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音高集合列表

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维基百科，自由的百科全书

这是按Forte编号（英语：Forte number）分类的音高集合列表。[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 对称). "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：hexachord）s, tetrachord（英语：tetrachord）s, trichord（英语：trichord）s, and pentachord（英语：pentachord）s for combinatoriality（英语：combinatoriality） in his article, "The Source Set and its Aggregate Formations" (1961).[8]

列表

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Forte编号（英语：Forte number） 质数形式 区间向量 Carter编号（英语：Carter number） 声音 可能间距 Forte编号（英语：Forte number） 质数形式 区间向量 Carter编号（英语：Carter number） 声音 可能间距
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> 试听声音ⓘ aggregate（英语：aggregate (music)）
1-1 [0] <0,0,0,0,0,0> 试听声音ⓘ 纯一度, 八度 11-1 [0,1,2,3,4,5,
 6,7,8,9,T]		 <T,T,T,T,T,5> 试听声音ⓘ ...
2-1 [0,1] <1,0,0,0,0,0> 1 试听声音ⓘ 半音, 大七度 10-1 [0,1,2,3,4,
 5,6,7,8,9]		 <9,8,8,8,8,4> 试听声音ⓘ ...
2-2 [0,2] <0,1,0,0,0,0> 2 试听声音ⓘ 大二度, 小七度 10-2 [0,1,2,3,4,
 5,6,7,8,T]		 <8,9,8,8,8,4> 试听声音ⓘ ...
2-3 [0,3] <0,0,1,0,0,0> 3 试听声音ⓘ 小三度, 大六度 10-3 [0,1,2,3,4,
 5,6,7,9,T]		 <8,8,9,8,8,4> 试听声音ⓘ ...
2-4 [0,4] <0,0,0,1,0,0> 4 试听声音ⓘ 大三度, 小六度 10-4 [0,1,2,3,4,
 5,6,8,9,T]		 <8,8,8,9,8,4> 试听声音ⓘ ...
2-5 [0,5] <0,0,0,0,1,0> 5 试听声音ⓘ 纯四度, 纯五度 10-5 [0,1,2,3,4,
 5,7,8,9,T]		 <8,8,8,8,9,4> 试听声音ⓘ ...
2-6 [0,6] <0,0,0,0,0,1> 6 试听声音ⓘ A4, 增四度 10-6 [0,1,2,3,4,
 6,7,8,9,T]		 <8,8,8,8,8,5> 试听声音ⓘ ...
3-1 [0,1,2] <2,1,0,0,0,0> 4 试听声音ⓘ ... 9-1 [0,1,2,3,4,
 5,6,7,8]		 <8,7,6,6,6,3> 试听声音ⓘ ...
3-2A [0,1,3] <1,1,1,0,0,0> 12 试听声音ⓘ ... 9-2A [0,1,2,3,4,
 5,6,7,9]		 <7,7,7,6,6,3> 试听声音ⓘ ...
3-2B [0,2,3] 试听声音ⓘ ... 9-2B [0,2,3,4,5,
 6,7,8,9]		 试听声音ⓘ ...
3-3A [0,1,4] <1,0,1,1,0,0> 11 试听声音ⓘ ... 9-3B [0,1,3,4,
 5,6,7,8,9]		 <7,6,7,7,6,3> 试听声音ⓘ ...
3-3B [0,3,4] 试听声音ⓘ ... 9-3A [0,1,2,3,4,
 5,6,8,9]		 试听声音ⓘ ...
3-4A [0,1,5] <1,0,0,1,1,0> 9 试听声音ⓘ ... 9-4B [0,1,2,4,5,
 6,7,8,9]		 <7,6,6,7,7,3> 试听声音ⓘ ...
3-4B [0,4,5] 试听声音ⓘ ... 9-4A [0,1,2,3,4,
 5,7,8,9]		 试听声音ⓘ ...
3-5A [0,1,6] <1,0,0,0,1,1> 7 试听声音ⓘ Viennese trichord（英语：Viennese trichord） 9-5B [0,1,2,3,5,
 6,7,8,9]		 <7,6,6,6,7,4> 试听声音ⓘ ...
3-5B [0,5,6] 试听声音ⓘ ... 9-5A [0,1,2,3,4,
 6,7,8,9]		 试听声音ⓘ ...
3-6 [0,2,4] <0,2,0,1,0,0> 3 试听声音ⓘ ... 9-6 [0,1,2,3,4,
 5,6,8,T]		 <6,8,6,7,6,3> 试听声音ⓘ ...
3-7A [0,2,5] <0,1,1,0,1,0> 10 试听声音ⓘ ... 9-7B [0,1,2,3,4,
 5,7,9,T]		 <6,7,7,6,7,3> 试听声音ⓘ ...
