ピッチクラス セット(pitch-class set)自由な無調音楽の集合論・分析法の一つで、1990年代に入ってからアメリカで積極的に用いられるようになった。 12等分平均律上の全ての音高を1オクターブ内に還元すると、12の異なった音高類(ピッチクラス)しか無い事になる。 このピッチクラスの3音から9音までの組み合わせをそこに含まれる音程によって整理したものがピッチクラスセットで、主なるものは208種ある。無調音楽に於ける統一的要素を抽出する分析法だが、作曲技法としても用いられる。 ピッチクラス(pitch-class)ある所定の音高がゼロまたは整数オクターブ移高されたもの、と云う条件全てを満たすピッチ全ての集合体。例えば全てのＤはピッチクラスＤに帰属する。ミルトン・バビット (Milton Babbitt ; MAY/10/1916-) によって導入されたこの用語は、それ以前には明確に定義されなかった基本的な音楽概念を示している。最初は十二音技法に関連して用いられたもので、十二音のセットは１２のピッチクラスの順序づけされた連なりからなる。 |
| Fortean set-name | Prime | Hieroglyphics | interval vector | Fortean set-name | Prime | Hieroglyphics | interval vector | ||
| 0-0 | (empty) | XXXXXXXXXXXX | <000000> | 12-1*(1) | (0,1,2,3,4,5,6,7,8,9,A,B) | OOOOOOOOOOOO | <12,12,12,12,12,12> | ||
| 1-1* | (0) | OXXXXXXXXXXX | <000000> | 11-1* | (0,1,2,3,4,5,6,7,8,9,A) | OOOOOOOOOOOX | <12,12,12,12,12,12> | ||
| 2-1* | (0,1) | OOXXXXXXXXXX | <100000> | 10-1* | (0,1,2,3,4,5,6,7,8,9) | OOOOOOOOOOXX | <988888> | ||
| 2-2* | (0,2) | OXOXXXXXXXXX | <010000> | 10-2* | (0,1,2,3,4,5,6,7,8,A) | OOOOOOOOOXOX | <898888> | ||
| 2-3* | (0,3) | OXXOXXXXXXXX | <001000> | 10-3* | (0,1,2,3,4,5,6,7,9,A) | OOOOOOOOXOOX | <889888> | ||
| 2-4* | (0,4) | OXXXOXXXXXXX | <000100> | 10-4* | (0,1,2,3,4,5,6,8,9,A) | OOOOOOOXOOOX | <888988> | ||
| 2-5* | (0,5) | OXXXXOXXXXXX | <000010> | 10-5* | (0,1,2,3,4,5,7,8,9,A) | OOOOOOXOOOOX | <888898> | ||
| 2-6*(6) | (0,6) | OXXXXXOXXXXX | <000001> | 10-6*(6) | (0,1,2,3,4,6,7,8,9,A) | OOOOOXOOOOOX | <888889> | ||
| 3-1* | (0,1,2) | OOOXXXXXXXXX | <210000> | 9-1* | (0,1,2,3,4,5,6,7,8) | OOOOOOOOOXXX | <876663> | ||
| 3-2 | (0,1,3) | OOXOXXXXXXXX | <111000> | 9-2 | (0,1,2,3,4,5,6,7,9) | OOOOOOOOXOXX | <777663> | ||
| 3-2B | (0,2,3) | OXOOXXXXXXXX | <111000> | 9-2B | (0,2,3,4,5,6,7,8,9) | OXOOOOOOOOXX | <777663> | ||
| 3-3 | (0,1,4) | OOXXOXXXXXXX | <101100> | 9-3 | (0,1,2,3,4,5,6,8,9) | OOOOOOOXOOXX | <767763> | ||
| 3-3B | (0,3,4) | OXXOOXXXXXXX | <101100> | 9-3B | (0,1,3,4,5,6,7,8,9) | OOXOOOOOOOXX | <767763> | ||
| 3-4 | (0,1,5) | OOXXXOXXXXXX | <100110> | 9-4 | (0,1,2,3,4,5,7,8,9) | OOOOOOXOOOXX | <766773> | ||
| 3-4B | (0,4,5) | OXXXOOXXXXXX | <100110> | 9-4B | (0,1,2,4,5,6,7,8,9) | OOOXOOOOOOXX | <766773> | ||
| 3-5 | (0,1,6) | OOXXXXOXXXXX | <100011> | 9-5 | (0,1,2,3,4,6,7,8,9) | OOOOOXOOOOXX | <766674> | ||
| 3-5B | (0,5,6) | OXXXXOOXXXXX | <100011> | 9-5B | (0,1,2,3,5,6,7,8,9) | OOOOXOOOOOXX | <766674> | ||
| 3-6* | (0,2,4) | OXOXOXXXXXXX | <020100> | 9-6* | (0,1,2,3,4,5,6,8,A) | OOOOOOOXOXOX | <686763> | ||
