate the beats.
3) In simple quadruple time the notes are sometimes joined for half a measure, e.g. .
4) As a general rule, do not group the notes from a weak beat over a strong beat, e.g. .
5) However, exceptions do exist in order to emphasize a particular rhythmic pattern, and, in some instances, for this purpose, notes have even been grouped over a bar line, e.g. . However, this is to be avoided in theoretical work.

6) In some music the normal accents are deliberately shifted so that the stresses are constantly occurring on weak beats, or on the weak parts of beats. This phenomenon is called SYNCOPATION and is very prevalent in jazz. This music is generally notated to emphasize the phenomenon:



instead of

Actual jazz not only abounds in syncopation, but the style of performance is such that the music is not really played exactly the way it is notated.

In the following figure (Fig. 15), A is a typical example of a jazz rhythm and it is essential to jazz musicians who are accustomed to reading and playing these rhythms that they be notated in this syncopated manner.

Example B is the same rhythm as example A, but notated in an academically correct manner. This would imply a "straight" performance of it rather than a jazzy one.


Figure 15

Try clapping the above examples.
7) These exceptions to normal grouping are rarely found in music in compound time.
8) Careful observation of a variety of music will clarify usual procedures and exceptions in rhythmic notation and the grouping of notes.

­


EXERCISES

1 . Categorize the time signatures of the following examples, and indicate by numbers (1, 2, 3 etc.) the location of the beginning of each beat in every measure:

2. Re-group the following according to the normal rules of grouping:
­

3. Complete the following bars with rests:

4. Re-write the following measures correcting all errors in pitch and rhythm notation:

­ 5. Define in your own words:
­ rhythm; metre; beat; simple time; compound time; tie; dot; triplet. ­

Index



(c) TEMPO

We have now dealt with most aspects of pitch and rhythm. Is this information adequate for a group of performers to enable them to give a proper if perhaps rough performance of the music? Not really. A TEMPO must be established for them. In this way, they start together, end together, and all perform according to the same basic pulse or beat. TEMPO refers to the speed of the pulse, and, in ensemble performance, this is usually provided by the conductor. If all players do not feel the same basic pulse, it is impossible for them to perform the music correctly.

This does not imply that tempo is unimportant to the solo performer. It is also very necessary for him, because it serves another and perhaps more important purpose. All music is composed with a definite tempo in mind, and, if it is performed with a pulse slower or faster than that intended, the character of the music will be changed. This is not to say that there is no leeway in matters of tempo, particularly in more romantic types of music. Different performers may interpret the same music differently and hence there may be variations in the tempo employed, but generally these variations are bound to be very slight.

Having established the importance of tempo, let us now see how composers provide this information. Two basic methods are employed, one more exact than the other. The precise way to indicate tempo is by means of a metronome mark. The metronome, a device first used in Beethoven's time, is a mechanical or electrical means of showing or sounding a steady pulse at any adjustable rate. One merely sets the desired speed, and the metronome gives an exact and steady rendering of this speed. Although a very useful device for practice, the metronome is actually too regular and mechanical for performance where slight and subtle deviations from the pulse are often desirable to humanize the musical performance and allow the music to breathe.

The metronome mark, as often indicated on a musical manuscript, refers to the number of pulsations per minute. For example,   = 60 means that the pulse rate of this music is sixty quarter notes per minute, or one per second. A typical march tempo would be   = 120. In compound time, the speed of the dotted note beat is usually given, for example,   = 96. In 3/4 waltz time where the main pulsation is usually one beat per measure the speed of the   would be indicated. Experienced performers and conductors can usually look at a metronome mark and instinctively perform at the correct tempo without actual recourse to the metronome itself.

In addition to the metronome mark, and, more frequently, in place of it, words are used to indicate tempo. This is a slightly more subjective method, and the word indication is more approximate, depending to some extent on the style of music to be performed. It is only through considerab1e experience with various musical styles that performers gain the ability to interpret verbal tempo indications, although there is always some divergence of opinion in these matters. Tempi are frequently indicated in the language of the composer, but Italian is the universal musical language and it is mostly Italian terms that are in use.

The following is a list of Italian terms commonly used in reference to tempo. Sometimes a term refers exclusively to matters of speed, and sometimes it also carries with it connotations regarding the character of the music.

				Very slow to slow
				Larghissimo
				Largo
				Larghetto
				Grave - slow and solemn
				Lento - slow and sad
				Adagio
				Adagietto

				Medium
				Andante - moderate walking pace
				Andantino
				Moderato

				Fast to very fast
				Allegretto
				Allegro
				Vivace - vivacious, lively
				Veloce
				Presto
				Prestissimo
				  
			   Changing tempi
			   accelerando (accel.) - gradually faster
			   ad libitum, or, a piacere - freely, at pleasure
			   allargando (allarg.) - gradually slower and broader
			   a tempo - return to the original speed
			   calando - gradually slower (and softer)
			   doppio movimento - at double the pace
			   l'istesso tempo - at the same speed
			   meno mosso - slower
			   piu mosso - faster
			   rallentando (rall.) - gradually slower
			   ritardando (ritard.) - gradually slower
			   ritenuto - at a steady pace, but slower than the preceding tempo
			   rubato - freely; lengthening certain notes at the expense of others
			   stringendo (string.) - gradually faster

			   General terms
			   alla marcia - march tempo
			   tempo di valse - waltz tempo


EXERCISES

1. Specifically, what does the metronome mark indicate?
2. Memorize the meaning of all the Italian terms.
3. Sing or play a piece of music in different tempi to note the differences of effect.

Index



(d) DYNAMICS

We now have sufficient information in notation to render a work accurately. However, if there were nothing more to a performance than the correct pitch, rhythm, and tempo, the music would often sound dull and lifeless. Other subtleties must be brought to bear on the performance. . An important aspect of musical shading is the contrast produced in volume - the relative loudness or softness of any given moment of a work. Sometimes the change is sudden, sometimes it is gradual, sometimes it is taken to extremes, sometimes the volume is deliberately held constant through lengthy passages. Musical shading achieved by changes in loudness and softness is known as DYNAMICS. Whatever the use of dynamics, it adds infinite contrast, variety, and interest to a musical performance, and the artistic use of dynamics is an important measure of a performer's skill.

Dynamic indications in music must be carefully handled by the performer in terms of the dynamic range of the entire composition, in terms of the style of the music being performed, and in terms of the instrument for which it was written. Certain instruments and certain registers of individual instruments are naturally loud or soft in a relative sense. Therefore, any change in dynamics will also be relative according to this situation, and a loud passage by one instrument will automatically be much louder than a "loud" passage on an essentially softer instrument. When a variety of instruments is used in combination, the interpretation of dynamics becomes even more complex, and the success of the total effect will depend to a large extent on the skill of the composer or arranger and the "balancing" skill of the conductor and performers. However, this aspect of dynamics will be dealt with more fully in the section on arranging. For the moment let us concern ourselves with the general meaning of the most commonly used words and symbols which refer to dynamics.

	Soft to loud
	pianissimo (pp) - very softly. (ppp means almost a whisper)
	piano (p) - softly
	mezzopiano (mp) - medium soft
	mezzoforte (mf) - medium loud
	forte (f) - loud
	fortissimo (ff) - very loud. (fff means extremely loud)

	Changing dynamics

An interesting sidelight in our study of dynamics is that the piano received its name (pianoforte) because it was the first keyboard instrument on which it was possible to change the dynamics gradually and effectively during performance.

	Terms and symbols used to indicate changing dynamics
	crescendo (cresc. or ) - gradually becoming louder
	diminuendo (dim. or ) - gradually becoming softer
	decrescendo (decresc.) - same as diminuendo
	morendo - becoming softer and slower; dying away
	calando - same as morendo
	fortepiano (fp) - loud, then suddenly soft



EXERCISES

1 . Memorize the meanings of all terms relating to dynamics.
2. Sing or play a piece of music correctly in pitch, rhythm, and tempo, but at a steady mf dynamic level. Then add the proper dynamic changes.
­

Index



(e) ARTICULATION

In vocal music articulation generally refers to the proper and effective rendering of the words. This involves all the subtleties of enunciating consonants and vowels to produce the most musically and interpretively effective performance. However, this type of articulation is not usually indicated in notation.

Articulation also refers to the various ways in which musical pitches can be sounded. Let us consider first the various instruments (including the voice) which produce musical sound. Each requires a unique physical approach to set a string (or vocal chord) vibrating, or to set off a vibrating column of air. Many forms of attacking a note are possible on these instruments, from drawing, bouncing, or hammering a bow, plucking a string or striking a key, to various uses of the tongue, the lips and the jaw on a wind instrument. We will not deal here with those articulations which are unique to particular instruments, for that falls rather into the province of arranging.

However, there are certain forms of attacking and sustaining pitches that are common to all instruments, and it is these that we shall elaborate in the following chart. Each articulation is displayed in notation, and then given a name, and explained in words.

  legato (slur)
Play the music smoothly.
This symbol is the same as that used for a tie, but it joins only notes of different pitch values.

  staccato
Play the music short and crisp.
This is sometimes interpreted as meaning: give each note half its value, but in practice, the shortness will depend upon the style and tempo of the music.

  marcato
Accent (stress the attack on the note).

  marcato
Heavier accent.

  sforzando (fz or sfz)
Very heavy accent.

  tenuto
Sustain the note for its full value. (This sign is sometimes used to indicate a slight accent in a generally smooth passage.)

  mezzo-staccato or portato
A gentle attack, and slight shortening of each note value - a throbbing effect.

These are the principal symbols and terms of articula­tion, although many more exist in connection with individual instruments. Like dynamic marks, articulation symbols are subject to interpretation according to the style and character of the music. A simple accent sign ( > ) may refer to a heavy stress in one situation and a very slight stress in another. Similarly, staccato dots may require the notes to be extremely short in one composition and only fairly short in another. Sometimes a tenuto symbol will mean a slight accent. The Italian term "marcato" means "with a clearly marked rhythm", and a passage with an occasional accent will not necessarily be marcato, whereas a marcato passage could be indicated by means of the word and not necessarily contain any accent symbols. A note without any articulation symbol or verbal direction will generally be played either like a tenuto or a mezzo-staccato according to the nature of the music.



ASSIGNMENT

Sing or play the following melodies, and then indicate what you feel is the proper tempo, dynamics, and articulation:

1.

2.

3.



.

Index

(f) MUSICAL ABBREVIATIONS

Musical notation is a very time consuming and often tedious task. Therefore, composers have devised various methods over the years to lighten the load by eliminating as much as possible any unnecessary writing. This is done by means of words or symbols which are a sort of musical shorthand. Of course, the use of these terms has no effect whatsoever on the ultimate performance of the music.

Here are the most common examples:

­

  This means:- repeat the section between the dots. If this-repeat sign is encountered and no similar sign facing it was passed, repeat the whole passage from the beginning.



  When a variation in the ending of a repeated passage is desired, this is the way it is indicated. Upon repetition, skip the first ending and play the second.





  This indicates:- repeat the previous measure of music. Any number of these repeat bars may be used consecutively.


  This means:- repeat the previous two measures.




When the music contains a series of repeated eighth or sixteenth notes they may be written in this manner:

­ Simply play repeated sixteenths or eighths for the value of the note.


  does not usually mean precisely to play repeated thirty-second notes, but is the notation for a tremolo most commonly identified with strings or percussion instruments. This requires a very very quick repetition of a note to convey a feeling of tension or suspense.


  This means a rapid alternation between two notes in sixteenth note values for the duration of a half note.



  This means a tremolo between two notes for the duration of a whole note.




D.C. al fine (Da capo al fine). Go back to the beginning and continue to the word "fine" (end).

D.S. al fine (Dal segno al fine). Go back to the sign   and continue to "fine".

A coda is a special ending to a composition and may be indicated by the Sign  . Instructions sometimes read D. C. al or D. S. al . In these cases proceed to the sign located somewhere in the music, and then jump down to the Coda located at the end of the music.

Traditionally, one does not repeat sections marked on a D.C. or D.S.

When a performer is required to rest for several consecutive measures, each measure is not written out, but the total is simply noted.   means five bars rest.

In operettas or other theatre music certain performers may not be used in an entire number. This is indicated on their parts by the word "tacet".

over a given passage means:- play that passage one octave higher.

 under a given passage means:- play that passage one octave lower.

Following the use of these symbols the word "loco" is often used as a reminder to continue the music exactly as written.

When a lengthy passage or an entire piece is to be performed with a particular articulation, often one or two measures of the notation of this articulation followed by the word "simile" indicates this fact. "Sempre staccato" means to play staccato throughout.



ASSIGNMENT

The following example contains many musical abbreviations. Re-write it in full notating exactly how it is to be performed.



Index

(g) ORNAMENTS

During the seventeenth and eighteenth centuries a whole series of standard ornaments evolved. These were conventional means of embellishing melodies and were well understood by the performers of the day. Therefore, they were simply indicated by certain standard notational symbols,   etc..

We will not go into these in great detail since they are not in common use today, since most editions of older music contain footnotes explaining their interpretation, and since this information may easily be found in musical dictionaries and other reference works. However, three of these are still used by composers today.

1) The trill, notated   means that the performer is to oscillate very rapidly between the indicated pitch and the pitch on the line or space directly above. In other words, it is a tremolo between neighboring tones.   or  means to sharp or flat the neighboring tone.

2) The grace note, indicated  , is a pitch that is attacked and left as quickly as possible on the beat so that a minimum of time is robbed from the main melodic note.

3 )  are groups of grace notes which are performed essentially in a similar manner to the single grace note.

Remember that these and other ornaments are merely embellishments which do not alter the basic melodic or rhythmic structure of the music, but they might affect its character.

Index

(h) MISCELLANEOUS ITEMS

The curved line used to indicate the tie and the slur is also sometimes used to indicate the phrasing of a piece of music, all the notes of the phrase being covered by this symbol. In vocal and wind music an apostrophe indicates where the performer is to take a breath (thus also more or less indicating the phrasing). A double bar line   . indicates the end of a composition. In longer works, sections are sometimes separated by this type of double bar,  . A fermata over a double bar,   also indicates the end of the music. This sign,  , indicates a relatively short break in the performance, where the pulse stops, and is again resumed. The letters GP are sometimes used when there is a grand pause, that is, when all performers have a simultaneous rest. Usually this would be used when the rest takes place during a stormy climactic section.

More Italian terms.
Composers try to aid the performers in matters of interpretation by means of verbal directions. Here are some common ones:

­
			agitato		-	agitated
			amoroso		-	lovingly
			animato		-	spirited
			appassionato	-	intensely; with deep feeling
			con brio	-	brilliantly
			con fusco	-	with fire; with energy
			cantabile	-	in a singing style
			dolce		-	sweetly
			expressivo	-	expressively
			giocoso		-	joyfully; jocosely
			grandioso	-	grand or noble style
			grazioso	-	gracefully
			leggiero	-	lightly
			maestoso	-	majestically
			pesante		-	heavily
			scherzando	-	playfully
			semplice	-	simply
			sostenuto	-	sustained
			tranquillo	-	tranquilly
			vivo		-	vivaciously

Miscellaneous terms:

			a capella	-	unaccompanied (choral music);"in the church style"
			assai		-	very
			attaca		-	continue on at once
			molto		-	much; very
			poco a poco	-	little by little
			seque		-	follow on at once
			V.S. 		-	turn the page quickly (volti subito)

Commonly used German and French terms:

			ausdrucksvoll	-	with expression
			einfach		-	simply
			lebhaft		-	lively
			sec		-	dry
			vif et gai	-	quick and lively

It is not recommended that students spend much time memorizing these terms. It is much more important that they be made aware of the significance of these words in relation to actual music and its performance.



