Printable Module 9: Imitative Polyphony
written by William Atkinson

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  1. Josquin des Prez, Missa Pangue Lingua, Gloria (c. 1510)
    Josquin des Prez, Gimell CDGIM 009

  2. J. S. Bach, The Well-Tempered Clavier, Book II, Fugue in E Minor (1738) (Keith Jarrett, harpsichord)

    J. S. Bach, The Well-Tempered Clavier, Book II, Fugue in E Minor (1738) (Glenn Gould, piano)

  3. Bela Bartok, Music for Strings, Percussion, and Celesta, first movement (1936)

  4. Ramin Amir Arjomand, Five, #1; #5(2000)
    All rights reserved by Ramin Amir Arjomand


E.E. Cummings, "Five", I

after all white horses are in bed

will you walking beside me, my very lady,
if scarcely the somewhat city
wiggles in considerable twilight

touch (now) with a suddenly unsaid

gesture lightly my eyes?
And send life out of me and the night
absolutely into me....a wise
and puerile moving of your arm will
do suddenly that

                                        will do
more than heroes beautifully in shrill
armour colliding on huge blue horses,
and the poets looked at them, and made verses,

through the sharp night cryingly as the knights flew.

-e. e. cummings


E.E. Cummings, "Five", V

if i have made, my lady, intricate
imperfect various things chiefly which wrong
your eyes (frailer than most deep dreams are frail)
songs less firm than your body's whitest song
upon my mind--if i have failed to snare
the glance too shy--if through my singing slips
the very skillful strangeness of your smile
the keen primeval silence of your hair

--let the world say "his most wise music stole
nothing from death"--
                                 you only will create
(who are so perfectly alive) my shame:
lady through whose profound and fragile lips
the sweet small clumsy feet of April came

into the ragged meadow of my soul.

-e. e. cummings


Questions on musical works

(Before answering the following questions, you may find it helpful to review Reading 1, the Sonic Glossary entry "Imitative Polyphony.")

For each of the musical works:

Is more than one melody imitated over the course of the work? (In the case of the Amir Arjomand work, the word "melody" is broadly defined.) If so, how are the melodies after the first one introduced?

How many voices participate in each round of imitation? (In cases where you can't decide on an exact number, make guesses.) In the examples by Josquin and Amir Arjomand, does the number of voices have any significance for the text that is imitated?

After all the voices enter, does the texture stay the same or does it change?

Is imitation of some kind always going on, or does it come and go?

Are the "points of imitation" (times when imitation happens) systematically deployed? That is, can you predict when the next one is going to happen?

Does a melody that is imitated come back later? If so, is it somehow modified or transformed when it comes back?



1. Imitative Polyphony

A musical texture featuring two or more equally prominent, simultaneous melodic lines, those lines being similar in shape and sound.

Polyphony is usually divided into two main types: imitative and non-imitative. Either the various melodic lines in a polyphonic passage may sound similar to one another, or they may be completely independent in their rhythm and contour. If the individual lines are similar in their shapes and sounds, the polyphony is termed imitative; but if the strands show little or no resemblance to each other, it is non-imitative. Each of these types may also mix with or succeed one other in a musical passage.

In contrast to the independence of the musical lines in non-imitative polyphony, imitative polyphony allows the members of a polyphonic texture to share audible features of the melodic material, as they echo portions of it among the various parts. Although imitative polyphony may appear in music from a variety of cultures, it is particularly prominent in Western European art music. Similarly, although it appears in medieval compositions from as early as the 13th century, imitative polyphonic textures were especially exploited in music from the later Renaissance and the Baroque periods, from approximately 1500-1750. In the following example of imitative polyphony--a vocal composition from the Renaissance written by Josquin des Prez--each of the four voice parts begins successively with the same musical phrase. This opening phrase begins alone in the highest of the parts, and then works its way down to the lowest voice in the texture. Each of the entering voices thus imitates its predecessor as it presents its material [Example 1: Josquin, Ave Maria, Virgo Serena, stanza 1].

