Poème du Délire


Bruce Mather


In 1979 I discussed with Ivan Wyschnegradsky two concert projects, one for the Fragments Symphoniques I, II, III for four pianos in quarter tones which I realized in January 1980 as a memorial concert (as Wyschnegradsky had passed away in September. 1979) and the first performance of his three works in sixths of tones for three pianos, Prélude et Fugue op 30 (1945), Composition op.46 No. 1 (1961) and Dialogue àTrois op.51 (1974). For the concert on April 21st, 1983 two Canadian colleagues wrote new pieces, Aspects of Jack Behrens and Le Parcours duJour of John Winiarz and I produced Poème du Délire. The following year the three Wyschnegradsky works plus those of Behrens and myself appeared on a vinyl disc of McGill University Records. Among Wyschnegradsky's manuscripts without opus numbers I discovered years later the Deux Mèditations also for three pianos in sixth of tones. I conducted the first performance of the work on May fifteenth, 1996 with pianists Pierrette LePage, Louis Philippe Pelletier and Paul Helmer.

As I had used for my quarter tone works the non-octaviant spaces in "régime onze" (i.e. cycles repeating at a major seventh), I opted for his analogous system for sixths of tones. In this system (see Appendix A) the interval of the major seventh (33 sixths of tones) is divided into three equal intervals of 11 sixths of tones (one sixth less than a major third). These notes are in white. Each interval of eleven sixths of tones is subdivided into three intervals of four, four and three sixths of tones (or 2/3 tone, 2/3 tone, semitone). For notation in sixths of tones I use only four new signs:


2_Page_244b.jpg        (a sixth tone higher)

2_Page_244c.jpg         (two sixths tone higher

d.jpg       (a sixth tone lower),

2_Page_244e.jpg        (two sixth tones lower).



 It should be explained that in Poème du Délire (and in the works of Wyschnegradsky in sixths of tones) Piano I is tuned a sixth of a tone sharp, Piano II at normal pitch and Piano III a sixth of a tone flat:


Figure 1: Tuning of Three Pianos in Sixth of Tones

From one position to the next, in the eleven positions one of the three notes rises a sixth of a tone. From position 1 to position 2 it is the 'white' note, from position 2 to 3 it is the first black note and from position 3 to 4 it is the second black note. The result is that, while in position 1 the division of each interval of 11 sixths of tones is 4,4,3, in position 2 it is 3,4,4 and in position 3 it is 4,3,4. In order to obtain smaller melodic intervals (1 or 2 sixths of tones) I combine two positions such as 1 and 6 (Example 2). This produces many intervals of thirds of tones and some sixths of tones.



Example 1: Combination of Positions 1 and 6


Example 2: Melodic Structure of Section B


Example 3: Harmonic Structure of Section B

Formally Poème du Délire is characterized by the presence of six different elements or textures, most of which return in a different context, duration or contour. Here are the six elements:


Here is the large-scale formal plan in four sections, determined by the return of the elements.


Figure 2: Large-Scale Formal Plan of Poème du Délire

It is interesting to observe the role of each element in the large-scale structure. "A" starts the work as a long slow monody. It ends the second and third sections as fast monodies. In the final section it overlaps with elements "B" and "C". In section I "B" starts with a higher melody joined soon in dialogue by a lower strand. In section II it appears, much shorter, with a low melody in fast groups of 2 or 3 notes. In section III the fast groups appear in a dialogue, high and low. In the final section the fast groups are transformed into element "A". Element "C" appears in section I and then in section IV, accompanying the monody "A" and then alone, ending the work. Element "D" appears in sections I, II, III in progressively shorter versions. Element "E" appears in sections I, II, III in the same position with durations of 11, 8 and 8 bars. It begins the final section with a large development of 48 bars. Element "F" appears only once, at the end of section I.

Detailed Analysis

Section 1 A

As shown in Example 2, the eleven phrases of A use the combine positions 1+6, 3+8, 4+10, 7+1 and 9+3. The scheme below shows the melodic shapes, the note values used for each phrase, and the intervals used (in sixths of tones). Note the ritardandos from phrases 4 to 6 and 7 to 11 (see Figure 3).

Section B Harmonic structure (see Example 3)

In each of the 11 positions a white note is followed by 2 black notes. The intervals (in sixths of tones) are 4,4,3 or 3,4,4 or 4,3,4, always a total of 11 (A sixth tone small than a major third). Chords built from the white notes carry the letter "a", those built from the first black note "b", and those built from the second black note "c".