3-7B [0,3,5] 试听声音ⓘ Blues trichord (五声音阶 subset)[9] 9-7A [0,1,2,3,4,
 5,7,8,T]		 试听声音ⓘ ...
3-8A [0,2,6] <0,1,0,1,0,1> 8 试听声音ⓘ 增六和弦 9-8B [0,1,2,3,4,
 6,8,9,T]		 <6,7,6,7,6,4> 试听声音ⓘ ...
3-8B [0,4,6] 试听声音ⓘ ... 9-8A [0,1,2,3,4,
 6,7,8,T]		 试听声音ⓘ ...
3-9 [0,2,7] <0,1,0,0,2,0> 5 试听声音ⓘ sus. chord（英语：suspended chord） 9-9 [0,1,2,3,5,
 6,7,8,T]		 <6,7,6,6,8,3> 试听声音ⓘ blues scale（英语：Blues scale）
3-10 [0,3,6] <0,0,2,0,0,1> 2 试听声音ⓘ 减三和弦 9-10 [0,1,2,3,4,
 6,7,9,T]		 <6,6,8,6,6,4> 试听声音ⓘ ...
3-11A [0,3,7] <0,0,1,1,1,0> 6 试听声音ⓘ 小三和弦 9-11B [0,1,2,3,5,
 6,8,9,T]		 <6,6,7,7,7,3> 试听声音ⓘ ...
3-11B [0,4,7] 试听声音ⓘ 大三和弦 9-11A [0,1,2,3,5,
 6,7,9,T]		 试听声音ⓘ ...
3-12 [0,4,8] <0,0,0,3,0,0> 1 试听声音ⓘ 增三和弦 9-12 [0,1,2,4,5,
 6,8,9,T]		 <6,6,6,9,6,3> 试听声音ⓘ ...
4-1 [0,1,2,3] <3,2,1,0,0,0> 1 试听声音ⓘ ... 8-1 [0,1,2,3,
 4,5,6,7]		 <7,6,5,4,4,2> 试听声音ⓘ ...
4-2A [0,1,2,4] <2,2,1,1,0,0> 17 试听声音ⓘ ... 8-2B [0,2,3,4,
 5,6,7,8]		 <6,6,5,5,4,2> 试听声音ⓘ ...
4-2B [0,2,3,4] 试听声音ⓘ ... 8-2A [0,1,2,3,
 4,5,6,8]		 试听声音ⓘ ...
4-3 [0,1,3,4] <2,1,2,1,0,0> 9 试听声音ⓘ ... 8-3 [0,1,2,3,
 4,5,6,9]		 <6,5,6,5,4,2> 试听声音ⓘ ...
4-4A [0,1,2,5] <2,1,1,1,1,0> 20 试听声音ⓘ ... 8-4B [0,1,3,4,
 5,6,7,8]		 <6,5,5,5,5,2> 试听声音ⓘ ...
4-4B [0,3,4,5] 试听声音ⓘ ... 8-4A [0,1,2,3,
 4,5,7,8]		 试听声音ⓘ ...
4-5A [0,1,2,6] <2,1,0,1,1,1> 22 试听声音ⓘ ... 8-5B [0,1,2,4,
 5,6,7,8]		 <6,5,4,5,5,3> 试听声音ⓘ ...
4-5B [0,4,5,6] 试听声音ⓘ ... 8-5A [0,1,2,3,
 4,6,7,8]		 试听声音ⓘ ...
4-6 [0,1,2,7] <2,1,0,0,2,1> 6 试听声音ⓘ dream chord（英语：dream chord） 8-6 [0,1,2,3,
 5,6,7,8]		 <6,5,4,4,6,3> 试听声音ⓘ ...
4-7 [0,1,4,5] <2,0,1,2,1,0> 8 试听声音ⓘ ... 8-7 [0,1,2,3,
 4,5,8,9]		 <6,4,5,6,5,2> 试听声音ⓘ ...
4-8 [0,1,5,6] <2,0,0,1,2,1> 10 试听声音ⓘ ... 8-8 [0,1,2,3,
 4,7,8,9]		 <6,4,4,5,6,3> 试听声音ⓘ ...
4-9 [0,1,6,7] <2,0,0,0,2,2> 2 试听声音ⓘ distance model（英语：distance model） 8-9 [0,1,2,3,
 6,7,8,9]		 <6,4,4,4,6,4> 试听声音ⓘ ...
4-10 [0,2,3,5] <1,2,2,0,1,0> 3 试听声音ⓘ ... 8-10 [0,2,3,4,
 5,6,7,9]		 <5,6,6,4,5,2> 试听声音ⓘ ...
4-11A [0,1,3,5] <1,2,1,1,1,0> 26 试听声音ⓘ ... 8-11B [0,2,4,5,
 6,7,8,9]		 <5,6,5,5,5,2> 试听声音ⓘ ...