But significantly, after each of the parts has sung its opening phrase, it does not resort to accompanying material; instead it continues to spin further melodic phrases that are also taken up by each member of the ensemble in turn. As a result, each of the four participants in this texture retains its musical identity and interest throughout this section of the piece--they all are thus truly polyphonic. And, since each of the parts also recalls the others with similar sounding material, the polyphonic texture is imitative. The same principles of sharing musical material among the various melodic lines can be heard in these two selections from instrumental compositions by the Baroque composer J.S. Bach. As in the previous example, each part enters individually with a similar musical phrase, and then continues to act as an important participant as the piece progresses. The first example shows the procedure in an orchestral context [Example 2: J.S. Bach: Third Orchestral Suite, "Overture"]. The second demonstrates imitative polyphony in a piece for solo harpsichord, played by a single performer. [Example 3: J.S. Bach: Well-Tempered Clavier, Book 1, Fugue no 2 in C minor (opening)]

Summary: Polyphony may be imitative or non-imitative, depending on how closely the various musical lines resemble each other. If the individual lines are similar in their shapes and sounds, the polyphony is termed imitative; but if the strands show little or no resemblance to each other, it is non-imitative. Each of these types may also mix with or succeed one another in a musical passage. Imitative polyphony is associated particularly with Western music from the later Renaissance and the Baroque periods.


2. Zarlino ÷ The Art of Counterpoint

Chapter 1

I have given sufficient attention in the two preceding books to the first part of music ÷ the theoretical or speculative ÷ and have covered things that are pertinent and necessary to the musician. There remains for me to discuss in the two books that follow the second or practical part of music. This consists of the compositions of songs or melodies for two ot more voices. Practitioners call it the art of counterpoint.

Since counterpoint is the principal study of this part, we shall first see what it is and why it is so named. I consider counterpoint to be that concordance or agreement which is born of a body with diverse parts, its various melodic lines accommodated to the total composition, arranged so that voices are separated by commensurable, harmonious intervals. This is what in Chapter 12 of Part II I called "proper harmony." It might also be said that counterpoint is a kind of harmony that contains diverse variations of sounds or steps, using rational intervallic proportions and temporal measurements; or that it is an artful union of diverse sounds reduced to concordance. From these definitions we may gather that the art of counterpoint is a discipline which teaches one to recognize the various elements in a composition and to arrange the sounds with proportional ratios and temporal measure.

Musicians once composed with only a few dots or points. Hence they called this counterpoint. They placed on against another as we now place one note against another. A dot represented a tone: just as a point is the beginning of a line as well as its end, a sound or tone marks the beginning and end of a melody and forms the consonance out of which counterpoint is made. Perhaps it would have been more reasonable to name this countersound rather than counterpoint, since one sound was placed against the other. Not to depart from popular usage, I have continued to call it counterpoint, by which we understand point against point or note against note.

There are two kinds of counterpoint: simple and diminished. The simple is composed solely of consonances and equal note-values ÷ whatever these may be ÷ placed against one another. Diminished counterpoint has dissonances as well as consonances, and may employ every kind of note-value, as the composer wishes. It proceeds by intervals or singable spaces, and its values are reckoned according to the measure of its tempus. It is in the nature of counterpoint that its various sounds or steps ascend and descend simultaneously in contrary motion, using intervals whose proportions are suited to consonance; for harmony has its origin in the joining together of a diversity of opposed elements. Counterpoint is considered best and most pleasing when the best manners, ornaments, and procedures are gracefully employed, and when this is done according to the rules that the art of good composition requires. It should be observed that by melodic interval is meant the silent passage made from one sound or step to the next; it is intelligible though inaudible.

