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音高集合列表

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這是按Forte編號英语Forte number分類的音高集合列表[1]

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This is a list of set classes by Forte number英语Forte number.[2] For a list of ordered collections, see: list of tone rows and series英语list of tone rows and series.

Sets are listed next to their complements英语Complement (music). 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英语Donald Martino had produced tables of hexachord英语hexachords, tetrachord英语tetrachords, trichord英语trichords, and pentachord英语pentachords for combinatoriality英语combinatoriality in his article, "The Source Set and its Aggregate Formations" (1961).[8]

列表

Forte編號英语Forte number 質數形式 區間向量 Carter編號英语Carter number 聲音 可能間距 Forte編號英语Forte number 質數形式 區間向量 Carter編號英语Carter number 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> 試聽聲音 aggregate英语aggregate (music)
1-1 [0] <0,0,0,0,0,0> 試聽聲音 純一度, 八度 11-1 [0,1,2,3,4,5,
 6,7,8,9,T]
<T,T,T,T,T,5> 試聽聲音 ...
2-1 [0,1] <1,0,0,0,0,0> 1 試聽聲音 半音, 大七度 10-1 [0,1,2,3,4,
 5,6,7,8,9]
<9,8,8,8,8,4> 試聽聲音 ...
2-2 [0,2] <0,1,0,0,0,0> 2 試聽聲音 大二度, 小七度 10-2 [0,1,2,3,4,
 5,6,7,8,T]
<8,9,8,8,8,4> 試聽聲音 ...
2-3 [0,3] <0,0,1,0,0,0> 3 試聽聲音 小三度, 大六度 10-3 [0,1,2,3,4,
 5,6,7,9,T]
<8,8,9,8,8,4> 試聽聲音 ...
2-4 [0,4] <0,0,0,1,0,0> 4 試聽聲音 大三度, 小六度 10-4 [0,1,2,3,4,
 5,6,8,9,T]
<8,8,8,9,8,4> 試聽聲音 ...
2-5 [0,5] <0,0,0,0,1,0> 5 試聽聲音 純四度, 纯五度 10-5 [0,1,2,3,4,
 5,7,8,9,T]
<8,8,8,8,9,4> 試聽聲音 ...
2-6 [0,6] <0,0,0,0,0,1> 6 試聽聲音 A4, 增四度 10-6 [0,1,2,3,4,
 6,7,8,9,T]
<8,8,8,8,8,5> 試聽聲音 ...
3-1 [0,1,2] <2,1,0,0,0,0> 4 試聽聲音 ... 9-1 [0,1,2,3,4,
 5,6,7,8]
<8,7,6,6,6,3> 試聽聲音 ...
3-2A [0,1,3] <1,1,1,0,0,0> 12 試聽聲音 ... 9-2A [0,1,2,3,4,
 5,6,7,9]
<7,7,7,6,6,3> 試聽聲音 ...
3-2B [0,2,3] 試聽聲音 ... 9-2B [0,2,3,4,5,
 6,7,8,9]
試聽聲音 ...
3-3A [0,1,4] <1,0,1,1,0,0> 11 試聽聲音 ... 9-3B [0,1,3,4,
 5,6,7,8,9]
<7,6,7,7,6,3> 試聽聲音 ...
3-3B [0,3,4] 試聽聲音 ... 9-3A [0,1,2,3,4,
 5,6,8,9]
試聽聲音 ...
3-4A [0,1,5] <1,0,0,1,1,0> 9 試聽聲音 ... 9-4B [0,1,2,4,5,
 6,7,8,9]
<7,6,6,7,7,3> 試聽聲音 ...
3-4B [0,4,5] 試聽聲音 ... 9-4A [0,1,2,3,4,
 5,7,8,9]
試聽聲音 ...
3-5A [0,1,6] <1,0,0,0,1,1> 7 試聽聲音 Viennese trichord英语Viennese trichord 9-5B [0,1,2,3,5,
 6,7,8,9]
<7,6,6,6,7,4> 試聽聲音 ...
3-5B [0,5,6] 試聽聲音 ... 9-5A [0,1,2,3,4,
 6,7,8,9]
試聽聲音 ...
3-6 [0,2,4] <0,2,0,1,0,0> 3 試聽聲音 ... 9-6 [0,1,2,3,4,
 5,6,8,T]
<6,8,6,7,6,3> 試聽聲音 ...
3-7A [0,2,5] <0,1,1,0,1,0> 10 試聽聲音 ... 9-7B [0,1,2,3,4,
 5,7,9,T]
<6,7,7,6,7,3> 試聽聲音 ...
3-7B [0,3,5] 試聽聲音 Blues trichord (五聲音階 subset)[9] 9-7A [0,1,2,3,4,
 5,7,8,T]
試聽聲音 ...