4-11B [0,2,4,5] 试听声音ⓘ ... 8-11A [0,1,2,3,
 4,5,7,9]		 试听声音ⓘ ...
4-12A [0,2,3,6] <1,1,2,1,0,1> 28 试听声音ⓘ ... 8-12A [0,1,3,4,
 5,6,7,9]		 <5,5,6,5,4,3> 试听声音ⓘ ...
4-12B [0,3,4,6] 试听声音ⓘ ... 8-12B [0,2,3,4,
 5,6,8,9]		 试听声音ⓘ ...
4-13A [0,1,3,6] <1,1,2,0,1,1> 7 试听声音ⓘ ... 8-13B [0,2,3,5,
 6,7,8,9]		 <5,5,6,4,5,3> 试听声音ⓘ ...
4-13B [0,3,5,6] 试听声音ⓘ ... 8-13A [0,1,2,3,
 4,6,7,9]		 试听声音ⓘ ...
4-14A [0,2,3,7] <1,1,1,1,2,0> 25 试听声音ⓘ ... 8-14A [0,1,2,4,
 5,6,7,9]		 <5,5,5,5,6,2> 试听声音ⓘ ...
4-14B [0,4,5,7] 试听声音ⓘ ... 8-14B [0,2,3,4,
 5,7,8,9]		 试听声音ⓘ ...
4-z15A [0,1,4,6] <1,1,1,1,1,1> 18 试听声音ⓘ all-interval tetrachord（英语：all-interval tetrachord） 8-z15B [0,1,3,5,
 6,7,8,9]		 <5,5,5,5,5,3> 试听声音ⓘ ...
4-z15B [0,2,5,6] 试听声音ⓘ all-interval tetrachord（英语：all-interval tetrachord） 8-z15A [0,1,2,3,
 4,6,8,9]		 试听声音ⓘ ...
4-16A [0,1,5,7] <1,1,0,1,2,1> 19 试听声音ⓘ ... 8-16B [0,1,2,4,
 6,7,8,9]		 <5,5,4,5,6,3> 试听声音ⓘ ...
4-16B [0,2,6,7] 试听声音ⓘ ... 8-16A [0,1,2,3,
 5,7,8,9]		 试听声音ⓘ ...
4-17 [0,3,4,7] <1,0,2,2,1,0> 13 试听声音ⓘ alpha chord（英语：alpha chord） 8-17 [0,1,3,4,
 5,6,8,9]		 <5,4,6,6,5,2> 试听声音ⓘ ...
4-18A [0,1,4,7] <1,0,2,1,1,1> 21 试听声音ⓘ 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> 试听声音ⓘ ...
4-18B [0,3,6,7] 试听声音ⓘ ... 8-18A [0,1,2,3,
 5,6,8,9]		 试听声音ⓘ ...
4-19A [0,1,4,8] <1,0,1,3,1,0> 24 试听声音ⓘ mM7 chord（英语：Minor major seventh chord） 8-19B [0,1,3,4,
 5,7,8,9]		 <5,4,5,7,5,2> 试听声音ⓘ ...
4-19B [0,3,4,8] 试听声音ⓘ ... 8-19A [0,1,2,4,
 5,6,8,9]		 试听声音ⓘ ...
4-20 [0,1,5,8] <1,0,1,2,2,0> 15 试听声音ⓘ 大七和弦 8-20 [0,1,2,4,
 5,7,8,9]		 <5,4,5,6,6,2> 试听声音ⓘ ...
4-21 [0,2,4,6] <0,3,0,2,0,1> 11 试听声音ⓘ ... 8-21 [0,1,2,3,
 4,6,8,T]		 <4,7,4,6,4,3> 试听声音ⓘ ...
4-22A [0,2,4,7] <0,2,1,1,2,0> 27 试听声音ⓘ 史提利·丹 8-22B [0,1,2,3,
 5,7,9,T]		 <4,6,5,5,6,2> 试听声音ⓘ ...
4-22B [0,3,5,7] 试听声音ⓘ ... 8-22A [0,1,2,3,
 5,6,8,T]		 试听声音ⓘ ...
4-23 [0,2,5,7] <0,2,1,0,3,0> 4 试听声音ⓘ quartal chord（英语：quartal chord） 8-23 [0,1,2,3,
 5,7,8,T]		 <4,6,5,4,7,2> 试听声音ⓘ bebop scale（英语：bebop scale）
4-24 [0,2,4,8] <0,2,0,3,0,1> 16 试听声音ⓘ A7 chord（英语：Augmented seventh chord） 8-24 [0,1,2,4,
 5,6,8,T]		 <4,6,4,7,4,3> 试听声音ⓘ ...