Figure 3: Section B Melodic/Intervallic and Shapes and Rhythmic Values

Of the ten chords most have seven notes but three (numbers 1,7,10) have 8 notes. The top notes of the ten chords are relatively static (from          to

2_Page_247c.jpg         ) but the ranges vary from just over two octaves (chord 3) to over 3 octaves (chord 7). Three intervals are used 11/6, 22/6 and 44/6. As can be seen below only two chords (numbers 4 and 9) have the same spacing:


Figure 4: Section B Chord Spacings

Divided among the three pianos, each piano has two or three notes of each chord (except for piano I in chord number 8 with only one note). The notes of each piano are presented in rhythmic ostinatos of 4, 5 or 6 values per half giving, respectively, eighths, quintuplets of eighths and triplets of eighths. The patterns of the triplets can be described as 7+(3), i.e. 7 notes in triplets then 3 in silence etc.                                     


2_Page_247f.jpgThe quintuplet pattern can be described as 5+(1), i.e. 5 notes in quintuplets plus one in silence                                                   etc.

The pattern in eighths is less regular as in Piano III p.2 (3+(2), 4+(1), etc.) As shown below the distribution of the ostinatos between the three pianos changes constantly:



Figure 5: Distribution of Ostinatos Between Piano in Section B



Example 4: Melodic Strands of Section B



Example 5: End of Section B




Example 6: Chord Vocabulary of Chorale:

Section B Melody

As shown in Example 4 a high melody (from m.2) is joined by a low melody (m.8). The two strands then converge. In order to create a rhythmic independence from the accompanying ostinatos the attacks of the melody are on the second or fourth sixteenth of the beat. In the first three phrases (over harmonic structures 4b, 5a, 6b) of 3, 5, and 5 notes, the actual perceived rhythm is h h h  \ q . h q q . h  \ q q q h h .The dialogue between the two strands starting at m. 8 can be represented thus:


Figure 6a: Representation of the Dialogue Between Two Strands at M. 8

The high line descends while the low line rises. The actual perceived rhythm for this passage is:


Figure 6b: Perceived Rhythm at M. 8

The values over chord 2_Page_249t.jpg are more complex with accelerations 6 , 4, 3, 3, 2 x s . At chord 2_Page_249u.jpg the two strands have the same melodic curve 2_Page_249v.jpgbut the durations of the first two notes are different. Each line creates an accelerando - ritardando pattern:


Figure 7: Rhythmic Contour in High and Low Strands

The phrase over chord 2_Page_249w.jpg is identical. Over the final chord 2_Page_249x.jpg the eighth-note pulsation returns with a dialogue similar to that at m. 8:



Figure 8: Dialogue of Eight-Note Pulsation in Final Chord of Section B

Example 6 shows the end of the section where the accompanying ostinatos stop, leaving the convergence of the two parts into a five-note ostinato in x s, then a trill and a final rising line with ritardando, all in position 2_Page_249y.jpg.




Example 7: Chordal Development of Chorale


In general the top notes of the chords of the seven phrases of this chorale (phrases of 4,4,4,4,3,3,2 chords) describe a slowly descending curve. The chords increase in density (3,5,8,13 notes, see Example 7). Durations in quarters are marked below each chord. Example 7 shows the vocabulary of chords of 3,5,8 and13 notes (all in position 1). The letters describe the range of the chords C (1 ¼ octaves), D (1 ¾ octaves) E (2 ½ octave), F 2 ¾ octaves), G (4 octaves), B (less than an octave).


This element is characterized by a melody in sixteenths or triplet eighths accompanied by chord in quarter, halves or dotted halves. Example 8 shows, in increasing range, the five-chord formations used: I, II, III, IV, V. Example 9 shows the actual chords and positions.

Example 8: Increasing Range in Section D



Example 9: Harmonic Structure in D

Figure 9 presents the various rhythmic patterns of the melody and the chords which are articulated in 2,3 or 4 attacks. There are patterns of 5, 6,7 and 9 beats for the 12 phrase which contain successively 6,6,7,5,7,5,9,9,5,5,6,6 beats.



Figure 9: 5-, 6-, and 9-Beat Rhythmic Patterns Between Melody and Chords in D


Example 10 shows the first melodic note of each phrase and its melodic direction (descending, rising descending and then rising, static). Example 11 shows the first two bars in sixth of tone notation.