3-8A [0,2,6] <0,1,0,1,0,1> 8 試聽聲音 增六和弦 9-8B [0,1,2,3,4,
 6,8,9,T]
<6,7,6,7,6,4> 試聽聲音 ...
3-8B [0,4,6] 試聽聲音 ... 9-8A [0,1,2,3,4,
 6,7,8,T]
試聽聲音 ...
3-9 [0,2,7] <0,1,0,0,2,0> 5 試聽聲音 sus. chord英语suspended chord 9-9 [0,1,2,3,5,
 6,7,8,T]
<6,7,6,6,8,3> 試聽聲音 blues scale英语Blues scale
3-10 [0,3,6] <0,0,2,0,0,1> 2 試聽聲音 減三和弦 9-10 [0,1,2,3,4,
 6,7,9,T]
<6,6,8,6,6,4> 試聽聲音 ...
3-11A [0,3,7] <0,0,1,1,1,0> 6 試聽聲音 小三和弦 9-11B [0,1,2,3,5,
 6,8,9,T]
<6,6,7,7,7,3> 試聽聲音 ...
3-11B [0,4,7] 試聽聲音 大三和弦 9-11A [0,1,2,3,5,
 6,7,9,T]
試聽聲音 ...
3-12 [0,4,8] <0,0,0,3,0,0> 1 試聽聲音 增三和弦 9-12 [0,1,2,4,5,
 6,8,9,T]
<6,6,6,9,6,3> 試聽聲音 ...
4-1 [0,1,2,3] <3,2,1,0,0,0> 1 試聽聲音 ... 8-1 [0,1,2,3,
 4,5,6,7]
<7,6,5,4,4,2> 試聽聲音 ...
4-2A [0,1,2,4] <2,2,1,1,0,0> 17 試聽聲音 ... 8-2B [0,2,3,4,
 5,6,7,8]
<6,6,5,5,4,2> 試聽聲音 ...
4-2B [0,2,3,4] 試聽聲音 ... 8-2A [0,1,2,3,
 4,5,6,8]
試聽聲音 ...
4-3 [0,1,3,4] <2,1,2,1,0,0> 9 試聽聲音 ... 8-3 [0,1,2,3,
 4,5,6,9]
<6,5,6,5,4,2> 試聽聲音 ...
4-4A [0,1,2,5] <2,1,1,1,1,0> 20 試聽聲音 ... 8-4B [0,1,3,4,
 5,6,7,8]
<6,5,5,5,5,2> 試聽聲音 ...
4-4B [0,3,4,5] 試聽聲音 ... 8-4A [0,1,2,3,
 4,5,7,8]
試聽聲音 ...
4-5A [0,1,2,6] <2,1,0,1,1,1> 22 試聽聲音 ... 8-5B [0,1,2,4,
 5,6,7,8]
<6,5,4,5,5,3> 試聽聲音 ...
4-5B [0,4,5,6] 試聽聲音 ... 8-5A [0,1,2,3,
 4,6,7,8]
試聽聲音 ...
4-6 [0,1,2,7] <2,1,0,0,2,1> 6 試聽聲音 dream chord英语dream chord 8-6 [0,1,2,3,
 5,6,7,8]
<6,5,4,4,6,3> 試聽聲音 ...
4-7 [0,1,4,5] <2,0,1,2,1,0> 8 試聽聲音 ... 8-7 [0,1,2,3,
 4,5,8,9]
<6,4,5,6,5,2> 試聽聲音 ...
4-8 [0,1,5,6] <2,0,0,1,2,1> 10 試聽聲音 ... 8-8 [0,1,2,3,
 4,7,8,9]
<6,4,4,5,6,3> 試聽聲音 ...
4-9 [0,1,6,7] <2,0,0,0,2,2> 2 試聽聲音 distance model英语distance model 8-9 [0,1,2,3,
 6,7,8,9]
<6,4,4,4,6,4> 試聽聲音 ...
4-10 [0,2,3,5] <1,2,2,0,1,0> 3 試聽聲音 ... 8-10 [0,2,3,4,
 5,6,7,9]
<5,6,6,4,5,2> 試聽聲音 ...
4-11A [0,1,3,5] <1,2,1,1,1,0> 26 試聽聲音 ... 8-11B [0,2,4,5,
 6,7,8,9]
<5,6,5,5,5,2> 試聽聲音 ...
4-11B [0,2,4,5] 試聽聲音 ... 8-11A [0,1,2,3,
 4,5,7,9]
試聽聲音 ...
4-12A [0,2,3,6] <1,1,2,1,0,1> 28 試聽聲音 ... 8-12A [0,1,3,4,
 5,6,7,9]
<5,5,6,5,4,3> 試聽聲音 ...
