音律周波数比表 1 純正律 Pure Temperament 音名┃平均律  cent│純正律   相対cent│純正律    │ │ │   ┃12 Equal │Pure (5-3) │Pure (5-3)' │Pure Q-39 (3-5) │Pure T-71 (5-3b) │ ━━╋━━━━━━━┿━━━━━━━━━━┿━━━━━━━━━━┿━━━━━━━━━━━━━━┿━━━━━━━━━━━━━━┿ C ┃2.000000 1200│ 2  -------  0.00│ 2  -------  0.00│ 2 ------- 1200.00 0.00│ 2 ------- 1200.00 0.00│   ┃       │  16/15      │ 16/15 │ 27/25 │ 250/243 │ H ┃1.887749 1100│15/8 ------- -11.73│15/8 ------- -11.73│50/27 ------- 1066.76 -33.24│243/125------ 1150.83 +50.83│   ┃       │  75/72 |    │ 25/24 | │ 25/24 | │ 27/25 | │ B ┃1.781797 1000│ 9/5 ---- 9/8 +17.60│ 9/5 ----10/9 +17.60│16/9 ---10/9 996.09 -3.91│ 9/5 --- 9/8 1017.60 +17.60│   ┃       │  27/25 |    │ 16/15 | │ 16/15 | │ 25/24 | │ A ┃1.681793  900│ 5/3 ------- -15.64│27/16------- +5.87│ 5/3 ------- 884.36 -15.64│216/125------ 946.92 +46.92│   ┃       │  25/24 |    │ 135/128| │ 16/15 | │ 16/15 │ G#┃1.587401  800│ 8/5 ----10/9 +13.69│ 8/5 ---- 9/8 +13.69│25/16 --- 9/8 772.63 -27.37│81/50 --- 835.19 +35.19│   ┃       │  16/15 |    │ 16/15 | │ 135/128| │ 27/25 │ G ┃1.498307  700│ 3/2 ------- +1.96│ 3/2 ------- +1.96│40/27 ------- 680.45 -19.55│ 3/2 ------- 701.96 +1.96│   ┃       │  16/15 |    │ 16/15 | │ 27/25 | │ 25/24 | │ F#┃1.414214  600│45/32 --- 9/8 -9.78│45/32 ---10/9 -9.78│25/18 --- 9/8 568.72 -31.28│36/25 ---10/9 631.28 +31.28│   ┃       │  135/128 |    │ 25/24 | │ 25/24 | │ 16/15 | │ F ┃1.334840 500│ 4/3 ------- -1.96│27/20------- +19.55│ 4/3 ------- 498.04 -1.96│27/20 ------- 519.55 +19.55│   ┃       │  16/15      │ 27/25 │ 16/15 │ 25/24 │ E ┃1.259921 400│ 5/4 ------- -13.69│ 5/4 ------- -13.69│ 5/4 ------- 386.31 -13.69│162/125------ 448.88 +48.88│   ┃       │  25/24 |    │ 25/24 | │ 135/128| │ 27/25 │ Eb┃1.189207 300│ 6/5 ----10/9 +15.64│ 6/5 ----10/9 +15.64│32/27 --- 9/8 294.13 -5.87│ 6/5 --- 315.64 +15.64│   ┃       │  16/15 |    │ 16/15 | │ 16/15 | │ 16/15 │ D ┃1.122462 200│ 9/8 -------- +3.91│ 9/8 -------- +3.91│10/9 ------- 182.40 -17.60│ 9/8 ------- 203.91 +3.91│   ┃       │  135/128 |    │ 16/15 | │ 16/15 | │ 25/24 | │ C#┃1.059463 100│16/15 --- 9/8 +11.73│135/128--- 9/8 -7.82│25/24 ---10/9 70.67 -29.33│27/25 --- 9/8 133.24 +33.24│   ┃       │  16/15 |    │ 135/128| │ 25/24 | │ 27/25 | │ C ┃1.000000 0│ 1 -------- 0.00│ 1 -------- 0.00│ 1 ------- 0.00 0.00│ 1 ------- 0.00 0.00│ 9/8 = 大全音 10/9 = 小全音 平均律比 2^(1/12) = 1.059463 = 100cent cent=1200*log2(比) Pure Pure' PureD-1 PureDb+2 A E H F# E H F# C# H -- F#-- C#-- G# C -- G -- D / / / / / / / / / \ \ \ F -- C -- G -- D C -- G -- D -- A G -- D -- A -- E Eb B F / / / / / / / / / \ \ \ C# Ab Eb B Ab Eb B F Eb-- B -- F -- C Gb Db Ab \ \ \ --:V(3/2) /:III(5/4) \:IIIm(6/5) A E H 音律周波数比表 2 音名┃メルセンヌ純正律 │ピタゴラス律 │中全音律   ┃Marin Mersenne │Pythagorean Scale │Meantone アロンミーントーン ━━╋━━━━━━━━━━━━━━┿━━━━━━━━━━━┿━━━━━━━━━━━━━ C ┃ 2  ------- 1200.00  0.00│ 2 -------  0.00│2 1200.00  0.0   ┃   16/15       │ 256/243 │            H ┃15/8 ------- 1088.27 -11.73│243/128 ------- +9.78│1.869186 1082.89 -17.11   ┃ 135/128| │ | │            B ┃16/9 --- 9/8 996.09 -3.91│ 16/9 --- 9/8 -3.91│1.788854 1006.84 +6.84   ┃ 16/15 | │ 256/243 │            A ┃ 5/3 ------- 884.36 -15.64│ 27/16 ------- +5.87│1.671851 889.74 -10.26   ┃ 16/15 | │ 256/243 │            G#┃25/16 ---10/9 772.63 -27.37│6561/4096 - 9/8 +15.64│25/16 772.63 -27.37   ┃ 25/24 | │ | │            G ┃ 3/2 ------- 701.96 +1.96│ 3/2 ------- +1.96│1.495349 696.58 -3.42   ┃ 27/25 | │ 256/243 │            F#┃25/18 --- 9/8 568.72 -31.28│729/512 9/8 +11.73│1.397542 579.47 -20.53   ┃ 25/24 | │Gb1024/729 | -11.73│            F ┃ 4/3 ------- 498.04 -1.96│ 4/3 ------- -1.96│1.337481 503.42 +3.42   ┃   16/15 │ 256/243 │            E ┃ 5/4 ------- 386.31 -13.69│ 81/64 ------- +7.82│5/4 386.31 -13.69   ┃ 16/15 | │ | │            Eb┃75/64 ---10/9 274.58 -25.42│ 32/27 --- 9/8 -5.87│1.196279 310.26 +10.26   ┃ 25/24 | │ 256/243 │            D ┃ 9/8 ------- 203.91 +3.91│ 9/8 ------- +3.91│1.118034 193.16 -6.84   ┃ 27/25 | │ 256/243 │ C#┃25/24 --- 9/8 70.67 -29.33│2187/2048 - 9/8 +13.69│1.044907 76.05 -23.95   ┃ 25/24 | │ 2187/2048 │            C ┃ 1 ------- 0.00 0.00│ 1 ------- 0.00│1   0.00  0.00 シントニック・コンマ SC = 5/4:81/64 = 81/80 = 21.51cent ピタゴラス・コンマ PC = (3/2)^12 / 2^7 = 531441/524288 Mersenne F# C# G# D# \ / / / A E H / / / B -- F -- C -- G -- D 5度補正 (3/2) * {PC,SC}^(補正) 5度円 Pythag. Eb B F C G D A E H F# C# G# Eb PC 0 0 0 0 0 0 0 0 0 0 0 -1 Mean Eb B F C G D A E H F# C# G# Eb SC -1/4 -1/4 -1/4 -1/4 -1/4 -1/4 -1/4 -1/4 -1/4 -1/4 -1/4 wolf wolf = 125/128 音律周波数比表 3 不等分律 Well-Tempered Temperament 音名┃キルンベルガー 第2  │キルンベルガー 第3  │キルン-ヴェルク │ヴェルク 第1技法第3番 │ヴェルクマイスター 第3'│ ┃Kirnberger 2 │Kirnberger 3 │Kirn-Werck (Werck 3) │Werckmeister 3 │Werckmeister 3' │ ━━╋━━━━━━━━━━━━┿━━━━━━━━━━━━┿━━━━━━━━━━━━┿━━━━━━━━━━━━┿━━━━━━━━━━━━┿ C ┃2.000000 1200.00 0.00│2.000000 1200.00 0.00│2.000000 1200.00 0.00│2.000000 1200.00 0.00│2.000000 1200.00 0.00│   ┃            │            │            │            │            │ H ┃15/8  1088.27 -11.73│15/8  1088.27 -11.73│1.880832 1093.65 -6.35│1.879241 1092.18 -7.82│1.885618 1098.05 -1.95│   ┃            │            │            │            │            │ B ┃16/9   996.09 -3.91│16/9   996.09 -3.91│16/9   996.09 -3.91│16/9   996.09 -3.91│1.783811 1001.96 +1.96│   ┃            │            │            │            │            │ A ┃1.677051  895.11 -4.89│1.671851  889.74 -10.26│1.671851  889.74 -10.26│1.670436  888.27 -11.73│1.681793 900.00 0.00│   ┃            │            │            │            │            │ G#┃128/81   792.18 -7.82│128/81   792.18 -7.82│128/81   792.18 -7.82│128/81   792.18 -7.82│128/81 792.18 -7.82│   ┃            │            │            │            │            │ G ┃3/2   701.96 +1.96│1.495349 696.58 -3.42│1.495349 696.58 -3.42│1.494927 696.09 -3.91│3/2 701.96 +1.96│   ┃            │            │            │            │            │ F#┃45/32   590.22 -9.78│45/32   590.22 -9.78│45/32   590.22 -9.78│1024/729  588.27 -11.73│1.414214 600.00 0.00│   ┃            │            │            │            │            │ F ┃4/3 498.04 -1.96│4/3 498.04 -1.96│4/3 498.04 -1.96│4/3 498.04 -1.96│1.337858 503.91 +3.91│   ┃            │            │            │            │            │ E ┃5/4 386.31 -13.69│5/4 386.31 -13.69│1.253888 391.69 -8.31│1.252827 390.22 -9.78│1.257079 396.09 -3.91│   ┃            │            │            │            │            │ Eb┃32/27 294.13 -5.87│32/27 294.13 -5.87│32/27 294.13 -5.87│32/27 294.13 -5.87│1.189207 300.00 0.00│   ┃            │            │            │            │            │ D ┃9/8 203.91 +3.91│1.118034 193.16 -6.84│1.118034 193.16 -6.84│1.117403 192.18 -7.82│9/8 203.91 +3.91│   ┃            │            │            │            │            │ C#┃256/243 90.22 -9.78│256/243 90.22 -9.78│256/243 90.22 -9.78│256/243 90.22 -9.78│1.057073 96.09 -3.91│   ┃            │            │            │            │            │ C ┃1.0 0.00 0.00│1.0 0.00 0.00│1.0 0.00 0.00│1.0 0.00 0.00│1.0 0.00 0.00│ 5度円 s:スキスマ Kirn 2 C# G# Eb B F C G D A E H F# C# SC 0 0 0 0 0 0 0 -1/2 -1/2 0 0 s Kirn 3 C# G# Eb B F C G D A E H F# C# SC 0 0 0 0 0 -1/4 -1/4 -1/4 -1/4 0 0 s Kirn-Werck C# G# Eb B F C G D A E H F# C# SC 0 0 0 0 0 -1/4 -1/4 -1/4 0 0 -1/4 s Werck 3 C# G# Eb B F C G D A E H F# C# PC 0 0 0 0 0 -1/4 -1/4 -1/4 0 0 -1/4 0 Werck 3' C# G# Eb B F C G D A E H F# C# G# PC -1/4 +1/4 0 0 -1/4 0 0 -1/4 -1/4 0 0 -1/4 -1/4 (?) 音律周波数比表 4 不等分律,N等分平均律 音名┃ラモー   │ヴァロッティ-ヤング │ヤング 第2   │43平均律 │53平均律     ━━╋━━━━━━━━━━━━┿━━━━━━━━━━━━┿━━━━━━━━━━━━┿━━━━━━━━━┿━━━━━━━━━━ C ┃2.000000 1200.00 0.00│2.000000 1200.00 0.00│2.000000 1200.00 0.00│43 1200.00  0.00│53 1200.00  0.00   ┃            │            │            │         │          H ┃1.869186 1082.89 -17.11│1.877120 1090.22 -9.78│1.877120 1090.22 -9.78│39 1088.37 -11.63│48 1086.79 -13.21   ┃            │            │            │         │          B ┃1.775938  994.30 -5.70│  1000.00 0.00│16/9   996.09 -3.91│36 1004.65 +4.65│44 996.23  -3.77   ┃            │            │            │         │          A ┃1.671851  889.74 -10.26│1.676105  894.13 -5.87│1.676105  894.13 -5.87│32 893.02 -6.98│39 883.02 -16.98   ┃            │            │            │         │          G#┃1.577126  788.76 -11.24│   796.09 -3.91│128/81   792.18 -7.82│29 809.30 +9.30│35 792.45  -7.55   ┃            │            │            │         │          G ┃1.495349  696.58 -3.42│1.496616 698.04 -1.96│1.496616 698.04 -1.95│25 697.67  -2.33│31 701.89 +1.89   ┃            │            │            │         │          F#┃1.401889  584.85 -15.15│   592.18 -7.82│1024/729  588.27 -11.73│22 613.95 +13.95│27 611.32 +11.32   ┃            │            │            │         │          F ┃1.337481 503.42 +3.42│ 501.96 1.96│4/3 498.04 -1.96│18 502.33 +2.33│22 498.11 -1.89   ┃            │            │            │         │          E ┃5/4 386.31 -13.69│1.254243 392.18 -7.82│1.254243 392.18 -7.82│14 390.70 -9.30│17 384.91 -15.09   ┃            │            │            │         │          Eb┃1.179066 