| 3-7 | (0,2,5) | OXOXXOXXXXXX | <011010> | 9-7 | (0,1,2,3,4,5,7,8,A) | OOOOOOXOOXOX | <677673> | ||
| 3-7B | (0,3,5) | OXXOXOXXXXXX | <011010> | 9-7B | (0,1,2,3,4,5,7,9,A) | OOOOOOXOXOOX | <677673> | ||
| 3-8 | (0,2,6) | OXOXXXOXXXXX | <010101> | 9-8 | (0,1,2,3,4,6,7,8,A) | OOOOOXOOOXOX | <676764> | ||
| 3-8B | (0,4,6) | OXXXOXOXXXXX | <010101> | 9-8B | (0,1,2,3,4,6,8,9,A) | OOOOOXOXOOOX | <676764> | ||
| 3-9* | (0,2,7) | OXOXXXXOXXXX | <010020> | 9-9* | (0,1,2,3,5,6,7,8,A) | OOOOXOOOOXOX | <676683> | ||
| 3-10* | (0,3,6) | OXXOXXOXXXXX | <002001> | 9-10* | (0,1,2,3,4,6,7,9,A) | OOOOOXOOXOOX | <668664> | ||
| 3-11 | (0,3,7) | OXXOXXXOXXXX | <001110> | 9-11 | (0,1,2,3,5,6,7,9,A) | OOOOXOOOXOOX | <667773> | ||
| 3-11B | (0,4,7) | OXXXOXXOXXXX | <001110> | 9-11B | (0,1,2,3,5,6,8,9,A) | OOOOXOOXOOOX | <667773> | ||
| 3-12*(4) | (0,4,8) | OXXXOXXXOXXX | <000300> | 9-12*(4) | (0,1,2,4,5,6,8,9,A) | OOOXOOOXOOOX | <666963> | ||
| 4-1* | (0,1,2,3) | OOOOXXXXXXXX | <321000> | 8-1* | (0,1,2,3,4,5,6,7) | OOOOOOOOXXXX | <765442> | ||
| 4-2 | (0,1,2,4) | OOOXOXXXXXXX | <221100> | 8-2 | (0,1,2,3,4,5,6,8) | OOOOOOOXOXXX | <665542> | ||
| 4-2B | (0,2,3,4) | OXOOOXXXXXXX | <221100> | 8-2B | (0,2,3,4,5,6,7,8) | OXOOOOOOOXXX | <665542> | ||
| 4-3* | (0,1,3,4) | OOXOOXXXXXXX | <212100> | 8-3* | (0,1,2,3,4,5,6,9) | OOOOOOOXXOXX | <656542> | ||
| 4-4 | (0,1,2,5) | OOOXXOXXXXXX | <211110> | 8-4 | (0,1,2,3,4,5,7,8) | OOOOOOXOOXXX | <655552> | ||
| 4-4B | (0,3,4,5) | OXXOOOXXXXXX | <211110> | 8-4B | (0,1,3,4,5,6,7,8) | OOXOOOOOOXXX | <655552> | ||
| 4-5 | (0,1,2,6) | OOOXXXOXXXXX | <210111> | 8-5 | (0,1,2,3,4,6,7,8) | OOOOOXOOOXXX | <654553> | ||
| 4-5B | (0,4,5,6) | OXXXOOOXXXXX | <210111> | 8-5B | (0,1,2,4,5,6,7,8) | OOOXOOOOOXXX | <654553> | ||
| 4-6* | (0,1,2,7) | OOOXXXXOXXXX | <210021> | 8-6* | (0,1,2,3,5,6,7,8) | OOOOXOOOOXXX | <654463> | ||
| 4-7* | (0,1,4,5) | OOXXOOXXXXXX | <201210> | 8-7* | (0,1,2,3,4,5,8,9) | OOOOOOXXOOXX | <645652> | ||
| 4-8* | (0,1,5,6) | OOXXXOOXXXXX | <200121> | 8-8* | (0,1,2,3,4,7,8,9) | OOOOOXXOOOXX | <644563> | ||
| 4-9*(6) | (0,1,6,7) | OOXXXXOOXXXX | <200022> | 8-9*(6) | (0,1,2,3,6,7,8,9) | OOOOXXOOOOXX | <644464> | ||
| 4-10* | (0,2,3,5) | OXOOXOXXXXXX | <122010> | 8-10* | (0,2,3,4,5,6,7,9) | OXOOOOOOXOXX | <566452> | ||
| 4-11 | (0,1,3,5) | OOXOXOXXXXXX | <121110> | 8-11 | (0,1,2,3,4,5,7,9) | OOOOOOXOXOXX | <565552> | ||
| 4-11B | (0,2,4,5) | OXOXOOXXXXXX | <121110> | 8-11B | (0,2.4.5.6.7.8.9) | OXOXOOOOOOXX | <565552> | ||