ASSIGNMENT

Compose a melody approximately eight measures long, in any metre, and for any instrument or for voice. Do it entirely intuitively, using accidentals as needed, and notate it fully with regard to pitch, rhythm, tempo, dynamics, articulation, and interpretation. It will be judged solely on the basis of how accurately it has been notated according to the composer's intention.

Index



Part Two
BASIC MUSICAL MATERIALS

Now that we have investigated the notation of musical sounds, let us turn our attention to the actual sound materials which form the basis of musical compositions. One might define a musical composition as the end result of the organization of musical sounds over a given span of time. The basic elements of music are pitch and rhythm, and the framework within which these elements are organized is referred to as the FORM of the music. TEXTURE is also an important consideration in a musical work, and it refers primarily to the manner in which pitches are combined to produce fullness or thinness of sound, lightness or heaviness, and the nature of the basic flow or lack of flow in the music. We are also attracted to the COLORS of a work produced primarily by a variety of instruments used singly or in combination. In this section we will concern ourselves exclusively with specific patterns of pitch which form the basis of a large body of music.

(a) SCALES

A scale is a sequence of pitches based upon a definite pattern of intervals. All commonly used scales are organized within the framework of an octave, and can be produced at any other octave level. Because of equal temperament tuning (a system of tuning instruments, developed roughly during the time of J.S. Bach, in which the octave is divided into exactly twelve equal semitones), a particular scale may begin on any desired pitch. Scales move continuously in one direction, and the descending pattern of any scale is usually the reverse of the ascending pattern, although there are significant exceptions. Each tone in a scale which contains seven tones or less is usually given a different letter name.

Historically, scales were derived theoretically by the analysis of a large body of music. In other words, the actual music was written before the materials upon which it was based were necessarily fully analyzed. In more recent times this procedure is sometimes reversed, and the basic pitch materials are first organized in a scale or some other form, and a composition based upon this material is then composed. In ancient music the complete pattern of the scale is rarely found in the music, but the scale used as the basis of a particular composition can generally be detected by the presence of certain characteristic melodic formulae. Toward the end of the sixteenth century complete scale passages became more and more a feature of the music ­ notably in instrumental music. The practising of scale patterns has long served as a basis for the development of technique on musical instruments.

The Major Scale (Click for example)

More music is probably based upon this scale than upon any other. Most people who have had any contact at all with music are familiar with the singing and the sound of the pattern DO RE MI FA SOL LA TI DO. Let us sing it now. This is the sound of a major scale.

The major scale consists of a sequence of eight pitches. There is an interval of a tone between each of these, except between the third and fourth, and the seventh and eighth pitches which are a semi tone apart. (A tone is an interval equal to the value of two semi tones.) The major scale pattern can be most readily heard and seen by simply sounding the white keys of the keyboard from C to C. Note that there is no black key between E and F, and between B and C, because they are only a semitone apart; there is a black key between each of the others and they are a tone apart. Another way of describing the major scale pattern is simply:- Tone Tone Semitone Tone Tone Tone Semitone. Note that the last note is the octave of the first.

Let us now construct a major scale beginning on a given note - Ab. Here is a suggested step by step procedure:
­ 1) Write up eight notes on successive lines and spaces beginning on Ab.


Figure 16

2) Number each note from 1 to 8 and indicate the semitones by means of a bracket, joining the third and fourth, and seventh and eighth notes.

3) Check each interval. If it is the correct interval, leave it alone; if not, change the upper of the two notes to make the interval correct. A piano keyboard (or a diagram of one) is a useful aid in checking intervals. Remember - ­ any two adjacent keys are a semitone apart; one intervening key between two notes means that the interval is a tone, two intervening keys indicates an interval of a tone and a half.

What is the interval between the first two tones, Ab to B?
A tone and a half.
What do we want, according to our definition of a major scale?
A tone.
How do we achieve this?
Change B to Bb.

What do we have now between 2 and 3 ?
A tone.
Since this is the interval we want, leave it alone.
What is the interval between 3 and 4?
A tone.
What do we want?
A semi tone.
What do we do?
Change D to Db.

Continue this process until the scale is complete. This should be your result. It is called the scale of Ab major.


Figure 17

(If you started on the Ab an octave lower and had all the same pitches an octave lower, it would also be correct.)

As a final check play what you have written on a keyboard or other instrument. It should sound like DO RE MI FA SOL LA TI DO.

Problem: ­ Notate the scale of F# major, using whole notes in the bass clef. Construct this scale by following the above procedure.

This should be your result.(Click for example) Check it out in sound.


Figure 18

Note:­ The numbers and brackets are merely aids in working out the scale, and are not really necessary in the completed notation.



ASSIGNMENT

Construct the following scales:

­ a) Bb major in treble clef, using whole notes.
b) C# major in alto clef, using whole notes.
c) A major in bass clef. Write this scale over four measures of compound duple metre, making up an interesting rhythm which could include the use of rests.
d) Db major, tenor clef, ascending and descending, using any metre, any rhythm, and of any length you choose.


Transposition

We have noted in writing and performing major scales that although different ones contain different pitches, they all sound basically the same, and are all, therefore, major scales. What is the one factor that is constant, and that causes the "tune" always to sound the same? Answer:- the pattern of intervals. What is true of a major scale is true of any piece of music. It can be started on any pitch and still come out right if the pattern of intervals is kept unchanged. This phenomenon of reproducing a given piece of music by starting it on a higher or lower pitch than the original is known as TRANSPOSITION. For instance, sing a familiar tune, and then sing it again starting on a different note. If the melody sounded the same in both instances, that was because the distance or interval between each adjacent pitch was kept unchanged. Of course, there will be some difference in the overall effect of each example because of the high or low range in which the melody is performed.

Degree names and keys
Each pitch of a major scale is referred to as a degree within that scale, and each degree has a special name. The name which is given to each degree indicates to some extent its importance as well as its location in the scale. These are the names:
­

I Tonic - the most important degree in the scale. Its magnetic power tends to draw all other pitches in the scale towards it, and most compositions end on the tonic. Major scales begin and end on the tonic (at the octave), and its name is assigned to the entire scale, e.g.,when the tonic is Ab , the scale is Ab major.

II Supertonic - the degree above the tonic.

III Mediant - comes halfway between the tonic and the second most important degree.

IV Sub dominant - the degree below the second most important note of the scale. Harmonically, it is third in importance, and it occupies the same relative position below the tonic as the dominant (see below) occupies above the tonic.

V Dominant - next in importance to the tonic. Its importance will be more clearly understood when we come to study harmony.

VI Submediant - occupies the same position between the tonic above and the subdominant below as the mediant occupies between the tonic and the dominant.

VII Leading tone - a semitone below the tonic, and has the natural tendency to rise into it.


Figure 19

Always use Roman numerals when referring to degrees of a scale.

Since all music is drawn toward, and ultimately into, the tonic, the tonic is also referred to as the "key-note". Consequently, any music which is built around the notes of any particular major scale is thought of as being in that major key and is labelled according to the key-note. For instance, if a piece revolves around the notes of the Db major scale, it is in Db major. Therefore, for every scale there is a corresponding key.



ASSIGNMENT

1) Write the D major scale using whole notes in the bass clef.
2) Compose a melody using these pitches. Make the melody approximately eight measures in length, in simple triple metre, beginning on the dominant and ending on the tonic.
3) Transpose this melody to the key of F major. Begin on the dominant of F major and reproduce the melody exactly as you had it in D major. (It might be a good idea to write out the F major scale first to find out what notes you will be using.)
4) Transpose the melody up one octave, re-writing it in the alto clef.

Key Signatures

We find that melodies based upon particular major scales utilize primarily. just the notes of that scale. Occasionally, tones not belonging to the scale are used to "color" the music. You may have noted in writing a melody in D major that you had to use F# and C# consistently throughout the music. The key signature is a device whereby the accidentals required consistently for music in any particular key are placed at the left hand side of each line of music on the lines or spaces of the notes to be altered, and the performer realizes that throughout the work these accidentals will always be applied to those particular notes. For example, in D major sharps are placed on F and C at the beginning of each line of music, and all F's and C's are played or sung F# and C#.

In actual sound, how many different major scales are possible within an octave? Twelve: one for each of the twelve semitones. In theory, it is possible to write many more major scales since for every pitch there are two or three enharmonic names. In practice only fifteen major scales are written, three of which occur in two enharmonic forms. The reason that no others are used is that they would necessitate double sharps or double flats, which are avoided whenever possible. The fifteen major scales used are:- C C# Db D Eb E F F# Gb G Ab A Bb B Cb. (It might be useful to construct on paper each of the fifteen scales.)

We know that, in constructing these scales, all except C require one to seven sharps or one to seven flats, but we have also noted that the sharps and flats are never mixed in the same scale. If we examine all the scales containing sharps we find that starting with G major which uses one sharp (F#) we progressively add a sharp to each of the six others until we reach C# major which uses seven sharps. The order in which these sharps were added is F# C# G# D# A# E# B#. Here is how the seven sharps would be notated in the key signature for C# major in the four clefs. For any other key signature using sharps simply drop the unnecessary sharps.


Figure 20

The same procedure as we have just used can be applied to flat keys. The order in which the flats occur is Bb Eb Ab Db Gb Cb Fb, exactly the reverse order of the sharps. Therefore, the key signature for Cb major requiring all seven flats is written as follows in the four clefs:


Figure 21

­

ASSIGNMENT

Study and memorize the placement of the seven sharps and flats in all four clefs.


The Cycle of Fifths

We have now discovered all the major key signatures by constructing major scales on each of the twelve semitones of the octave. Let us now seek another relationship which might exist between all major scales. Examine the following C major scale and see if you can discover any aspect of its construction other than the basic tone semi tone relationship.


Figure 22

Did you notice that if you split the scale right down the middle the top half is identical in construction to the bottom half? Therefore, the top half of C major might be considered the bottom half of G major. What accidentals are required for G major? (One sharp - F#.) Let us now examine the G major scale in the same way. We find that its top half is the bottom half of the D major scale. What accidentals are needed in D major? (Two sharps - F# C#) We can follow this same process straight through all the sharp and flat keys. The fifth degree of each major scale is the first degree of another major scale requiring one additional sharp. This phenomenon is known as the Cycle of Fifths and can be charted as follows:


Figure 23

­

If you know your order of sharps and flats, this chart might be useful as a memory guide to your major key signatures. However, its main purpose is to demonstrate the underlying theoretical relationship between all major keys. It also serves to point out the relative closeness of relationship between various keys. This will become clearer in the study of harmony, and particularly in connection with modulation.

Other points to note on the chart of the Cycle of Fifths:
­ 1) The three enharmonic keys in use, and the fact that the equivalent flat key signature is derived from a given sharp signature by subtracting the number of sharps from twelve. (The reverse is also true.)
2) When we add a sharp to a key signature in flats we simply cancel out the last flat. Conversely, one or more flats added to a sharp signature will cancel out that number of sharps.


ASSIGNMENT

1) Memorize all major key signatures thoroughly. This knowledge is the basis of all subsequent work.
2) Using the proper key signatures, write the following major scales:
  (a) Eb major, alto clef; three measures in 3/8 time.
  (b) F major, tenor clef; four measures in 5/8 time.
  (c) F# major, bass clef; four measures in 6/8 time.
  (d) E major, treble clef; three measures in 4/2 time.

­ Utilize rests, and write interesting rhythmic patterns which you should then be able to sing and play.

The Minor Mode

Let us sing and play the following melody.(Click for example):


Figure 24

What adjectives might you use to describe this tune? (Possible answers:- sad, haunting, melancholy, exotic.) Does it sound like a major key melody? No. The reason is, of course, that it is not based upon the major mode. (We shall use the term "mode" from now on to describe the specific tonal resource of a particular piece of music.) Although perhaps the majority of melodies with which you are familiar are based upon the major mode, a considerable amount of music is based upon other modes.

If this work (Fig. 24) were in the major mode, " according to its key signature it would be in C major. However, what pitch is in fact its tonic? (The last note would be the most significant clue.) Its tonic is A, the submediant of C major, and this piece is based upon the Minor mode. Let us sing the scale of the Minor mode from A to A, all pitches natural. Perhaps it would be simpler to sing the syllables "la" to "la". This is called the Natural Minor Scale, and the best description of its sound would be to say that it is like singing "la ti do re mi fa sol la " . (Remember that the Major scale is the sound from "do" to "do".) Sing some minor scales starting on different pitches:- B, Bb, D. (Use the "solfa" syllables.) Although, of course, this scale has its own tone semi tone structure, we shall not concern ourselves with it as we did with the major scale. Which degree of this scale contrasts it most significantly with the major scale? The third degree, just a semi tone above the second, seems to be predominant in creating the characteristic minor quality of sound.

Relative and Tonic Minor
We have derived the minor scale from a given major scale, and, because of this, it is very closely related in sound to that major scale. It has the same key signature, and therefore utilizes all the same pitches. A minor scale with that type of relationship to a given major scale is called a Relative Minor scale; it has the same key signature and begins on the submediant degree of the major scale. What is the relative minor of E major? C# minor. Let us sing it, starting on C#, but singing the syllable names ("la" to "la").

Let us now sing a minor scale starting on the same pitch as our given major (E) using the syllable names. What actual pitches did we sing? E F# G A B C D E. Therefore, this minor scale has a key signature of one sharp. A minor scale which starts on the same pitch as a given major is called the Tonic Minor. In this case the Tonic Minor of E major is E minor. What must be done to a major key signature to change it to its Tonic Minor key signature? Add three flats. A Tonic Minor scale, then, starts on the same note as a given major, but its key signature contains three additional flats. (Flats cancel out existing sharps, so if we add three flats to a key signature consisting of one sharp, we end up with a key signature of two flats).

Summary:  ­ A Relative Minor scale has the same key signature as a given major scale but starts on the submediant degree of the major scale. A Tonic Minor scale starts on the same pitch as a given major scale but requires three additional flats in the key signature.



ASSIGNMENT

1) Name the Relative Minor of the following major scales and state the key signature: ­ Bb D Db B.

2) Name the Tonic Minor of the following major scales and state the key signature: ­ Bb D C# B.



Harmonic and Melodic Minor Scales
What is the most critical difference between the natural minor scale we have been singing, and a major scale? The lack of a leading tone. This lack will become much more obvious when we get into the study of harmony. The fact that the seventh degree of the minor scale did not lead into the tonic by a semi tone step also troubled many composers of the past. They overcame this problem by a habit of altering the seventh degree of the scale and making it into a true leading tone. Let us write the A minor scale, and then alter the seventh degree to make it into a true leading tone. This is done by raising the natural to a sharp. (If the seventh degree were a flat, we would make it natural. If it were a sharp, we would make it a double sharp.)(Click for example)


Figure 25

Sing this scale now. In this form it was now apparently suitable for harmonization, but melodically it was still unsatisfactory to the tastes of many composers. Where is the problem now? The unusual interval between the sixth and seventh degrees (augmented second). Therefore, another form of minor had to evolve for melodic purposes. Raise the sixth as well as the seventh degree of the A minor scale and sing it now. This is called the Melodic Minor scale. In its descending form it is converted back to the natural minor since the raised leading tone is no longer necessary. We always write melodic minor scales in ascending and descending forms, as follows:(Click for example)

­


Figure 26

It should be noted that in the music of Bach, Beethoven, and others, the harmonic minor scale was on occasion used melodically, and this particular sound is actually favored in certain parts of the world.