285.17 -14.83│32/27 298.04 -1.96│32/27 294.13 -5.87│11 306.98 +6.98│13 294.34 -5.66   ┃            │            │            │         │          D ┃1.118034 193.16 -6.84│1.119930 196.09 -3.91│1.119930 196.09 -3.91│ 7 195.35 -4.65│ 9 203.77 +3.77   ┃            │            │            │         │          C#┃1.051417 86.80 -13.20│ 94.13 -5.87│256/243 90.22 -9.78│ 4 111.63 +11.63│ 5 113.21 +13.21   ┃            │            │            │         │          C ┃1.0 0.00 0.00│1.0 0.00 0.00│1.0 0.00 0.00│ 1 0.00 0.00│ 1 0.00 0.00 5度円 ラモー Eb B F C G D A E H F# C# G# Eb SC +1/3 +1/3 -1/4 -1/4 -1/4 -1/4 -1/4 -1/4 0 0 0 s' ?ヴァロヤング Eb B F C G D A E H F# C# G# Eb PC 0 0 -1/6 -1/6 -1/6 -1/6 -1/6 -1/6 0 0 0 0 ヤング 2 Eb B F C G D A E H F# C# G# Eb PC 0 0 0 -1/6 -1/6 -1/6 -1/6 -1/6 -1/6 0 0 0 音律周波数比表 5 民族音律 音名┃タイ音階 cent│ジャワ音階 cent │インドHindu音階 cent ━━╋━━━━━━━┿━━━━━━━━┿━━━━━━━━━━ C ┃1200.00 0.00│1200.00 0.00 │             ┃       │        │           B ┃       │1066.67 -33.33 │Ni 243/128 1110   ┃       │        │Ni 15/8 1088 A#┃1028.57 +28.57│        │Ni 9/5 1018   ┃       │        │Ni 16/9 996 A ┃ 857.14 -42.86│ 933.33 +33.33 │Dha 27/16 906   ┃       │        │Dha 5/3 884 G#┃       │ 800.00 0.0 │Dha 8/5 814   ┃       │        │Dha 128/81 792 G ┃ 685.71 -14.29│ 666.67 -33.33 │Fa 3/2 702   ┃       │        │Pa 64/45 600 F#┃       │        │Ma 45/32 590   ┃       │        │Ma 27/20 520 F ┃ 514.29 +14.29│ 533.33 +33.33 │Ma 4/3 498   ┃       │        │Ga 81/64 408 E ┃ 342.86 -57.14│ 400.00 0.0 │Ga 5/4 386   ┃       │        │Ga 6/5 316 D#┃       │ 266.67 -33.33 │Ga 32/27 294   ┃       │        │Ri 9/8 204 D ┃ 171.43 -28.57│        │Ri 10/9 182   ┃       │        │Ri 16/15 112 C#┃       │ 133.33 +33.33 │Ri 256/243 90   ┃       │        │Pramana 81/80 22 C ┃     0.00│     0.00 │Sa 0.00 純正律比表 -- : V (3/2) / : III (5/4) \ : IIIm(6/5) C#'' -------- G#' -------- D#' -------- A#' -------- E# 500/486 125/81 125/108 125/72 125/96 \ / \ / \ / \ / \ \ / \ / \ / \ / \ E' -------- H' -------- F#' -------- C# -------- G# -------- D# -------- A# -------- E#' 100/81 50/27 25/18 25/24 25/16 75/64 225/128 675/512 \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / G' -------- D' -------- A -------- E -------- H -------- F# -------- C#' 40/27 10/9 5/3 5/4 15/8 45/32 135/128 / \ / \ / \ / \ / \ / \ / / \ / \ / \ / \ / \ / \ / Ab''------- Eb' -------- B -------- F -------- C -------- G -------- D -------- A' -------- E' -------- H'' 128/81 32/27 16/9 4/3 1/1 3/2 9/8 27/16 81/64 243/128 / \ / \ / \ / \ / \ / \ / / \ / \ / \ / \ / \ / \ / Cb' -------- Gb' -------- Db -------- Ab -------- Eb -------- Hb -------- F' 256/135 64/45 16/15 8/5 6/5 9/5 27/20 / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ Abb' -------- Ebb' -------- Bb -------- Fb -------- Cb -------- Gb -------- Db' -------- Ab' 128/75 32/25 48/25 36/25 27/25 81/50 \ / \ / \ / \ / \ \ / \ / \ / \ / \ Abb -------- Ebb -------- Bb' -------- Fb' -------- H''' 192/125 144/125 216/125 162/125 243/125