4-25 [0,2,6,8] <0,2,0,2,0,2> 12 试听声音ⓘ 增六和弦 8-25 [0,1,2,4,
 6,7,8,T]		 <4,6,4,6,4,4> 试听声音ⓘ ...
4-26 [0,3,5,8] <0,1,2,1,2,0> 14 试听声音ⓘ 小七和弦 8-26 [0,1,3,4,
 5,7,8,T][b]		 <4,5,6,5,6,2> 试听声音ⓘ ...
4-27A [0,2,5,8] <0,1,2,1,1,1> 29 试听声音ⓘ 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> 试听声音ⓘ ...
4-27B [0,3,6,8] 试听声音ⓘ 属七和弦 8-27A [0,1,2,4,
 5,7,8,T]		 试听声音ⓘ ...
4-28 [0,3,6,9] <0,0,4,0,0,2> 5 试听声音ⓘ dim. 7th chord（英语：Diminished seventh chord） 8-28 [0,1,3,4,
 6,7,9,T]		 <4,4,8,4,4,4> 试听声音ⓘ octatonic scale
4-z29A [0,1,3,7] <1,1,1,1,1,1> 23 试听声音ⓘ all-interval tetrachord（英语：all-interval tetrachord） 8-z29B [0,2,3,4,
 6,7,8,9]		 <5,5,5,5,5,3> 试听声音ⓘ ...
4-z29B [0,4,6,7] 试听声音ⓘ all-interval tetrachord（英语：all-interval tetrachord） 8-z29A [0,1,2,3,
 5,6,7,9]		 试听声音ⓘ ...
5-1 [0,1,2,3,4] <4,3,2,1,0,0> 试听声音ⓘ ... 7-1 [0,1,2,3,
 4,5,6]		 <6,5,4,3,2,1> 1 试听声音ⓘ ...
5-2A [0,1,2,3,5] <3,3,2,1,1,0> 试听声音ⓘ ... 7-2B [0,2,3,4,
 5,6,7]		 <5,5,4,3,3,1> 11 试听声音ⓘ ...
5-2B [0,2,3,4,5] 试听声音ⓘ ... 7-2A [0,1,2,3,
 4,5,7]		 试听声音ⓘ ...
5-3A [0,1,2,4,5] <3,2,2,2,1,0> 试听声音ⓘ ... 7-3B [0,3,4,5,
 6,7,8]		 <5,4,4,4,3,1> 14 试听声音ⓘ ...
5-3B [0,1,3,4,5] 试听声音ⓘ ... 7-3A [0,1,2,3,
 4,5,8]		 试听声音ⓘ ...
5-4A [0,1,2,3,6] <3,2,2,1,1,1> 试听声音ⓘ ... 7-4B [0,1,3,4,
 5,6,7]		 <5,4,4,3,3,2> 12 试听声音ⓘ ...
5-4B [0,3,4,5,6] 试听声音ⓘ ... 7-4A [0,1,2,3,
 4,6,7]		 试听声音ⓘ ...
5-5A [0,1,2,3,7] <3,2,1,1,2,1> 试听声音ⓘ ... 7-5B [0,1,2,4,
 5,6,7]		 <5,4,3,3,4,2> 13 试听声音ⓘ ...
5-5B [0,4,5,6,7] 试听声音ⓘ ... 7-5A [0,1,2,3,
 5,6,7]		 试听声音ⓘ ...
5-6A [0,1,2,5,6] <3,1,1,2,2,1> 试听声音ⓘ ... 7-6B [0,1,4,5,
 6,7,8]		 <5,3,3,4,4,2> 27 试听声音ⓘ ...
5-6B [0,1,4,5,6] 试听声音ⓘ ... 7-6A [0,1,2,3,
 4,7,8]		 试听声音ⓘ ...
5-7A [0,1,2,6,7] <3,1,0,1,3,2> 试听声音ⓘ ... 7-7B [0,1,2,5,
 6,7,8]		 <5,3,2,3,5,3> 30 试听声音ⓘ ...
5-7B [0,1,5,6,7] 试听声音ⓘ ... 7-7A [0,1,2,3,
 6,7,8]		 试听声音ⓘ ...
5-8 [0,2,3,4,6] <2,3,2,2,0,1> 试听声音ⓘ ... 7-8 [0,2,3,4,
 5,6,8]		 <4,5,4,4,2,2> 2 试听声音ⓘ ...
5-9A [0,1,2,4,6] <2,3,1,2,1,1> 试听声音ⓘ ... 7-9B [0,2,4,5,
 6,7,8]		 <4,5,3,4,3,2> 15 试听声音ⓘ ...
5-9B [0,2,4,5,6] 试听声音ⓘ ... 7-9A [0,1,2,3,
 4,6,8]		 试听声音ⓘ ...