Chapter 27

As I have said, every composition, counterpoint, or harmony is composed principally of consonances. Nevertheless, for greater beauty and charm dissonances are used, incidentally and secondarily. Although these dissonances are not pleasing in isolation, when they are properly placed according to the precepts to be given, the ear not only endures them but derives great pleasure and delight from them. They are of double utility to the musician (in addition to other uses of no small value). The first has been mentioned: with their aid we may pass from one consonance to another. The second is that a dissonance causes the consonance which follows it to sound more agreeable. The ear then grasps and appreciates the consonance with greater pleasure, just as light is more delightful to the sight after darkness, and the tastes of sweets are delicious after something bitter. We daily have the experience that after the ear is offended by a dissonance for a short time, the consonance following it becomes all the more sweet and pleasant. Therefore the musicians of older times held that compositions should include not only perfect and imperfect consonances, but also dissonances; for they realized that their work would achieve more beauty and charm with them than without them. Had they composed solely with consonance, they might have produced agreeable effects, but nonetheless their compositions (being unmixed with dissonance) would have been somehow imperfect; and this from the standpoint of singing as well as of composition, for they would have lacked the great grace that stems from these dissonances.

Though I have said that in composing we use consonances primarily, and dissonances incidentally, it must not be thought that these dissonances can be placed in counterpoints or compositions without rule or order, as is sometimes done, for confusion would result. Care should be taken to use them in an orderly, regular fashion, so that all may turn out well. Two things must be borne in mind above others, and I believe all the beauty and charm of every composition resides in these: the movements of the melodic parts, ascending and descending in similar or contrary motion; and the proper collocation of the consonances in the texture. Of these things, with GodÔs help, I intend to speak; indeed this has always been my main purpose...

Chapter 51

...The voice that begins the fugue, whether strict or free, is called the guide, and the voice that follows it is called the consequent. When these voices are separated from one another by a minim or semibreve rest, or certain other rests, the resulting fugues are the most intelligible because of the proximity of the parts to one another. The ear comprehends their relationship best when the voices are close together in time, and for this reason composers strive to keep them so, if possible, in fugal writing. But constant practice of this close imitation has resulted in such a common idiom that a fugal pattern cannot be found that has not been used thousands of times by various composers.

To achieve some variety in our work, let us use only rarely this close imitation, and thus we shall depart from those consequences that are so common. Let us apply all our ingenuity to write fugues that are fresher. By separating somewhat the guide from the consequent [in time], as by rests of three or five minims, we will undoubtedly achieve something novel. I do not wish to imply that fugues at the distance of a minim or semibreve [i.e., the second voice starts only a few seconds after the first voice] should never be written, but I suggest that their use be sparing, so that we do not fall into the cliches found in every book of music, which I refrain from illustrating for fear of being tedious or offending someone...


3. Marpurg's Abhandlung von der Fuge (Paper on Fugue): Imitation and fugue in general

1. The restatement of a subject by use of the same tones in the same part is called repetition. The restatement of a subject by use of different tones in the same part is called transposition. The restatement of a subject through repetition in different parts is called imitation...

3. The alternating use of one subject in various parts may occur not only at the unison but also at all other intervals. Hence there are eight general species of imitation [corresponding to eight standardized sizes of interval]...

4. imitation in similar motion is that kind of imitation in which one voice answers the other, using the same direction of interval progressions; an imitation in dissimilar or inverted motion is that kind of imitation in which the ascending intervals in the preceding part become descending in the following part, or vice versa...

6. In some instances of imitation, the second part will follow the first part, using changed note values. If this occurs with increased note values, for example with notes twice the original value, so that eighth notes become quarters and quarters become half notes [i.e. twice as long, twice as slow], it is called imitation in augmentation. If it occurs with decreased note values, for example with notes half their original value, so that half notes become quarters and quarters become eighth notes, it is called imitation in diminution.

10. All the kinds of imitation which have been discussed are either periodic or canonic.

a) Periodic imitation is that form of imitation in which the part which follows uses only a short portion of the opening part...

b) Canonic imitation is that form of imitation in which the part which follows uses the melodic line of the opening part, note for note throughout. [A round, such as "Row, row, row your boat," involves canonic imitation.]

11. Periodic imitation in all its kinds and species may be used in two ways:

a) Incidental periodic imitation, which, according to the judgment of the composer, may occur here and there in various instrumental and vocal compositions, such as solo sonatas, duets, trios, quartets, concertos, symphonies, cantatas, and arias.

b) Formal periodic imitation, which restricts the imitative use of a basic subject by certain rules to certain places. Such a composition, which is based on a definite theme imitatively developed in various voices under certain rules in a continuous, uninterrupted manner, is called a periodic fugue.