Summary:
­ The natural minor scale sounds like singing from "la" to "la", or the playing of the white keys from A to A, or performing from submediant to submediant of any major key. To form the Harmonic Minor, simply raise the leading tone one semitone.

To form the Melodic Minor, raise the sixth and seventh degrees ascending by one semitone, and convert the descending form of the scale back to natural minor.

We have not bothered about the interval pattern of the various minor scales, but, of course, each scale has its own specific pattern of intervals which the student can discover for himself or herself.

Here are all minor key signatures as charted on the cycle of fifths:

­ ­


Figure 27



ASSIGNMENT

Write the following minor scales using key Signatures:
­ (a) The relative minor of D major, harmonic, bass clef, in 6/4 metre over three measures.
(b)  In simple triple metre over five measures, write the tonic minor of A major melodic, alto clef.
(c)  In compound quadruple metre, four measures, write the scale of Eb minor, melodic, treble clef.


Other Modes
Let us sing the following melody (either on "ah" or using "solfa" syllables):(Click for example)

­


Figure 28

Upon what scale or mode is this melody based? It is pentatonic, using only five notes. It is neither major nor minor, but resembles minor more closely because of the last note and some of the melodic patterns it contains.

A great deal of music, particularly folk music, is based upon the pentatonic scale. Its main characteristic is that it contains only five different pitches within the octave of a major or minor scale, and has no semitones. You can derive it by removing "fa" and "ti" (subdominant and leading tone in the major, or supertonic and submediant in the natural minor), or simply by playing on the black keys of the keyboard.

Let us now sing this melody:(Click for example)
­


Figure 29

Find the keynote, and then write the scale upon which this tune is based. {D E F G A B C D.) Is it major or minor? Neither. The pattern of intervals is that formed by playing the white keys from D to D or by singing from "re" to "re". This is called the Dorian mode and its use goes back to the Middle Ages. The body of music known as Gregorian Chant is based upon the church modes, one of which is the Dorian. Some folk songs are also based upon this mode and many contemporary composers are again using it in their works. Like any other scale or mode, it can of course be transposed to any key. There are two basic ways of doing this: one is to analyze the interval structure of the Dorian mode (T S T T T S T) and simply apply it to any key note; the other is to determine the new key signature by considering the key-note of the Dorian key as the "re" of a major key ( remember that the Dorian mode is a scale from "re" to "re").

For example, write the A Dorian mode. If we construct it on the interval pattern we get A B C D E F# G A. If we think of A as "re" in a major key, we have the key signature of G major, one sharp, and arrive at the same answer.(Click for example)

­


Figure 30

Three other modes which we have inherited from the Middle Ages are:
­ Phrygian - E to E, or "mi" to "mi" (S T T T S T T).
Lydian - F to F, or "fa" to "fa" (T T T S T T S).
Mixolydian - G to G, or "sol" to "sol" (T T S T T S T).

Let us sing and play these in different keys. Note that Dorian has a slight resemblance to minor, Lydian and Mixolydian have qualities of the major mode, whereas Phrygian seems to be a law unto itself. An interesting theoretical point to note about Phrygian is that it has the same interval pattern in its ascending form as the descending form of major, and vice versa. Another way of:saying this is that the Phrygian mode is the inversion of the major mode.

A scale form which is strictly a development of recent times is the Whole Tone Scale. This scale contains only six notes within the octave, with an interval pattern of T T T T T. Music based upon this scale has a unique exotic quality, and, because there are no semitones, there is no strong feeling of tonic. There are only two tonal possiblities for this scale - one starting on C and one starting on Db. If you start on any other pitch, you have simply a variant of one of these two scales. Sing and play whole tone scales starting on different notes.

A Chromatic scale is the sequence of the twelve semitones within the octave. There is only one tonal possibility for this. This particular scale is not really usable as the basis of a musical composition. However, a modern technique in musical composition utilizes the twelve semitones of the octave in a particular manner as a basis for composition. This is called the "twelve tone" or "dodecaphonic" ­ style of composition, and this kind of music is often referred to as "atonal" music.

Simply stated, this is how the technique operates: the composer arranges the twelve tones of the octave in a sequence of his own invention. He then proceeds to use this "tone row", the main rule being that the notes must always be presented in sequence, although they can be in any rhythmic pattern, and can occur either consecutively or simultaneously. The resultant music differs radically in effect from all music of the past. Further information on this technique, invented by Schoenberg, can be found in any number of books and articles on music.

The above are the principal scale patterns used as the foundation for most western music of the last fifteen hundred years. Of course, new "synthetic" scales can be, and are, sometimes invented by composers who are seeking out new sonorities.

The important point to remember is that the scale itself is not significant except for its use in actual music, and that any scale may be transposed to any tonality with a minimal sacrifice of its intrinsic quality.

As an illustration of the variety of sound possible in music, here are ten scales,. all in the tonality of D. It may be interesting to test a group in their ability to identify these various modes by ear. However, remember that this is not any easy task for the inexperienced ear.

­






Figure 31



ASSIGNMENT

1) In whole notes, treble clef, using the proper accidentals, write:
­ (a) The Dorian mode on B .
 (b) The whole tone scale on B .
 (c) A pentatonic scale on B
. (d) The Mixolydian mode on B .

2) Sing each of the above examples.

3) Compose a melody based upon any mode or scale other than major or minor.

Index



(b) INTERVALS

An interval is the distance in sound between any two pitches sounded concurrently or consecutively. Each different musical interval has its own name for purposes of identification, although as in the naming of single pitches more than one name is possible for each interval. Here are two intervals with which you are already familiar (Click for example) :

­ ­


Figure 32

They are the perfect octave and the semitone. The perfect octave produces a sound as pure as it is possible for two notes to produce without actually being the same note (unison). In other words, when you hear an octave, it is almost like hearing one note, but not quite: Therefore, the octave would have to be considered our most consonant interval. The semitone , on the other hand, is a sort of paradox, as the distance between the two notes is as small as is possible in conventional tuning, but when the two notes are sounded simultaneously, extreme dissonance is produced which implies that in sound the two notes are actually very far apart.

Each interval can be reproduced from any pitch provided that the distance between the two notes (i.e. the number of semitones) remains constant. Here are some other examples of octaves and semitones (Click for example) :

­ ­


Figure 33

Let us see if we can identify a few intervals by ear. This is the sound of the perfect fifth, perfect fourth, and major third (Click for example) :

­ ­


Figure 34

(Play various perfect octaves, perfect fifths, perfect fourths, and major thirds for ear training. (Click for examples - Perfect 5th, Major 3rd, Octave, Perfect 4th, Octave, Perfect 5th, Perfect 5th, Perfect 4th) Do them consecutively, playing the lower note first; but it often helps if the lower note is sustained while the second note is being sounded. As much practice of this type as is possible is desirable.)

The Naming of Intervals
As you probably have noticed, the name of each interval has two parts, e.g. Perfect Fifth. The first part is called the quality and the second part is called the number. Let us now find out how we apply names to intervals. We will deal first with the number.

Procedure:  ­ To determine the number of any interval count each successive letter name from the lower note to the higher, including both. If the number is greater than an octave, the interval might be called Compound, e.g. octave plus third is compound third, or it might be called the actual number (a tenth). Ninths are usually called ninths, although intervals greater in number are often called compound.

What is the number of the following intervals?

­


Figure 35

(Answers:- 6th, 2nd, 7th, compound 3rd or tenth, 4th, and 9th.)

Now we will investigate how we name the quality of the intervals. There are five possible names in use for intervals - major, minor, perfect, diminished, augmented. 2nds, 3rds, 6ths and 7ths may be major, minor, diminished or augmented. Unisons, 4ths, 5ths, and octaves may be perfect, diminished or augmented. The relationship between these various names is as follows:

­ augmented = semitone larger than major
major
minor = semitone smaller than major
diminished = semitone smaller than minor

augmented = semi tone larger than perfect
perfect
diminished = semitone smaller than perfect

Therefore, to determine the quality name of an interval, we must first decide whether the interval is major or perfect, and then work from there.

Rule:- If the top note is a part of a major scale of which the bottom note is the tonic, then the interval is major or perfect according to its number. Your first step must be then to look at the lower note of an interval and think of it as the tonic of a major scale.

We will now work out the names of a few intervals.
­


Figure 36

1) is a fifth - since B is a part of the scale of E major, it is a perfect fifth.
2) is a sixth - since C# is in the scale of E major it is a major sixth.
3) Bb would have been a perfect fourth. Since this interval is a semitone larger it is an augmented fourth.
4) minor seventh.
5) F would be a major second, therefore this is an augmented second.
6) Since E is in the scale of F major, that would have been a major seventh. Eb would make it a minor seventh, and Ebb makes it a diminished seventh.
7) compound major third, or major tenth.
8) Since we do not have a scale of Fb major, let us raise the lower note to F, but to keep the interval the same we must also raise the upper note by one semitone to C#. We can now work out this interval as an augmented fifth. Remember that an interval is the distance between two notes, and, regardless of the notes, as long as the distance is kept the same, the interval remains the same.
9) augmented sixth.

Before one can do intervals with any degree of fluency, one must be extremely familiar with all major key signatures. Always associate the names of intervals with their sounds, and practise hearing intervals as much as possible.

Enharmonic names
Name the following intervals:

­ ­


Figure 37

(From now on we will utilize the following symbols to denote the quality of intervals:­ + major, - minor, P perfect, ° diminished, x augmented.)

Play the intervals (Figure 37) and check their sounds.(Click for example) Actually, we have only three sounds, although we have six names. This phenomenon of enharmonic names, whether applied to single pitches or to intervals, is not new to us.

How many possible different interval sounds are there actually within an octave?
There are only the following thirteen:­ ­


Figure 38

The above are listed according to size. Let us now reorganize these intervals according to relative consonance and dissonance. In order to determine this aurally, the two notes should be played or sung simultaneously. There is a scientific method of explaining relative consonance and dissonance, but we will do it more or less strictly on aural intuition, and this is what we come up with:­

­


Figure 39

Awareness of the sound of intervals in this manner may help us in hearing and identifying different intervals. Two things to be particularly aware of are whether the pitches are close together or far apart, and whether they are relatively consonant or dissonant.

Besides being able to name intervals, we also have to write intervals above and below given notes. Writing an interval above a given note should not present any difficulty if one can name intervals properly. However, writing an interval below a given note does bring up a few problems in procedure because of the fact that all intervals are named by checking the number and quality from bottom to top. In other words, the bottom note is your main reference note.

Let us review the steps involved in writing an interval above a given note; a minor seventh above Bb .
1) Count up seven steps from Bb to find the top note which is A.
2) Is A in the Bb major scale? Yes, therefore we have a major seventh.
3) Reduce the interval by one semitone in order to produce a minor seventh. A becomes Ab.

Practice writing intervals above given notes.

Let us now examine the steps we would take to write a minor seventh below Ab.

1) Count down seven steps and you arrive at B.
2)What is the interval from B to Ab? A diminished seventh.
3) Since we require a minor seventh, an interval a semitone larger, we must change the B to Bb.

Notice that a flat added to the lower note increases an interval, and an added sharp would reduce the interval. Practice writing intervals below given notes.

Inversion of intervals.
Sing a P5 above E. Now sing a P4 below E. What have you discovered? In both cases the note B (an octave apart) produced the correct interval. The second interval you sang is called the inversion of the first one, and vice versa. Each interval has its corresponding inversion. For instance, C up to E is a major third. Drop the E an octave below C and you have a minor sixth. Similarly, what is an augmented 2nd above C? D#. When the D# is dropped below the C, a diminished 7th is now produced.

From these observations what general conclusions can we arrive at regarding inversions?
1) An inversion of an interval is simply the completion of an interval to its octave.
2) The number of an interval plus the number of its inversion adds up to nine. In order to determine the number of the inversion of an interval, subtract the number of the interval from nine.
3) Major intervals become minor, and vice versa.
4)Perfect intervals remain perfect.
5)Diminished intervals become augmented, and vice versa.

Knowledge of inversions is particularly useful in writing intervals below a given note, because the correct note can now be found simply by writing the inversion of the required interval above the given note and then transposing it down an octave. This knowledge becomes particularly pertinent when we come to deal with triads. In making the inversion of a compound interval consider it in its simple form; in writing it, complete the interval to two octaves.



ASSIGNMENT

1) Name the following intervals:
­­

2) Write the following intervals above the given notes:
­­

­ 3) Write the inversions of the above intervals, and re-name them.
4) Write the intervals of #2 below the given notes.
5) Write the inversions of these new intervals, and re-name them.
6) Do as much aural identification and singing of intervals as possible.


Measuring intervals by semitones

A less practical, although perhaps more meaningful, means of measuring intervals is simply by counting the number of semitones within each interval.

The numbers of semitones contained in each interval within the octave are as follows:
­
   Twelve  -  perfect octave, augmented seventh, diminished ninth.
   Eleven  -  major seventh, diminished octave.
   Ten     -  minor seventh, augmented sixth.
   Nine    -  major sixth, diminished seventh.
   Eight   -  minor sixth, augmented fifth.
   Seven   -  perfect fifth, diminished sixth.  
   Six     -  diminished fifth, augmented fourth.
   Five    -  perfect fourth, augmented third.
   Four    -  major third, diminished fourth.
   Three   -  minor third, augmented second. 
   Two     -  major second, diminished third.
   One     -  minor second, augmented unison.

This is useful information for the student, but the preceding method of writing and naming intervals is felt to be the more practical one. However, it is the end result (fluency) that counts, and any means that assists in attaining this goal is acceptable.

Index



(c) CHORDS

The simultaneous sounding of any number of tones constitute what we might consider a chord. Sometimes a chord may be "broken" so that the pitches are sounded consecutively, but the chord feeling remains, either because each tone is sustained against the succeeding one, or because of the familiarity of this combination of tones as a chord sound. The purpose of chords is to provide a fullness to the musical tex­ ture, often as accompaniment to a melodic line, and also to provide a certain tonal direction to the music. As we get into our study of harmony these concepts will become clearer.

The TRIAD is the most familiar and most basic chord form. It consists of three pitches, each one the interval of a third higher than its predecessor. The fundamental note of the triad is called the ROOT, the third above it is called the THIRD, and the fifth above it is called the FIFTH (makes sense). Therefore, we can also analyze the structure of a triad by saying that it comprises an interval of a third and an interval of a fifth above a given root.

Let us sing a triad. One group will sing C, one will sing E, and one will sing G. (Sing it on "ah" and stress a good clear ringing major triad.)Click here for example This is what we sang:

­


Figure 40

It is a MAJOR triad, consisting of a +3 and P5 above the root.
Those singing the third, change it now to Eb.Click here for example
­


Figure 41

This gives us a MINOR triad consisting of -3 and P5 above the root.
Now change the fifth to a Gb. Check the intonation and listen carefully to the overall sound.Click here for example
­


Figure 42

This is a DIMINISHED triad with a -3 and °5 above the root.
Now we will sing the following.Click here for example:
­


Figure 43

.­ This is an AUGMENTED triad, consisting of +3 and x5 above the root.
These are our four basic triad forms and can be transposed to any degree of the chromatic scale.

Summary:
MAJOR = +3, P5 above the root, or a -3 superimposed on a +3
MINOR = -3, P5 above the root, or a +3 superimposed on a -3.
DIMINISHED = -3, °5 above the root, or a -3 superimposed on a -3.
AUGMENTED = +3, x5 above the root, or a +3 superimposed on a +3.

Triads are named according to the root and the kind. For example, we have just sung and written a C major, C minor, C diminished, and C augmented triad.