4-12B [0,3,4,6] 試聽聲音 ... 8-12B [0,2,3,4,
 5,6,8,9]
試聽聲音 ...
4-13A [0,1,3,6] <1,1,2,0,1,1> 7 試聽聲音 ... 8-13B [0,2,3,5,
 6,7,8,9]
<5,5,6,4,5,3> 試聽聲音 ...
4-13B [0,3,5,6] 試聽聲音 ... 8-13A [0,1,2,3,
 4,6,7,9]
試聽聲音 ...
4-14A [0,2,3,7] <1,1,1,1,2,0> 25 試聽聲音 ... 8-14A [0,1,2,4,
 5,6,7,9]
<5,5,5,5,6,2> 試聽聲音 ...
4-14B [0,4,5,7] 試聽聲音 ... 8-14B [0,2,3,4,
 5,7,8,9]
試聽聲音 ...
4-z15A [0,1,4,6] <1,1,1,1,1,1> 18 試聽聲音 all-interval tetrachord英语all-interval tetrachord 8-z15B [0,1,3,5,
 6,7,8,9]
<5,5,5,5,5,3> 試聽聲音 ...
4-z15B [0,2,5,6] 試聽聲音 all-interval tetrachord英语all-interval tetrachord 8-z15A [0,1,2,3,
 4,6,8,9]
試聽聲音 ...
4-16A [0,1,5,7] <1,1,0,1,2,1> 19 試聽聲音 ... 8-16B [0,1,2,4,
 6,7,8,9]
<5,5,4,5,6,3> 試聽聲音 ...
4-16B [0,2,6,7] 試聽聲音 ... 8-16A [0,1,2,3,
 5,7,8,9]
試聽聲音 ...
4-17 [0,3,4,7] <1,0,2,2,1,0> 13 試聽聲音 alpha chord英语alpha chord 8-17 [0,1,3,4,
 5,6,8,9]
<5,4,6,6,5,2> 試聽聲音 ...
4-18A [0,1,4,7] <1,0,2,1,1,1> 21 試聽聲音 dim. M7 chord英语Diminished major seventh chord 8-18B [0,1,3,4,
 6,7,8,9]
<5,4,6,5,5,3> 試聽聲音 ...
4-18B [0,3,6,7] 試聽聲音 ... 8-18A [0,1,2,3,
 5,6,8,9]
試聽聲音 ...
4-19A [0,1,4,8] <1,0,1,3,1,0> 24 試聽聲音 mM7 chord英语Minor major seventh chord 8-19B [0,1,3,4,
 5,7,8,9]
<5,4,5,7,5,2> 試聽聲音 ...
4-19B [0,3,4,8] 試聽聲音 ... 8-19A [0,1,2,4,
 5,6,8,9]
試聽聲音 ...
4-20 [0,1,5,8] <1,0,1,2,2,0> 15 試聽聲音 大七和弦 8-20 [0,1,2,4,
 5,7,8,9]
<5,4,5,6,6,2> 試聽聲音 ...
4-21 [0,2,4,6] <0,3,0,2,0,1> 11 試聽聲音 ... 8-21 [0,1,2,3,
 4,6,8,T]
<4,7,4,6,4,3> 試聽聲音 ...
4-22A [0,2,4,7] <0,2,1,1,2,0> 27 試聽聲音 史提利·丹 8-22B [0,1,2,3,
 5,7,9,T]
<4,6,5,5,6,2> 試聽聲音 ...
4-22B [0,3,5,7] 試聽聲音 ... 8-22A [0,1,2,3,
 5,6,8,T]
試聽聲音 ...
4-23 [0,2,5,7] <0,2,1,0,3,0> 4 試聽聲音 quartal chord英语quartal chord 8-23 [0,1,2,3,
 5,7,8,T]
<4,6,5,4,7,2> 試聽聲音 bebop scale英语bebop scale
4-24 [0,2,4,8] <0,2,0,3,0,1> 16 試聽聲音 A7 chord英语Augmented seventh chord 8-24 [0,1,2,4,
 5,6,8,T]
<4,6,4,7,4,3> 試聽聲音 ...
4-25 [0,2,6,8] <0,2,0,2,0,2> 12 試聽聲音 增六和弦 8-25 [0,1,2,4,
 6,7,8,T]
<4,6,4,6,4,4> 試聽聲音 ...
4-26 [0,3,5,8] <0,1,2,1,2,0> 14 試聽聲音 小七和弦 8-26 [0,1,3,4,
 5,7,8,T]
[b]
<4,5,6,5,6,2> 試聽聲音 ...
4-27A [0,2,5,8] <0,1,2,1,1,1> 29 試聽聲音 Half-diminished seventh chord英语Half-diminished seventh chord 8-27B [0,1,2,4,
 6,7,9,T]
<4,5,6,5,5,3> 試聽聲音 ...