5-10A [0,1,3,4,6] <2,2,3,1,1,1> 试听声音ⓘ ... 7-10B [0,2,3,4,
 5,6,9]		 <4,4,5,3,3,2> 19 试听声音ⓘ ...
5-10B [0,2,3,5,6] 试听声音ⓘ ... 7-10A [0,1,2,3,
 4,6,9]		 试听声音ⓘ ...
5-11A [0,2,3,4,7] <2,2,2,2,2,0> 试听声音ⓘ ... 7-11B [0,2,3,4,
 5,7,8]		 <4,4,4,4,4,1> 18 试听声音ⓘ ...
5-11B [0,3,4,5,7] 试听声音ⓘ ... 7-11A [0,1,3,4,
 5,6,8]		 试听声音ⓘ ...
5-z12 [0,1,3,5,6] <2,2,2,1,2,1> 试听声音ⓘ ... 7-z12 [0,1,2,3,
 4,7,9]		 <4,4,4,3,4,2> 5 试听声音ⓘ ...
5-13A [0,1,2,4,8] <2,2,1,3,1,1> 试听声音ⓘ ... 7-13B [0,2,3,4,
 6,7,8]		 <4,4,3,5,3,2> 17 试听声音ⓘ ...
5-13B [0,2,3,4,8] 试听声音ⓘ ... 7-13A [0,1,2,4,
 5,6,8]		 试听声音ⓘ ...
5-14A [0,1,2,5,7] <2,2,1,1,3,1> 试听声音ⓘ ... 7-14B [0,1,3,5,
 6,7,8]		 <4,4,3,3,5,2> 28 试听声音ⓘ ...
5-14B [0,2,5,6,7] 试听声音ⓘ ... 7-14A [0,1,2,3,
 5,7,8]		 试听声音ⓘ ...
5-15 [0,1,2,6,8] <2,2,0,2,2,2> 试听声音ⓘ ... 7-15 [0,1,2,4,
 6,7,8]		 <4,4,2,4,4,3> 4 试听声音ⓘ ...
5-16A [0,1,3,4,7] <2,1,3,2,1,1> 试听声音ⓘ ... 7-16B [0,1,3,4,
 5,6,9]		 <4,3,5,4,3,2> 20 试听声音ⓘ ...
5-16B [0,3,4,6,7] 试听声音ⓘ ... 7-16A [0,1,2,3,
 5,6,9]		 试听声音ⓘ ...
5-z17 [0,1,3,4,8] <2,1,2,3,2,0> 试听声音ⓘ Farben chord（英语：Farben chord） 7-z17 [0,1,2,4,
 5,6,9]		 <4,3,4,5,4,1> 10 试听声音ⓘ ...
5-z18A [0,1,4,5,7] <2,1,2,2,2,1> 试听声音ⓘ ... 7-z18A [0,1,4,5,
 6,7,9][c]		 <4,3,4,4,4,2> 35 试听声音ⓘ ...
5-z18B [0,2,3,6,7] 试听声音ⓘ ... 7-z18B [0,1,4,6,
 7,8,9]		 试听声音ⓘ ...
5-19A [0,1,3,6,7] <2,1,2,1,2,2> 试听声音ⓘ ... 7-19B [0,1,2,3,
 6,8,9]		 <4,3,4,3,4,3> 31 试听声音ⓘ ...
5-19B [0,1,4,6,7] 试听声音ⓘ ... 7-19A [0,1,2,3,
 6,7,9]		 试听声音ⓘ ...
5-20A [0,1,5,6,8][d] <2,1,1,2,3,1> 试听声音ⓘ ... 7-20B [0,1,2,5,
 7,8,9]		 <4,3,3,4,5,2> 34 试听声音ⓘ ...
5-20B [0,2,3,7,8] 试听声音ⓘ In scale（英语：In scale） 7-20A [0,1,2,5,
 6,7,9][e]		 试听声音ⓘ Persian scale（英语：Persian scale）
5-21A [0,1,4,5,8] <2,0,2,4,2,0> 试听声音ⓘ ... 7-21B [0,1,3,4,
 5,8,9]		 <4,2,4,6,4,1> 21 试听声音ⓘ ...
5-21B [0,3,4,7,8] 试听声音ⓘ ... 7-21A [0,1,2,4,
 5,8,9]		 试听声音ⓘ ...
5-22 [0,1,4,7,8] <2,0,2,3,2,1> 试听声音ⓘ ... 7-22 [0,1,2,5,
 6,8,9]		 <4,2,4,5,4,2> 8 试听声音ⓘ double harmonic scale（英语：double harmonic scale）
5-23A [0,2,3,5,7] <1,3,2,1,3,0> 试听声音ⓘ ... 7-23B [0,2,4,5,
 6,7,9]		 <3,5,4,3,5,1> 25 试听声音ⓘ ...
