音高集合列表
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This is a list of set classes by Forte number.[2] For a list of ordered collections, see: list of tone rows and series.
Sets are listed next to their complements. 转位 are marked "B" (sets not marked "A" or "B" are 對稱). "T" and "E" are conventionally used in sets to notate 10 and 11, respectively, as single characters.
There are two slightly different methods of obtaining a normal form.[a] This results in two different normal form sets for the same Forte number in a few cases. The alternative notation for those chords are listed in the footnotes.[4][5]
艾略特·卡特 had earlier (1960–67) produced a numbered listing of pitch class sets, or "chords", as Carter referred to them, for his own use.[6][7] Donald Martino had produced tables of hexachords, tetrachords, trichords, and pentachords for combinatoriality in his article, "The Source Set and its Aggregate Formations" (1961).[8]
列表
[编辑]Forte編號 | 質數形式 | 區間向量 | Carter編號 | 聲音 | 可能間距 | Forte編號 | 質數形式 | 區間向量 | Carter編號 | 聲音 | 可能間距 |
---|---|---|---|---|---|---|---|---|---|---|---|
0-1 | [] | <0,0,0,0,0,0> | 空集 | 12-1 | [0,1,2,3,4,5, 6,7,8,9,T,E] |
<C,C,C,C,C,6> | ⓘ | aggregate | |||
1-1 | [0] | <0,0,0,0,0,0> | ⓘ | 純一度, 八度 | 11-1 | [0,1,2,3,4,5, 6,7,8,9,T] |
<T,T,T,T,T,5> | ⓘ | ... | ||
2-1 | [0,1] | <1,0,0,0,0,0> | 1 | ⓘ | 半音, 大七度 | 10-1 | [0,1,2,3,4, 5,6,7,8,9] |
<9,8,8,8,8,4> | ⓘ | ... | |
2-2 | [0,2] | <0,1,0,0,0,0> | 2 | ⓘ | 大二度, 小七度 | 10-2 | [0,1,2,3,4, 5,6,7,8,T] |
<8,9,8,8,8,4> | ⓘ | ... | |
2-3 | [0,3] | <0,0,1,0,0,0> | 3 | ⓘ | 小三度, 大六度 | 10-3 | [0,1,2,3,4, 5,6,7,9,T] |
<8,8,9,8,8,4> | ⓘ | ... | |
2-4 | [0,4] | <0,0,0,1,0,0> | 4 | ⓘ | 大三度, 小六度 | 10-4 | [0,1,2,3,4, 5,6,8,9,T] |
<8,8,8,9,8,4> | ⓘ | ... | |
2-5 | [0,5] | <0,0,0,0,1,0> | 5 | ⓘ | 純四度, 纯五度 | 10-5 | [0,1,2,3,4, 5,7,8,9,T] |
<8,8,8,8,9,4> | ⓘ | ... | |
2-6 | [0,6] | <0,0,0,0,0,1> | 6 | ⓘ | A4, 增四度 | 10-6 | [0,1,2,3,4, 6,7,8,9,T] |
<8,8,8,8,8,5> | ⓘ | ... | |
3-1 | [0,1,2] | <2,1,0,0,0,0> | 4 | ⓘ | ... | 9-1 | [0,1,2,3,4, 5,6,7,8] |
<8,7,6,6,6,3> | ⓘ | ... | |
3-2A | [0,1,3] | <1,1,1,0,0,0> | 12 | ⓘ | ... | 9-2A | [0,1,2,3,4, 5,6,7,9] |
<7,7,7,6,6,3> | ⓘ | ... | |
3-2B | [0,2,3] | ⓘ | ... | 9-2B | [0,2,3,4,5, 6,7,8,9] |
ⓘ | ... | ||||
3-3A | [0,1,4] | <1,0,1,1,0,0> | 11 | ⓘ | ... | 9-3B | [0,1,3,4, 5,6,7,8,9] |
<7,6,7,7,6,3> | ⓘ | ... | |
3-3B | [0,3,4] | ⓘ | ... | 9-3A | [0,1,2,3,4, 5,6,8,9] |
ⓘ | ... | ||||
3-4A | [0,1,5] | <1,0,0,1,1,0> | 9 | ⓘ | ... | 9-4B | [0,1,2,4,5, 6,7,8,9] |
<7,6,6,7,7,3> | ⓘ | ... | |
3-4B | [0,4,5] | ⓘ | ... | 9-4A | [0,1,2,3,4, 5,7,8,9] |