4-27B [0,3,6,8] 試聽聲音 属七和弦 8-27A [0,1,2,4,
 5,7,8,T]
試聽聲音 ...
4-28 [0,3,6,9] <0,0,4,0,0,2> 5 試聽聲音 dim. 7th chord英语Diminished seventh chord 8-28 [0,1,3,4,
 6,7,9,T]
<4,4,8,4,4,4> 試聽聲音 octatonic scale
4-z29A [0,1,3,7] <1,1,1,1,1,1> 23 試聽聲音 all-interval tetrachord英语all-interval tetrachord 8-z29B [0,2,3,4,
 6,7,8,9]
<5,5,5,5,5,3> 試聽聲音 ...
4-z29B [0,4,6,7] 試聽聲音 all-interval tetrachord英语all-interval tetrachord 8-z29A [0,1,2,3,
 5,6,7,9]
試聽聲音 ...
5-1 [0,1,2,3,4] <4,3,2,1,0,0> 試聽聲音 ... 7-1 [0,1,2,3,
 4,5,6]
<6,5,4,3,2,1> 1 試聽聲音 ...
5-2A [0,1,2,3,5] <3,3,2,1,1,0> 試聽聲音 ... 7-2B [0,2,3,4,
 5,6,7]
<5,5,4,3,3,1> 11 試聽聲音 ...
5-2B [0,2,3,4,5] 試聽聲音 ... 7-2A [0,1,2,3,
 4,5,7]
試聽聲音 ...
5-3A [0,1,2,4,5] <3,2,2,2,1,0> 試聽聲音 ... 7-3B [0,3,4,5,
 6,7,8]
<5,4,4,4,3,1> 14 試聽聲音 ...
5-3B [0,1,3,4,5] 試聽聲音 ... 7-3A [0,1,2,3,
 4,5,8]
試聽聲音 ...
5-4A [0,1,2,3,6] <3,2,2,1,1,1> 試聽聲音 ... 7-4B [0,1,3,4,
 5,6,7]
<5,4,4,3,3,2> 12 試聽聲音 ...
5-4B [0,3,4,5,6] 試聽聲音 ... 7-4A [0,1,2,3,
 4,6,7]
試聽聲音 ...
5-5A [0,1,2,3,7] <3,2,1,1,2,1> 試聽聲音 ... 7-5B [0,1,2,4,
 5,6,7]
<5,4,3,3,4,2> 13 試聽聲音 ...
5-5B [0,4,5,6,7] 試聽聲音 ... 7-5A [0,1,2,3,
 5,6,7]
試聽聲音 ...
5-6A [0,1,2,5,6] <3,1,1,2,2,1> 試聽聲音 ... 7-6B [0,1,4,5,
 6,7,8]
<5,3,3,4,4,2> 27 試聽聲音 ...
5-6B [0,1,4,5,6] 試聽聲音 ... 7-6A [0,1,2,3,
 4,7,8]
試聽聲音 ...
5-7A [0,1,2,6,7] <3,1,0,1,3,2> 試聽聲音 ... 7-7B [0,1,2,5,
 6,7,8]
<5,3,2,3,5,3> 30 試聽聲音 ...
5-7B [0,1,5,6,7] 試聽聲音 ... 7-7A [0,1,2,3,
 6,7,8]
試聽聲音 ...
5-8 [0,2,3,4,6] <2,3,2,2,0,1> 試聽聲音 ... 7-8 [0,2,3,4,
 5,6,8]
<4,5,4,4,2,2> 2 試聽聲音 ...
5-9A [0,1,2,4,6] <2,3,1,2,1,1> 試聽聲音 ... 7-9B [0,2,4,5,
 6,7,8]
<4,5,3,4,3,2> 15 試聽聲音 ...
5-9B [0,2,4,5,6] 試聽聲音 ... 7-9A [0,1,2,3,
 4,6,8]
試聽聲音 ...
5-10A [0,1,3,4,6] <2,2,3,1,1,1> 試聽聲音 ... 7-10B [0,2,3,4,
 5,6,9]
<4,4,5,3,3,2> 19 試聽聲音 ...
5-10B [0,2,3,5,6] 試聽聲音 ... 7-10A [0,1,2,3,
 4,6,9]
試聽聲音 ...
5-11A [0,2,3,4,7] <2,2,2,2,2,0> 試聽聲音 ... 7-11B [0,2,3,4,
 5,7,8]
<4,4,4,4,4,1> 18 試聽聲音 ...
5-11B [0,3,4,5,7] 試聽聲音 ... 7-11A [0,1,3,4,
 5,6,8]
試聽聲音 ...