Example 10: Contour Structure in Section D


Example 11: Opening Measures of Section D


Section E

The first section of trill motives marked "leger, envolé: (q = 150) lasts 11 bars. In fact the successive 5-note broken chords of the accompaniment last 6,6,6,10,9,7,7,6,6 beats as shown in Example 12. The five-note chords are constructed with intervals of 11 and 22 sixths of tones in three different formats:


Figure 10: Interval Formats for Construction of 5-Note Chords in E

Example 12 also gives the first note of each trill or chromatic scale motive which lasts a quarter, half or dotted-half. The motives pass from one piano to another in the order III, I, II, I, III, II, III, I, II etc. At the beginning the successive notes of departure are relatively conjunct (intervals of three and four sixths of tones) but the line becomes more and more mobile. At the end one has intervals of 11 and 22 sixths of tones.



Example 12: Opening Succession of 5-Note Chords in Section E



Example 13: Harmonic Structure of "Broken Chords" Section

Broken Chords p. 5 m.5

Following the first appearance of the trill motives this section acts as a parenthesis. As shown in Example 13, the seven chords are of 34, 21, 21, 13, 13 8 different notes following the numbers of the Fibonacci series with a progressively reduced range and dynamic level. The successive positions used are 3(+8), 6(+11), 9(+3), 1(+6),4, 7(+1),10.

Since there are only 36 different notes per octave in the scale in sixths of tones and since I wished to avoid octaves, I was obliged to used the resources of two positions in many cases (3+8, 6+11, 9+3 etc.) Example 13 shows that the chords are constructed first with the intervals of 22 and 11 sixth of tones with smaller intervals in the upper register.

The chords are broken in various ways. Chords 1,2, and 4 have a fast arpeggio followed by a solid chord (pp) in the upper register. Chord 6 is a solid chord (pp). Chord 3 is expressed in triplets (q =80), three notes at a time. Chord seven is expressed in 3+2+3 notes and chord five as single notes in triplet (q =120).

"F" - Tremolandos pg. 8

Already at the end of page three (at the end of B) we have a preview of the tremolando. Exclusively in the high register, this passage is in three parts. The first consists of tremolando clusters of six notes (two in each piano) rising through an octave followed by a descending monody.

Example 13 shows the notes from positions 10 and 4 and the actual notes played by each piano, 5 notes for piano I, eight for piano III and seven for piano III. Example 15 gives the descending monody in sixth of tones notation and a "diatonic version" allowing us to see more clearly the melodic curve in descending groups of 3,2,2,4,2,3 notes.


Example 14: Distribution of Notes from Positions 10 and 4 Among the Three Pianos in Section F

Example 15: Descending Monody in Section F

The second part starts with six note clusters like the first part but this develops into rapid ostinatos of five and six notes for each piano ending with a rapid broken chord of 21 notes. It uses positions 2+7. The third part is a counterpart to the first but with descending clusters and a rising monody. It uses positions 5+10.


Section Two

As already mentioned this section recapitulates some of the elements of section I with various modifications, the most extremes being A which is now a fast rather than a slow melody and is placed at the end rather than at the beginning of the section.




Marked "mystérieux, menaçant" this passage is only half the length of B in section I. The seven slowly rising chords of 9 or 10 notes use positions 5a, 6b, 7a, 8a, 8b, 10a, 11a (see Example 10). Instead of broken chord ostinatos exclusively of 4,5, or 6 notes per half there ar two new arrangements, one slower (3,4,5) and one faster (5,6,7) as follows:


The last chord is articulated ff with repeated three-note chords in each piano. The melodic element, exclusively in the low register, is reduced to two or three note "calls in x s (in chords 2 - 6) moving in third or sixth tones. In Example 16 these are indicated in 'black' notes.



Example 16: Harmonic Structure in B'

D p. 10

This passage lasts only seven bars (as opposed to 12 bars for D in section I). The melodic line is quite static but descends gradually (except for the last bar which rises to prepare for E). The bar lengths are 7,5,7,5,6,6,6 q s. Example 17 shows the seven harmonic structures, at first with a large span (three octaves) then converging to less than two octaves. The Roman numerals refer to the same chord construction used for D in section I.



Example 17: Harmonic/Registral Development of D pg.10


E end of p. 10

The general curve of this passage is descending. Example 18 shows that the seven successive structures (built with intervals of 11 and 22 sixth of tones) widens and then contracts. Example 18 also shows the first note of each trill pattern. They follow the following descending and rising patterns:


A' p.11 m.7

This rising monody (see Example 19) is developed rhythmically by the filtering of one six-beat pattern:


Figure 11: Rhythmic Filtering of 6-Beat Patterning in A'

Section III

The section has the same elements in the same order as section II, - B' and D being shorter, A' longer and E the same length.