Let us practice writing a few triads: F# °, Ab +, B x, Bb -. Simply follow the proceedure of writing the proper third and fifth above the root.

­


Figure 44

Ear training: Play some triads, block form or broken and have the class try to identify their kind.

Inversions of Triads
Let us first write and then sing a D+ triad. (Have male voices all sing lowest part, or if there is a fairly equal mixture of men and women, divide both groups into three parts.)

­


(a) Figure 45

We have just sung this major triad in what is known as ROOT POSITION. This means that the lowest voice is the root of the triad. Its effect is one of clarity and strength. We will continue to sing this same D+ triad, but change the voicing so that the third, and then the fifth become the lowest parts.

­


(b) (c) Figure 46

(b) is a D+ triad in FIRST INVERSION.
(c) is a D+ triad in SECOND INVERSION.

Notice the subtle differences of effect produced by the different inversions.Click here for example

All triads of all kinds can be inverted in this manner. For convenience, a numbering is often used to specify the inversion.

Root position is 5/3, a fifth and third above the bass. First inversion is 6/3, a sixth and third above the bass. Second inversion is 6/4, a sixth and fourth above the bass.

Examples:
­­


Figure 47

NOTE: In order to determine the root and the kind of any given triad in first or second inversion, it is desirable to first re-juggle the pitches to revert the triad to root position, and then analyze.



ASSIGNMENT

1) Write the following triads:
(a) Eb minor, root position, bass clef.
(b) Eb major, second inversion, alto clef.
(c) A diminished, first inversion, treble clef.
(d) G# augmented, root position, tenor clef.
2) Write the proper triads above the given notes according to the figuring. If a sharp or flat is placed beside a figure, sharpen or flatten that note.
­

3) Name fully the root, kind, and inversion of each triad in #2.


Triads in relation to major keys
So far, we have been considering triads. as isolated entities. In the study and practice of harmony, we tend to think more of triads as they relate to a given key. Let us consider the variety of triads available to any major key. For purposes of convenience, we will work in C major, but what is true of C major is true of all major keys.

Write the scale of C major in the treble clef, and then write a triad in root position above each degree of this scale using only the pitches of C major.

We will divide in three parts and sing what we have written.(Click for example) Now we will number each degree with the proper Roman Numeral and analyze each triad to determine its kind.

­­


Figure 48

Analysis: Tonic (I) is major.
Supertonic (ii) is minor.
Mediant (iii) is minor.
Subdominant (IV) is major.
Dominant (V) is major.
Submediant (vi) is minor.
Leading tone (vii°) is diminished.
(For greater clarity, we will use the lower case Roman numerals for minor and diminished triads.)

Therefore, in any major key, there are three major, three minor, and one diminished triad which will be used as the primary materials for harmonization. The most important or key triads are the major ones, I, V, and IV. The others are secondary, but are useful for additional color and variety.

We must become extremely fluent in identifying and writing triads on any degree of any key. We will limit our work at this point strictly to major keys. Remember, what­ ever the major key, vii° is always diminished, ii is always minor, etc.



ASSIGNMENT

1) Write the following triads using the proper key signature:
(a) Supertonic of E major, 1st inversion, bass clef.
(b) Dominantt of Ab major, root position, treble clef.
(c) Leading note of Bb major, 2nd inversion, alto clef.
(d) Subdominant of B major, root position, tenor clef.
(e) Submediant of F major, 1st inversion, treble clef.

2) Name fully each of the triads in #1 (root and kind).

3) Write the following triads according to the given figured bass, and name fully.
­­

N.B. A "bass" is the lowest note of a triad irrespective of what clef is used.

Index



Part Three
HARMONY

In a sense, we have already been dealing with harmony, since one concept of the meaning of the word "harmony" suggests the blending together of different sounds. In writing and singing triads (and intervals) we have already produced harmony in this sense. However, there is also another aspect to the meaning of the word, and it is with this aspect that we shall be mainly concerned at this point.

(a) CHORD PROGRESSION

What is being referred to here is the relationship or interconnection between chords. When we think of the musical effect of a series of chords, we are thinking of CHORD PROGRESSION. With every melody there is a logical sequence of chords which can be used to enhance and accompany it. Sometimes there are several possibilities available in choice of chords which would be almost equally effective, and that is why harmony is to some extent a creative endeavour. However, if one's objectives are clear, then there are certain rules of style and logic which can be used as guides in the choice of chords.

In order to successfully harmonize melodies, you must be thoroughly familiar with the tone materials with which you will be working. What are these materials?

1.   Theoretically, any kind of chord, or series of chords is available. However, for the present, we will limit ourselves to all the diatonic triads within any given key and mode. You should know which ones are major, minor, diminished and augmented.
2.   You must now also think of the music in connection with a definite medium. You must know if you are harmonizing for voices, or for any particular instrument or combination of instruments. The same chord progression written for different media would in each case be handled differently, and would produce a somewhat different result. The manner, or the medium, in which harmonies are presented, is often thought of as the TEXTURE of the music.

Let us illustrate this point together. We will select a chord progression, and write it and perform it in different media. We will work in C major, although what is done in C major, theoretically, could be transposed to any other key. However, certain limitations now begin to affect our choice of key: primarily, these are the limitations of range and technical flexibility of any given voice or instrument.

The progression of triads that we will write and perform in C major is as follows: I vi ii V I. We will arrange this chord progression for (a) the autoharp (b)the piano and (c) four voices.

The Autoharp
On this instrument the names of certain chords are written directly on each of the bars that are used in playing the instrument. When a particular bar is depressed it blocks off or dampens all the strings that are not needed for that chord, and when one strums the instrument only the notes required for the selected chord will sound. What is it then that we must know in order to play our progression on the auto­ harp?

Answer: The names of the chords needed.

What are they? (I vi ii V I in C major)

Answer:   C major; A minor; D minor; G major; C major.

(Play the progression on the autoharp )

You will notice that in playing the progression on the auto­harp we do not concern ourselves with individual notes since this is taken care of for us by the instrument. However, we should decide on a particular rhythm, and know how long we wish to retain each chord.
For example, in 4/4 time we might play it like this:(Click for example)

­­


Figure 49

What other possibilities can you suggest? (try different ones) Of course, this would depend upon the type of song you were accompanying, its rhythm and its metre.

Harmonic Rhythm
This term refers to the relative duration of chords within a given piece of music. If, as in Bach chorales, the chord changes are frequent (more or less one on every beat), then the harmonic rhythm is considered to be fast. If, on the other hand, the tendency is to retain the same chord over one or several measures as in many simple folk songs, then the harmonic rhythm is considered to be slow. Harmonic rhythm usually affects the character of music and more tension is generally built up with a fast harmonic rhythm. (Comparisons might be made in this regard between the music of Bach or Handel, and that of Mozart or Haydn.)

It is possible to play our chord progression on the guitar similarly to the way in which we played it on the autoharp. Many guitarists do not concern themselves with individual notes or chords, but simply with the finger pattern they must use for each chord. Therefore, the music for the guitarist is often written in the form of a tablature, showing the placement of the fingers on the frets and strings for each chord. The vertical lines represent the strings, the horizontal lines represent the frets, and the black dots represent the fingers. The selection of harmonic rhythm would be the same as that of the autoharp.

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Figure 50

The Piano
To write this chord progression for piano, what additional information must we have?

Answer: We must know the exact notes needed for each triad, and we must notate them properly for the pianist. Let us plan to write this progression as the left hand accompaniment to a waltz. First, we will write out the chords in full on a staff so that we will know what notes are required. Write each triad in root position.

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Figure 51

Now let us write this progression for the left hand in a waltz accompaniment pattern -- oom pa pa ; 3/4 time. The usual way to do this is to strike the root of the chord in octaves on the first beat of each measure, and the complete triad on the second and third beats. In writing out the second and third beats, don't worry about writing the triad in root position since the feeling of the octave on the first beat will carry through the bar. Therefore, our concern should be in making the triads connect as smoothly as possible, one to the other. (Work this out on the blackboard together with the class). Most logical result: ­­


Figure 52

(Play the example or Click here)

Of course, it is possible on the piano to set this harmonic progression to an infinite variety of textures and rhythms.

Voices

Let us now write this same harmonic progression for the standard mixed voice choir -- soprano, alto, tenor, . and bass.

Before we can do this, we must be familiar with the workable ranges of these voices. Here they are:

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Figure 53

In writing four part harmony for the mixed choir, we will use only treble and bass clef, putting the soprano and alto on the treble and the tenor and bass on the bass staff. Often these parts are placed on four separate staves (the tenor part being written an octave higher than it actually sounds in the treble clef). However, it is easier for beginners to read the harmony on two rather than four staves. One way of writing our progression for SATB is as follows:Click for example

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Figure 54

Let us divide into four parts and sing this example to the syllable "ah". Once the class has learned to sing this progression properly, the teacher can play many popular melodies such as "Heart and Soul", "Blue Moon" and "These Foolish Things" on the piano or other instrument to the accompaniment of this chorus).

Now study the music and point out any features you notice.

Answers:

1.   It is necessary to double one of the notes of each triad because of the four voices. In each case the root of the triad is the note that is doubled.

2.   Because each chord is in root position, the bass line is fixed.

3.   The other parts move as smoothly as possible, staying on the same note or proceeding by step in most cases.

4.   The spacing between the voices is fairly equal, with the largest intervals occuring between tenor and bass.

5.   The motion between soprano and bass (the two most import­ant voices) is mainly contrary or oblique.

We will pursue our study of harmony for the present in the SATB medium. We will be concerned with discovering, writing, and singing various harmonic progressions using the diatonic chords in a given key. Because it is necessary for the beginner to have definite limitations within which to work, we will impose some rules. These rules are, in a sense, arbitrary, but they are justified by being part of a long tradition of choral music.

Voice Leading

This term refers to the individual movement or melodic character of each volce as considered in isolation as well as in relation to the other voices. Here are rules to follow for the present:

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1.   Make each voice as smooth as possible avoiding any unnecessary leaps. Wherever possible, keep the common tone between two adjacent chords in the same voice.

2.   Consider the relationship between soprano and bass parts. There should be a fair amount of contrary motion (when one part moves up, the other part moves down and vice versa), some oblique motion (one part stands still while the other moves) and occasional similar motion.

3.   Consecutive perfect fifths or perfect octaves between any two parts are strictly forbidden.

4.   The leading note should rise to tonic.

Spacing
This refers to the interval between any two adjacent parts: soprano and alto, alto and tenor, tenor and bass. An interval greater than an octave is allowed only between tenor and bass. The interval between the other parts should always be an octave or less.

Doubling
For the present, always double the root of the chord. Occasionally, it will be found necessary to triple the root of a chord and omit the fifth. This is acceptable. The third of a triad may never be omitted.

These are our basic rules, although many exceptions will gradually be introduced.

ASSIGNMENT

1)   Transpose the choral setting of our harmonic progression to the keys of E major and A major. Sing and discuss these transpositions with regard to any alteration of effect, or any special problems they present.

2)   Utilizing the rules of doubling and voice leading so far established, continue the I vi ii V I progression in half notes, root position, from the following opening chord:





The Cadence
Certain chord progressions come to be recognized as standard formulas or clichés through constant and recurring use in similar musical situations. When one hears a progression of this type, one immediately receives clues regarding the structure and direction of the music. 0f course, when these formulas are deliberately used in an unpredictable manner, then the opposite effect, usually one of surprise, is created.

The most common of these musical clichés are called CADENCES or cadential formulas. Cadences serve the dual purpose of establishing a key or tonality, and of clarifying the form or structure of the music. When cadences are deliberately avoided, both form and tonality become less clearly defined, and the music assumes a quality of vagueness. A cadence operates much in the same manner as punctuation, signifying the end of a phrase or section in the music, and the degree of finality inherent in this ending; it also emphasizes the key or tonal region reached at this point.

Most cadence formulas consist of two chords, but a third chord is often necessary in order to clearly establish the key. This will be made evident when we study our first cadence.

The Perfect Cadence
This cadence would be similar to a period in language punctuation in that it generally denotes a full stop. The basic chord progression for the perfect cadence is V 5/3 to I 5/3. This is what it looks like in four parts. (Sing it on "ah" and play it on the piano.)(Click for example)

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Figure 55

Notice two things about this cadence:

1.   The two chords in isolation do not definitely establish the tonality. This same progression might be thought of as I to IV in G major. In order to clearly establish C major, a third chord is necessary to precede this. The chord must have an F natural in it (ii, IV, or vii°).(Click for example)

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Figure 56

2.   This example contains the root of the I chord in the soprano. It would still be a perfect cadence if the 3rd and 5th were used, but the strength and finality of the cadence would be weakened. Let us write and sing examples of perfect cadences with either root, 3rd, or 5th of the tonic chord in the soprano in various keys.

By and large, the part writing in each example will be the same. That is, the root, third and fifth of the V chord will always logically progress to the same note of the I chord. This follows the basic rule of moving as smoothly as possible within any given part, and keeping the common tone wherever possible. Also of having leading tone go to tonic. However, if the fifth of V is made to go to the root (rather than the third) of I, you will notice that we end up with a I chord containing three roots and a third. This is quite acceptable and for the time being we will consider it the only solution to this problem.(Click for example)

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Figure 57

Plagal Cadence
This cadence is not really a cadence at all, but rather a conventional musical tag, or epilogue. It is always preceded by a perfect cadence, and is the familiar "amen" found at the end of hymn tunes. Its formula is IV 5/3 to I 5/3.(Click for example)

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Figure 58

Sing it to the word "A-men."

Note these points:

1)   Because it is preceded by a Perfect Cadence, tonality is clearly established. Otherwise it might also be considered as I to V in F major.

2)  Conventionally, the root of I is in the soprano. Write examples in various keys with the third and fifth of I in the soprano, and note the difference in effect.

3)   Regardless of what note is given to the soprano, the voice leading never varies in this cadence formula.

Let us now write a Perfect Cadence followed by a Plagal Cadence in Eb major. Remember that all chords should be in root position.(Click for example)

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Figure 59

Sometimes, in writing this progression (V I IV I) the IV - I is thought of purely as an extension of the Perfect cadence, and when the bass first sounds the root of the I chord, it sustains it right to the end. This puts the IV chord in second inversion, and its fifth is the conventional note to double in this case. ­­


Figure 60

Sing this progression.(Click for example)

Note that the basic effect of this prognession is a sustained tonic chord with a slight ornamentation in the two inner voices. A sustained bass note which contains chord changes above it is called a PEDAL tone. It is a common device found particularly at the end of many organ works in which an organ pedal is sustained for several measures, and changing harmonies occur above it.

The Half Cadence

As the perfect cadence resembles the period in punctuation, the half cadence resembles the comma. It is, therefore, to be found at the end of various phrases in a musical work, but never at the end of a section. Frequently, one finds a musical sentence made up of two balanced phrases. This is often referred to as question and answer, or thesis and antithesis. In this case, the first phrase would normally end with a half cadence and the second phrase with a perfect cadence.(Click for example)

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Figure 61

There are various forms possible of the half cadence, but in all cases the second of the two chords is a V 5/3. It can be preceded by any triad (iii or vii° would be rarely used) in either root position or first inversion.

Let us write various possibilities of half cadences in A major.