5-z12 [0,1,3,5,6] <2,2,2,1,2,1> 試聽聲音 ... 7-z12 [0,1,2,3,
 4,7,9]
<4,4,4,3,4,2> 5 試聽聲音 ...
5-13A [0,1,2,4,8] <2,2,1,3,1,1> 試聽聲音 ... 7-13B [0,2,3,4,
 6,7,8]
<4,4,3,5,3,2> 17 試聽聲音 ...
5-13B [0,2,3,4,8] 試聽聲音 ... 7-13A [0,1,2,4,
 5,6,8]
試聽聲音 ...
5-14A [0,1,2,5,7] <2,2,1,1,3,1> 試聽聲音 ... 7-14B [0,1,3,5,
 6,7,8]
<4,4,3,3,5,2> 28 試聽聲音 ...
5-14B [0,2,5,6,7] 試聽聲音 ... 7-14A [0,1,2,3,
 5,7,8]
試聽聲音 ...
5-15 [0,1,2,6,8] <2,2,0,2,2,2> 試聽聲音 ... 7-15 [0,1,2,4,
 6,7,8]
<4,4,2,4,4,3> 4 試聽聲音 ...
5-16A [0,1,3,4,7] <2,1,3,2,1,1> 試聽聲音 ... 7-16B [0,1,3,4,
 5,6,9]
<4,3,5,4,3,2> 20 試聽聲音 ...
5-16B [0,3,4,6,7] 試聽聲音 ... 7-16A [0,1,2,3,
 5,6,9]
試聽聲音 ...
5-z17 [0,1,3,4,8] <2,1,2,3,2,0> 試聽聲音 Farben chord英语Farben chord 7-z17 [0,1,2,4,
 5,6,9]
<4,3,4,5,4,1> 10 試聽聲音 ...
5-z18A [0,1,4,5,7] <2,1,2,2,2,1> 試聽聲音 ... 7-z18A [0,1,4,5,
 6,7,9]
[c]
<4,3,4,4,4,2> 35 試聽聲音 ...
5-z18B [0,2,3,6,7] 試聽聲音 ... 7-z18B [0,1,4,6,
 7,8,9]
試聽聲音 ...
5-19A [0,1,3,6,7] <2,1,2,1,2,2> 試聽聲音 ... 7-19B [0,1,2,3,
 6,8,9]
<4,3,4,3,4,3> 31 試聽聲音 ...
5-19B [0,1,4,6,7] 試聽聲音 ... 7-19A [0,1,2,3,
 6,7,9]
試聽聲音 ...
5-20A [0,1,5,6,8][d] <2,1,1,2,3,1> 試聽聲音 ... 7-20B [0,1,2,5,
 7,8,9]
<4,3,3,4,5,2> 34 試聽聲音 ...
5-20B [0,2,3,7,8] 試聽聲音 In scale英语In scale 7-20A [0,1,2,5,
 6,7,9]
[e]
試聽聲音 Persian scale英语Persian scale
5-21A [0,1,4,5,8] <2,0,2,4,2,0> 試聽聲音 ... 7-21B [0,1,3,4,
 5,8,9]
<4,2,4,6,4,1> 21 試聽聲音 ...
5-21B [0,3,4,7,8] 試聽聲音 ... 7-21A [0,1,2,4,
 5,8,9]
試聽聲音 ...
5-22 [0,1,4,7,8] <2,0,2,3,2,1> 試聽聲音 ... 7-22 [0,1,2,5,
 6,8,9]
<4,2,4,5,4,2> 8 試聽聲音 double harmonic scale英语double harmonic scale
5-23A [0,2,3,5,7] <1,3,2,1,3,0> 試聽聲音 ... 7-23B [0,2,4,5,
 6,7,9]
<3,5,4,3,5,1> 25 試聽聲音 ...
5-23B [0,2,4,5,7] 試聽聲音 ... 7-23A [0,2,3,4,
 5,7,9]
試聽聲音 ...
5-24A [0,1,3,5,7] <1,3,1,2,2,1> 試聽聲音 ... 7-24B [0,2,4,6,
 7,8,9]
<3,5,3,4,4,2> 22 試聽聲音 enigmatic scale英语enigmatic scale
5-24B [0,2,4,6,7] 試聽聲音 ... 7-24A [0,1,2,3,
 5,7,9]
試聽聲音 ...
5-25A [0,2,3,5,8] <1,2,3,1,2,1> 試聽聲音 Seven six chord英语Seven six chord 7-25B [0,2,3,5,
 6,7,9]
<3,4,5,3,4,2> 24 試聽聲音 ...
5-25B [0,3,5,6,8] 試聽聲音 ... 7-25A [0,2,3,4,
 6,7,9]
試聽聲音 ...