| 4-12< | (0,2,3,6) | OXOOXXOXXXXX | <112101> | 8-12< | (0,1,3,4,5,6,7,9) | OOXOOOOOXOXX | <556543> | ||
| 4-12B< | (0,3,4,6) | OXXOOXOXXXXX | <112101> | 8-12B< | (0,2,3,4,5,6,8,9) | OXOOOOOXOOXX | <556543> | ||
| 4-13 | (0,1,3,6) | OOXOXXOXXXXX | <112011> | 8-13 | (0,1,2,3,4,6,7,9) | OOOOOXOOXOXX | <556453> | ||
| 4-13B | (0,3,5,6) | OOXOXXOXXXXX | <112011> | 8-13B | (0,2,3,5,6,7,8,9) | OXOOXOOOOOXX | <556453> | ||
| 4-14< | (0,2,3,7) | OXOOXXXOXXXX | <111120> | 8-14< | (0,1,2,4,5,6,7,9) | OOOXOOOOXOXX | <555562> | ||
| 4-14B< | (0,4,5,7) | OXXXOOXOXXXX | <111120> | 8-14B< | (0,2,3,4,5,7,8,9) | OXOOOOXOOOXX | <555562> | ||
| 4-Z15..29 | (0,1,4,6) | OOXXOXOXXXXX | <111111> | 8-Z15..29 | (0,1,2,3,4,6,8,9) | OOOOOXOXOOXX | <555553> | ||
| 4-Z15B..29 | (0,2,5,6) | OXOXXOOXXXXX | <111111> | 8-Z15B..29 | (0,1,3,5,6,7,8,9) | OOXOXOOOOOXX | <555553> | ||
| 4-16 | (0,1,5,7) | OOXXXOXOXXXX | <110121> | 8-16 | (0,1,2,3,5,7,8,9) | OOOOXOXOOOXX | <554563> | ||
| 4-16B | (0,2,6,7) | OXOXXXOOXXXX | <110121> | 8-16B | (0,1,2,4,6,7,8,9) | OOOXOXOOOOXX | <554563> | ||
| 4-17* | (0,3,4,7) | OXXOOXXOXXXX | <102210> | 8-17* | (0,1,3,4,5,6,8,9) | OOXOOOOXOOXX | <546652> | ||
| 4-18 | (0,1,4,7) | OOXXOXXOXXXX | <102111> | 8-18 | (0,1,2,3,5,6,8,9) | OOOOXOOXOOXX | <546553> | ||
| 4-18B | (0,3,6,7) | OXXOXXOOXXXX | <102111> | 8-18B | (0,1,3,4,6,7,8,9) | OOXOOXOOOOXX | <546553> | ||
| 4-19 | (0,1,4,8) | OOXXOXXXOXXX | <101310> | 8-19 | (0,1,2,4,5,6,8,9) | OOOXOOOXOOXX | <545752> | ||
| 4-19B | (0,3,4,8) | OXXOOXXXOXXX | <101310> | 8-19B | (0,1,3,4,5,7,8,9) | OOXOOOXOOOXX | <545752> | ||
| 4-20* | (0,1,5,8) | OOXXXOXXOXXX | <101220> | 8-20* | (0,1,2,4,5,7,8,9) | OOOXOOXOOOXX | <545662> | ||
| 4-21* | (0,2,4,6) | OXOXOXOXXXXX | <030201> | 8-21* | (0,1,2,3,4,6,8,A) | OOOOOXOXOXOX | <474643> | ||
| 4-22 | (0,2,4,7) | OXOXOXXOXXXX | <021120> | 8-22 | (0,1,2,3,5,6,8,A) | OOOOXOOXOXOX | <465562> | ||
| 4-22B | (0,3,5,7) | OXXOXOXOXXXX | <021120> | 8-22B | (0,1,2,3,5,7,9,A) | OOOOXOXOXOOX | <465562> | ||
| 4-23* | (0,2,5,7) | OXOXXOXOXXXX | <021030> | 8-23* | (0,1,2,3,5,7,8,A) | OOOOXOXOOXOX | <465472> | ||
| 4-24* | (0,2,4,8) | OXOXOXXXOXXX | <020301> | 8-24* | (0,1,2,4,5,6,8,A) | OOOXOOOXOXOX | <464743> | ||
| 4-25*(6) | (0,2,6,8) | OXOXXXOXOXXX | <020202> | 8-25*(6) | (0,1,2,4,6,7,8,A) | OOOXOXOOOXOX | <464644> | ||
| 4-26* | (0,3,5,8) | OXXOXOXXOXXX | <012120> | 8-26* | (0,1,2,4,5,7,9,A) | OOOXOOXOXOOX | <456562> | ||
| 4-27 | (0,2,5,8) | OXOXXOXXOXXX | <012111> | 8-27 | (0,1,2,4,5,7,8,A) | OOOXOOXOOXOX | <456553> | ||