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Figure 62

The Deceptive Cadence

Sing the following perfect cadence in D major: ­­


Figure 63

Now let us sing this progression:

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Figure 64

This new cadence formula is called "deceptive" for obvious reasons. It starts out like a perfect cadence but its course is altered. Thus, we are deceived or thwarted. V 5/3 to vi 5/3 is the standard formula for this cadence. Note . the unusual doubling in the vi chord. What is it? (Third). Why do you think it is used? The third of the vi chord is the tonic note of the key, and thus the same note is doubled as would have been doubled if this chord was a I. Thus the ambiguity of this particular cadence is re-inforced. Actually, any chord other than I following V 5/3 would be considered deceptive. However, V to vi is the only form we will consider here. In some ways the word cadence in connection with this formula is a misnomer since it is more likely to occur in the middle rather than at the end of phrases.

Write deceptive cadences in various keys.

Ear Training

1.   Identify the following cadences:

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Figure 65

2.   After being informed of the key, write these cadences. (Supplement these examples with others.)

ASSIGNMENT

Above the given bass notes, write the cadences they suggest. Name each cadence, and fully number each triad with the Roman numeral for degree and Arabic numerals for inversion.

Index



(b) HARMONIZATION OF MELODIES
We will now proceed.with studies related to the harmonization of melodies. We will pursue two approaches more or less concurrently. One will be the harmonization of chorale phrases in four parts in a style imitative of Bach. In this work certain rules derived from analyses of the Bach chorales, as well as comparisons of our own harmonizations with those of Bach will be of key importance. Simultaneously, we will also practise harmonization of folk songs and other simple melodies using simple chordal accompanihments. Here, our ear and our intuition will play predominant roles.

Normal Progression

In harmonizing a melody, our primary concerns are with the selecton of chords and with the frequency of chord change: Chord progression and harmonic rhythm. In Bach chorales the harmonic rhythm is relatively fast; generally one chord change on each beat of the measure. McHose (McHose, A. I., Basic Principles of the Technique of 18th and 19th Century Composition, Appleton-Century Crofts, Inc., 1951), through an exhaustive study of Bach chorales has arrived at a basic concept of chord progression which he refers to as "normal progression." Although exceptions are many, normal progression implies the usual chord choices one would find in Bach chorales. The following diagram is a simple depiction of normal progression:

                ---------------------->
                I   iii   IV   V    I
                          ii   vii°
                     
                     Figure 66

This diagram indicates which chord would normally follow any other given chord. However, this does not suggest that each chord must be used, but only that the direction as indicated by the arrow be maintained. In other words VI to V to I would be normal progression. I ii V I would also be normal progression. V IV vi would not be normal progression. Note that the supertonic and subdominant triads, as well as the dominant and leading tone triads are interchangeable in function. If both are used consecutively, it is usually stronger to go from IV to ii (rather than vice versa) and from Vll° to V.

Of course, if we analyze a large number of Bach chorales, we will probably detect many instances when normal progression is not followed, but until a student attains a certain proficiency and a certain insight into this style, he should utilize normal progression in every instance where it is possible to do so. Occasionally a situation arises where it is impossible, and then, of course, it cannot be used.

That having been said, three common exceptions can now be given:
1)   V - vi is acceptable, since this is our familiar deceptive cadence. (Remember the unusual doubling.)
2)   vi - iii is a common exception and may be used, although sparingly.
3)   iii vi and ii should not go directly to I.

Other points to note:

iii is relatively infrequently used.
vii° should always be in first inversion, and the bass (3rd of the chord) is the note normally doubled. Some­ times the 5th may be doubled, but the leading tone is never doubled.

Summary of basic rules of chord progression in Bach Chorale style.

I can go to any chord
ii usually to V, sometimes to vii°
iii usually to VI; could also go to IV or V
IV could progress equally to V ii or I
V usually to I, sometimes to vi
vi could go to IV ii V or vii° sometimes to iii
vii° usually goes to I; sometimes to V

Let us now harmonize together a phrase from a chorale so that we may discover a suitable working procedure.

Here is the melody. Sing it over. Remember that although there are many rules and guidelines which help us in harmonization, our ultimate criterion is always the sound. Usually it is possible to come up with more than one correct result, and, therefore, within certain limitations, one's choice of chords is purely subjective and should be based upon what one eventually will be able to identify as typically Bach style.

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Figure 67

Suggestions for procedure in the harmonization of this tune:

1)   Note the key - A major. Know the chords in this key.
2)  Check the cadence at the end. It looks like a Perfect cadence with the third in the soprano of the tonic chord. A deceptive cadence wouldn't work because it would produce parallel fifths between bass and soprano.
3)   Proceed with chord selection. Two things should be borne mind in this work: (a) try for strong normal progression; (b) try for an interesting bass line. The expression an "interesting bass line" is a somewhat abstract concept. It should be interesting mainly in relation to the soprano and the two parts together should sound quite well. Generally speaking, the bass line should have a certain melodic interest, with some leaps, some stepwise motion, and a pleasing contour. It is frequently desirable to have some contrary motion with the soprano (that is when the soprano moves downward, the. bass moves upward, and vice versa), and some conjunct motion (both parts moving in the same direction).
Here are all the chord possibilities for this tune:
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Figure 68

­ 4)   Now make your selection bearing in mind the rules (and. exceptions) dealing with normal progression, and the resultant bass line. If you are set on a chord progression and wish to improve the bass line, the occasional chord can be. used in first inversion. Do not write chords in second inversion.
5)   Now complete the inner parts making them as smooth as possible, and making certain that no basic rules are being broken. Here they are as a review:
(a) No consecutive perfect fifths or perfect octaves between any two voices.
(b) The leading note should move to tonic.
(c) No more than an octave between any two adjacent voices, except tenor and bass which may be any distance apart.
(d) Double the root of the chord wherever possible. The next most desirable note to double would be the fifth, often effective in a first inversion chord. Never double the leading note. Double the 3rd of vi in a V-­vi progression; and the 3rd of the vii° chord which must be in first inversion.
(e) Avoid awkward leaps in a voice (augmented 4th, major seventh), and as a general principle, when a fairly large leap is made, the next note should return.within the leap.
6)   Keep fthe parts within a comfortable singing range. Some extremely high or low pitches may be used but be aware of very high or very low tessitura.
7)   Play your work over many times to become familiar with its sound.

These seem like quite a few rules to remember, and they are, but with practice and correction, they will become more or less second nature. Your primary guides are the models themselves -- the Bach Chorales, and each of the phrases you will be given to harmonize will be actual phrases that Bach has harmonized. After you have completed each exercise to the best of your ability, comparisons should be made with the original. Differences, of course, should be noted, but it is not to be expected that your harmonization will be the same as Bach's.

This is the Bach harmonization (modified to eliminate some elements not yet covered) of the phrase you have completed. It is the first phrase of the Chorale "Nun lob; mein Seel', den Herren".

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Figure 69

Note these points:
1)   Normal progression is followed with the exception of vi - iii which has been noted as a common exception.
2)   The first two chords of the second last measure are both in first inversion (root position would have produced parallel octaves).
3)   The root of the chord is doubled in each case, except in the ii 6/3 chord where the fifth is doubled. Note that the doubling of the root here would have produced parallel octaves between tenor and soprano.
4)   There is some contrary motion, between soprano and bass, some similar motion, and some oblique motion. The bass is an interesting melody in its own right. Play, sing, and listen carefully to this harmonization.



ASSIGNMENT

Harmonize the following phrases in four parts. Note that this is the same melody as the one we have just done but in a different key and a different metre. Bach does not harmonize it exactly the same as the previous one; therefore, approach it from a fresh view point.

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From this point on, the work of individual students will have to be corrected for technical errors as well as stylistic weaknesses. However, the Bach models should still be studied by the class after each harmonization is completed and retained for reference. This is Bach's harmonization of "O Herre Gott, dein gottlich Wort." (Slightly modified.)(Click for example))

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Figure 70

It is not always necessary to decide upon a complete chord progression and bass line for a phrase before doing the inner parts. Sometimes, it might be found desirable to sketch in a few bass notes and then complete the inner parts, and continue along in this manner. Often, it is desirable to do the cadences first and then go back to the beginning. Any method which produces good results is acceptable.

Voice Leading

We have been discussing harmonization so far primarily in terms of chord progression. The selection of an effective chord progression is fundamental, and at this stage of development a harmonization should mainly be the result of a methodical selection of chords. However, the importance of a good bass line has already been indicated, and this to some extent will determine chord choices. As one becomes more adept at this work, the melodic interest in the bass, as well as the innier parts, will more and more become determining factors of the harmony, although the underlying chord structure will always predominate. The main point here relates to a method of working. At this stage in the study of harmony, the student will first work out the chord progression, and then consider the voice leading (melodic interest of the individual parts). Sometimes an inversion or a chord will be changed to improve the voice leading. At a more advanced stage, the voice leading and the chord progression will be determined more or less simultaneously, with both factors having equal importance.

The following is an example taken from Piston (Piston, Walter, Harmony ( 3rd edition), W.W. Norton and Co. Co.Inc., 1962, Page 22 and 28.) illustrating how voice leading might be improved in a predetermined harmonic progression. The basic approach is to open up the spacing between the parts. Note changes in doublings and instances where the common tone is not kept in the same voice in successive chords.(Click for example))

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Figure 71

The dominant seventh chord.

Triads are not the only available tonal material which can be used in the harmonization of melodies. By super imposing an additional third on the two existing thirds of the triad, we form a new type of chord called the seventh chord. This is a thicker, much fuller sounding chord. Any triad can be converted into a seventh chord. The most common and important of these seventh chords is the Dominant Seventh, the seventh chord constructed on the dominant degree of a scale. Here is the dominant seventh of C major. It is frequently familiarly known as G7.

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Figure 72

This chord is used functionally in exactly the same way as the ordinary dominant triad. In four part writing, the problem of doubling does not usually exist since this is a four note chord. However, occasionally the fifth might be dropped, and then the root would be the logical note to double. The basic rules of voice leading in the use of V7 are that the seventh always descends by step, and the leading note, of course, rises by step to tonic. This is V7 to I in C major (a Perfect Cadence).(Click for example))

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Figure 73

The Dominant Seventh chord can be written in any inversion. The following are the four inversions of the chord with their full numberings. (Remember that the numbers simply indicate the intervals above the bass.) The full numberings are not used in actual practice and the bracketed numbers indicate the ones which are omitted.

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Figure 74

Here are the V7 to I progression in first, second, and third inversion. Notice the voice leading. Notice the necessity for I 6/3 in the third inversion; this is a very useful progression. Play and sing these examples and listen carefully to the sounds.(Click for example))

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Figure 75

ASSIGNMENT

Write the followingprogressions in four parts:
(a) V7 to I 5/3 in Bb major
(b) V 6/5 to I 5/3 in D major
(c) V 4/3 to I 5/3 in Ab major
(d) V 4/2 to I 6/3 in F# Major


Index

(c) KEYBOARD HARMONIZATION OF SIMPLE SONGS
We will now turn to a form of harmonization which will necessitate a different approach from the Bach chorale style -- keyboard chording of simple song. In this work, intuition and ear, rather than rule will be of primary importance. However, a theoretical understanding of the processes should not be dismissed if the most effective results are to be achieved. (In conjunction with, or in lieu of a keyboard, a guitar, or an autoharp with a sufficient number of chords on it can be used.) The harmonic rhythm in most songs is much slower than in the Bach chorales, and frequently one chord will last for several measures. Relatively few chords will satisfactorily harmonize many songs -- I, IV, and V or V7 are often all that are needed.

Let us sing the following well known melody and then try to harmonize it.
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Figure 76

Procedure:
1)   Sing the melody.
2)  Determine the key (Eb +) and write out I IV V and V 7 in block form in bass clef. (To play a thick chordal accompaniment is not always musically very satisfactory, but the primary purpose of this exercise is chord selection and the chords should be very easy to perform.)
3)    Work out the chord selection together with the class primarily by a trial and error method. Play little bits of the melody and find out what chords are needed as you go along. Strike one chord per measure even if it is a repetition.

The most logical chord choice for this piece is as indicated in Figure 76.

Analysis of Result:
1)   Only the three chords I IV and V7 were needed
2)   Frequently the melody provides clues by outlining parts of chords or complete chords (bar 1, bar 9, bar 13).
3)   There are several instances of notes which do not belong to a chord, but which nevertheless fit in well with a particular chord. These are called "non-chord tones" and are very important to our study of harmony. These non-chord tones serve to keep the music moving, add tension to it, and color the harmony. (Examples: D in bar 3, C in bar 4, G in bar 5, etc.) We will study the various types in more detail later, but for the time being be aware of their existence. It is these non-chord tones, particularly when they are located on strong beats, which make it most difficult to determine the correct chord, and it is in these instances that one's ear must be most keenly attuned to what is needed.

Do the following tune together with the class. They probably will have great difficulty in discovering the key to the correct harmonization of this, which is the fact that the first beat of practically every measure is a non-chord tone. When this is discovered the chord progressions turns out to be very simple. Without the proper harmonization the basic rhythmic drive of this tune would be lacking.

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Figure 77

ASSIGNMENT

In the same manner harmonize the following tune (or tunes). It might be advisable to give out several tunes to a group, with different people doing different ones, or allow students to select their own from a song book. For the time being stick to major keys, and only material that can be harmonized simply with three or four chords. The students should play their own solutions at the keyboard, and suggestions for improvement, if necessary, be made by teacher and fellow students. Suggested tunes for harmonization. ­­


Figure 78

This work can be continued at spaced intervals interspersed with the chorale type of harmonization.

Index



(d) NON-CHORD TONES
We have already noted the presence of non-chord tones in the songs we have been harmonizing. Let us now take a closer look at them to see if we can discover the different varieties of non-chord tone. All the circled notes in the following example are non Chord tones.

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Figure 79

1)   Unaccented passing tone -- moves stepwise between two chord tones and occurs on weak beat - bar 3.
2)   Suspension-dissonance occurs on strong beat and is a chord tone held over from previous chord. Usually resolves down­ ward by step. - bar 4.
All the rest are unaccented passing tones.
­­


Figure 80

1)   Appogiatura - unprepared dissonance on strong beat; resolves downward by step - bar 1.
2)    Suspensions - bars 2 and 3.
3)  Appogiaturas - bars 4 and 5.
All the rest are similarly suspension or appogiaturas.

These are the principal non-chord tones, although a few other types do exist.

Let us now see examples of all of them in a four part setting, with definitions. This material is taken from McHose (see above).
1. Passing tone - when a non-harmonic tone is interpolated stepwise between two harmonic tones of different pitch, it is called a passing tone.


Click to play example

2. Suspension - if,in a progression of two chords, any of the tones of the first chord are delayed from their normal stepwise movement at the moment the second chord appears, the non-harmonic dissonant effect is called a suspension.


Click to play example

3. Neighboring tone - when a non-harmonic tone is interpolated stepwise between two harmonic tones of the same pitch, it is called a neighboring tone. ­­


Click to play example

4. Anticipation - if in a progression of two chords, any of the tones of the first chord move stepwise to forecast the consonant intervals of the second chord, the dissonance is called an anticipation. ­­


Click to play example

5. Escape tone - if a non-harmonic tone is derived stepwise and leaps to a harmonic tone, it is called an escape tone. ­­


Click to play example

6. Appoggiatura - if a non-harmonic tone is derived by leap, and resolved stepwise, it is called an appoggiatura. ­­


Click to play example

7. Changing tones - if a non-harmonic tone is derived stepwise, and leaps an interval of a third in the opposite direction to another non-harmonic tone which is resolved stepwise, the dissonant tones are called Changing tones. ­­


Click to play example

Figure 81

Possibilities for the use of non-chord tones in harmonization are as follows:
1.   An unaccented passing tone may be inserted when any given voice leaps a third.
2.   A suspension may be inserted when any given voice decends by step.
3.   A neighboring tone may be inserted when any given voice repeats a tone on two consecutive beats.
4.   An anticipation may be used when any given voice descends by step.
5.   An escape tone may be inserted when a part descends by step.
6.  An appogiatura might be inserted anywhere if it sounds effective.
7.   A changing tone might be used when a voice stands still or leaps a third.