5-26A [0,2,4,5,8] <1,2,2,3,1,1> 試聽聲音 ... 7-26A [0,1,3,4,
 5,7,9]
<3,4,4,5,3,2> 26 試聽聲音 ...
5-26B [0,3,4,6,8] 試聽聲音 ... 7-26B [0,2,4,5,
 6,8,9]
試聽聲音 ...
5-27A [0,1,3,5,8] <1,2,2,2,3,0> 試聽聲音 ... 7-27B [0,2,4,5,
 7,8,9]
<3,4,4,4,5,1> 23 試聽聲音 ...
5-27B [0,3,5,7,8] 試聽聲音 ... 7-27A [0,1,2,4,
 5,7,9]
試聽聲音 ...
5-28A [0,2,3,6,8] <1,2,2,2,1,2> 試聽聲音 ... 7-28A [0,1,3,5,
 6,7,9]
<3,4,4,4,3,3> 36 試聽聲音 ...
5-28B [0,2,5,6,8] 試聽聲音 ... 7-28B [0,2,3,4,
 6,8,9]
試聽聲音 ...
5-29A [0,1,3,6,8] <1,2,2,1,3,1> 試聽聲音 ... 7-29B [0,2,3,5,
 7,8,9]
<3,4,4,3,5,2> 32 試聽聲音 ...
5-29B [0,2,5,7,8] 試聽聲音 ... 7-29A [0,1,2,4,
 6,7,9]
試聽聲音 ...
5-30A [0,1,4,6,8] <1,2,1,3,2,1> 試聽聲音 ... 7-30B [0,1,3,5,
 7,8,9]
<3,4,3,5,4,2> 37 試聽聲音 ...
5-30B [0,2,4,7,8] 試聽聲音 ... 7-30A [0,1,2,4,
 6,8,9]
試聽聲音 minor Neapolitan scale英语minor Neapolitan scale
5-31A [0,1,3,6,9] <1,1,4,1,1,2> 試聽聲音 beta chord 7-31B [0,2,3,5,
 6,8,9]
<3,3,6,3,3,3> 38 試聽聲音 ...
5-31B [0,2,3,6,9] 試聽聲音 Dominant minor ninth chord英语Dominant minor ninth chord 7-31A [0,1,3,4,
 6,7,9]
試聽聲音 Hungarian major scale英语Hungarian major scale
5-32A [0,1,4,6,9] <1,1,3,2,2,1> 試聽聲音 ... 7-32B [0,1,3,5,
 6,8,9]
<3,3,5,4,4,2> 33 試聽聲音 和声大调
5-32B [0,3,5,8,9] 試聽聲音 Elektra chord英语Elektra chord, gamma chord英语gamma chord 7-32A [0,1,3,4,
 6,8,9]
試聽聲音 harmonic minor scale英语harmonic minor scale
5-33 [0,2,4,6,8] <0,4,0,4,0,2> 試聽聲音 ... 7-33 [0,1,2,4,
 6,8,T]
<2,6,2,6,2,3> 6 試聽聲音 M Locrian scale英语Major Locrian scale
5-34 [0,2,4,6,9] <0,3,2,2,2,1> 試聽聲音 Dominant ninth chord 7-34 [0,1,3,4,
 6,8,T]
<2,5,4,4,4,2> 9 試聽聲音 altered scale英语altered scale
5-35 [0,2,4,7,9] <0,3,2,1,4,0> 試聽聲音 五聲音階 7-35 [0,1,3,5,
 6,8,T]
<2,5,4,3,6,1> 7 試聽聲音 自然音阶
5-z36A [0,1,2,4,7] <2,2,2,1,2,1> 試聽聲音 ... 7-z36B [0,2,3,5,
 6,7,8]
<4,4,4,3,4,2> 16 試聽聲音 ...
5-z36B [0,3,5,6,7] 試聽聲音 ... 7-z36A [0,1,2,3,
 5,6,8]
試聽聲音 ...
5-z37 [0,3,4,5,8] <2,1,2,3,2,0> 試聽聲音 ... 7-z37 [0,1,3,4,
 5,7,8]
<4,3,4,5,4,1> 3 試聽聲音 ...
5-z38A [0,1,2,5,8] <2,1,2,2,2,1> 試聽聲音 ... 7-z38B [0,1,3,4,
 6,7,8]
<4,3,4,4,4,2> 29 試聽聲音 ...
5-z38B [0,3,6,7,8] 試聽聲音 ... 7-z38A [0,1,2,4,
 5,7,8]
試聽聲音 ...
6-1 [0,1,2,3,4,5] <5,4,3,2,1,0> 4 試聽聲音 chromatic hexachord英语chromatic hexachord
6-2A [0,1,2,3,4,6] <4,4,3,2,1,1> 19 試聽聲音 ...
6-2B [0,2,3,4,5,6] 試聽聲音 ...