| 4-27B | (0,3,6,8) | OXXOXXOXOXXX | <012111> | 8-27B | (0,1,2,4,6,7,9,A) | OOOXOXOOXOOX | <456553> | ||
| 4-28*(3) | (0,3,6,9) | OXXOXXOXXOXX | <004002> | 8-28*(3) | (0,1,3,4,6,7,9,A) | OOXOOXOOXOOX | <448444> | ||
| 8-Z29..15 | (0,1,3,7) | OOXOXXXOXXXX | <111111> | 8-Z29..15 | (0,1,2,3,5,6,7,9) | OOOOXOOOXOXX | <555553> | ||
| 8-Z29B..15 | (0,4,6,7) | OXXXOXOOXXXX | <111111> | 8-Z29B..15 | (0,2,3,4,6,7,8,9) | OXOOOXOOOOXX | <555553> | ||
| 5-1* | (0,1,2,3,4) | OOOOOXXXXXXX | <432100> | 7-1* | (0,1,2,3,4,5,6) | OOOOOOOXXXXX | <654321> | ||
| 5-2 | (0,1,2,3,5) | OOOOXOXXXXXX | <332110> | 7-2 | (0,1,2,3,4,5,7) | OOOOOOXOXXXX | <554331> | ||
| 5-2B | (0,2,3,4,5) | OXOOOOXXXXXX | <332110> | 7-2B | (0,2,3,4,5,6,7) | OXOOOOOOXXXX | <554331> | ||
| 5-3 | (0,1,2,4,5) | OOOXOOXXXXXX | <322210> | 7-3 | (0,1,2,3,4,5,8) | OOOOOOXXOXXX | <544431> | ||
| 5-3B | (0,1,3,4,5) | OOXOOOXXXXXX | <322210> | 7-3B | (0,3,4,5,6,7,8) | OXXOOOOOOXXX | <544431> | ||
| 5-4 | (0,1,2,3,6) | OOOOXXOXXXXX | <322111> | 7-4 | (0,1,2,3,4,6,7) | OOOOOXOOXXXX | <544332> | ||
| 5-4B | (0,3,4,5,6) | OXXOOOOXXXXX | <322111> | 7-4B | (0,1,3,4,5,6,7) | OOXOOOOOXXXX | <544332> | ||
| 5-5 | (0,1,2,3,7) | OOOOXXXOXXXX | <321121> | 7-5 | (0,1,2,3,5,6,7) | OOOOXOOOXXXX | <543342> | ||
| 5-5B | (0,4,5,6,7) | OXXXOOOOXXXX | <321121> | 7-5B | (0,1,2,4,5,6,7) | OOOXOOOOXXXX | <543342> | ||
| 5-6 | (0,1,2,5,6) | OOOXXOOXXXXX | <311221> | 7-6 | (0,1,2,3,4,7,8) | OOOOOXXOOXXX | <533442> | ||
| 5-6B | (0,1,4,5,6) | OOXXOOOXXXXX | <311221> | 7-6B | (0,1,4,5,6,7,8) | OOXXOOOOOXXX | <533442> | ||
| 5-7 | (0,1,2,6,7) | OOOXXXOOXXXX | <310132> | 7-7 | (0,1,2,3,6,7,8) | OOOOXXOOOXXX | <532353> | ||
| 5-7B | (0,1,5,6,7) | OOXXXOOOXXXX | <310132> | 7-7B | (0,1,2,5,6,7,8) | OOOXXOOOOXXX | <532353> | ||
| 5-8* | (0,2,3,4,6) | OXOOOXOXXXXX | <232201> | 7-8* | (0,2,3,4,5,6,8) | OXOOOOOXOXXX | <454422> | ||
| 5-9 | (0,1,2,4,6) | OOOXOXOXXXXX | <231211> | 7-9 | (0,1,2,3,4,6,8) | OOOOOXOXOXXX | <453432> | ||
| 5-9B | (0,2,4,5,6) | OXOXOOOXXXXX | <231211> | 7-9B | (0,2,4,5,6,7,8) | OXOXOOOOOXXX | <453432> | ||
| 5-10 | (0,1,3,4,6) | OOXOOXOXXXXX | <223111> | 7-10 | (0,1,2,3,4,6,9) | OOOOOXOXXOXX | <445332> | ||
| 5-10B | (0,2,3,5,6) | OXOOXOOXXXXX | <223111> | 7-10B | (0,2,3,4,5,6,9) | OXOOOOOXXOXX | <445332> | ||
| 5-11 | (0,2,3,4,7) | OXOOOXXOXXXX | <222220> | 7-11 | (0,1,3,4,5,6,8) | OOXOOOOXOXXX | <444441> | ||
| 5-11B | (0,3,4,5,7) | OXXOOOXOXXXX | <222220> | 7-11B | (0,2,3,4,5,7,8) | OXOOOOXOOXXX | <444441> | ||