5-23B [0,2,4,5,7] 试听声音ⓘ ... 7-23A [0,2,3,4,
 5,7,9]		 试听声音ⓘ ...
5-24A [0,1,3,5,7] <1,3,1,2,2,1> 试听声音ⓘ ... 7-24B [0,2,4,6,
 7,8,9]		 <3,5,3,4,4,2> 22 试听声音ⓘ enigmatic scale（英语：enigmatic scale）
5-24B [0,2,4,6,7] 试听声音ⓘ ... 7-24A [0,1,2,3,
 5,7,9]		 试听声音ⓘ ...
5-25A [0,2,3,5,8] <1,2,3,1,2,1> 试听声音ⓘ Seven six chord（英语：Seven six chord） 7-25B [0,2,3,5,
 6,7,9]		 <3,4,5,3,4,2> 24 试听声音ⓘ ...
5-25B [0,3,5,6,8] 试听声音ⓘ ... 7-25A [0,2,3,4,
 6,7,9]		 试听声音ⓘ ...
5-26A [0,2,4,5,8] <1,2,2,3,1,1> 试听声音ⓘ ... 7-26A [0,1,3,4,
 5,7,9]		 <3,4,4,5,3,2> 26 试听声音ⓘ ...
5-26B [0,3,4,6,8] 试听声音ⓘ ... 7-26B [0,2,4,5,
 6,8,9]		 试听声音ⓘ ...
5-27A [0,1,3,5,8] <1,2,2,2,3,0> 试听声音ⓘ ... 7-27B [0,2,4,5,
 7,8,9]		 <3,4,4,4,5,1> 23 试听声音ⓘ ...
5-27B [0,3,5,7,8] 试听声音ⓘ ... 7-27A [0,1,2,4,
 5,7,9]		 试听声音ⓘ ...
5-28A [0,2,3,6,8] <1,2,2,2,1,2> 试听声音ⓘ ... 7-28A [0,1,3,5,
 6,7,9]		 <3,4,4,4,3,3> 36 试听声音ⓘ ...
5-28B [0,2,5,6,8] 试听声音ⓘ ... 7-28B [0,2,3,4,
 6,8,9]		 试听声音ⓘ ...
5-29A [0,1,3,6,8] <1,2,2,1,3,1> 试听声音ⓘ ... 7-29B [0,2,3,5,
 7,8,9]		 <3,4,4,3,5,2> 32 试听声音ⓘ ...
5-29B [0,2,5,7,8] 试听声音ⓘ ... 7-29A [0,1,2,4,
 6,7,9]		 试听声音ⓘ ...
5-30A [0,1,4,6,8] <1,2,1,3,2,1> 试听声音ⓘ ... 7-30B [0,1,3,5,
 7,8,9]		 <3,4,3,5,4,2> 37 试听声音ⓘ ...
5-30B [0,2,4,7,8] 试听声音ⓘ ... 7-30A [0,1,2,4,
 6,8,9]		 试听声音ⓘ minor Neapolitan scale（英语：minor Neapolitan scale）
5-31A [0,1,3,6,9] <1,1,4,1,1,2> 试听声音ⓘ beta chord 7-31B [0,2,3,5,
 6,8,9]		 <3,3,6,3,3,3> 38 试听声音ⓘ ...
5-31B [0,2,3,6,9] 试听声音ⓘ Dominant minor ninth chord（英语：Dominant minor ninth chord） 7-31A [0,1,3,4,
 6,7,9]		 试听声音ⓘ Hungarian major scale（英语：Hungarian major scale）
5-32A [0,1,4,6,9] <1,1,3,2,2,1> 试听声音ⓘ ... 7-32B [0,1,3,5,
 6,8,9]		 <3,3,5,4,4,2> 33 试听声音ⓘ 和声大调
5-32B [0,3,5,8,9] 试听声音ⓘ Elektra chord（英语：Elektra chord）, gamma chord（英语：gamma chord） 7-32A [0,1,3,4,
 6,8,9]		 试听声音ⓘ harmonic minor scale（英语：harmonic minor scale）
5-33 [0,2,4,6,8] <0,4,0,4,0,2> 试听声音ⓘ ... 7-33 [0,1,2,4,
 6,8,T]		 <2,6,2,6,2,3> 6 试听声音ⓘ M Locrian scale（英语：Major Locrian scale）
5-34 [0,2,4,6,9] <0,3,2,2,2,1> 试听声音ⓘ Dominant ninth chord 7-34 [0,1,3,4,
 6,8,T]		 <2,5,4,4,4,2> 9 试听声音ⓘ altered scale（英语：altered scale）
5-35 [0,2,4,7,9] <0,3,2,1,4,0> 试听声音ⓘ 五声音阶 7-35 [0,1,3,5,
 6,8,T]		 <2,5,4,3,6,1> 7 试听声音ⓘ 自然音阶
5-z36A [0,1,2,4,7] <2,2,2,1,2,1> 试听声音ⓘ ... 7-z36B [0,2,3,5,
 6,7,8]		 <4,4,4,3,4,2> 16 试听声音ⓘ ...