B' p. 12

The four slowly-rising chord structures have 8,9,9,9 notes in positions 1a, 2b, 3c, 4a (see Example 20). The ostinatos create an accelerando as follows:


Figure 11: Resultant Accelerando From Combination of Chords Structures in B'



Example 18: Harmonic/Registral Development of E on pg.10



Example 19: Rising Monody in A' pg.11



Example 20: Rising Chord Structure of B' on pg. 12

The new element is the dialogue between low and high two- and three-note "calls". This can be shown as follows:


Figure 12: Registral "Dialogue" in B'

In Example 20 they are shown in 'black' notes.

2_Page_258c.jpg2_Page_258b.jpgD p. 12 m. 10

The melody of this passage starts higher than D of section II and descends constantly from                       to               . The four chords of eight notes use positions 4,5,6,7 and decrease in range (see Example 21). Note that the bass notes descend with small intervals (semitones and 2/3 tones) and the top notes of the chords with large intervals. The durations of the four chords increase: 5,5,6,9 q s.


Example 21: Registral/Harmonic Development of D on pg. 12

E p.13 m.3

Contrary to section II the design here is ascending. The eight basic chords (Example 22) have durations of 6,4,6,4,6,6,7,7 q s. The melody is in four rising phrases and chord in two expanding formation (1-4, 5-8) using positions 8a, 10b, 1c, 3a, 5b, 7a, 9bm 11c.



This fast monody lasts thirteen bars (as opposed to seven bars before A' of section II, see Example 23). As in A' in Section it develops through a rhythmic filtering of the same six-beat pattern (see Figure 13). Sometimes only 2,3,4 or 5 beats of the original pattern are used as a basis for the filtering.


Example 22: Harmonic/Melodic Development of E on Pg. 13




Example 23: Monody of A' on pg. 13



Figure 13: Filtering of 6-Beat Pattern in A'


Section IV

E p.14 m.9

Example 24 gives the first note of each trill pattern for the six parts of this passage:


Example 24: Trill Contour of E on pg. 14:

I Each of the four phrases has a descending and rising curve. The four phrases have 5,5,5,7 notes, each lasting two or three beats.

II The five phrase create an almost continuous descent with the following rhythmic pattern: h h h \ h q q q  : \ h h h h h h.

III This part features an alternation of registers with mostly three-note phrases



There is an effect of rallentando with only q  at the beginning and only h  at the end.

IV The five rising phrases of 5,5,7,7,5 notes feature only h at the beginning but introduce more and more q.

V This continuously rising passage is almost an inversion of II


2_Page_261b.jpgVI The four phrases of 5,5,6,3 notes feature mainly large intervals (22 sixths of tones). The five-note phrase  have the same design :           .

 The third phrase rises in intervals of eleven sixth of tones.

Example 25 shows the harmonic vocabulary of the 5-note accompanying chords with increasing range (a,b,c,d,e) and variations within each range (c1,c2,d1,d2,d3,d4).Example 26 gives the accompanying chords for the six parts:




Example 25: Harmonic Vocabulary in E on Pg. 14



Example 26: Accompanying Chords in E on Pg. 14




Example 27: Coda Pg.18



Coda p.18 m.2

In the final passage the elements B, A and C gradually melt one into the other. As shown in Example 27 there are five chords of eight notes in converging registers. These five chord are displayed in ostinatos thus:


Figure 14: Ostenato Organization in Coda

After the third and fourth chords there ar pauses. At this point the two and three-note "calls" are transformed into a melodic line (element A). Starting at p. 10 m.6 the element C starts with chord of 5,5,8,13,21,13 and 21 notes. Between these chords the melody dissolves in motives of 2,3,2 and 3 notes. The twenty-one-note chord is presented first in two parts (15 high notes then 6 low notes) and secondly in three parts rising (3+6+12).

Poème du Délire is dedicated to the memory of Alexander Scriabine (1871-1915) and his disciple Ivan Wyschnegradsky (1893-1979). Although it stylistically very different from the works of Scriabin, there is nevertheless a certain influence of the spirit of "Poème de l'Extase" and "Poème du Feu". In any case both Scriabin and Wyschnegradsky are composers whose music I treasure deeply.


APPENDIX A: "Régime Onze"