For the time being use only unaccented passing tones, suspensions, and neighboring tones when harmonizing a melody. However, consider that any of these non-chord tones might be present in the given melody. Add the non-chord tones after the harmonization has been completed, and use them judiciously; do not overuse them. Generally speaking, non-chord tones serve to keep the music moving, and in chorale style are usually in the form of eighth notes. They also serve to spice up the harmony and to create points of tension. They are usually sprinkled throughout the texture, occuring at various points in all the voices. However, sometimes they are used more or less continuously in a single voice, mainly the bass. Suspensions are numbered according to the interval between the dissonance and the bass (see figure 81, number 2: 4-3 sus, 7-6 sus, 9-8 sus). The 4 - 3 is the most effective suspension. Avoid doubling the suspended note. The 9 - 8 is the next most effective suspension. The suspended note in this case is obviously doubled in the bass.



ASSIGNMENT

Harmonize the following chorale phrase in four parts. The dominant seventh chord may be used, as well as all triads in either root position or first inversion.. Also try to use some passing tones in alto, tenor, or bass parts. (Give the students the melody from the following four part harmonization.)
Bach's solution of #54 "Lobt Gott, ihr Christen, allzugleich."(Click to play example). ­­


Figure 81a

Index



(e) DICTATION
The following dictation exercises should be given periodically interspersed with the other work. Intensive training in ear training and sight singing are beyond the scope of this book.

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Figure 82

The melodies of the following chorale phrases may be assigned for harmonization. Bach's harmonizations involve primarily triads (with the occasional use or suggestion of a dominant seventh) and a moderate use of non-chord tones.

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Figure 83

In your study of Bach's solutions, note particularly instances when "basic rules" of chord progression, voice leading, and doubling are broken. Try to determine the reasons for this wherever possible. Frequently, it is simply a matter of achieving a more interesting melodic line in a particular voice or avoiding parallel fifths or octaves. However, various reasons may be ascribed to these situations, including the subjective one that "Bach did this because he liked the sound."

Index

(f) SECONDARY SEVENTHS
We have already noted in our study of the Dominant Seventh Chord, that a seventh chord can be constructed on any degree of a scale. Simply add another third (a seventh above the root) to the existing triad.

Let us write out the scale of F major, and then complete the seventh chord for each degree of the scale

. ­­


Figure 84

These seventh chords are all in root position. It is also possible to use them in any inversion. Remember the commonly used numberings for seventh chords - root position = 7, first inversion = 6/5, second inversion = 4/3, and third inversion = 4/2. These seventh chords are not all alike. Let us analyze them to determine the differences in sound and construction. What we will discover about the sound, construction and use of seventh chords in F major will be information that can be readily transposed to any major key.

Results of analysis:

There are four types of seventh chord which can be constructed (diatonically) over a major scale.
(a) Dominant seventh on V which has been discussed earlier. Only one seventh chord of this type can be derived diatonically in a major key.
(b) Major seventh on I and IV. This chord consists of a +3 P 5 and +7. Note its sound which has a certain sharpness of quality. It is frequently found in popular music as well as some early twentieth century serious music, particularly of the French school.
(c) Minor seventh on ii, iii, and vi. This chord consists of a -3 P5, and -7. It has a smoother quality of sound than the major seventh and was very commonly found in Bach's music as well as all other music through the centuries.
(d) Half diminished seventh on vii°. This chord consists of a -3 °5 and -7. It was favored by late romantic composers such as Wagner.

Let us construct an example of each of these four types of seventh chord on E. Write it in root position and in each of its inversions, in block form, treble clef. Play and listen to the results.

­­


Figure 85

Analyze fully the following chorale phrase:
Procedure:
1) Sing and then play the example.
2) Indicate the root of each chord - Roman numerals.
3) Indicate the inversion - Arabic numerals.
4) Circle all non-chords tones and state their type (PT - passing tone, APP - appogiatura, UNT or LNT - upper or lower neighboring tone, SUSP - suspension. The suspension also has to be explained in terms of its movement from dissonance to resolution over the bass: 4 - 3, 9 - 8, etc.) Remember that non-chord tones are exactly what their name implies, and any note that can be explained as part of a triad or seventh chord should not be classified as a non-chord tone even though it sometimes appears to function melodically as one.
5) Note unusual and interesting features. In this example, note particularly the use and writing of seventh chords.
6) Sing and play the example again.

­­


Figure 86

Summary:
In terms of chord progression, secondary sevenths are used in exactly the same way as triads. The main difference between using a. seventh chord or a triad in one of sonority, not function. In the Bach chorales we frequently find the minor sevenths, particularly on ii and vi, where as the others are much less frequently used. They are as often used in first inversion as in root position and the progression ii 6/5,V, I can be considered a standard cadence formula. Here it is in F major (note the 4 - 3 suspension) : ­­


Figure 87

In regard to voice leading, note that the seventh is always made to drop by step. It is frequently prepared by being present in the same voice in the previous chord, thus assuming the guise of a suspension, but this preparation is not essential.



ASSIGNMENT

Harmonize the following chorale phrase in four parts using some secondary sevenths and some non-chord tones:

­­


Figure 87a

(Click for example)


The leading note
As you must have noticed from analyses of Bach harmonizations, Bach is rather cavalier in his treatment of the leading note and it certainly does not frequently rise to tonic. Note the very unusual resolution of the leading note in the pre­vious example. More commonly, Bach has the leading note drop a third to the fifth of the tonic chord at a cadence. However, this only occurs when the leading note is in an inner part. When the leading note is in soprano or bass, it still should resolve upwards directly to tonic.

Harmonizing a figured bass
The basis for the harmonic style with which we are at present dealing assumed its definitive form in the seventeenth century. It became established simultaneously with the concept of BASSO CONTINUO. This concept emphasized the dominance of chord progression over voice leading as the determining factor in harmony. The basso continuo specifically is a figured bass part (a bass line with figures indicating the inversion and content of each chord) given to the harpsichordist who improvises an accompaniment from this music. He performs the bass line as written and fills in the chords from the figuring in an interesting manner above the bass line. The bass line is also usually doubled on another bass instrument such as cello, bassoon, etc.

So far we have approached the Bach chorales from the point of view of analysis of existing harmonizations, and from our own experience in harmonizing the melodies and comparing them with Bach's harmonizations. One can also do a given figured bass. This approach is easier than the harmonization of a melody since the chords are spelled out for us. Our primary challenge, next to interpreting the figured bass correctly, is to write an interesting melody (soprano) to go with this bass, and also to write satisfying inner parts.

Let us harmonize the following figured bass together: (#3, 1st phrase). ­­


Figure 88

Procedure:
(1)   According to the numbering, figure out the notes in each chord. If necessary, each chord can be jotted down in block form on a separate sheet so that you will be perfectly clear about the tonal material being used. A sharp beside a number means to raise that note one semi tone. A flat, of course, would indicate the reverse.
(2)  Think primarily of an interesting melody to go with this bass. It should involve a certain amount of contrary motion, and might include the odd passing tone.
(3)   Jot down a few notes of the melody, and then fill in the inner parts to see if they work. Continue along in this manner.
(4)   Play over the exercise, and then compare it with the Bach harmonization.

("Ach, Gott, von Himmel sieh' darein."(Click for example)) ) ­­


Figure 89

Let us now proceed to analyze this chorale phrase because you must have noticed by now that it is not in a major key. What is the tonic? Answer: A. What key is it in? Answer: A minor.

Harmonization in the minor mode

When harmonizing in a minor mode, we should still essentially utilize normal progression as we do in major mode melodies. The same basic cadence formulas will still apply --­ V or V7 to i, IV to i, V to VI and i, ii°, IV or VI to V. However, there is more complication in working the minor due to the fact that sometimes harmonic minor and sometimes melodic minor scale forms are used. Let us write out the harmonic minor scale and the melodic minor scale and see what triads would occur as a result of these scale forms.

­­


Figure 90

Bach chorale phrases can frequentiy be harmonized using the material of the harmonic minor scale, and we should utilize, particularly at the beginning, just those chords. Note that we have now two diminished triads, ii°and vii° and in both cases it is desirable to write them in first inversion and double the bass note. The deceptive cadence in this scale is particularly effective with both V and VI being major triads. The usual doubling should still be utilized if possible. The mediant triad is now augmented and can be used as a quasi dominant triad with III× to i being a possible progression. When harmonizing with this scale, the melodic interval of the augmented second may occur.

­­


Figure 91

This is generally frowned upon and the F (sixth degree) is frequently raised to F# . However, Bach does not always disdain the augmented second, and therefore, it can sometimes be allowed, and sound very effective.

The melodic minor scale presents a whole new range of chord possibilities. Look them over carefully. The use of some of them, on the descending form will generally suggest a modulation (see next section) to the relative major. This will allow the possibility of vacillating between major and minor mode and still essentially retain strong normal progression.

The chords on ii, IV and vi° on the ascending form might suggest a modulation to VII (the natural leading note key). If no modulation occurs, they can sometimes be used to avoid the augmented second interval, but are otherwise not too strong and should be sparingly used. No real feeling of dominant harmony exists in the minor mode without the use of the raised leading note.



Index

(g) MODULATION

ASSIGNMENT

Do a simple block chord keyboard harmonization of the following melody. This can be done with a few basic chords, but use your musical intuition if you run into any difficulty. This is the simplest logical solution.

­­



Figure 92

Take up these points:
(1)   Key is G major
(2)   I IV and V7 suffice for most of it. However, Em7 and A7 are needed on the first line of the refrain.

The reason that these chords are needed (particularly the A7 which does not belong diatonically to G major), is that the melody modulates to a new key, D major. In D major these chords are simply ii7 and V7 -- a very normal progression.

Modulation is very common in music, and creates many new melodic and harmonic possiblities. A modulation can be very smooth and practically imperceptible as the music glides from one key into another, or a modulation might be very abrupt and obvious.

In order to effect a smooth modulation which is what we will be primarily concerned with at this point, the music should move to a RELATED KEY by means of a PIVOT CHORD.

Related keys

In simplest terms, a related key is a key which has the same key signature, or one sharp more, or one flat more than the key from which it emanated. For example, the related keys to G major are E minor, D major, B minor, C major and A minor. Give examples of related keys to any given major or minor keys.

Another way of looking at the concept of related keys is to interpret the keys to which the music modulates in relation to the original key, which is considered a tonic. For instance, if music is in a major key, its supertonic, mediant, sub­ dominant, dominant, and submediant keys are all related keys. If the original key was A major, its related keys would be B minor, C# minor, D major, E major, and F# minor. The related keys emanating from a minor key have to be considered on the natural minor scale and are the keys of the mediant, subdominant, dominant, submediant, and flat leading tone. Music that starts out in F minor and modulates to Bb minor is modulating to the key of the subdominant, a related key. A modulation from D major to E minor would be a modulation to the supertonic.

If music starts out in a major key, the most common modulation would be to the key of the dominant. Its next most likely modulation would be to the submediant or relative minor. The third most likely modulation would be to the subdominant key. Of course, there is no hard and fast rule; it depends on the melody and the desires of the composer. From the minor, the key of the mediant (or relative major) is the most frequent modulation, then probably the key of the flat leading tone. Example, A minor to G major. However, any related key is a possible modulation.

The Pivot Chord
Since our aim at this point is to effect very smooth modulations, these must be done by means of a pivot chord. The pivot chord is a chord which is diatonically common to both keys, and can be considered the point at which the modulation begins to take place. In Figure 92, the progression at the point of modulation is:

­­


Figure 93

The pivot chord is the one enclosed in a box: V in G major becoming I in D major. Note that the modulation is to the key of the dominant. In the return to the tonic key, I of D major becomes V of G major.

In the previous section dealing with the minor mode, we noted two common modulations from the minor. An example which contains both modulations is as follows:
"Puer Natus in Bethleham."

­­


Figure 94

Points to note:
1)   The two pivot chords.
2)   The suggestions of a 6/4 chord in the second. measure to retain movement in the bass.
3)   The rare use of a pIagal cadence to end a phrase.

Summary regarding modulation

Modulation is one means of extending our harmonic vocabulary. Some melodies obviously suggest modulation (Figure 92). In others, modulation is optional, and they can be harmonized with or without certain modulations. It is simply a matter of taste and style. The melody of Figure 94, for example, could have been harmonized with only the modulation to G major. However, Bach also found it desirable to include a modulation to C major. Frequently we will find two identical phrases in Bach chorales harmonized differently, and the difference is very likely to involve a modulation.

For the present we will concern ourselves only with modulation to related keys by means of a pivot chord.

ASSIGNMENT

Harmonize the following chorale phrases. Your harmonization may include modulation as well as non-chord tones and seventh chords. (Once the exercises have been cleared of all purely technical errors, compare the harmonizations with those of Bach in all aspects -- chord progression, voice leading, doubling, spacing, and non-chord tones. Only the melodies will be given to the students. The complete harmonizations will be used later for comparison. These exercises do not all have to be done at once, but can be spread out over a period of time interspersed with ear training, keyboard harmony , and analysis.

Interesting points to note in Bach's harmonizations:
"Ach Gott, von Himmel sieh' darein".

1.   Although this chorale is in the minor mode, it uses strong normal progression.
2.   Note that the submediant F is sharp when rising to G sharp, but is natural when dropping to E.
3.   The last chord of the second measure is a diminished seventh chord. This is a seventh chord built on the raised leading note and contains a minor third, diminished fifth, and diminished seventh above the root. It is dramatically very effective, and can be used in any inversion. Commonly, all parts resolve by step as they do here.
4.   Note the interesting use of non-chord tones throughout this chorale.
5.   The last measure is basically i 6/4 V 5/3 i 5/3. This chord progression can be considered a cliché cadential formula and is very frequently used. In the i 6/4 the bass note (the fifth of the chord) is always doubled. In this instance there is added interest because of the G# appogiatura and the 4-3 suspension. Notice also the unusual resolution of the leading note.

"Aus meines Herzens Grunde."

1.   The tenor note F sharp in bar two falls below the bass G. This is called overlapping and is usually to be avoided.
2.   Note the chord changes below the soprano half notes. In two instances good secondary sevenths are produced.
3.   Parallel tenths between tenor and bass in the second phrase produce good sonority.

"Ermuntre dich, mein schwacher Geist."

1.   Modulations to dominant and submediant keys. The first modulation is smooth, effected by the pivot chord I in G becoming IV in D. The second modulation is abrupt and is produced by a chromatic shift in the bass - D to D sharp. This type of modulation occurs often between phrases, and in this instance is very fleeting as we are immediately back in G major.
2.   Note the almost continuous use of eighth note movement distributed throughout the voices.

"Wach 'auf, mein Herz."

1.   In contrast to the previous example, the modulations in this beautiful harmonization are not demanded by the melody.
2.   Although most of these modulations can be explained by means of a pivot chord or a chromatic shift, some of them, particularly those in the last phrase, really come under the designation of altered chords within a key, a concept beyond the scope of this book.
3.   Notice the use of anticipations at the third and fourth cadences.
4.   Notice how the harmony of the last phrase is predominately governed by the sequential movement of the bass.

Detailed analysis of Bach's chorale harmonizations is intriguing in itself, and will amply repay the effort. At this stage the subtle mutual interdependence between chord progression and part writing will begin to be noted. The judicious and effective use of non-chord tones, seventh chords, and modulation are also factors which are mutually interrelated, and the overriding feeling of strength, tension, and variety are what underlie the characteristic harmonic style of Bach.