5-z36B [0,3,5,6,7] 试听声音ⓘ ... 7-z36A [0,1,2,3,
 5,6,8]		 试听声音ⓘ ...
5-z37 [0,3,4,5,8] <2,1,2,3,2,0> 试听声音ⓘ ... 7-z37 [0,1,3,4,
 5,7,8]		 <4,3,4,5,4,1> 3 试听声音ⓘ ...
5-z38A [0,1,2,5,8] <2,1,2,2,2,1> 试听声音ⓘ ... 7-z38B [0,1,3,4,
 6,7,8]		 <4,3,4,4,4,2> 29 试听声音ⓘ ...
5-z38B [0,3,6,7,8] 试听声音ⓘ ... 7-z38A [0,1,2,4,
 5,7,8]		 试听声音ⓘ ...
6-1 [0,1,2,3,4,5] <5,4,3,2,1,0> 4 试听声音ⓘ chromatic hexachord（英语：chromatic hexachord）
6-2A [0,1,2,3,4,6] <4,4,3,2,1,1> 19 试听声音ⓘ ...
6-2B [0,2,3,4,5,6] 试听声音ⓘ ...
6-z3A [0,1,2,3,5,6] <4,3,3,2,2,1> 49 试听声音ⓘ ... 6-z36B [0,3,4,5,6,7] <4,3,3,2,2,1> 50 试听声音ⓘ ...
6-z3B [0,1,3,4,5,6] 试听声音ⓘ ... 6-z36A [0,1,2,3,4,7] 试听声音ⓘ ...
6-z4 [0,1,2,4,5,6] <4,3,2,3,2,1> 24 试听声音ⓘ ... 6-z37 [0,1,2,3,4,8] <4,3,2,3,2,1> 23 试听声音ⓘ ...
6-5A [0,1,2,3,6,7] <4,2,2,2,3,2> 16 试听声音ⓘ ...
6-5B [0,1,4,5,6,7] 试听声音ⓘ ...
6-z6 [0,1,2,5,6,7] <4,2,1,2,4,2> 33 试听声音ⓘ ... 6-z38 [0,1,2,3,7,8] <4,2,1,2,4,2> 34 试听声音ⓘ ...
6-7 [0,1,2,6,7,8] <4,2,0,2,4,3> 7 试听声音ⓘ ...
6-8 [0,2,3,4,5,7] <3,4,3,2,3,0> 5 试听声音ⓘ ...
6-9A [0,1,2,3,5,7] <3,4,2,2,3,1> 20 试听声音ⓘ ...
6-9B [0,2,4,5,6,7] 试听声音ⓘ ...
6-z10A [0,1,3,4,5,7] <3,3,3,3,2,1> 42 试听声音ⓘ ... 6-z39B [0,3,4,5,6,8] <3,3,3,3,2,1> 41 试听声音ⓘ ...
6-z10B [0,2,3,4,6,7] 试听声音ⓘ ... 6-z39A [0,2,3,4,5,8] 试听声音ⓘ ...
6-z11A [0,1,2,4,5,7] <3,3,3,2,3,1> 47 试听声音ⓘ ... 6-z40B [0,3,5,6,7,8] <3,3,3,2,3,1> 48 试听声音ⓘ ...
6-z11B [0,2,3,5,6,7] 试听声音ⓘ Sacher hexachord（英语：Sacher hexachord） 6-z40A [0,1,2,3,5,8] 试听声音ⓘ ...
6-z12A [0,1,2,4,6,7] <3,3,2,2,3,2> 46 试听声音ⓘ ... 6-z41B [0,2,5,6,7,8] <3,3,2,2,3,2> 45 试听声音ⓘ ...
6-z12B [0,1,3,5,6,7] 试听声音ⓘ ... 6-z41A [0,1,2,3,6,8] 试听声音ⓘ ...
6-z13 [0,1,3,4,6,7] <3,2,4,2,2,2> 29 试听声音ⓘ ... 6-z42 [0,1,2,3,6,9] <3,2,4,2,2,2> 30 试听声音ⓘ ...
6-14A [0,1,3,4,5,8] <3,2,3,4,3,0> 3 试听声音ⓘ ...
6-14B [0,3,4,5,7,8] 试听声音ⓘ ...
6-15A [0,1,2,4,5,8] <3,2,3,4,2,1> 13 试听声音ⓘ ...
6-15B [0,3,4,6,7,8] 试听声音ⓘ ...
6-16A [0,1,4,5,6,8] <3,2,2,4,3,1> 11 试听声音ⓘ ...