| 5-Z12*..36 | (0,1,3,5,6) | OOXOXOOXXXXX | <222121> | 7-Z12*..36 | (0,1,2,3,4,7,9) | OOOOOXXOXOXX | <444342> | ||
| 5-13 | (0,1,2,4,8) | OOOXOXXXOXXX | <221311> | 7-13 | (0,1,2,4,5,6,8) | OOOXOOOXOXXX | <443532> | ||
| 5-13B | (0,2,3,4,8) | OXOOOXXXOXXX | <221311> | 7-13B | (0,2,3,4,6,7,8) | OXOOOXOOOXXX | <443532> | ||
| 5-14 | (0,1,2,5,7) | OOOXXOXOXXXX | <221131> | 7-14 | (0,1,2,3,5,7,8) | OOOOXOXOOXXX | <443352> | ||
| 5-14B | (0,2,5,6,7) | OXOXXOOOXXXX | <221131> | 7-14B | (0,1,3,5,6,7,8) | OOXOXOOOOXXX | <443352> | ||
| 5-15* | (0,1,2,6,8) | OOOXXXOXOXXX | <220222> | 7-15* | (0,1,2,4,6,7,8) | OOOXOXOOOXXX | <442443> | ||
| 5-16 | (0,1,3,4,7) | OOXOOXXOXXXX | <213211> | 7-16 | (0,1,2,3,5,6,9) | OOOOXOOXXOXX | <435432> | ||
| 5-16B | (0,3,4,6,7) | OXXOOXOOXXXX | <213211> | 7-16B | (0,1,3,4,5,6,9) | OOXOOOOXXOXX | <435432> | ||
| 5-Z17*..37 | (0,1,3,4,8) | OOXOOXXXOXXX | <212320> | 7-Z17*..37 | (0,1,2,4,5,6,9) | OOOXOOOXXOXX | <434541> | ||
| 5-Z18<..38 | (0,1,4,5,7) | OOXXOOXOXXXX | <212221> | 7-Z18<..38 | (0,1,2,3,5,8,9) | OOOOXOXXOOXX | <434442> | ||
| 5-Z18B<..38 | (0,2,3,6,7) | OXOOXXOOXXXX | <212221> | 7-Z18B<..38 | (0,1,4,6,7,8,9) | OOXXOXOOOOXX | <434442> | ||
| 5-19 | (0,1,3,6,7) | OOXOXXOOXXXX | <212122> | 7-19 | (0,1,2,3,6,7,9) | OOOOXXOOXOXX | <434343> | ||
| 5-19B | (0,1,4,6,7) | OOXXOXOOXXXX | <212122> | 7-19B | (0,1,2,3,6,8,9) | OOOOXXOXOOXX | <434343> | ||
| 5-20 | (0,1,3,7,8) | OOXOXXXOOXXX | <211231> | 7-20 | (0,1,2,4,7,8,9) | OOOXOXXOOOXX | <433452> | ||
| 5-20B | (0,1,5,7,8) | OOXXXOXOOXXX | <211231> | 7-20B | (0,1,2,5,7,8,9) | OOOXXOXOOOXX | <433452> | ||
| 5-21 | (0,1,4,5,8) | OOXXOOXXOXXX | <202420> | 7-21 | (0,1,2,4,5,8,9) | OOOXOOXXOOXX | <424641> | ||
| 5-21B | (0,3,4,7,8) | OXXOOXXOOXXX | <202420> | 7-21B | (0,1,3,4,5,8,9) | OOXOOOXXOOXX | <424641> | ||
| 5-22* | (0,1,4,7,8) | OOXXOXXOOXXX | <202321> | 7-22* | (0,1,2,5,6,8,9) | OOOXXOOXOOXX | <424542> | ||
| 5-23 | (0,2,3,5,7) | OXOOXOXOXXXX | <132130> | 7-23 | (0,2,3,4,5,7,9) | OXOOOOXOXOXX | <354351> | ||
| 5-23B | (0,2,4,5,7) | OXOXOOXOXXXX | <132130> | 7-23B | (0,2,4,5,6,7,9) | OXOXOOOOXOXX | <354351> | ||
| 5-24 | (0,1,3,5,7) | OOXOXOXOXXXX | <131221> | 7-24 | (0,1,2,3,5,7,9) | OOOOXOXOXOXX | <353442> | ||
| 5-24B | (0,2,4,6,7) | OXOXOXOOXXXX | <131221> | 7-24B | (0,2,4,6,7,8,9) | OXOXOXOOOOXX | <353442> | ||
| 5-25 | (0,2,3,5,8) | OXOOXOXXOXXX | <123121> | 7-25 | (0,2,3,4,6,7,9) | OXOOOXOOXOXX | <345342> | ||