Index



Part Four
ARRANGING (Studies in texture)

So far, in our work in harmony, we have only worked idiomatically in one medium, the SATB choir. We used the piano in our keyboard harmonizations,. but it was primarily used as a convenient means of selecting chords, and no special consideration was given to the quality of the sound produced. Each medium of performance places the music which it is presenting in a particular context of color. Each medium also has its characteristic ways of presenting music (i.e. textures), and when the music seems to be ideally suited to the medium so that the resultant effect enhances both the music and the instruments or voices which are performing it, then we say that the music is idiomatically written, or well arranged.

Arranging, like harmonizing, is an art, and what may please some ears will possibly displease others. There are certain conventional ways of using and combining instruments that have been established by many composers and arrangers, but once the fundamentals regarding the uses, limitations, and potential of instruments have been learned, there is considerable scope for originality and experimentation in arranging. The arranger, on any given occasion, can choose to do something conventional or something unusual depending upon his own tastes, the effect he wishes to produce and the purposes for which his arrangement was written.

We will approach this subject on a very practical level, and undertake two projects. One will be to arrange a chorale (which we have harmonized ourselves) for winds, and the other will be to write a proper piano accompaniment to a song. Analysis and experimentation again play a major role in the learning process. Score study and listening to recorded or live performances, as well as writing our own arrangements and having them performed are the ways of developing skill in arranging. Our two projects can only serve as an introduction to this vast subject, but through them we can begin to grasp some of the concepts regarding the uses of instruments, as well as acquire some insight in to the whole area of arranging.

Index

(a) WRITING FOR BAND
Let us first harmonize one of the following chorale melodies: ­­


Figure 96

(These harmonizations should be checked for errors and weaknesses, and then re-worked by the student until they are acceptable. Since this is an exercise in harmonization as well as arranging, the Bach harmonization can be used for comparison and analysis as before. )

The decision as to whether the arrangement should be written for full band, or small wind ensemble will depend upon what is available to the group as well as the preference of the teacher. Even if a full band is available it might be worthwhile to have students select their own ensembles of a minimum number of instruments (perhaps ten). If more work is desired in this area, then some arrangements could be written for full band and some for small ensembles. However, we will use a full band score for investigation some of the fundamentals.

Our two-stave chorale harmonization will ultimately be converted in to a full score for all the instruments. involved. The parts for the individual players will then be copied from the score. Remember that actual performance is the aim of this project, and therefore, the arrangement can only be written for instruments which are available, and within the abilities of the participating performers.

Question:
What must we know before we can write this chorale arrangement for winds ?
Possible answers:
1.  The choice of instruments involved.
2.  The capabilities of these instruments and players.
3. The correct notation of score and parts.
4.  The sound of these instruments, individually and in combination, and some ideas for arranging.

Let us begin by looking at a page from an actual band score. This is an arrangement of a chorale for full band. Study it carefully. What information does it provide?

­ ­


Figure 97

(Taken from '142 Chorales for Band', Ed. Philip Gordon, Bourne Co., 136 W 52nd St., N. Y. 19.)

Points to Note:
I.  The instruments involved.
2.  The division of some instruments (e.g. trumpets, clarinets, etc.)
3. The order in which they are listed on the score.
4.  The various keys (some are transposing instruments).
5.  Detailed analysis can also provide information regarding matters of blend, balance and disposition of the four voices of the chorale.

It might be useful to note here that in a band there are usually several instruments to certain parts. The personnel of bands varies according to availability, playing ability, and the preferances of the director. Here is the make-up of an ideal band as recommended by the College Band Directors National Association:
(House, Robert W., Instrumental Music for Today's Schools, Prentice Hall, Englewood Cliffs, N.J., p. 106.)

flute - 6; oboe - 2; English horn - 1; E flat clarinet 1; B flat clarinet - 18; E flat alto clarinet - 6; B flat bass clarinet - 3; contrabass clarinet - 2; bassoon - 2; B flat soprano saxophone - 1; E flat alto saxophone - 1; B flat tenor saxophone - 1; E flat baritone saxophone - 1; B flat bass saxophone - 1; French horn - 4; E flat cornet,- 1; B flat cornet - 3; B flat trumpet - 3; trombone - 3; bass trombone - 1; euphonium (baritone) - 1; tuba - 3; percussion - 5.

Parts for English horn, contrabass clarinet, soprano and bass saxophones, and E flat cornet are rare, and are not included in the arrangement we are studying. On the other hand, a part for piccolo (usually one player) is quite common. Some arrangements have separate parts for trumpet and cornet.

Let us now investigate each of the instruments we will be using to find out some of its limitations and capabilities. ­ When we talk about capabilities of a given instrument, we must distinguish between the skilled professional and the performer at our disposal - the ideal and the real. Therefore, our major source of information should be our own performers who can provide us with all the pertinent facts, but we will also indicate here the "ideal" -- (theoretical information regarding the potential of each instrument,­ its lowest and highest possible note etc.) We will provide the full range as well as a suggested range for amateurs (which can be modified according to the abilities of your performers). All ranges will be notated at actual pitch, and the transpositions which affect certain instruments will be explained later. . In addition, we will provide certain facts regarding the practical uses of various instruments. These are open to discussion, expansion, and demonstrion by your own players.


FLUTE
See Figure 98 (Click the 'Back' button on your browser to return)

The lowest notes can only be played softly in relation to most other instruments. On the other hand, the notes of the top octave are difficult to play softly.
The PICCOLO is pitched roughly one octave higher than the flute. It has a sharper, thinner, more penetrating sound.


OBOE
See Figure 99 (Click the 'Back' button on your browser to return)

The lower notes of the oboe are very difficult to play softly. Although this is a challenging instrument to master, and intonation is often a problem, its distinctive tone quality makes it a welcome addition to a wind ensemble.


E FLAT CLARINET
B FLAT CLARINET
E FLAT ALTO CLARINET
B FLAT BASS CLARINET
See Figure 100 (Click the 'Back' button on your browser to return)

There are four distinct registers of tone quality in the clarinet: the bottom fifth - full rich sounds; the next octave - ­ tending to thinness and some awkwardness of fingering; the next octave - ­bright and clear; the top octave - tone, intonation, and fingering problems.

Compare these registers on the different clarinets and note the tone differences -- for instance between the second highest octave on the B flat clarinet and the Bass clarinet.


BASSOON
See Figure 101 (Click the 'Back' button on your browser to return)

The lowest notes on the bassoon are full and penetrating, and like the oboe cannot be played softly. The highest notes have some resemblance to an alto saxophone. Like the oboe, a fairly rare and difficult instrument, but a very welcome addition to the group.


ALTO SAXOPHONE
TENOR SAXOPHONE
BARITONE SAXOPHONE
See Figure 102 (Click the 'Back' button on your browser to return)

The lowest notes on the saxophone are generally loud and difficult to control. Otherwise, it is probably the most fluent of all wind instruments.


B Flat TRUMPET (or CORNET)
See Figure 103 (Click the 'Back' button on your browser to return)

The tone quality of the cornet is lighter than that of the trumpet.


HORN in F
See Figure 104 (Click the 'Back' button on your browser to return)

The French horn can blend as readily with woodwind as with brass instruments.


TROMBONE AND BARITONE
See Figure 105 (Click the 'Back' button on your browser to return)

Although they have the same range, there is quite a difference in tone between the trombone and baritone. The tone of the baritone is much closer to that of the tuba. The Bass Trombone extends the range downward by a fourth.


TUBA
See Figure 106 (Click the 'Back' button on your browser to return)

It provides a solid bass foundation to the brass instruments.

Range on brass instruments varies a great deal according to the experience and ability of the player. It is very difficult for performers to play softly in the upper extremity of their range, and the lowest notes are generally muffled or wooly sounding.


Percussion and string bass will be omitted from our considerations here. However, some of the percussion instruments can be used to good effect in a chorale arrangement. Investigation of the instruments themselves, and the playing techniques can be made through demonstration by the percussionists, and notation as well as some ideas in scoring can be learned through a perusal of some scores.

TRANSPOSITION

As we have already noted, not all instruments actually sound the pitches they are reading. A number of instruments are reading in a key quite different from the actual key of the music, but are sounding the pitches of the real key. Also, some instruments are sounding pitches an octave higher or lower than the notated pitch. These instruments are all TRANSPOSING INSTRU­ MENTS

.

Let us refer to the score and locate and list all the non-transposing instruments.

What is the actual (concert pitch) key of this chorale? B flat major.

The concert pitch instruments are:
  flute, oboe, bassoon, trombone, baritone, tuba (basses),
  piccolo sounds an octave higher than written.
  string bass and timpani sound an octave lower than written.
  (Percussion are of no definite pitch).

The other instruments can now be categorized as:
B flat instruments, E flat instruments, and F instruments.
B flat instruments: B flat clarinet, bass clarinet, tenor saxophone, B flat trumpet (or cornet).
E flat instruments: E flat clarinet, alto clarinet, alto saxophone, baritone saxophone.
F instruments: French horns.

A simple rule can put us into perspective with these transposing instruments: when the instrument plays its C, it sounds its name. (e.g. When an alto saxophone plays C, it sounds E flat; when a trumpet or French horn plays C, they sound B flat and F respectively).

Here are the rules for the proper notation of these transposing instruments.
1.  B flat clarinet and B flat trumpet (or cornet):
Transpose everything up one tone. Practical procedure: add two sharps to the key signature (remember that one sharp cancels out one flat), and raise everything one degree. Accidentals in the original will remain as accidentals and everything else will fall into place.

See Figure 107 (Click the 'Back' button on your browser to return)

2.  Bass clarinet and tenor saxophone:
All the clarinets have exactly the same fingering and read exactly the same notation. The same is true of all the saxophones. (note that only the treble clef is used).
See Figure 108 (Click the 'Back' button on your browser to return)

However, in actual pitch these instruments cover a wide range. Therefore, clef changes and octave transpositions are also necessary in notating some of these instruments. Practical procedure for bass clarinet and tenor saxophone: Add two sharps to the key signature and transpose everything up one tone plus one octave into the treble clef.
See Figure 109 (Click the 'Back' button on your browser to return)

3.  E flat clarinet:
Transpose everything down a minor third. Practical procedure: Add three sharps to the key signature and lower every­thing a (minor) third.
See Figure 110 (Click the 'Back' button on your browser to return)

4.  Alto Clarinet and Alto Saxophone:
Transpose everything up a major sixth. Practical procedure: Add three sharps to the key signature and raise every­ thing a (major) sixth.
See Figure 111 (Click the 'Back' button on your browser to return)

5.  Baritone Saxophone:
Transpose everything up a major sixth plus an octave. Practical procedure: Add three sharps to the key signature and transpose as stated into the treble clef.
See Figure 112 (Click the 'Back' button on your browser to return)

6.  French Horn:
French horns read in treble clef, up a perfect fifth. Practical procedure: Add one sharp to the key signature and transpose everything up a (perfect) fifth.
See Figure 113 (Click the 'Back' button on your browser to return)


BLENDING AND BALANCE

Identical instruments playing ensemble music will produce the most homogeneous blend. Instruments of the same family (e.g. clarinets, saxophones, recorders, strings) will be the next most homogeneous combination and, of course, are capable of a wider range of pitch. However, even within these homogeneous families there are definite distinctions of tone color between the different instruments (e.g. alto and tenor saxophone or violin and string bass). Actually, a single instrument like a clarinet in its different registers is already producing a variety of tone colors. In combining instruments, one cannot separate matters of blend from the problems of balance. One must think not only of proper choice of instruments, but also of suitable dynamic markings, and careful rehearsal of the performers before the desired result is achieved. A perfectly homogeneous sound is not always desirable, especially if you wish to underline the shape of the individual voices. If only identical instruments are used, the balance should be right with an equal number of instruments on each part. If a family of instruments is used, this should also be the case, although normally in a string section there are more violins to a part than violas, more violas then cellos, and more cellos than basses. However, in a simple four voice section .of music, basses frequently double cellos an octave lower, and a similar combination of baritone and tuba is often used in a wind ensemble to good effect.

All the brass instruments might be considered a fairly homogeneous family providing that one bore in mind the distinctions that do exist. Although one French horn is often written to equal one trumpet and one trombone in a small ensemble, it might be more reasonable to think of two French horns as being equal in strength to one trumpet or one trombone. Listen to, and become aware of the subtle distinctions in tone color which exist between the cornet, trumpet, French horn, trombone, baritone, and tuba. These could possibly be paired off in terms of blend in the following manner: cornet and French horn; trumpet and trombone; baritone and tuba.

As has already been mentioned, the indication of dynamics is extremely important in arranging. Not only can they be used to compensate for what might be a lack of balance, but sometimes to indicate emphasis of a particular part. Of course, dynamics are basically used in terms of the whole ensemble to produce fluctuations and contrasts in volume. At best, they can only be approximate guides to performance, and the performer must interpret the dynamic indication (as indeed he must interpret all notation) in the light of what he feels the composer's or arranger's intentions are. Similarly, notation of articulation is very important. Remember that the wind player interprets the slur as a clear direction regarding tongueing and non-tongueing. Therefore, notate it scrupulously with this in mind, and also remember the use of the tenuto, the half-staccato, and the verbal direction "legato".

In arranging a chorale for winds, it is possible and even desirable to double individual voices in octaves. For instance, the soprano is frequently given to the first trumpet and doubled an actave higher by the flutes. It is practically useless to use the flutes in their bottom octave when used in combination with brasses. Similarly, the bass part is, frequently given to the baritone and doubled an octave lower by the tuba. Clarinets may also be used to double inner parts an octave higher. If it is impossible to achieve a perfect balance, it would be logical to give some extra weight to the soprano and bass parts.

Most wind music for amateur groups is written or arranged in the "flat" keys F major (or D minor) through to A flat major (or F minor) are the most common range of keys. These are the easiest keys to play in, and generally produce the most felicitous tonal results. There is some validity and justification to utilize these keys for practicality, but is unfortunate that some quite competent wind players never evolve beyond them, and this is very limiting not only in terms of the music that one hears, but also in terms of their development as performers.

Let us now have a closer look at Figure 97 to see exactly how this particular chorale was arranged for band.

ASSIGNMENT

Reduce this portion to a two stave, four part harmonization.
Result:
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Figure 114

This little assignment has given us an insight into this particular arrangement. Now let us further summarize by noting exactly what each instrument is doing. The simplest procedure would be to take each voice of the chorale and see how it has been scored. (Notice how this harmonization differs from a typical Bach chorale harmonization and how there has been a re-scoring in the second phrase) .