ⓘ | ... | ||||
3-5A | [0,1,6] | <1,0,0,0,1,1> | 7 | ⓘ | Viennese trichord | 9-5B | [0,1,2,3,5, 6,7,8,9] |
<7,6,6,6,7,4> | ⓘ | ... | |
3-5B | [0,5,6] | ⓘ | ... | 9-5A | [0,1,2,3,4, 6,7,8,9] |
ⓘ | ... | ||||
3-6 | [0,2,4] | <0,2,0,1,0,0> | 3 | ⓘ | ... | 9-6 | [0,1,2,3,4, 5,6,8,T] |
<6,8,6,7,6,3> | ⓘ | ... | |
3-7A | [0,2,5] | <0,1,1,0,1,0> | 10 | ⓘ | ... | 9-7B | [0,1,2,3,4, 5,7,9,T] |
<6,7,7,6,7,3> | ⓘ | ... | |
3-7B | [0,3,5] | ⓘ | Blues trichord (五聲音階 subset)[9] | 9-7A | [0,1,2,3,4, 5,7,8,T] |
ⓘ | ... | ||||
3-8A | [0,2,6] | <0,1,0,1,0,1> | 8 | ⓘ | 增六和弦 | 9-8B | [0,1,2,3,4, 6,8,9,T] |
<6,7,6,7,6,4> | ⓘ | ... | |
3-8B | [0,4,6] | ⓘ | ... | 9-8A | [0,1,2,3,4, 6,7,8,T] |
ⓘ | ... | ||||
3-9 | [0,2,7] | <0,1,0,0,2,0> | 5 | ⓘ | sus. chord | 9-9 | [0,1,2,3,5, 6,7,8,T] |
<6,7,6,6,8,3> | ⓘ | blues scale | |
3-10 | [0,3,6] | <0,0,2,0,0,1> | 2 | ⓘ | 減三和弦 | 9-10 | [0,1,2,3,4, 6,7,9,T] |
<6,6,8,6,6,4> | ⓘ | ... | |
3-11A | [0,3,7] | <0,0,1,1,1,0> | 6 | ⓘ | 小三和弦 | 9-11B | [0,1,2,3,5, 6,8,9,T] |
<6,6,7,7,7,3> | ⓘ | ... | |
3-11B | [0,4,7] | ⓘ | 大三和弦 | 9-11A | [0,1,2,3,5, 6,7,9,T] |
ⓘ | ... | ||||
3-12 | [0,4,8] | <0,0,0,3,0,0> | 1 | ⓘ | 增三和弦 | 9-12 | [0,1,2,4,5, 6,8,9,T] |
<6,6,6,9,6,3> | ⓘ | ... | |
4-1 | [0,1,2,3] | <3,2,1,0,0,0> | 1 | ⓘ | ... | 8-1 | [0,1,2,3, 4,5,6,7] |
<7,6,5,4,4,2> | ⓘ | ... | |
4-2A | [0,1,2,4] | <2,2,1,1,0,0> | 17 | ⓘ | ... | 8-2B | [0,2,3,4, 5,6,7,8] |
<6,6,5,5,4,2> | ⓘ | ... | |
4-2B | [0,2,3,4] | ⓘ | ... | 8-2A | [0,1,2,3, 4,5,6,8] |
ⓘ | ... | ||||
4-3 | [0,1,3,4] | <2,1,2,1,0,0> | 9 | ⓘ | ... | 8-3 | [0,1,2,3, 4,5,6,9] |
<6,5,6,5,4,2> | ⓘ | ... | |
4-4A | [0,1,2,5] | <2,1,1,1,1,0> | 20 | ⓘ | ... | 8-4B | [0,1,3,4, 5,6,7,8] |
<6,5,5,5,5,2> | ⓘ | ... | |
4-4B | [0,3,4,5] | ⓘ | ... | 8-4A | [0,1,2,3, 4,5,7,8] |
ⓘ | ... | ||||
4-5A | [0,1,2,6] | <2,1,0,1,1,1> | 22 | ⓘ | ... | 8-5B | [0,1,2,4, 5,6,7,8] |
<6,5,4,5,5,3> | ⓘ | ... | |
4-5B | [0,4,5,6] | ⓘ | ... | 8-5A | [0,1,2,3, 4,6,7,8] |
ⓘ | ... | ||||
4-6 | [0,1,2,7] | <2,1,0,0,2,1> | 6 | ⓘ | dream chord | 8-6 | [0,1,2,3, 5,6,7,8] |
<6,5,4,4,6,3> | ⓘ | ... | |
4-7 | [0,1,4,5] | <2,0,1,2,1,0> | 8 | ⓘ | ... | 8-7 | [0,1,2,3, 4,5,8,9] |
<6,4,5,6,5,2> | ⓘ | ... | |
4-8 | [0,1,5,6] | <2,0,0,1,2,1> | 10 | ⓘ | ... | 8-8 | [0,1,2,3, 4,7,8,9] |
<6,4,4,5,6,3> | ⓘ | ... | |
4-9 | [0,1,6,7] | <2,0,0,0,2,2> | 2 | ⓘ | distance model | 8-9 | [0,1,2,3, 6,7,8,9] |
<6,4,4,4,6,4> | ⓘ | ... | |
4-10 | [0,2,3,5] | <1,2,2,0,1,0> | 3 | ⓘ | ... | 8-10 | [0,2,3,4, 5,6,7,9] |
<5,6,6,4,5,2> | ⓘ | ... | |
4-11A | [0,1,3,5] | <1,2,1,1,1,0> | 26 | ⓘ | ... | 8-11B | [0,2,4,5, 6,7,8,9] |