| 5-25B | (0,3,5,6,8) | OXXOXOOXOXXX | <123121> | 7-25B | (0,2,3,5,6,7,9) | OXOOXOOOXOXX | <345342> | ||
| 5-26< | (0,2,4,5,8) | OXOXOOXXOXXX | <122311> | 7-26< | (0,1,3,4,5,7,9) | OOXOOOXOXOXX | <344532> | ||
| 5-26B< | (0,3,4,6,8) | OXXOOXOXOXXX | <122311> | 7-26B< | (02,4,5,6,8,9) | OXOXOOOXOOXX | <344532> | ||
| 5-27 | (0,1,3,5,8) | OOXOXOXXOXXX | <122230> | 7-27 | (0,1,2,4,5,7,9) | OOOXOOXOXOXX | <344451> | ||
| 5-27B | (0,3,5,7,8) | OXXOXOXOOXXX | <122230> | 7-27B | (0,2,4,5,7,8,9) | OXOXOOXOOOXX | <344451> | ||
| 5-28< | (0,2,3,6,8) | OXOOXXOXOXXX | <122212> | 7-28< | (0,1,3,5,6,7,9) | OOXOXOOOXOXX | <344433> | ||
| 5-28B< | (0,2,5,6,8) | OXOXXOOXOXXX | <122212> | 7-28B< | (0,2,3,4,6,8,9) | OXOOOXOXOOXX | <344433> | ||
| 5-29 | (0,1,3,6,8) | OOXOXXOXOXXX | <122131> | 7-29 | (0,1,2,4,6,7,9) | OOOXOXOOXOXX | <344352> | ||
| 5-29B | (0,2,5,7,8) | OXOXXOXOOXXX | <122131> | 7-29B | (0,2,3,5,7,8,9) | OXOOXOXOOOXX | <344352> | ||
| 5-30 | (0,1,4,6,8) | OOXXOXOXOXXX | <121321> | 7-30 | (0,1,2,4,6,8,9) | OOOXOXOXOOXX | <343542> | ||
| 5-30B | (0,2,4,7,8) | OXOXOXXOOXXX | <121321> | 7-30B | (0,1,3,5,7,8,9) | OOXOXOXOOOXX | <343542> | ||
| 5-31 | (0,1,3,6,9) | OOXOXXOXXOXX | <114112> | 7-31 | (0,1,3,4,6,7,9) | OOXOOXOOXOXX | <336333> | ||
| 5-31B | (0,2,3,6,9) | OXOOXXOXXOXX | <114112> | 7-31B | (0,2,3,5,6,8,9) | OXOOXOOXOOXX | <336333> | ||
| 5-32 | (0,1,4,6,9) | OOXXOXOXXOXX | <113221> | 7-32 | (0,1,3,4,6,8,9) | OOXOOXOXOOXX | <335442> | ||
| 5-32B | (0,1,4,7,9) | OOXXOXXOXOXX | <113221> | 7-32B | (0,1,3,5,6,8,9) | OOXOXOOXOOXX | <335442> | ||
| 5-33* | (0,2,4,6,8) | OXOXOXOXOXXX | <040402> | 7-33 | (0,1,2,4,6,8,A) | OOOXOXOXOXOX | <262623> | ||
| 5-34* | (0,2,4,6,9) | OXOXOXOXXOXX | <032221> | 7-34 | (0,1,3,4,6,8,A) | OOXOOXOXOXOX | <254442> | ||
| 5-35* | (0,2,4,7,9) | OXOXOXXOXOXX | <032140> | 7-35 | (0,1,3,5,6,8,A) | OOXOXOOXOXOX | <254361> | ||
| 5-Z36..12 | (0,1,2,4,7) | OOOXOXXOXXXX | <222121> | 7-Z36..12 | (0,1,2,3,5,6,8) | OOOOXOOXOXXX | <444342> | ||
| 5-Z36B..12 | (0,3,5,6,7) | OXXOXOOOXXXX | <222121> | 7-Z36B..12 | (0,2,3,5,6,7,8) | OXOOXOOOOXXX | <444342> | ||
| 5-Z37*..17 | (0,3,4,5,8) | OXXOOOXXOXXX | <212320> | 7-Z37*..17 | (0,1,3,4,5,7,8) | OOXOOOXOOXXX | <434541> | ||
| 5-Z38 | (0,1,2,5,8) | OOOXXOXXOXXX | <212221> | 7-Z38 | (0,1,2,4,5,7,8) | OOOXOOXOOXXX | <434442> | ||
| 5-Z38B | (0,3,6,7,8) | OXXOXXOOOXXX | <212221> | 7-Z38B | (0,1,3,4,6,7,8) | OOXOOXOOOXXX | <434442> | ||
| 6-1* | (0,1,2,3,4,5) | OOOOOOXXXXXX | <543210> | 6-Z25..47B | (0,1,3,5,6,8) | OOXOXOOXOXXX | <233241> | ||
