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Theory IV Class Notes Messiaen of 7




Class notes

Drs. Gill / Folio / Brinkman

ISORYTHM IN MACHAUT AND MESSIAEN

Isorhythm: a structural principle frequently used in 14

th

-century motets, particularly in the tenorline. Its main feature is the use of a reiterated scheme of time values for the presentation of aliturgical cantus firmus. The repeated scheme of time values is called talea and the repeated

scheme of melodic tones is called color .

Machaut: De Bon Espoir—Puisque la Douce Rosee—Speravi

In the following examples, the rhythm = talea and the melody = color

Tenor:

Rhythm (mm. 1-102): #$ #$ #$ #% # #$ #& #$ #' #& #' #$ #& # #$ #& #= 34 ' ’s

-beginning in m. 103 this is halved to:

Rhythm (mm. 103-152): $ #' #' #' #& #$ #' #( #' #) #( #) #' #( #$ #' #( #= 17 ' ’s

-there are 12 rhythmic events per series (not including rests)

Melody: do re mi fa mi re mi fa mi re do re mi re do re re do-there are 18 melodic events per series

Rhythmic and melodic series line up after 3 rhythmic and 2 melodic statements (since 3x12 =

2x18). This happens twice: once at m. 103 (where the talea is subsequently halved) and again atthe end of the motet (the penultimate note of the talea is reduced by ! in its final statement to

facilitate the final cadence; this is why there are only 50 measures between 103-152 as opposedto the expected 51 [= " of 102]).

The Triplum and Motetus parts feature a more free rhythmic series (within each part). The

rhythms of the first 34 measures are repeated (with variations) as 35-68 and again as 69-102.The beginnings of these varied repetitions coincide with the beginnings of the talea in the Tenor.




ISORHYTHM IN MACHAUT AND MESSIAEN (cont.)

Messiaen: Liturgie de cristal from Quatuor pour la fin du temp s

In the following examples, the rhythm = talea and the melody or harmony = color

Cello:

Rhythm: '##) ##'##'##*##*#) ##*##*##*##*##) ##*##*##'#= 33 *#’s-there are 15 rhythmic events per series

Melody: 0 4 2 6 A

-there are 5 melodic events per series

Rhythmic and melodic series line up after 1 rhythmic and 3 melodic statements (since 1x15 =3x5).

Piano:

Rhythm: )##)##)##*##* ##*##*##*##*##* ##* ##* ##+##*##* ##)##'#= 26 *#’s-there are 17 rhythmic events per series

Harmony (bottom note listed): 5 5 5 5 5 5 5 5 5 5 5 5 8 8 6 6 9 A 0 1 6 6 5 4 2 1 B 8 6-there are 29 harmonic events per series

Rhythmic and harmonic series (potentially) line up after 29 rhythmic and 17 harmonic

statements (since 29x17 = 17x29).

The rhythmic series in the cello (33 *#’s) and the piano (26 * ‘s) line up after 853 * ‘s, or

142.2 measures.

The whole process would (potentially) line up again in a little less than 2 hours.




Notes:

• All of the sets are fairly dissonant; all have ic 1 except 5-35 (pentatonic set) • Several set classes occur more than once: 7-20 (4x), 7-35(4x), 5-25(2x), 5-25(2x), 5-27(2x),

4-29(5x), 6-15(3x). The others occur once each: 7-34, 6-34, 6-16, 6-23, 6-21, 6-14. • 15 different set classes are used in the 29 chord series. [ratio = 15/29 = 0.517] • The last four chords (and chord #24) are sc 4-29 (one of the two all-interval tetracords). The

last three chords are exact transpositions of each other (parallelism). Perhaps this is meant to

help us hear the end of the series. • The only complementary pair Messiaen uses is 7-35 (diatonic set) and 5-35 (pentatonic)

• Messiaen doesn’t use any Z- or M-related sets. • See the table on the next page for more information




PC Sets in the Piano Chords of Christal Litergy

Chord PCs N.O. Op. Set Class IC Vector M-Set Z-Set1 57a03b4 ab03457 TaP 7-20 (0125679) [433452] 6 02 57a0392 9a02357 T9P 7-35 (013568a) [254361] 1 0

3 58a1392 89a1235 T8P 7-20 (0125679) [433452] 6 04 59a1370 9a01357 T

9P 7-34 (013468a) [254442] 8 0

5 57a26b0 567ab02 T5P 7-20 (0125679) [433452] 6 06 57a2490 4579a02 T4P 7-35 (013568a) [254361] 1 07 5902716 0125679 T0P 7-20 (0125679) [433452] 6 08 59027b4 b024579 TbP 7-35 (013568a) [254361] 1 0

9 5a164 a1456 T6I 5-38 (01258) [212221] 18 18

10 5b2747 b2457 T7I 5-25 (02358) [123121] 10 0

11 50387 03578 T8I 5-27 (01358) [122230] 3 0

12 51497b 4579b1 T4P 6-34 (013579) [142422] 21 0

13 836a36b 368ab TbI 5-27 (01358) [122230] 3 0

14 932a15a 9a1235 T9P 6-16 (014568) [322431] 16 0

15 61838b3 b1368 TbP 5-35 (02479) [032140] 1 0

16 61a25a2 a1256 T6I 5-21 (01458) [202420] 21 0

17 9026a16a1 69a012 T2I 6-15 (012458) [323421] 31 018 a1480280 8a0124 T4I 6-21 (023468) [242412] 34 0

19 0259149 901245 T5I 6-14 (013458) [323430] 14 0

20 146a25 a12456 T6I 6-15 (012458) [323421] 31 0

21 58a269 25689a TaI 6-15 (012458) [323421] 31 0

22 69b358 35689b T3P 6-23 (023568) [234222] 23 45

23 5a247 2457a T2P 5-25 (02358) [123121] 10 0

24 4812 1248 T1P 4-29 (0137) [111111] 15 15

25 27b14 b1247 TbP 5-25 (02358) [123121] 10 0

26 15ab5 ab15 TaP 4-29 (0137) [111111] 15 15

27 b48a 48ab TbI 4-29 (0137) [111111] 15 15

28 8157 1578 T8I 4-29 (0137) [111111] 15 15

29 6b35 B356 T6I 4-29 (0137) [111111] 15 15

Non-Retrogradable Rhythms: Messiaen’s term for rhythmic palindromes. In this excerpt each

measure is a non-retrogradable rhythm. (From Dance de la fureur, pour les sept trompettes.)




Examples from Messiaen, Techniques of My Musical Language. (See also bottom of previous page and next page.)




Additive Rhythm: Non-metric music in which the composer sets up a regular pulse, and thenadds a small value (16

th or dot) to shift the pulse. In this example, the added values are indicated

by “+”.