<5,6,5,5,5,2> | ⓘ | ... | |
4-11B | [0,2,4,5] | ⓘ | ... | 8-11A | [0,1,2,3, 4,5,7,9] |
ⓘ | ... | ||||
4-12A | [0,2,3,6] | <1,1,2,1,0,1> | 28 | ⓘ | ... | 8-12A | [0,1,3,4, 5,6,7,9] |
<5,5,6,5,4,3> | ⓘ | ... | |
4-12B | [0,3,4,6] | ⓘ | ... | 8-12B | [0,2,3,4, 5,6,8,9] |
ⓘ | ... | ||||
4-13A | [0,1,3,6] | <1,1,2,0,1,1> | 7 | ⓘ | ... | 8-13B | [0,2,3,5, 6,7,8,9] |
<5,5,6,4,5,3> | ⓘ | ... | |
4-13B | [0,3,5,6] | ⓘ | ... | 8-13A | [0,1,2,3, 4,6,7,9] |
ⓘ | ... | ||||
4-14A | [0,2,3,7] | <1,1,1,1,2,0> | 25 | ⓘ | ... | 8-14A | [0,1,2,4, 5,6,7,9] |
<5,5,5,5,6,2> | ⓘ | ... | |
4-14B | [0,4,5,7] | ⓘ | ... | 8-14B | [0,2,3,4, 5,7,8,9] |
ⓘ | ... | ||||
4-z15A | [0,1,4,6] | <1,1,1,1,1,1> | 18 | ⓘ | all-interval tetrachord | 8-z15B | [0,1,3,5, 6,7,8,9] |
<5,5,5,5,5,3> | ⓘ | ... | |
4-z15B | [0,2,5,6] | ⓘ | all-interval tetrachord | 8-z15A | [0,1,2,3, 4,6,8,9] |
ⓘ | ... | ||||
4-16A | [0,1,5,7] | <1,1,0,1,2,1> | 19 | ⓘ | ... | 8-16B | [0,1,2,4, 6,7,8,9] |
<5,5,4,5,6,3> | ⓘ | ... | |
4-16B | [0,2,6,7] | ⓘ | ... | 8-16A | [0,1,2,3, 5,7,8,9] |
ⓘ | ... | ||||
4-17 | [0,3,4,7] | <1,0,2,2,1,0> | 13 | ⓘ | alpha chord | 8-17 | [0,1,3,4, 5,6,8,9] |
<5,4,6,6,5,2> | ⓘ | ... | |
4-18A | [0,1,4,7] | <1,0,2,1,1,1> | 21 | ⓘ | dim. M7 chord | 8-18B | [0,1,3,4, 6,7,8,9] |
<5,4,6,5,5,3> | ⓘ | ... | |
4-18B | [0,3,6,7] | ⓘ | ... | 8-18A | [0,1,2,3, 5,6,8,9] |
ⓘ | ... | ||||
4-19A | [0,1,4,8] | <1,0,1,3,1,0> | 24 | ⓘ | mM7 chord | 8-19B | [0,1,3,4, 5,7,8,9] |
<5,4,5,7,5,2> | ⓘ | ... | |
4-19B | [0,3,4,8] | ⓘ | ... | 8-19A | [0,1,2,4, 5,6,8,9] |
ⓘ | ... | ||||
4-20 | [0,1,5,8] | <1,0,1,2,2,0> | 15 | ⓘ | 大七和弦 | 8-20 | [0,1,2,4, 5,7,8,9] |
<5,4,5,6,6,2> | ⓘ | ... | |
4-21 | [0,2,4,6] | <0,3,0,2,0,1> | 11 | ⓘ | ... | 8-21 | [0,1,2,3, 4,6,8,T] |
<4,7,4,6,4,3> | ⓘ | ... | |
4-22A | [0,2,4,7] | <0,2,1,1,2,0> | 27 | ⓘ | 史提利·丹 | 8-22B | [0,1,2,3, 5,7,9,T] |
<4,6,5,5,6,2> | ⓘ | ... | |
4-22B | [0,3,5,7] | ⓘ | ... | 8-22A | [0,1,2,3, 5,6,8,T] |
ⓘ | ... | ||||
4-23 | [0,2,5,7] | <0,2,1,0,3,0> | 4 | ⓘ | quartal chord | 8-23 | [0,1,2,3, 5,7,8,T] |
<4,6,5,4,7,2> | ⓘ | bebop scale | |
4-24 | [0,2,4,8] | <0,2,0,3,0,1> | 16 | ⓘ | A7 chord | 8-24 | [0,1,2,4, 5,6,8,T] |
<4,6,4,7,4,3> | ⓘ | ... | |
4-25 | [0,2,6,8] | <0,2,0,2,0,2> | 12 | ⓘ | 增六和弦 | 8-25 | [0,1,2,4, 6,7,8,T] |
<4,6,4,6,4,4> | ⓘ | ... | |
4-26 | [0,3,5,8] | <0,1,2,1,2,0> | 14 | ⓘ | 小七和弦 | 8-26 | [0,1,3,4, 5,7,8,T][b] |
<4,5,6,5,6,2> | ⓘ | ... | |
4-27A | [0,2,5,8] | <0,1,2,1,1,1> | 29 | ⓘ | Half-diminished seventh chord | 8-27B | [0,1,2,4, 6,7,9,T] |
<4,5,6,5,5,3> | ⓘ | ... | |