12. Thus there are two major categories of fugues, namely canonic and periodic. This treatise encompasses both categories. We shall follow common usage, however, and call the canonic fugue simply canon and the periodic fugue, simply fugue.

13. Since a fugue can be written with two, three, four, or more parts, we have to distinguish between two-part fugues, three-part fugues, four-part fugues, and fugues for more than four parts.

14. In all fugues five characteristic elements are to be distinguished:

a) The first or opening statement, or the theme: phonagogos in Greek; dux, thema, subjectum, vox antecedens in Latin; sujet in French. All of these terms refer to the basic melodic line with which the fugue opens.

b) The answer or second statement: comes, vox consequens in Latin; risposta or conseguenza in Italian; reponse in French. These terms refer to the repetition of the opening melodic line as it appears in another voice transposed to a higher or lower register.

c) The exposition: repercussio in Latin. This term applies to the arrangement by which the opening statement and the answer are alternately heard in different registers [i.e., high and low]. It is often wrongly used to designate the answer.

d) The counterpart or counterparts [sometimes referred to as countersubject]. These terms are used for the free melodic writing in the parts which are placed against the fugal theme.

e) The episodes. This term refers to the portions which serve as connection between the different expositions while the theme is not used.

15. A fugue, the characteristic elements of which are properly arranged according to the rules, is called a regular fugue. A fugue in which these elements are not so arranged but rather are arbitrarily handled is called an irregular fugue. There are different kinds of irregular fugues, distinguished according to the various ways in which one consideration or another may be followed. No special instructions are needed in this respect, since it is easier to depart from the rules than to follow them. Irregular fugues have often appeared under the title caprice in the keyboard literature. On the other hand, regular fugues were often given the name caprice by Frescobaldi, Froberger, d'Anglebert, and other masters of their time. In such a case, the term was applied to fugues written on a theme using short note values, so that the entire composition showed rather quick movement. During this period, a composition entitled fugue was allowed slow and deliberate rhythmic movement only...

16. A regular fugue is either strict or free, according to the treatment of the theme.

a) A strict fugue is a fugue which deals throughout its course with almost nothing but the theme. The theme will reappear immediately after the first exposition, if not in its entirety at least in various components. From the theme, or from the counterpart which is set against the answer which repeats the theme, are derived all other accompanying melodic lines and all episodes by either abbreviation, augmentation, diminution, change of rhythm, or the like. All these forms of the original thematic material are then logically combined in harmonic treatment. If such a strict fugue is carried out at length, and if it contains a number of contrapuntal artifices, such as various kinds of imitation, double counterpoint, canonic writing, and modulations, it may be given the Italian name ricercare or ricercata ÷ a fugue showing utmost skill, a master fugue. Such are most of the fugues of J. S. Bach.

b) A free fugue is a fugue which does not deal with the theme throughout. The theme or its various components do not appear at all times, though rather often; and whenever the theme is relinquished, the techniques of imitation and transposition are applied to a short, well-chosen secondary subject which is related in character to the theme or its counterpart, but not necessarily derived directly from them. Such are most of the fugues by Handel.


Questions on readings


Reading 2: Gioseffo Zarlino

After laying the basic groundwork of counterpoint in Chapters 1 and 27 (and in many other chapters not included here), Zarlino discusses in Chapter 51 the issue of the time delay between imitative entries. How well do the works in this module satisfy Zarlino's preferences?

Reading 3: Friedrich Wilhelm Marpurg

In the fugue by Bach, can you locate the five elements listed by Marpurg in point 14? Can you locate them in the movement by Bartok, which is also considered a fugue? Is the Bach fugue a strict fugue or a free fugue, according to Marpurg's distinction in point 16? (Put another way: Marpurg claims that Bach's fugues are mostly strict fugues. Is he right about this one?) Is the Bartok fugue strict or free?