6-16B [0,2,3,4,7,8] 试听声音ⓘ ...
6-z17A [0,1,2,4,7,8] <3,2,2,3,3,2> 35 试听声音ⓘ all-trichord hexachord（英语：all-trichord hexachord） 6-z43B [0,2,3,6,7,8] <3,2,2,3,3,2> 36 试听声音ⓘ ...
6-z17B [0,1,4,6,7,8] 试听声音ⓘ ... 6-z43A [0,1,2,5,6,8] 试听声音ⓘ ...
6-18A [0,1,2,5,7,8] <3,2,2,2,4,2> 17 试听声音ⓘ ...
6-18B [0,1,3,6,7,8] 试听声音ⓘ ...
6-z19A [0,1,3,4,7,8] <3,1,3,4,3,1> 37 试听声音ⓘ ... 6-z44B [0,3,4,7,8,9] <3,1,3,4,3,1> 38 试听声音ⓘ ...
6-z19B [0,1,4,5,7,8] 试听声音ⓘ ... 6-z44A [0,1,2,5,6,9] 试听声音ⓘ Schoenberg hexachord（英语：Schoenberg hexachord）
6-20 [0,1,4,5,8,9] <3,0,3,6,3,0> 2 试听声音ⓘ "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 试听声音ⓘ ...
6-21B [0,2,4,5,6,8] 试听声音ⓘ ...
6-22A [0,1,2,4,6,8] <2,4,1,4,2,2> 10 试听声音ⓘ ...
6-22B [0,2,4,6,7,8] 试听声音ⓘ ...
6-z23 [0,2,3,5,6,8] <2,3,4,2,2,2> 27 试听声音ⓘ ... 6-z45 [0,2,3,4,6,9] <2,3,4,2,2,2> 28 试听声音ⓘ ...
6-z24A [0,1,3,4,6,8] <2,3,3,3,3,1> 39 试听声音ⓘ ... 6-z46B [0,3,5,7,8,9] <2,3,3,3,3,1> 40 试听声音ⓘ ...
6-z24B [0,2,4,5,7,8] 试听声音ⓘ ... 6-z46A [0,1,2,4,6,9] 试听声音ⓘ ...
6-z25A [0,1,3,5,6,8] <2,3,3,2,4,1> 43 试听声音ⓘ Major eleventh chord（英语：Major eleventh chord） 6-z47B [0,2,5,7,8,9] <2,3,3,2,4,1> 44 试听声音ⓘ blues scale（英语：Blues scale）
6-z25B [0,2,3,5,7,8] 试听声音ⓘ ... 6-z47A [0,1,2,4,7,9] 试听声音ⓘ ...
6-z26 [0,1,3,5,7,8] <2,3,2,3,4,1> 26 试听声音ⓘ ... 6-z48 [0,1,2,5,7,9] <2,3,2,3,4,1> 25 试听声音ⓘ ...
6-27A [0,1,3,4,6,9] <2,2,5,2,2,2> 14 试听声音ⓘ ...
6-27B [0,3,5,6,8,9] 试听声音ⓘ ...
6-z28 [0,1,3,5,6,9] <2,2,4,3,2,2> 21 试听声音ⓘ ... 6-z49 [0,1,3,4,7,9] <2,2,4,3,2,2> 22 试听声音ⓘ ...
6-z29 [0,2,3,6,7,9][f] <2,2,4,2,3,2> 32 试听声音ⓘ Bridge chord（英语：Bridge chord） 6-z50 [0,1,4,6,7,9] <2,2,4,2,3,2> 31 试听声音ⓘ ...
6-30A [0,1,3,6,7,9] <2,2,4,2,2,3> 15 试听声音ⓘ ...
6-30B [0,2,3,6,8,9] 试听声音ⓘ Petrushka chord（英语：Petrushka chord）
6-31A [0,1,4,5,7,9][g] <2,2,3,4,3,1> 8 试听声音ⓘ ...
6-31B [0,2,4,5,8,9][h] 试听声音ⓘ ...
6-32 [0,2,4,5,7,9] <1,4,3,2,5,0> 6 试听声音ⓘ diatonic hexachord（英语：diatonic hexachord）
6-33A [0,2,3,5,7,9] <1,4,3,2,4,1> 18 试听声音ⓘ ...
6-33B [0,2,4,6,7,9] 试听声音ⓘ Dominant eleventh chord
6-34A [0,1,3,5,7,9] <1,4,2,4,2,2> 9 试听声音ⓘ mystic chord（英语：mystic chord）
6-34B [0,2,4,6,8,9] 试听声音ⓘ ...
6-35 [0,2,4,6,8,T] <0,6,0,6,0,3> 1 试听声音ⓘ 全音音阶

参见

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注

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  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]

参考

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  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.

外部链接

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