Analysis of Chorale Arrangement (a one note deviation from the SATB vocal line will be ignored here):
1.  Soprano in normal range:
     Alto Sax I; Cornet I; Oboe (second phrase);
2.  Soprano one octave higher:
     Flute (Piccolo is two octaves higher); E flat clarinet;
     Clarinet I (first phrase);
3.  Soprano one octave lower:
     Horn IV; Trombone I (second phrase);
4.  Alto in normal range:
     Alto Sax II (slight deviation); Cornet II;
5.  Alto one octave higher:
     Clarinet II (first Phrase) ;
6.  Alto one octave lower:
     Trombone II (second phrase);
7.  Tenor in normal range:
     Tenor sax (slight deviation); Cornet III; Horn I (second phrase);
8.  Tenor one octave higher:
     Clarinet III (first phrase) ;
9.  Bass in normal range:
     Alto Clarinet; Bass Clarinet (some notes an octave lower); Bassoon; Baritone Sax; Trombone III; Baritone;
10. Bass one octave lower:
      Tuba; String Bass;
11.  other (instrumental parts which combine two or more of the SATB voices).:
      Oboe (first phrase); Clarinet I (second phrase); Clarinet II (second phrase); Clarinet III (second phrase) ; Horn I (first       phrase); Horn II; Horn III; Trombone I (first phrase); Trombone II (first phrase)

Summary
This detailed investigation should give us some idea as to how the arranger worked with this particular chorale. One of his reasons for varying the arrangement in the second phrase was to avoid placing the Clarinet I in the top octave. He sought to utilize the full possibilities of the total band range, to maintain a full texture and to keep instruments within easy playing ranges. Of the original SATB harmonization, only the bass and the soprano come through clearly as definite lines. The alto and tenor become obscured in the thickness of the texture. Instruments which are obviously used to fill out texture are the French Horns, and to a lesser extent the First and Second Trombone. This is a fairly conventional chorale arrangement and should give us sufficient insight into the problems ihvolved. We are now ready to proceed with our own arrangements, where we might follow this procedure or do something quite different.

ASSIGNMENT

Arrange your chorale harmonization of Figure 96 for winds writing it out in full score With all dynamics and articulation fully notated. (The score can be done with all parts written in concert pi tch.) Then write out the parts properly for the players involved and conduct your own arrangement.

Index

(b) WRITING A PIANO ACCOMPANIMENT
Let us analyze the following examples of piano accompaniment noting all features of the texture that we would find distinctive and interesting. It would also be useful to analyze the harmony so that we could see how a particular harmonization is worked into a piano texture, and how sometimes the harmony itself is influenced by the kind of texture that is utilized. Some of the chords will be unfamiliar to us but we will not discuss these here since our primary concern is texture. However, these encounters with unfamiliar progressions may widen our harmonic horizons and spur us on to further study in this area.

(The following examples of piano accompaniments are taken from Guide and Accompaniments To The Canadian Singer, Book 5, W. J. Gage Ltd., Toronto, Canada)

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Figure 115

1.  A simple four part texture with the tune in the top part.
2.  Spacing in the right hand comprises mainly thirds, and the left hand emphasizes fifths and octaves.
3.  The harmony is simple With a judicious sprinkling of non-chord tones, and generally one chord per bar, with an accelerated harmonic rhythm toward the end.

Summary: A simple, effective example of straight four part writing for piano. Note the spacing in particular.
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Figure 116

1.  The accompaniment has a significantly independent rhythmic pattern which complements the vocal line.
2.  The melody is actually discreetly outlined in the top notes of the right hand.
3.  The left hand is primarily unison or octave with the right hand in two or three parts completing the chords.

Summary:
An attractive rhythmic pattern and harmonization using some altered chords. Effective for piano.

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Figure 117

1.  Melody not present in accompaniment.
2.  Typical off-beat rhythmic pattern. Note range and spacing. Note how accompaniment pattern changes to complement the sustained notes in melody.
3.  Some of the chord changes are introduced simply to add interest to the bass line.

Summary:
A conventional accompaniment appropriate for this tune.

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Figure 118

1.  Melody is present in the right hand.
2.  Two bar introduction derived from a fragment of the tune.
3.  The texture is generally appropriately delicate to go with the delicate tune. Notice how the texture shifts from unison, two part, three part, and four part.
4. Notice the inner pedal on A from bars 10 to 13.
5. Notice the details of dynamics and articulations.
6. Notice the changes in harmonic rhythm.

Surnmary:
This accompaniment is quite complex. and artistic; worth careful study.

(From this point, the harmonic analysis will be dropped.)

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Figure 119

The texture of this accompaniment is consistent throughout. A typical 3/4 rhythm in the left hand stating the chords. The melody is present in the right hand filled out with chord tones and often doubled in octaves.

Summary:
A full, rather cliché accompaniment suitable for a sentimental song.

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Figure 120

This is an interesting example of simple two part counter­ point. One part is the tune itself (right hand), and the second part is a complementary melody. Although the two part texture is consistent throughout, the simple chord progression upon which it is based can easily be detected. Note the balance of motion between the parts; when one part moves in longer note values when the other moves in eighth notes. Notice how the left hand of the third measure seems to be an imitation of the right hand of the first measure. The middle section of the song ("Then came a piper ....." ) is treated slightly differently. It is placed at a higher pitch level and is largely similar motion in tenths with little bits of more independent movement occuring occasionally in the left hand.

Summary: A simple charming treatment of a simple tune.

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Figure 121

This is an illustration of an accompaniment creating an atmospheric background suitable to a particular kind of tune (lullaby).

Final Summary: Accompaniments may or may not contain the melody. Sometimes the melody is suggested rather than presented entirely. .'When the melody is absent, the purpose of the accompaniment is either used to state a basic rhythm or to create atmospheric background. Ths texture of the first bar or two is often consistent throughout, but it may be varied to coincide with a change .in the melody. The left hand frequently consists of unison, octaves, or fifths with the fuller sounds reserved for the right hand. The kind of tune for which the accompaniment has been written frequently dictates the style of the accompaniment - i.e. sentimental, humorous, rhythmic, atmospheric, etc. However, it is mainly dependent upon the taste and inclinations of the arranger, and good solutions are possible for each tune.

ASSIGNMENT

Write a piano accompaniment for the following melody: ­ ­

Select your own chord progression and your own style of accompaniment, and notate it in full on three staves (voice and piano) including all markings of dynamics and articulation. (The teacher may substitute any fairly simple melody for this one, or give additional assignments along these lines using other tunes. If more intensive work is desired in this area, specific accompaniment styles can be assigned for the students to imitate, but the intention here is simply to introduce the topic and to provide scope for creativity.)

Two modern arrangements
We present here for interest, but without comment, treatments of folksongs by two eminent twentieth century composers, Igor Stravinsky and Bela Bartok. The Stravinsky example is a reduction of an orchestration while the Bartok was written specifically for piano. Note the harmony as well as the texture of these examples.

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Figure 122a

Austin, William W., Music in the Twentieth Century, W. W. Norton and Company, Inc., N. Y., p. 269.
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Figure 122b

Bartok, Selected Works for the Piano, G. Schirmer, Inc., N. Y.

Index



Part Five
MELODY WRITING (Studies in form)

We now turn to melodic analysis as our final item for study. When we have completed this we will have dealt with all basic elements in music - melody, harmony, texture, instrumentation, and form, although only to a very limited degree. The aim of this section will be to gain some experience in composing melodies, and then to combine melody with harmony and texture to produce an original composition.

It is impossible to think of melody without also thinking in terms of form. How long will the music be? What shape will it take? Will there be a climax? Where? How? Should there be repetition ? Form involves all these factors and more. Just as a story is broken down into chapters, paragraphs, sentences, clauses, phrases and words, a musical composition is similarly composed of movements, sentences (or periods), phrases, and motives. When we begin to see how these elements are juxtaposed, and how all the fragments serve to produce a unified and meaningful whole, we begin to understand the form.

We will analyze a few melodies in order to discover the logic behind them. Then we will turn to writing melodies of our own. We may prefer to write intuitively, and be able to do something quite satisfactory in this way, but it is always an advantage to be able to stand back and scrutinize your endeavours objectively and intelligently. Through this means you can frequently detect ways in which your creation can be improved and refined.

Definition of Terms
Sentence or period - a complete musical statement having a clearly defined beginning, middle, and end.
Phrase - the largest portion of a sentence which is apparently complete in itself (analogous to a clause in language) . In performance, the shape of the phrase must be presented clearly, unbroken by undue breathing or other disruptions.
Motive - a fragment of melody, within a phrase, which has some identifiable characteristic of rhythm and interval, and is found repeated in its original or in varied forms throughout the work.
Sequence - a form of repetition of a phrase or motive, beginning on a different pitch. The repetition may be exact in interval and rhythm or there may be some variation, but not enough to render the phrase or motive unrecognizable.
Inversion - the reversal of direction of the intervals of a phrase or motive.
Climax - the obvious point of focus in a work. This is the point to which everything has been developing, and from which there is a subsiding of tension. !t is usually characterized by being the highest and loudest point in a work. However, a strong feeling of climax is not an essential element in a musical composition.

We will now look at some melodies to see what secrets they yield. Some of these tunes are already familiar to us. Since they are the same ones we looked at in terms of their Accompaniments.

1.   "Our Country" See Figure 115 (Click the 'Back' button on your browser to return)
Questions:
(a) How many phrases are there? Four - two measures each.
(b)What is the form in terms of the phrasing? AA (sequence) BC.
(c) How many characteristic motives are there? Three - Bar one (a), Bar two (b), Bar six (c).
(d) Where is the climax? Bars five and six.

We can see that this is a highly integrated little melody consisting entirely of three motives leading to a climax just past the midpoint and descending to a conclusion. Rather than any direct repetition of phrase or motive, there is considerable sequence.

. The form may be described as follows (upper case=phrase, lower case=motive, s=sequence):
A (a + b)
As(as + bs)
B (as + c) {climax}
C (cs + bs )

2.   "Had A Little Dog" See Figure 116 (Click the 'Back' button on your browser to return)
(a) How many phrases are there? Five - two measures each.
(b) What is the form? AA (variation) ABC
(c) What are the characteristic motives and where are they found?
The characteristic motives are bar one (a), the descending major third, and bar two (b) the descending perfect fourth. The second phrase presents these same motives in variation. The fourth phrase contains only motive (b) in sequence ( C to G, B flat to F) and With some variation. The final phrase is an entirely new rising motive bringing the song to a conclusion.

.

This song is interesting because of the unusual number of phrases - five. Normal phrasing would consist of two, four, or eight measure phrases, either two, four, or eight in number making up a sentence. This song has no obvious climax but the music seems to push relentlessly toward the last note.

3.   "Strawberry Fair" See Figure 118 (Click the 'Back' button on your browser to return)

Ignore the two bar introduction.
Phrasing ( 4 + 4 + 4 + 4 measures)
Motives     (a) rising second                        (bar 1)
            (b) rising fourth                        (bar 3)
            (c) three note descending pattern        (bar 9)
            We can find thse three motives in every bar of the song.

Bar 1    (b) anacrusis (a)
Bar 2    repeat of bar 1
Bar 3    (b)
Bar 4    (c) ornamented
Bar 5     repeat of bar 1
Bar 6     repeat of bar 1
Bar 7 & 8 (c) anacrusis inverted - climax - 
              (high point, sustained note, rhythmic tension)
Bar 9     (c) sequence
Bar 10    repeat of bar 9
Bar 11    repeat of bar 9
Bar 12    (c) sequence
Bar 13    (b) anacrusis (a) (b)
Bar 14    (c)
Bar 15    repeat of bar 13
Bar 16    (c) ornamented

We can see from this detailed analysis that the form of this melody is quite complex, and that it contains a high degree of unity as well as great diversity. The ornamentation, sequencing, inversion, and juxtapositions of these three basic motives all contribute to the creation of this finely wrought melody. We may hear the argument at this point that all these details of motivic development were not in the composer's mind when he made up this tune, but this does not alter the fact that they are there.

The broad form of the tune seems to be AABA but the second A is thwarted by the leap to the climax, and the last A contains a telescoping and a re-juxtaposition of the motives of the first A. We find here, then, variation and development of material on a small scale similar to the variation and development found in the master works of the great composers.

4.   "The Moon"

See previous assignment (Click the 'Back' button on your browser to return)

Phrasing - (4 + 6)
Here we have an example of two unbalanced phrases. The second phrase is extended by means of a two bar interpolation. Play or sing through this song omitting bars 7 and 8. This makes it sound normal and complete. The last four measures were essentially a repeat of the first four measures.

What material is present in the interpolation? In order to discover this we will have to reduce the first phrase to its motives - (a) bar 1, (a sequence) bar 2, (b) bar 3, and (a varied) bar 4. The second phrase contains (a) bar 5, (a inverted and varied) bar 6; bar 7 contains another variation of (a) derived rhythmically from bar 6 and melodically from bar 2. Bar 8 is a repeat of bar 7. The effect of this interpolation is a momentary pause, followed by bar 9 which repeats motive (b) and bar 10, another variation and inversion of (a) derived from bar 6.

The shape of the first part of the song is a smooth arch leading to a small climax in the third measure. The second part through its variants, rises more rapidly, but this is counter­ balanced by the two bar interpolation which produces a moment of calm, and the expected climax is then reached. (The word "climax" is used here in a technical rather than a dramatic sense).

5.   "Autumn Holiday"

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Figure 124

Sentence I    (4 + 4)
Sentence II    (4 + 6)
Sentence III   (4 + 4)

The two measure extension on the second phrase of Sentence II is primarily for the purpose of establishing the modulation to the key of the Dominant. If we called sentence I A, the essential form is A A1 A2. Key motives are (a) bars 1 and 2, (b) bars 11 and 12, and (c) bars 13 and 14. Most of the other material is derived from these motives.

This song, by one of the great composers of the late 19th Century, merits careful scrutiny, but we will not deal any further With it here. Note, however, the modulation and the extension of the fouth phrase.



ASSIGNMENT

Continue the following openings of melodies to any reasonable length which you think will constitute a complete sentence. You may attempt to do it intuitively or you may consciously work it out in terms of motive, sequence, repetition, etc. Either way, once the melody has been completed, view it critically, playing or singing it over several times. In this way you may find ways of improving it. The matenal presented in the first few bars should re-occur in one form or other throughout the melody, although this does not necessarily obviate the use of some new material. (After these melodies have been discussed, it would be interesting to look at the complete original melody, bearing in mind that any resemblance between it and the results of the assignment would be purely coincidental.)

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Figure 125

Conclusion
We are now ready to experiment with original compos­ itions of our own. Since experimentation is our primary objective, these compositions can be of any sort, in any style. We can remove all restrictions except the practical one, that these works should be suitable for performance by available performers. As we require more information, we must seek it out from available sources - scores, reference books, professional musicians.

Of course, one can also continue the study of musical composition more academically. The field is vast. We have just begun to explore matters of harmony, texture, orchestration, and form. The musical masterworks of the past, as well as the great variety of musical approaches found in our own time provide us with a boundless treasure of material for performance and study. Numerous interesting texts have been written on various facets of the art.

Even if you are not inclined toward composition or musical scholarship, a basic understanding of the mechanics of music will always serve you well as a performer or simply as an interested listener.



BIBLIOGRAPHY

Apel, Willi, The Harvard Dictionary of Music, Harvard University Press, Cambridge, Mass.
Austin, William W., Music in the Twentieth Century , W. W. Norton and Co., I nc., N. Y.
Bach, Riemenschneider, 371 Harmonized Chorales and 69 Chorale Melodies with Figured Bass, G. Schirmer, Inc., N. Y.
Bartok, Bela, Selected Works For The Piano, G. Schirmer, Inc., N. Y.
The Canadian Singer, Books 4, 5, and 6, Beattie, Wolverton, Wilson, Hinga (ed.), W. J. Gage Ltd., Toronto.
Guide and Accompaniments To The Canadian Singer,-Book 5, W. J. Gage Ltd., Toronto.
McHose, Allen Irvine, Basic Principles of the Technique of 18th and 19th Century Composition, Appleton - Century - Crofts, Inc ., N. Y.
42 Chorales For Band, Philip Gordon (arranger and editor), Bourne Co., 136 West 52nd St., N. Y. 19.
Piston, Walter, Harmony, W. W. Norton and Co., Inc., N. Y.
Piston, Walter, Orchestration, W. W. Norton and Co., Inc., N. Y.



Index