4-27B | [0,3,6,8] | ⓘ | 属七和弦 | 8-27A | [0,1,2,4, 5,7,8,T] |
ⓘ | ... | ||||
4-28 | [0,3,6,9] | <0,0,4,0,0,2> | 5 | ⓘ | dim. 7th chord | 8-28 | [0,1,3,4, 6,7,9,T] |
<4,4,8,4,4,4> | ⓘ | octatonic scale | |
4-z29A | [0,1,3,7] | <1,1,1,1,1,1> | 23 | ⓘ | all-interval tetrachord | 8-z29B | [0,2,3,4, 6,7,8,9] |
<5,5,5,5,5,3> | ⓘ | ... | |
4-z29B | [0,4,6,7] | ⓘ | all-interval tetrachord | 8-z29A | [0,1,2,3, 5,6,7,9] |
ⓘ | ... | ||||
5-1 | [0,1,2,3,4] | <4,3,2,1,0,0> | ⓘ | ... | 7-1 | [0,1,2,3, 4,5,6] |
<6,5,4,3,2,1> | 1 | ⓘ | ... | |
5-2A | [0,1,2,3,5] | <3,3,2,1,1,0> | ⓘ | ... | 7-2B | [0,2,3,4, 5,6,7] |
<5,5,4,3,3,1> | 11 | ⓘ | ... | |
5-2B | [0,2,3,4,5] | ⓘ | ... | 7-2A | [0,1,2,3, 4,5,7] |
ⓘ | ... | ||||
5-3A | [0,1,2,4,5] | <3,2,2,2,1,0> | ⓘ | ... | 7-3B | [0,3,4,5, 6,7,8] |
<5,4,4,4,3,1> | 14 | ⓘ | ... | |
5-3B | [0,1,3,4,5] | ⓘ | ... | 7-3A | [0,1,2,3, 4,5,8] |
ⓘ | ... | ||||
5-4A | [0,1,2,3,6] | <3,2,2,1,1,1> | ⓘ | ... | 7-4B | [0,1,3,4, 5,6,7] |
<5,4,4,3,3,2> | 12 | ⓘ | ... | |
5-4B | [0,3,4,5,6] | ⓘ | ... | 7-4A | [0,1,2,3, 4,6,7] |
ⓘ | ... | ||||
5-5A | [0,1,2,3,7] | <3,2,1,1,2,1> | ⓘ | ... | 7-5B | [0,1,2,4, 5,6,7] |
<5,4,3,3,4,2> | 13 | ⓘ | ... | |
5-5B | [0,4,5,6,7] | ⓘ | ... | 7-5A | [0,1,2,3, 5,6,7] |
ⓘ | ... | ||||
5-6A | [0,1,2,5,6] | <3,1,1,2,2,1> | ⓘ | ... | 7-6B | [0,1,4,5, 6,7,8] |
<5,3,3,4,4,2> | 27 | ⓘ | ... | |
5-6B | [0,1,4,5,6] | ⓘ | ... | 7-6A | [0,1,2,3, 4,7,8] |
ⓘ | ... | ||||
5-7A | [0,1,2,6,7] | <3,1,0,1,3,2> | ⓘ | ... | 7-7B | [0,1,2,5, 6,7,8] |
<5,3,2,3,5,3> | 30 | ⓘ | ... | |
5-7B | [0,1,5,6,7] | ⓘ | ... | 7-7A | [0,1,2,3, 6,7,8] |
ⓘ | ... | ||||
5-8 | [0,2,3,4,6] | <2,3,2,2,0,1> | ⓘ | ... | 7-8 | [0,2,3,4, 5,6,8] |
<4,5,4,4,2,2> | 2 | ⓘ | ... | |
5-9A | [0,1,2,4,6] | <2,3,1,2,1,1> | ⓘ | ... | 7-9B | [0,2,4,5, 6,7,8] |
<4,5,3,4,3,2> | 15 | ⓘ | ... | |
5-9B | [0,2,4,5,6] | ⓘ | ... | 7-9A | [0,1,2,3, 4,6,8] |
ⓘ | ... | ||||
5-10A | [0,1,3,4,6] | <2,2,3,1,1,1> | ⓘ | ... | 7-10B | [0,2,3,4, 5,6,9] |
<4,4,5,3,3,2> | 19 | ⓘ | ... | |
5-10B | [0,2,3,5,6] | ⓘ | ... | 7-10A | [0,1,2,3, 4,6,9] |
ⓘ | ... | ||||
5-11A | [0,2,3,4,7] | <2,2,2,2,2,0> | ⓘ | ... | 7-11B | [0,2,3,4, 5,7,8] |
<4,4,4,4,4,1> | 18 | ⓘ | ... | |
5-11B | [0,3,4,5,7] | ⓘ | ... | 7-11A | [0,1,3,4, 5,6,8] |
ⓘ | ... | ||||
5-z12 | [0,1,3,5,6] | <2,2,2,1,2,1> | ⓘ | ... | 7-z12 | [0,1,2,3, 4,7,9] |
<4,4,4,3,4,2> | 5 | ⓘ | ... | |
5-13A | [0,1,2,4,8] | <2,2,1,3,1,1> | ⓘ | ... | 7-13B | [0,2,3,4, 6,7,8] |
<4,4,3,5,3,2> | 17 | ⓘ | ... | |
5-13B | [0,2,3,4,8] | ⓘ | ... | 7-13A | [0,1,2,4, 5,6,8] |
ⓘ | ... | ||||
5-14A | [0,1,2,5,7] | <2,2,1,1,3,1> | ⓘ | ... | 7-14B | [0,1,3,5, 6,7,8] |
