Class Notes on Machaut and Messiaen (Isorhythm)

Theory IV <strong>Class</strong> <strong>Notes</strong> Messiaen Page 1 of 7

Theory IV <strong>Class</strong> <strong>Notes</strong> Messiaen Page 3 of 7ISORHYTHM IN MACHAUT AND MESSIAEN (cont.)Messiaen: Liturgie de cristal from Quatuor pour la fin du tempsIn the following examples, the rhythm = talea and the melody or harmony = colorCello:Rhythm: = 33 ’s-there are 15 rhythmic events per seriesMelody: 0 4 2 6 A-there are 5 melodic events per seriesRhythmic 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 seriesHarmony (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 seriesRhythmic and harmonic series (potentially) line up after 29 rhythmic and 17 harmonicstatements (since 29x17 = 17x29).The rhythmic series in the cello (33 ’s) and the piano (26 ‘s) line up after 853 ‘s, or142.2 measures.The whole process would (potentially) line up again in a little less than 2 hours.

Theory IV <strong>Class</strong> <strong>Notes</strong> Messiaen Page 4 of 7<strong>Notes</strong>:• 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). Thelast three chords are exact transpositions of each other (parallelism). Perhaps this is meant tohelp 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

Theory IV <strong>Class</strong> <strong>Notes</strong> Messiaen Page 5 of 7PC Sets in the Piano Chords of Christal LitergyChord PCs N.O. Op. Set <strong>Class</strong> IC Vector M-Set Z-Set1 57a03b4 ab03457 T a P 7-20 (0125679) [433452] 6 02 57a0392 9a02357 T 9 P 7-35 (013568a) [254361] 1 03 58a1392 89a1235 T 8 P 7-20 (0125679) [433452] 6 04 59a1370 9a01357 T 9 P 7-34 (013468a) [254442] 8 05 57a26b0 567ab02 T 5 P 7-20 (0125679) [433452] 6 06 57a2490 4579a02 T 4 P 7-35 (013568a) [254361] 1 07 5902716 0125679 T 0 P 7-20 (0125679) [433452] 6 08 59027b4 b024579 T b P 7-35 (013568a) [254361] 1 09 5a164 a1456 T 6 I 5-38 (01258) [212221] 18 1810 5b2747 b2457 T 7 I 5-25 (02358) [123121] 10 011 50387 03578 T 8 I 5-27 (01358) [122230] 3 012 51497b 4579b1 T 4 P 6-34 (013579) [142422] 21 013 836a36b 368ab T b I 5-27 (01358) [122230] 3 014 932a15a 9a1235 T 9 P 6-16 (014568) [322431] 16 015 61838b3 b1368 T b P 5-35 (02479) [032140] 1 016 61a25a2 a1256 T 6 I 5-21 (01458) [202420] 21 017 9026a16a1 69a012 T 2 I 6-15 (012458) [323421] 31 018 a1480280 8a0124 T 4 I 6-21 (023468) [242412] 34 019 0259149 901245 T 5 I 6-14 (013458) [323430] 14 020 146a25 a12456 T 6 I 6-15 (012458) [323421] 31 021 58a269 25689a T a I 6-15 (012458) [323421] 31 022 69b358 35689b T 3 P 6-23 (023568) [234222] 23 4523 5a247 2457a T 2 P 5-25 (02358) [123121] 10 024 4812 1248 T 1 P 4-29 (0137) [111111] 15 1525 27b14 b1247 T b P 5-25 (02358) [123121] 10 026 15ab5 ab15 T a P 4-29 (0137) [111111] 15 1527 b48a 48ab T b I 4-29 (0137) [111111] 15 1528 8157 1578 T 8 I 4-29 (0137) [111111] 15 1529 6b35 B356 T 6 I 4-29 (0137) [111111] 15 15Non-Retrogradable Rhythms: Messiaen’s term for rhythmic palindromes. In this excerpt eachmeasure is a non-retrogradable rhythm. (From Dance de la fureur, pour les sept trompettes.)

Theory IV <strong>Class</strong> <strong>Notes</strong> Messiaen Page 7 of 7Additive 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 indicatedby “+”.