6-z3A [0,1,2,3,5,6] <4,3,3,2,2,1> 49 試聽聲音 ... 6-z36B [0,3,4,5,6,7] <4,3,3,2,2,1> 50 試聽聲音 ...
6-z3B [0,1,3,4,5,6] 試聽聲音 ... 6-z36A [0,1,2,3,4,7] 試聽聲音 ...
6-z4 [0,1,2,4,5,6] <4,3,2,3,2,1> 24 試聽聲音 ... 6-z37 [0,1,2,3,4,8] <4,3,2,3,2,1> 23 試聽聲音 ...
6-5A [0,1,2,3,6,7] <4,2,2,2,3,2> 16 試聽聲音 ...
6-5B [0,1,4,5,6,7] 試聽聲音 ...
6-z6 [0,1,2,5,6,7] <4,2,1,2,4,2> 33 試聽聲音 ... 6-z38 [0,1,2,3,7,8] <4,2,1,2,4,2> 34 試聽聲音 ...
6-7 [0,1,2,6,7,8] <4,2,0,2,4,3> 7 試聽聲音 ...
6-8 [0,2,3,4,5,7] <3,4,3,2,3,0> 5 試聽聲音 ...
6-9A [0,1,2,3,5,7] <3,4,2,2,3,1> 20 試聽聲音 ...
6-9B [0,2,4,5,6,7] 試聽聲音 ...
6-z10A [0,1,3,4,5,7] <3,3,3,3,2,1> 42 試聽聲音 ... 6-z39B [0,3,4,5,6,8] <3,3,3,3,2,1> 41 試聽聲音 ...
6-z10B [0,2,3,4,6,7] 試聽聲音 ... 6-z39A [0,2,3,4,5,8] 試聽聲音 ...
6-z11A [0,1,2,4,5,7] <3,3,3,2,3,1> 47 試聽聲音 ... 6-z40B [0,3,5,6,7,8] <3,3,3,2,3,1> 48 試聽聲音 ...
6-z11B [0,2,3,5,6,7] 試聽聲音 Sacher hexachord英语Sacher hexachord 6-z40A [0,1,2,3,5,8] 試聽聲音 ...
6-z12A [0,1,2,4,6,7] <3,3,2,2,3,2> 46 試聽聲音 ... 6-z41B [0,2,5,6,7,8] <3,3,2,2,3,2> 45 試聽聲音 ...
6-z12B [0,1,3,5,6,7] 試聽聲音 ... 6-z41A [0,1,2,3,6,8] 試聽聲音 ...
6-z13 [0,1,3,4,6,7] <3,2,4,2,2,2> 29 試聽聲音 ... 6-z42 [0,1,2,3,6,9] <3,2,4,2,2,2> 30 試聽聲音 ...
6-14A [0,1,3,4,5,8] <3,2,3,4,3,0> 3 試聽聲音 ...
6-14B [0,3,4,5,7,8] 試聽聲音 ...
6-15A [0,1,2,4,5,8] <3,2,3,4,2,1> 13 試聽聲音 ...
6-15B [0,3,4,6,7,8] 試聽聲音 ...
6-16A [0,1,4,5,6,8] <3,2,2,4,3,1> 11 試聽聲音 ...
6-16B [0,2,3,4,7,8] 試聽聲音 ...
6-z17A [0,1,2,4,7,8] <3,2,2,3,3,2> 35 試聽聲音 all-trichord hexachord英语all-trichord hexachord 6-z43B [0,2,3,6,7,8] <3,2,2,3,3,2> 36 試聽聲音 ...
6-z17B [0,1,4,6,7,8] 試聽聲音 ... 6-z43A [0,1,2,5,6,8] 試聽聲音 ...
6-18A [0,1,2,5,7,8] <3,2,2,2,4,2> 17 試聽聲音 ...
6-18B [0,1,3,6,7,8] 試聽聲音 ...
6-z19A [0,1,3,4,7,8] <3,1,3,4,3,1> 37 試聽聲音 ... 6-z44B [0,3,4,7,8,9] <3,1,3,4,3,1> 38 試聽聲音 ...
6-z19B [0,1,4,5,7,8] 試聽聲音 ... 6-z44A [0,1,2,5,6,9] 試聽聲音 Schoenberg hexachord英语Schoenberg hexachord
6-20 [0,1,4,5,8,9] <3,0,3,6,3,0> 2 試聽聲音 "Ode-to-Napoleon" hexachord英语"Ode-to-Napoleon" hexachord
6-21A [0,2,3,4,6,8] <2,4,2,4,1,2> 12 試聽聲音 ...
6-21B [0,2,4,5,6,8] 試聽聲音 ...
6-22A [0,1,2,4,6,8] <2,4,1,4,2,2> 10 試聽聲音 ...