| 6-2 | (0,1,2,3,4,6) | OOOOOXOXXXXX | <443211> | 6-Z25B..47 | (0,2,3,5,7,8) | OXOOXOXOOXXX | <233241> | ||
| 6-2B | (0,2,3,4,5,6) | OXOOOOOXXXXX | <443211> | 6-Z26*..48 | (0,1,3,5,7,8) | OOXOXOXOOXXX | <232341> | ||
| 6-Z3..36B | (0,1,2,3,5,6) | OOOOXOOXXXXX | <433221> | 6-27 | (0,1,3,4,6,9) | OOXOOXOXXOXX | <225222> | ||
| 6-Z3B..36 | (0,1,3,4,5,6) | OOXOOOOXXXXX | <433221> | 6-27B | (0,2,3,5,6,9) | OXOOXOOXXOXX | <225222> | ||
| 6-Z4*..37 | (0,1,2,4,5,6) | OOOXOOOXXXXX | <432321> | 6-Z28*..49 | (0,1,3,5,6,9) | OOXOXOOXXOXX | <224322> | ||
| 6-5 | (0,1,2,3,6,7) | OOOOXXOOXXXX | <422232> | 6-Z29*..50 | (0,1,3,6,8,9) | OOXOXXOXOOXX | <224232> | ||
| 6-5B | (0,1,4,5,6,7) | OOXXOOOOXXXX | <422232> | 6-30 (6) | (0,1,3,6,7,9) | OOXOXXOOXOXX | <224223> | ||
| 6-Z6*..38 | (0,1,2,5,6,7) | OOOXXOOOXXXX | <421242> | 6-30B (6) | (0,2,3,6,8,9) | OXOOXXOXOOXX | <224223> | ||
| 6-7* (6) | (0,1,2,6,7,8) | OOOXXXOOOXXX | <420243> | 6-31 | (0,1,3,5,8,9) | OOXOXOXXOOXX | <223431> | ||
| 6-8* | (0,2,3,4,5,7) | OXOOOOXOXXXX | <343230> | 6-31B | (0,1,4,6,8,9) | OOXXOXOXOOXX | <223431> | ||
| 6-9 | (0,1,2,3,5,7) | OOOOXOXOXXXX | <342231> | 6-32* | (0,2,4,5,7,9) | OXOXOOXOXOXX | <143250> | ||
| 6-9B | (0,2,4,5,6,7) | OXOXOOOOXXXX | <342231> | 6-33 | (0,2,3,5,7,9) | OXOOXOXOXOXX | <143241> | ||
| 6-Z10..39 | (0,1,3,4,5,7) | OOXOOOXOXXXX | <333321> | 6-33B | (0,2,4,6,7,9) | OXOXOXOOXOXX | <143241> | ||
| 6-Z10B..39B | (0,2,3,4,6,7) | OXOOOXOOXXXX | <333321> | 6-34 | (0,1,3,5,7,9) | OOXOXOXOXOXX | <142422> | ||
| 6-Z11..40B | (0,1,2,4,5,7) | OOOXOOXOXXXX | <333231> | 6-34B | (0,2,4,6,8,9) | OXOXOXOXOOXX | <142422> | ||
| 6-Z11B..40 | (0,2,3,5,6,7) | OXOOXOOOXXXX | <333231> | 6-35*(2) | (0,2,4,6,8,A) | OXOXOXOXOXOX | <060603> | ||
| 6-Z12..41B | (0,1,2,4,6,7) | OOOXOXOOXXXX | <332232> | 6-Z36..3B | (0,1,2,3,4,7) | OOOOOXXOXXXX | <433221> | ||
| 6-Z12B..41 | (0,1,3,5,6,7) | OOXOXOOOXXXX | <332232> | 6-Z36B..3 | (0,3,4,5,6,7) | OXXOOOOOXXXX | <433221> | ||
| 6-Z13*..42 | (0,1,3,4,6,7) | OOXOOXOOXXXX | <324222> | 6-Z37*..4 | (0,1,2,3,4,8) | OOOOOXXXOXXX | <432321> | ||
| 6-14..14 | (0,1,3,4,5,8) | OOXOOOXXOXXX | <323430> | 6-Z38*..6 | (0,1,2,3,7,8) | OOOOXXXOOXXX | <421242> | ||
| 6-14B..14B | (0,3,4,5,7,8) | OXXOOOXOOXXX | <323430> | 6-Z39..10 | (0,2,3,4,5,8) | OXOOOOXXOXXX | <333321> | ||
| 6-15 | (0,1,2,4,5,8) | OOOXOOXXOXXX | <323421> | 6-Z39B..10B | (0,3,4,5,6,8) | OXXOOOOXOXXX | <333321> | ||