<4,4,3,3,5,2> | 28 | ⓘ | ... | |
5-14B | [0,2,5,6,7] | ⓘ | ... | 7-14A | [0,1,2,3, 5,7,8] |
ⓘ | ... | ||||
5-15 | [0,1,2,6,8] | <2,2,0,2,2,2> | ⓘ | ... | 7-15 | [0,1,2,4, 6,7,8] |
<4,4,2,4,4,3> | 4 | ⓘ | ... | |
5-16A | [0,1,3,4,7] | <2,1,3,2,1,1> | ⓘ | ... | 7-16B | [0,1,3,4, 5,6,9] |
<4,3,5,4,3,2> | 20 | ⓘ | ... | |
5-16B | [0,3,4,6,7] | ⓘ | ... | 7-16A | [0,1,2,3, 5,6,9] |
ⓘ | ... | ||||
5-z17 | [0,1,3,4,8] | <2,1,2,3,2,0> | ⓘ | Farben chord | 7-z17 | [0,1,2,4, 5,6,9] |
<4,3,4,5,4,1> | 10 | ⓘ | ... | |
5-z18A | [0,1,4,5,7] | <2,1,2,2,2,1> | ⓘ | ... | 7-z18A | [0,1,4,5, 6,7,9][c] |
<4,3,4,4,4,2> | 35 | ⓘ | ... | |
5-z18B | [0,2,3,6,7] | ⓘ | ... | 7-z18B | [0,1,4,6, 7,8,9] |
ⓘ | ... | ||||
5-19A | [0,1,3,6,7] | <2,1,2,1,2,2> | ⓘ | ... | 7-19B | [0,1,2,3, 6,8,9] |
<4,3,4,3,4,3> | 31 | ⓘ | ... | |
5-19B | [0,1,4,6,7] | ⓘ | ... | 7-19A | [0,1,2,3, 6,7,9] |
ⓘ | ... | ||||
5-20A | [0,1,5,6,8][d] | <2,1,1,2,3,1> | ⓘ | ... | 7-20B | [0,1,2,5, 7,8,9] |
<4,3,3,4,5,2> | 34 | ⓘ | ... | |
5-20B | [0,2,3,7,8] | ⓘ | In scale | 7-20A | [0,1,2,5, 6,7,9][e] |
ⓘ | Persian scale | ||||
5-21A | [0,1,4,5,8] | <2,0,2,4,2,0> | ⓘ | ... | 7-21B | [0,1,3,4, 5,8,9] |
<4,2,4,6,4,1> | 21 | ⓘ | ... | |
5-21B | [0,3,4,7,8] | ⓘ | ... | 7-21A | [0,1,2,4, 5,8,9] |
ⓘ | ... | ||||
5-22 | [0,1,4,7,8] | <2,0,2,3,2,1> | ⓘ | ... | 7-22 | [0,1,2,5, 6,8,9] |
<4,2,4,5,4,2> | 8 | ⓘ | double harmonic scale | |
5-23A | [0,2,3,5,7] | <1,3,2,1,3,0> | ⓘ | ... | 7-23B | [0,2,4,5, 6,7,9] |
<3,5,4,3,5,1> | 25 | ⓘ | ... | |
5-23B | [0,2,4,5,7] | ⓘ | ... | 7-23A | [0,2,3,4, 5,7,9] |
ⓘ | ... | ||||
5-24A | [0,1,3,5,7] | <1,3,1,2,2,1> | ⓘ | ... | 7-24B | [0,2,4,6, 7,8,9] |
<3,5,3,4,4,2> | 22 | ⓘ | enigmatic scale | |
5-24B | [0,2,4,6,7] | ⓘ | ... | 7-24A | [0,1,2,3, 5,7,9] |
ⓘ | ... | ||||
5-25A | [0,2,3,5,8] | <1,2,3,1,2,1> | ⓘ | Seven six chord | 7-25B | [0,2,3,5, 6,7,9] |
<3,4,5,3,4,2> | 24 | ⓘ | ... | |
5-25B | [0,3,5,6,8] | ⓘ | ... | 7-25A | [0,2,3,4, 6,7,9] |
ⓘ | ... | ||||
5-26A | [0,2,4,5,8] | <1,2,2,3,1,1> | ⓘ | ... | 7-26A | [0,1,3,4, 5,7,9] |
<3,4,4,5,3,2> | 26 | ⓘ | ... | |
5-26B | [0,3,4,6,8] | ⓘ | ... | 7-26B | [0,2,4,5, 6,8,9] |
ⓘ | ... | ||||
5-27A | [0,1,3,5,8] | <1,2,2,2,3,0> | ⓘ | ... | 7-27B | [0,2,4,5, 7,8,9] |
<3,4,4,4,5,1> | 23 | ⓘ | ... | |
5-27B | [0,3,5,7,8] | ⓘ | ... | 7-27A | [0,1,2,4, 5,7,9] |
ⓘ | ... | ||||
5-28A | [0,2,3,6,8] | <1,2,2,2,1,2> | ⓘ | ... | 7-28A | [0,1,3,5, 6,7,9] |
<3,4,4,4,3,3> | 36 | ⓘ | ... | |
5-28B | [0,2,5,6,8] | ⓘ | ... | 7-28B | [0,2,3,4, 6,8,9] |
ⓘ | ... | ||||
5-29A | [0,1,3,6,8] | <1,2,2,1,3,1> | ⓘ | ... | 7-29B | [0,2,3,5, 7,8,9] |
<3,4,4,3,5,2> | 32 | ⓘ | ... | |
5-29B | [0,2,5,7,8] | ⓘ | ... | 7-29A | [0,1,2,4, 6,7,9] |
ⓘ | ... | ||||
5-30A | [0,1,4,6,8] | <1,2,1,3,2,1> | ⓘ | ... | 7-30B | [0,1,3,5, 7,8,9] |
<3,4,3,5,4,2> | 37 | ⓘ | ... | |
5-30B | [0,2,4,7,8] | ⓘ | ... | 7-30A | [0,1,2,4, 6,8,9] |
ⓘ | minor Neapolitan scale | ||||
5-31A | [0,1,3,6,9] | <1,1,4,1,1,2> | ⓘ | beta chord | 7-31B | [0,2,3,5, 6,8,9] |
<3,3,6,3,3,3> | 38 | ⓘ | ... | |
5-31B | [0,2,3,6,9] | ⓘ | Dominant minor ninth chord | 7-31A | [0,1,3,4, 6,7,9] |
ⓘ | Hungarian major scale | ||||
5-32A | [0,1,4,6,9] | <1,1,3,2,2,1> | ⓘ | ... | 7-32B | [0,1,3,5, 6,8,9] |
<3,3,5,4,4,2> | 33 | ⓘ | 和声大调 | |
5-32B | [0,3,5,8,9] | ⓘ | Elektra chord, gamma chord | 7-32A | [0,1,3,4, 6,8,9] |
ⓘ | harmonic minor scale | ||||
5-33 | [0,2,4,6,8] | <0,4,0,4,0,2> | ⓘ | ... | 7-33 | [0,1,2,4, 6,8,T] |
<2,6,2,6,2,3> | 6 | ⓘ | M Locrian scale | |
5-34 | [0,2,4,6,9] | <0,3,2,2,2,1> | ⓘ | Dominant ninth chord | 7-34 | [0,1,3,4, 6,8,T] |
<2,5,4,4,4,2> | 9 | ⓘ | altered scale | |
5-35 | [0,2,4,7,9] | <0,3,2,1,4,0> | ⓘ | 五聲音階 | 7-35 | [0,1,3,5, 6,8,T] |
<2,5,4,3,6,1> | 7 | ⓘ | 自然音阶 | |
5-z36A | [0,1,2,4,7] | <2,2,2,1,2,1> | ⓘ | ... | 7-z36B | [0,2,3,5, 6,7,8] |
<4,4,4,3,4,2> | 16 | ⓘ | ... | |
5-z36B | [0,3,5,6,7] | ⓘ | ... | 7-z36A | [0,1,2,3, 5,6,8] |
ⓘ | ... | ||||
5-z37 | [0,3,4,5,8] | <2,1,2,3,2,0> | ⓘ | ... | 7-z37 | [0,1,3,4, 5,7,8] |
<4,3,4,5,4,1> | 3 | ⓘ | ... | |
5-z38A | [0,1,2,5,8] | <2,1,2,2,2,1> | ⓘ | ... | 7-z38B | [0,1,3,4, 6,7,8] |
<4,3,4,4,4,2> | 29 | ⓘ | ... | |
5-z38B | [0,3,6,7,8] | ⓘ | ... | 7-z38A | [0,1,2,4, 5,7,8] |
ⓘ | ... | ||||
6-1 | [0,1,2,3,4,5] | <5,4,3,2,1,0> | 4 | ⓘ | chromatic hexachord | ||||||
6-2A | [0,1,2,3,4,6] | <4,4,3,2,1,1> | 19 | ⓘ | ... | ||||||
6-2B | [0,2,3,4,5,6] | ⓘ | ... | ||||||||
6-z3A | [0,1,2,3,5,6] | <4,3,3,2,2,1> | 49 | ⓘ | ... | 6-z36B | [0,3,4,5,6,7] | <4,3,3,2,2,1> | 50 | ⓘ | ... |
6-z3B | [0,1,3,4,5,6] | ⓘ | ... | 6-z36A | [0,1,2,3,4,7] | ⓘ | ... | ||||
6-z4 | [0,1,2,4,5,6] | <4,3,2,3,2,1> | 24 | ⓘ | ... | 6-z37 | [0,1,2,3,4,8] | <4,3,2,3,2,1> | 23 | ⓘ | ... |
6-5A | [0,1,2,3,6,7] | <4,2,2,2,3,2> | 16 | ⓘ | ... | ||||||
6-5B | [0,1,4,5,6,7] | ⓘ | ... | ||||||||
6-z6 | [0,1,2,5,6,7] | <4,2,1,2,4,2> | 33 | ⓘ | ... | 6-z38 | [0,1,2,3,7,8] | <4,2,1,2,4,2> | 34 | ⓘ | ... |
6-7 | [0,1,2,6,7,8] | <4,2,0,2,4,3> | 7 | ⓘ | ... | ||||||
6-8 | [0,2,3,4,5,7] | <3,4,3,2,3,0> | 5 | ⓘ | ... | ||||||
6-9A | [0,1,2,3,5,7] | <3,4,2,2,3,1> | 20 | ⓘ | ... | ||||||
6-9B | [0,2,4,5,6,7] | ⓘ | ... | ||||||||
6-z10A | [0,1,3,4,5,7] | <3,3,3,3,2,1> | 42 | ⓘ | ... | 6-z39B | [0,3,4,5,6,8] | <3,3,3,3,2,1> | 41 | ⓘ | ... |
6-z10B | [0,2,3,4,6,7] | ⓘ | ... | 6-z39A | [0,2,3,4,5,8] | ⓘ | ... | ||||
6-z11A | [0,1,2,4,5,7] | <3,3,3,2,3,1> | 47 | ⓘ | ... | 6-z40B | [0,3,5,6,7,8] | <3,3,3,2,3,1> | 48 | ⓘ | ... |
6-z11B | [0,2,3,5,6,7] | ⓘ | Sacher hexachord | 6-z40A | [0,1,2,3,5,8] | ⓘ | ... | ||||
6-z12A | [0,1,2,4,6,7] | <3,3,2,2,3,2> | 46 | ⓘ | ... | 6-z41B | [0,2,5,6,7,8] | <3,3,2,2,3,2> | 45 | ⓘ | ... |
6-z12B | [0,1,3,5,6,7] | ⓘ | ... | 6-z41A | [0,1,2,3,6,8] | ⓘ | ... | ||||
6-z13 | [0,1,3,4,6,7] | <3,2,4,2,2,2> | 29 | ⓘ | ... | 6-z42 | [0,1,2,3,6,9] | <3,2,4,2,2,2> | 30 | ⓘ | ... |
6-14A | [0,1,3,4,5,8] | <3,2,3,4,3,0> | 3 | ⓘ | ... | ||||||
6-14B | [0,3,4,5,7,8] | ⓘ | ... | ||||||||
6-15A | [0,1,2,4,5,8] | <3,2,3,4,2,1> | 13 | ⓘ | ... | ||||||
6-15B | [0,3,4,6,7,8] | ⓘ | ... | ||||||||
6-16A | [0,1,4,5,6,8] | <3,2,2,4,3,1> | 11 | ⓘ | ... | ||||||
6-16B | [0,2,3,4,7,8] | ⓘ | ... | ||||||||
6-z17A | [0,1,2,4,7,8] | <3,2,2,3,3,2> | 35 | ⓘ | all-trichord hexachord | 6-z43B | [0,2,3,6,7,8] | <3,2,2,3,3,2> | 36 | ⓘ | ... |
6-z17B | [0,1,4,6,7,8] | ⓘ | ... | 6-z43A | [0,1,2,5,6,8] | ⓘ | ... | ||||
6-18A | [0,1,2,5,7,8] | <3,2,2,2,4,2> | 17 | ⓘ | ... | ||||||
6-18B | [0,1,3,6,7,8] | ⓘ | ... | ||||||||
6-z19A | [0,1,3,4,7,8] | <3,1,3,4,3,1> | 37 | ⓘ | ... | 6-z44B | [0,3,4,7,8,9] | <3,1,3,4,3,1> | 38 | ⓘ | ... |
6-z19B | [0,1,4,5,7,8] | ⓘ | ... | 6-z44A | [0,1,2,5,6,9] | ⓘ | Schoenberg hexachord | ||||
6-20 | [0,1,4,5,8,9] | <3,0,3,6,3,0> | 2 | ⓘ | "Ode-to-Napoleon" hexachord | ||||||
6-21A | [0,2,3,4,6,8] | <2,4,2,4,1,2> | 12 | ⓘ | ... | ||||||
6-21B | [0,2,4,5,6,8] | ⓘ | ... | ||||||||
6-22A | [0,1,2,4,6,8] | <2,4,1,4,2,2> | 10 | ⓘ | ... | ||||||
6-22B | [0,2,4,6,7,8] | ⓘ | ... | ||||||||
6-z23 | [0,2,3,5,6,8] | <2,3,4,2,2,2> | 27 | ⓘ | ... | 6-z45 | [0,2,3,4,6,9] | <2,3,4,2,2,2> | 28 | ⓘ | ... |
6-z24A | [0,1,3,4,6,8] | <2,3,3,3,3,1> | 39 | ⓘ | ... | 6-z46B | [0,3,5,7,8,9] | <2,3,3,3,3,1> | 40 | ⓘ | ... |
6-z24B | [0,2,4,5,7,8] | ⓘ | ... | 6-z46A | [0,1,2,4,6,9] | ⓘ | ... | ||||
6-z25A | [0,1,3,5,6,8] | <2,3,3,2,4,1> | 43 | ⓘ | Major eleventh chord | 6-z47B | [0,2,5,7,8,9] | <2,3,3,2,4,1> | 44 | ⓘ | blues scale |
6-z25B | [0,2,3,5,7,8] | ⓘ | ... | 6-z47A | [0,1,2,4,7,9] | ⓘ | ... | ||||
6-z26 | [0,1,3,5,7,8] | <2,3,2,3,4,1> | 26 | ⓘ | ... | 6-z48 | [0,1,2,5,7,9] | <2,3,2,3,4,1> | 25 | ⓘ | ... |
6-27A | [0,1,3,4,6,9] | <2,2,5,2,2,2> | 14 | ⓘ | ... | ||||||
6-27B | [0,3,5,6,8,9] | ⓘ | ... | ||||||||
6-z28 | [0,1,3,5,6,9] | <2,2,4,3,2,2> | 21 | ⓘ | ... | 6-z49 | [0,1,3,4,7,9] | <2,2,4,3,2,2> | 22 | ⓘ | ... |
6-z29 | [0,2,3,6,7,9][f] | <2,2,4,2,3,2> | 32 | ⓘ | Bridge chord | 6-z50 | [0,1,4,6,7,9] | <2,2,4,2,3,2> | 31 | ⓘ | ... |
6-30A | [0,1,3,6,7,9] | <2,2,4,2,2,3> | 15 | ⓘ | ... | ||||||
6-30B | [0,2,3,6,8,9] | ⓘ | Petrushka chord | ||||||||
6-31A | [0,1,4,5,7,9][g] | <2,2,3,4,3,1> | 8 | ⓘ | ... | ||||||
6-31B | [0,2,4,5,8,9][h] | ⓘ | ... | ||||||||
6-32 | [0,2,4,5,7,9] | <1,4,3,2,5,0> | 6 | ⓘ | diatonic hexachord | ||||||
6-33A | [0,2,3,5,7,9] | <1,4,3,2,4,1> | 18 | ⓘ | ... | ||||||
6-33B | [0,2,4,6,7,9] | ⓘ | Dominant eleventh chord | ||||||||
6-34A | [0,1,3,5,7,9] | <1,4,2,4,2,2> | 9 | ⓘ | mystic chord | ||||||
6-34B | [0,2,4,6,8,9] | ⓘ | ... | ||||||||
6-35 | [0,2,4,6,8,T] | <0,6,0,6,0,3> | 1 | ⓘ | 全音音階 |
參見
[编辑]註
[编辑]- ^ Forte and Rahn both list 集合 (音乐) as the most left-packed possible version of a set. However, Forte packs from the left and Rahn packs from the right ("making the small numbers smaller," versus making, "the larger numbers ... smaller"[3]).
- ^ Forte 8-26: [0,1,2,4,5,7,9,T]
- ^ Forte 7-z18A: [0,1,2,3,5,8,9]
- ^ Forte 5-20A: [0,1,3,7,8]
- ^ Forte 7-20A: [0,1,2,4,7,8,9]
- ^ Forte 6-z29: [0,1,3,6,8,9]
- ^ Forte 6-31A: [0,1,3,5,8,9]
- ^ Forte 6-31B: [0,1,4,6,8,9]
參考
[编辑]- ^ 阿伦·福特 (1973). The Structure of Atonal Music. Yale University Press. ISBN 0-300-02120-8.
- ^ 阿伦·福特 (1973). The Structure of Atonal Music. Yale University Press. ISBN 0-300-02120-8.
- ^ Nelson, Paul (2004). "Two Algorithms for Computing the Prime Form", ComposerTools.com.
- ^ Rahn, John (1980). Basic Atonal Theory. New York: Longman. ISBN 978-0028731605.
- ^ Straus, Joseph N. (1990). Introduction to Post-Tonal Theory. Prentice-Hall. ISBN 9780131898905.
- ^ Schiff, David (1983/1998). The Music of Elliott Carter.
- ^ Carter, Elliott (2002). The Harmony Book, "Appendix 1". ISBN 9780825845949.
- ^ Schuijer, Michael (2008). Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts, p.97. University of Rochester. ISBN 978-1-58046-270-9.
- ^ Everett, Walter (2008). The Foundations of Rock, p.169. Oxford. ISBN 9780199718702.
外部鏈接
[编辑]- Solomon, Larry (2005). "The Table of Pitch Class Sets (页面存档备份,存于互联网档案馆)", SolomonsMusic.net.
- Tucker, Gary (2001). "Table of pc set classes (页面存档备份,存于互联网档案馆)", A Brief Introduction to Pitch-Class Set Analysis.
- Nelson, Paul (2004). "Table of Prime Forms (页面存档备份,存于互联网档案馆)", ComposerTools.com.
- "PC Set Calculator (页面存档备份,存于互联网档案馆)", MtA.Ca.
- "Chord Analyzer (PC Set Calculator) (页面存档备份,存于互联网档案馆)"
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