6-22B [0,2,4,6,7,8] 試聽聲音 ...
6-z23 [0,2,3,5,6,8] <2,3,4,2,2,2> 27 試聽聲音 ... 6-z45 [0,2,3,4,6,9] <2,3,4,2,2,2> 28 試聽聲音 ...
6-z24A [0,1,3,4,6,8] <2,3,3,3,3,1> 39 試聽聲音 ... 6-z46B [0,3,5,7,8,9] <2,3,3,3,3,1> 40 試聽聲音 ...
6-z24B [0,2,4,5,7,8] 試聽聲音 ... 6-z46A [0,1,2,4,6,9] 試聽聲音 ...
6-z25A [0,1,3,5,6,8] <2,3,3,2,4,1> 43 試聽聲音 Major eleventh chord英语Major eleventh chord 6-z47B [0,2,5,7,8,9] <2,3,3,2,4,1> 44 試聽聲音 blues scale英语Blues scale
6-z25B [0,2,3,5,7,8] 試聽聲音 ... 6-z47A [0,1,2,4,7,9] 試聽聲音 ...
6-z26 [0,1,3,5,7,8] <2,3,2,3,4,1> 26 試聽聲音 ... 6-z48 [0,1,2,5,7,9] <2,3,2,3,4,1> 25 試聽聲音 ...
6-27A [0,1,3,4,6,9] <2,2,5,2,2,2> 14 試聽聲音 ...
6-27B [0,3,5,6,8,9] 試聽聲音 ...
6-z28 [0,1,3,5,6,9] <2,2,4,3,2,2> 21 試聽聲音 ... 6-z49 [0,1,3,4,7,9] <2,2,4,3,2,2> 22 試聽聲音 ...
6-z29 [0,2,3,6,7,9][f] <2,2,4,2,3,2> 32 試聽聲音 Bridge chord英语Bridge chord 6-z50 [0,1,4,6,7,9] <2,2,4,2,3,2> 31 試聽聲音 ...
6-30A [0,1,3,6,7,9] <2,2,4,2,2,3> 15 試聽聲音 ...
6-30B [0,2,3,6,8,9] 試聽聲音 Petrushka chord英语Petrushka chord
6-31A [0,1,4,5,7,9][g] <2,2,3,4,3,1> 8 試聽聲音 ...
6-31B [0,2,4,5,8,9][h] 試聽聲音 ...
6-32 [0,2,4,5,7,9] <1,4,3,2,5,0> 6 試聽聲音 diatonic hexachord英语diatonic hexachord
6-33A [0,2,3,5,7,9] <1,4,3,2,4,1> 18 試聽聲音 ...
6-33B [0,2,4,6,7,9] 試聽聲音 Dominant eleventh chord
6-34A [0,1,3,5,7,9] <1,4,2,4,2,2> 9 試聽聲音 mystic chord英语mystic chord
6-34B [0,2,4,6,8,9] 試聽聲音 ...
6-35 [0,2,4,6,8,T] <0,6,0,6,0,3> 1 試聽聲音 全音音階

參見

  1. ^ 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]).
  2. ^ Forte 8-26: [0,1,2,4,5,7,9,T]
  3. ^ Forte 7-z18A: [0,1,2,3,5,8,9]
  4. ^ Forte 5-20A: [0,1,3,7,8]
  5. ^ Forte 7-20A: [0,1,2,4,7,8,9]
  6. ^ Forte 6-z29: [0,1,3,6,8,9]
  7. ^ Forte 6-31A: [0,1,3,5,8,9]
  8. ^ Forte 6-31B: [0,1,4,6,8,9]

參考

  1. ^ 阿伦·福特 (1973). The Structure of Atonal Music. Yale University Press. ISBN 0-300-02120-8.
  2. ^ 阿伦·福特 (1973). The Structure of Atonal Music. Yale University Press. ISBN 0-300-02120-8.
  3. ^ Nelson, Paul (2004). "Two Algorithms for Computing the Prime Form", ComposerTools.com.
  4. ^ Rahn, John (1980). Basic Atonal Theory. New York: Longman. ISBN 978-0028731605.
  5. ^ Straus, Joseph N. (1990). Introduction to Post-Tonal Theory. Prentice-Hall. ISBN 9780131898905.
  6. ^ Schiff, David (1983/1998). The Music of Elliott Carter.
  7. ^ Carter, Elliott (2002). The Harmony Book, "Appendix 1". ISBN 9780825845949.
  8. ^ Schuijer, Michael (2008). Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts, p.97. University of Rochester. ISBN 978-1-58046-270-9.
  9. ^ Everett, Walter (2008). The Foundations of Rock, p.169. Oxford. ISBN 9780199718702.

外部鏈接