| 6-15B | (0,3,4,6,7,8) | OXXOOXOOOXXX | <323421> | 6-Z40..11B | (0,1,2,3,5,8) | OOOOXOXXOXXX | <333231> | ||
| 6-16 | (0,1,4,5,6,8) | OOXXOOOXOXXX | <322431> | 6-Z40B..11 | (0,3,5,6,7,8) | OXXOXOOOOXXX | <333231> | ||
| 6-16B | (0,2,3,4,7,8) | OXOOOXXOOXXX | <322431> | 6-Z41..12B | (0,1,2,3,6,8) | OOOOXXOXOXXX | <332232> | ||
| 6-Z17..43B | (0,1,2,4,7,8) | OOOXOXXOOXXX | <322332> | 6-Z41B..12 | (0,2,5,6,7,8) | OXOXXOOOOXXX | <332232> | ||
| 6-Z17B..43 | (0,1,4,6,7,8) | OOXXOXOOOXXX | <322332> | 6-Z42*..13 | (0,1,2,3,6,9) | OOOOXXOXXOXX | <324222> | ||
| 6-18 | (0,1,2,5,7,8) | OOOXXOXOOXXX | <322242> | 6-Z43..17B | (0,1,2,5,6,8) | OOOXXOOXOXXX | <322332> | ||
| 6-18B | (0,1,3,6,7,8) | OOXOXXOOOXXX | <322242> | 6-Z43B..17 | (0,2,3,6,7,8) | OXOOXXOOOXXX | <322332> | ||
| 6-Z19..44B | (0,1,3,4,7,8) | OOXOOXXOOXXX | <313431> | 6-Z44..19B | (0,1,2,5,6,9) | OOOXXOOXXOXX | <313431> | ||
| 6-Z19B..44 | (0,1,4,5,7,8) | OOXXOOXOOXXX | <313431> | 6-Z44B..19 | (0,1,2,5,8,9) | OOOXXOXXOOXX | <313431> | ||
| 6-20*(4) | (0,1,4,5,8,9) | OOXXOOXXOOXX | <303630> | 6-Z45*..23 | (0,2,3,4,6,9) | OXOOOXOXXOXX | <234222> | ||
| 6-21 | (0,2,3,4,6,8) | OXOOOXOXOXXX | <242412> | 6-Z46..24B | (0,1,2,4,6,9) | OOOXOXOXXOXX | <233331> | ||
| 6-21B | (0,2,4,5,6,8) | OXOXOOOXOXXX | <242412> | 6-Z46B..24 | (0,2,4,5,6,9) | OXOXOOOXXOXX | <233331> | ||
| 6-22 | (0,1,2,4,6,8) | OOOXOXOXOXXX | <241422> | 6-Z47..25B | (0,1,2,4,7,9) | OOOXOXXOXOXX | <233241> | ||
| 6-22B | (0,2,4,6,7,8) | OXOXOXOOOXXX | <241422> | 6-Z47B..25 | (0,2,3,4,7,9) | OXOOOXXOXOXX | <233241> | ||
| 6-Z23*..45 | (0,2,3,5,6,8) | OXOOXOOXOXXX | <234222> | 6-Z48*..26 | (0,1,2,5,7,9) | OOOXXOXOXOXX | <232341> | ||
| 6-Z24..46B | (0,1,3,4,6,8) | OOXOOXOXOXXX | <233331> | 6-Z49*..28 | (0,1,3,4,7,9) | OOXOOXXOXOXX | <224322> | ||
| 6-Z24B..46 | (0,2,4,5,7,8) | OXOXOOXOOXXX | <233331> | 6-Z50*..29 | (0,1,4,6,7,9) | OOXXOXOOXOXX | <224232> |
Combination possibilities in our twelve-tone system: Duotonic: (12.11/2!-6)/12 + 1= 6 (= the six intervall-classes) Tritonic: (12.11.10/3! -6)/12 +1 = 19 (=19 triads) Tetratonic: (12.11.10.9 / 4! -15)/12 +3 = 43 (=43 tetrachords) Pentatonic: (12.11.10.9.8 /5!)/12 = 66 (=66 pentatonic combinations) Hexatonic: (12.11.10.9.8.7 /6! - 24)/12 +5 = 80 Heptatonic: (12.11.10.9.8.7.6 /7!) /12 = 66 (inversion of pentatonisism) Octotonic: ......................=43 (inversion of tetratonisism) Enneatonic: .....................=19 (inversion of tritonisism) Decatonic: ......................=6 (inversion of Duotonisism)参考文献:
