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94edo: Difference between revisions

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BudjarnLambeth (talk | contribs)
autopatrolled
18,159 edits
CompactStar (talk | contribs)
5,020 edits
Resorted the table using some code (I will properly fix it and add ups and downs notation later)
Line 24: Line 24:
!Cents
!Cents
!13-limit
!13-limit
!23-limit
!Short-form WED
!Short-form WED
!Long-form WED
!Diatonic
!Diatonic
!Long-form WED
!23-limit
|-
|-
| 1
| 1
|12.766
|12.766
|896/891, 243/242, (3125/3072, 245/243, 100/99, 99/98)
|896/891, 243/242, (3125/3072, 245/243, 100/99, 99/98)
|85/84
|L1, R1
|L1, R1
|large unison, rastma
|
|
|large unison, rastma
|85/84
|-
|-
| 2
| 2
|25.532
|25.532
|81/80, 64/63, (50/49)
|81/80, 64/63, (50/49)
|
|K1, S1
|K1, S1
|
|komma, super unison  
|komma, super unison  
|
|
Line 48: Line 48:
|38.298
|38.298
|45/44, 40/39, (250/243, 49/48)
|45/44, 40/39, (250/243, 49/48)
|46/45
|O1, H1
|O1, H1
|on unison, hyper unison
|
|
|on unison, hyper unison
|46/45
|-
|-
|4
|4
| 51.064
| 51.064
|33/32, (128/125, 36/35, 35/34, 34/33)
|33/32, (128/125, 36/35, 35/34, 34/33)
|
|U1, T1, hm2
|U1, T1, hm2
|
|uber unison, tall unison, hypo minor second
|uber unison, tall unison, hypo minor second
|
|
Line 64: Line 64:
|63.830
|63.830
|28/27, 729/704, 27/26, (25/24)
|28/27, 729/704, 27/26, (25/24)
|
|sm2, uA1, tA1, (kkA1)
|sm2, uA1, tA1, (kkA1)
|sub minor second, unter augmented unison, tiny augmented unison, (classic augmented unison)
|dd3
|dd3
|sub minor second, unter augmented unison, tiny augmented unison, (classic augmented unison)
|
|-
|-
| 6
| 6
|76.596
|76.596
|22/21, (648/625, 26/25)
|22/21, (648/625, 26/25)
|23/22, 24/23
|lm2, oA1
|lm2, oA1
|little minor second, off augmented unison
|
|
|little minor second, off augmented unison
|23/22, 24/23
|-
|-
|7
|7
|89.362
|89.362
|256/243, 135/128, (21/20)
|256/243, 135/128, (21/20)
|19/18, 20/19
|m2, kA1
|m2, kA1
|minor second, komma-down augmented unison
|m2
|m2
|minor second, komma-down augmented unison
|19/18, 20/19
|-
|-
|8
|8
|102.128
|102.128
|128/121, (35/33)
|128/121, (35/33)
|17/16, 18/17
|Rm2, rA1
|Rm2, rA1
|rastmic minor second, rastmic augmented unison
|
|
|rastmic minor second, rastmic augmented unison
|17/16, 18/17
|-
|-
|9
|9
|114.894
|114.894
|16/15, (15/14)
|16/15, (15/14)
|
|Km2, A1
|Km2, A1
|classic minor second, augmented unison
|A1
|A1
|classic minor second, augmented unison
|
|-
|-
|10
|10
|127.660
|127.660
|320/297, 189/176, (14/13)
|320/297, 189/176, (14/13)
|
|Om2, LA1
|Om2, LA1
|
|oceanic minor second, large augmented unison
|oceanic minor second, large augmented unison
|
|
Line 112: Line 112:
|140.426
|140.426
|88/81, 13/12, 243/224, (27/25)
|88/81, 13/12, 243/224, (27/25)
|25/23, 38/35
|n2, Tm2, SA1, (KKm2)
|n2, Tm2, SA1, (KKm2)
|lesser neutral second, tall minor second, super augmented unison, (2-komma-up minor second)
|
|
|lesser neutral second, tall minor second, super augmented unison, (2-komma-up minor second)
|25/23, 38/35
|-
|-
|12
|12
|153.191
|153.191
|12/11, (35/32)
|12/11, (35/32)
|23/21
|N2, tM2, HA1
|N2, tM2, HA1
|greater netral second, tiny major second, hyper augmented unison
|ddd4
|ddd4
|greater netral second, tiny major second, hyper augmented unison
|23/21
|-
|-
|13
|13
| 165.957
| 165.957
|11/10
|11/10
|
|oM2
|oM2
|
|off major second
|off major second
|
|
Line 136: Line 136:
|178.723
|178.723
|10/9
|10/9
|21/19
|kM2
|kM2
|komma-down major second
|d3
|d3
|komma-down major second
|21/19
|-
|-
|15
|15
| 191.489
| 191.489
|121/108, (49/44, 39/35)
|121/108, (49/44, 39/35)
|19/17
|rM2
|rM2
|rastmic major second
|
|
|rastmic major second
|19/17
|-
|-
|16
|16
|204.255
|204.255
|9/8
|9/8
|
|M2
|M2
|major second
|M2
|M2
|major second
|
|-
|-
|17
|17
|217.021
|217.021
|112/99, (25/22)
|112/99, (25/22)
|17/15, 26/23
|LM2
|LM2
|large major second
|
|
|large major second
|17/15, 26/23
|-
|-
|18
|18
|229.787
|229.787
|8/7
|8/7
|
|SM2
|SM2
|super major second
|AA1
|AA1
|super major second
|
|-
|-
|19
|19
|242.553
|242.553
|15/13
|15/13
|23/20, 38/33
|HM2
|HM2
|hyper major second
|
|
|hyper major second
|23/20, 38/33
|-
|-
| 20
| 20
|255.319
|255.319
|52/45
|52/45
|22/19
|hm3
|hm3
|hypo minor third
|
|
|hypo minor third
|22/19
|-
|-
|21
|21
|268.085
|268.085
|7/6, (75/64)
|7/6, (75/64)
|
|sm3, (kkA2)
|sm3, (kkA2)
|sub minor third, (classic augmented second)
|dd4
|dd4
|sub minor third, (classic augmented second)
|
|-
|-
| 22
| 22
|280.851
|280.851
|33/28
|33/28
|20/17, 27/23
|lm3
|lm3
|little minor third
|
|
|little minor third
|20/17, 27/23
|-
|-
| 23
| 23
|293.617
|293.617
|32/27, (25/21, 13/11)
|32/27, (25/21, 13/11)
|19/16
|m3
|m3
|minor third
|m3
|m3
|minor third
|19/16
|-
|-
|24
|24
| 306.383
| 306.383
|144/121, (81/70)
|144/121, (81/70)
|
|Rm3
|Rm3
|
|rastmic minor third
|rastmic minor third
|
|
Line 224: Line 224:
|319.149
|319.149
|6/5
|6/5
|
|Km3
|Km3
|classic minor third
|A2
|A2
|classic minor third
|
|-
|-
|26
|26
|331.915
|331.915
|40/33
|40/33
|17/14, 23/19
|Om3
|Om3
|on minor third
|
|
|on minor third
|17/14, 23/19
|-
|-
|27
|27
|344.681
|344.681
|11/9, 39/32, (243/200, 60/49)
|11/9, 39/32, (243/200, 60/49)
|28/23
|n3, Tm3
|n3, Tm3
|lesser neutral third, tall minor third
|AAA1
|AAA1
|lesser neutral third, tall minor third
|28/23
|-
|-
|28
|28
|357.447
|357.447
|27/22, 16/13, (100/81,49/40)
|27/22, 16/13, (100/81,49/40)
|
|N3, tM3
|N3, tM3
|greater neutral third, tiny major third
|ddd5
|ddd5
|greater neutral third, tiny major third
|
|-
|-
|29
|29
|370.213
|370.213
|99/80, (26/21)
|99/80, (26/21)
|21/17
|oM3
|oM3
|off major third
|
|
|off major third
|21/17
|-
|-
| 30
| 30
|382.979
|382.979
|5/4
|5/4
|
|kM3
|kM3
|classic major third
|d4
|d4
|classic major third
|
|-
|-
|31
|31
|395.745
|395.745
|121/96, (34/27)
|121/96, (34/27)
|
|rM3
|rM3
|
|rastmic major third
|rastmic major third
|
|
Line 280: Line 280:
| 408.511
| 408.511
|81/64, (33/26)
|81/64, (33/26)
|19/15, 24/19
|M3
|M3
|major third
|M3
|M3
|major third
|19/15, 24/19
|-
|-
|33
|33
|421.277
|421.277
|14/11
|14/11
|23/18
|LM3
|LM3
|large major third
|
|
|large major third
|23/18
|-
|-
|34
|34
|434.043
|434.043
|9/7, (32/25)
|9/7, (32/25)
|
|SM3, (KKd4)
|SM3, (KKd4)
|super major third, (classic diminished fourth)
|AA2
|AA2
|super major third, (classic diminished fourth)
|
|-
|-
| 35
| 35
| 446.809
| 446.809
|135/104, (35/27)
|135/104, (35/27)
|22/17
|HM3
|HM3
|hyper major third
|ddd6
|ddd6
|hyper major third
|22/17
|-
|-
|36
|36
|459.574
|459.574
|13/10
|13/10
|17/13, 30/23
|h4
|h4
|hypo fourth
|
|
|hypo fourth
|17/13, 30/23
|-
|-
|37
|37
| 472.340
| 472.340
|21/16
|21/16
|25/19, 46/35
|s4
|s4
|sub fourth
|dd5
|dd5
|sub fourth
|25/19, 46/35
|-
|-
|38
|38
|485.106
|485.106
|297/224
|297/224
|
|l4
|l4
|
|little fourth
|little fourth
|
|
Line 336: Line 336:
|497.872
|497.872
|4/3
|4/3
|
|P4
|P4
|perfect fourth
|P4
|P4
|perfect fourth
|
|-
|-
| 40
| 40
|510.638
|510.638
|162/121, (35/26)
|162/121, (35/26)
|
|R4
|R4
|
|rastmic fourth
|rastmic fourth
|
|
Line 352: Line 352:
|523.404
|523.404
|27/20
|27/20
|19/14, 23/17
|K4
|K4
|komma-up fourth
|A3
|A3
|komma-up fourth
|19/14, 23/17
|-
|-
|42
|42
|536.170
|536.170
|15/11
|15/11
|34/25
|O4
|O4
|on fourth
|
|
|on fourth
|34/25
|-
|-
|43
|43
|548.936
|548.936
|11/8
|11/8
|26/19
|U4, T4
|U4, T4
|uber/undecimal fourth, tall fourth
|AAA2
|AAA2
|uber/undecimal fourth, tall fourth
|26/19
|-
|-
|44
|44
|561.702
|561.702
|18/13, (25/18)
|18/13, (25/18)
|
|tA4, uA4, (kkA4)
|tA4, uA4, (kkA4)
|tiny augmented fourth, unter augmented fourth, (classic augmented fourth)
|dd6
|dd6
|tiny augmented fourth, unter augmented fourth, (classic augmented fourth)
|
|-
|-
|45
|45
|574.468
|574.468
|88/63
|88/63
|32/23, 46/33
|ld5, oA4
|ld5, oA4
|little diminished fifth, off augmented fourth
|
|
|little diminished fifth, off augmented fourth
|32/23, 46/33
|-
|-
| 46
| 46
|587.234
|587.234
|45/32, (7/5)
|45/32, (7/5)
|38/27
|kA4
|kA4
|komma-down augmented fourth
|d5
|d5
|komma-down augmented fourth
|38/27
|-
|-
| 47
| 47
|600.000
|600.000
|363/256, 512/363, (99/70)
|363/256, 512/363, (99/70)
|17/12, 24/17
|rA4, Rd5
|rA4, Rd5
|rastmic augmented fourth, rastmic diminished fifth
|
|
|rastmic augmented fourth, rastmic diminished fifth
|17/12, 24/17
|-
|-
|48
|48
|612.766
|612.766
|64/45, (10/7)
|64/45, (10/7)
|27/19
|Kd5
|Kd5
|komma-up diminished fifth
|A4
|A4
|komma-up diminished fifth
|27/19
|-
|-
|49
|49
|625.532
|625.532
|63/44
|63/44
|23/16, 33/23
|LA4, Od5
|LA4, Od5
|large augmented fourth, off diminished fifth
|
|
|large augmented fourth, off diminished fifth
|23/16, 33/23
|-
|-
| 50
| 50
|638.298
|638.298
|13/9, (36/25)
|13/9, (36/25)
|
|Td5, Ud5, (KKd5)
|Td5, Ud5, (KKd5)
|tall diminished fifth, uber diminished fifth, (classic diminished fifth)
|AA3
|AA3
|tall diminished fifth, uber diminished fifth, (classic diminished fifth)
|
|-
|-
|51
|51
|651.064
|651.064
|16/11
|16/11
|19/13
|u5, t5
|u5, t5
|unter/undecimal fifth, tiny fifth
|ddd7
|ddd7
|unter/undecimal fifth, tiny fifth
|19/13
|-
|-
| 52
| 52
|663.830
|663.830
|22/15
|22/15
|25/17
|o5
|o5
|off fifth
|
|
|off fifth
|25/17
|-
|-
|53
|53
|676.596
|676.596
|40/27
|40/27
|28/19, 34/23
|k5
|k5
|komma-down fifth
|d6
|d6
|komma-down fifth
|28/19, 34/23
|-
|-
|54
|54
| 689.362
| 689.362
|121/81, (52/35)
|121/81, (52/35)
|
|r5
|r5
|
|rastmic fifth
|rastmic fifth
|
|
Line 464: Line 464:
|702.128
|702.128
|3/2
|3/2
|
|P5
|P5
|perfect fifth
|P5
|P5
|perfect fifth
|
|-
|-
|56
|56
|714.894
|714.894
|448/297
|448/297
|
|L5
|L5
|
|large fifth
|large fifth
|
|
Line 480: Line 480:
| 727.660
| 727.660
|32/21
|32/21
|38/25, 35/23
|S5
|S5
|super fifth
|AA4
|AA4
|super fifth
|38/25, 35/23
|-
|-
|58
|58
|740.426
|740.426
|20/13
|20/13
|26/17, 23/15
|H5
|H5
|hyper fifth
|
|
|hyper fifth
|26/17, 23/15
|-
|-
|59
|59
|753.191
|753.191
|208/135
|208/135
|17/11
|hm6
|hm6
|hypo minor sixth
|AAA3
|AAA3
|hypo minor sixth
|17/11
|-
|-
|60
|60
|765.957
|765.957
|14/9, (128/75)
|14/9, (128/75)
|
|sm6, (kkA5)
|sm6, (kkA5)
|sub minor sixth, (classic augmented fifth)
|dd7
|dd7
|sub minor sixth, (classic augmented fifth)
|
|-
|-
| 61
| 61
|778.723
|778.723
|11/7
|11/7
|36/23
|lm6
|lm6
|little minor sixth
|
|
|little minor sixth
|36/23
|-
|-
|62
|62
|791.489
|791.489
|128/81
|128/81
|19/12, 30/19
|m6
|m6
|minor sixth
|m6
|m6
|minor sixth
|19/12, 30/19
|-
|-
|63
|63
|804.255
|804.255
|192/121
|192/121
|27/17
|Rm6
|Rm6
|rastmic minor sixth
|
|
|rastmic minor sixth
|27/17
|-
|-
|64
|64
|817.021
|817.021
|8/5
|8/5
|
|Km6
|Km6
|classic minor sixth
|A5
|A5
|classic minor sixth
|
|-
|-
|65
|65
|829.787
|829.787
|160/99, (21/13)
|160/99, (21/13)
|34/21
|Om6
|Om6
|on minor sixth
|
|
|on minor sixth
|34/21
|-
|-
|66
|66
|842.553
|842.553
|44/27, 13/8, (81/50, 80/49)
|44/27, 13/8, (81/50, 80/49)
|
|n6, Tm6
|n6, Tm6
|less neutral sixth, tall minor sixth
|AAA4
|AAA4
|less neutral sixth, tall minor sixth
|
|-
|-
|67
|67
| 855.319
| 855.319
|18/11, 64/39, (400/243, 49/30)
|18/11, 64/39, (400/243, 49/30)
|23/14
|N6, tM6
|N6, tM6
|greater neutral sixth, tiny minor sixth
|ddd8
|ddd8
|greater neutral sixth, tiny minor sixth
|23/14
|-
|-
|68
|68
| 868.085
| 868.085
|33/20
|33/20
|28/17, 38/23
|oM6
|oM6
|off major sixth
|
|
|off major sixth
|28/17, 38/23
|-
|-
|69
|69
|880.851
|880.851
|5/3
|5/3
|
|kM6
|kM6
|classic major sixth
|d7
|d7
|classic major sixth
|
|-
|-
|70
|70
|893.617
|893.617
|121/72
|121/72
|
|rM6
|rM6
|
|rastmic major sixth
|rastmic major sixth
|
|
Line 592: Line 592:
|906.383
|906.383
|27/16, (42/35, 22/13)
|27/16, (42/35, 22/13)
|32/19
|M6
|M6
|major sixth
|M6
|M6
|major sixth
|32/19
|-
|-
|72
|72
|919.149
|919.149
|56/33
|56/33
|17/10, 46/27
|LM6
|LM6
|large major sixth
|
|
|large major sixth
|17/10, 46/27
|-
|-
|73
|73
|931.915
|931.915
|12/7, 128/75
|12/7, 128/75
|
|SM6, (KKd7)
|SM6, (KKd7)
|super major sixth (classic diminished seventh)
|AA5
|AA5
|super major sixth (classic diminished seventh)
|
|-
|-
|74
|74
|944.681
|944.681
|45/26
|45/26
|19/11
|HM6
|HM6
|hyper major sixth
|
|
|hyper major sixth
|19/11
|-
|-
|75
|75
|957.447
|957.447
|26/15
|26/15
|40/23, 33/19
|hm7
|hm7
|hypo minor seventh
|
|
|hypo minor seventh
|40/23, 33/19
|-
|-
|76
|76
|970.213
|970.213
|7/4
|7/4
|
|sm7
|sm7
|sub minor seventh
|dd8
|dd8
|sub minor seventh
|
|-
|-
|77
|77
|982.979
|982.979
|99/56, (44/25)
|99/56, (44/25)
|30/17, 23/13
|lm7
|lm7
|little minor seventh
|
|
|little minor seventh
|30/17, 23/13
|-
|-
|78
|78
|995.745
|995.745
|16/9
|16/9
|
|m7
|m7
|minor seventh
|m7
|m7
|minor seventh
|
|-
|-
| 79
| 79
|1008.511
|1008.511
|216/121
|216/121
|34/19
|Rm7
|Rm7
|rastmic minor seventh
|
|
|rastmic minor seventh
|34/19
|-
|-
|80
|80
|1021.277
|1021.277
|9/5
|9/5
|38/21
|Km7
|Km7
|classic minor seventh
|A6
|A6
|classic minor seventh
|38/21
|-
|-
|81
|81
|1034.043
|1034.043
|20/11
|20/11
|
|Om7
|Om7
|
|on minor seventh
|on minor seventh
|
|
Line 680: Line 680:
| 1046.809
| 1046.809
|11/6, (64/35)
|11/6, (64/35)
|42/23
|n7, Tm7, hd8
|n7, Tm7, hd8
|less neutral seventh, tall minor seventh, hypo diminished octave
|AAA5
|AAA5
|less neutral seventh, tall minor seventh, hypo diminished octave
|42/23
|-
|-
|83
|83
|1059.574
|1059.574
|81/44, 24/13, (50/27)
|81/44, 24/13, (50/27)
|46/25, 35/19
|N7, tM7, sd8, (kkM7)
|N7, tM7, sd8, (kkM7)
|greater neutral seventh, tiny major seventh, sub diminished octave, (2-comma down major seventh)
|
|
|greater neutral seventh, tiny major seventh, sub diminished octave, (2-comma down major seventh)
|46/25, 35/19
|-
|-
|84
|84
|1072.340
|1072.340
|297/160, 144/91, (13/7)
|297/160, 144/91, (13/7)
|
|oM7, ld8
|oM7, ld8
|
|off major seventh, little diminished octave
|off major seventh, little diminished octave
|
|
Line 704: Line 704:
|1085.106
|1085.106
|15/8, (28/15)
|15/8, (28/15)
|
|kM7, d8
|kM7, d8
|classic major seventh, diminished octave
|d8
|d8
|classic major seventh, diminished octave
|
|-
|-
|86
|86
|1097.872
|1097.872
|121/64
|121/64
|32/17, 17/9
|rM7, Rd8
|rM7, Rd8
|rastmic major seventh, rastmic diminished octave
|
|
|rastmic major seventh, rastmic diminished octave
|32/17, 17/9
|-
|-
|87
|87
|1110.638
|1110.638
|243/128, 256/135, (40/21)
|243/128, 256/135, (40/21)
|36/19, 19/10
|M7, Kd8
|M7, Kd8
|major seventh, komma-up diminished octave
|M7
|M7
|major seventh, komma-up diminished octave
|36/19, 19/10
|-
|-
|88
|88
|1123.404
|1123.404
|21/11, (25/13)
|21/11, (25/13)
|44/23, 23/12
|LM7, Od8
|LM7, Od8
|large major seventh, on diminished octave
|
|
|large major seventh, on diminished octave
|44/23, 23/12
|-
|-
|89
|89
|1136.170
|1136.170
|27/14, 52/27, (48/25)
|27/14, 52/27, (48/25)
|
|SM7, Td8, Ud8, (KKd8)
|SM7, Td8, Ud8, (KKd8)
|super major seventh, tall diminished octave, unter diminished octave, (classic diminished octave)
|AA6
|AA6
|super major seventh, tall diminished octave, unter diminished octave, (classic diminished octave)
|
|-
|-
|90
|90
|1148.936
|1148.936
|64/33, (35/18, 68/35, 33/17)
|64/33, (35/18, 68/35, 33/17)
|33/17
|u8, t8, HM7
|u8, t8, HM7
|unter octave, tiny octave, hyper major seventh
|
|
|unter octave, tiny octave, hyper major seventh
|33/17
|-
|-
|91
|91
| 1161.702
| 1161.702
|88/45, 39/20
|88/45, 39/20
|45/23
|o8, h8
|o8, h8
|off octave, hypo octave
|
|
|off octave, hypo octave
|45/23
|-
|-
|92
|92
|1174.468
|1174.468
|160/81, 63/32, (49/25)
|160/81, 63/32, (49/25)
|
|k8, s8
|k8, s8
|
|komma-down octave, sub octave
|komma-down octave, sub octave
|
|
Line 768: Line 768:
|1187.234
|1187.234
|891/448, 484/243, (486/245, 99/50, 196/99)
|891/448, 484/243, (486/245, 99/50, 196/99)
|
|l8, r8
|l8, r8
|
|little octave, octave - rastma
|little octave, octave - rastma
|
|
Line 776: Line 776:
|1200.000
|1200.000
|2/1
|2/1
|
|P8
|P8
|perfect octave
|P8
|P8
|perfect octave
|
|}
There are perhaps nine functional minor thirds varying between 242.553 cents and 344.681 cents, and one can even go beyond those boundaries under the right conditions, so musicians playing in 94edo have a lot more flexibility in terms of the particular interval shadings they might use depending on context.
The perfect fifth has three, or perhaps even five, functional options, each differing by one step. Although in most timbres only the central perfect fifth at 702.128 cents sounds consonant and stable, the lower and higher variants provide a change in interval quality, and can be helpful in creating subsets which mimic other edos, and close the circle of fifths in different numbers of pitches. For example, a close approximation to 41edo can be made using a chain of forty 702.128 cent fifths and one wide fifth at 714.894 cents, with an improvement on the tuning of most simple consonances in close keys, but a 1-step variation in interval quality as one modulates to more distant keys.
Every odd-numbered interval can generate the entire tuning of 94edo except for the 600-cent [[tritone]] (47\94), which divides the octave exactly in half.
The regular major second divisible into 16 equal parts can be helpful for realising some of the subtle tunings of Ancient Greek [[tetrachord]]al theory, [[Indian]] raga and Turkish [[maqam]], though it has not been used historically as a division in those musical cultures.
While having the whole gamut of 94 intervals available on a keyboard or other instrument would be quite a feat, one can get a lot out of a 41-tone chain of fifths (with the odd fifth one degree wide) or a 53-tone chain of fifths (with the odd fifth one degree narrow), where the subset behaves much like a well-temperament, arguably usable in all keys but with some interval size variation between closer and more distant keys.
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 149 -94 }}
| [{{val| 94 149 }}]
| -0.054
| 0.054
| 0.43
|-
| 2.3.5
| 32805/32768, 9765625/9565938
| [{{val| 94 149 218 }}]
| +0.442
| 0.704
| 5.52
|-
| 2.3.5.7
| 225/224, 3125/3087, 118098/117649
| [{{val| 94 149 218 264 }}]
| +0.208
| 0.732
| 5.74
|-
| 2.3.5.7.11
| 225/224, 385/384, 1331/1323, 2200/2187
| [{{val| 94 149 218 264 325 }}]
| +0.304
| 0.683
| 5.35
|-
| 2.3.5.7.11.13
| 225/224, 275/273, 325/324, 385/384, 1331/1323
| [{{val| 94 149 218 264 325 348 }}]
| +0.162
| 0.699
| 5.48
|-
| 2.3.5.7.11.13.17
| 170/169, 225/224, 275/273, 289/288, 325/324, 385/384
| [{{val| 94 149 218 264 325 348 384 }}]
| +0.238
| 0.674
| 5.28
|-
| 2.3.5.7.11.13.17.19
| 170/169, 190/189, 225/224, 275/273, 289/288, 325/324, 385/384
| [{{val| 94 149 218 264 325 348 384 399 }}]
| +0.323
| 0.669
| 5.24
|-
| 2.3.5.7.11.13.17.19.23
| 170/169, 190/189, 209/208, 225/224, 275/273, 289/288, 300/299, 323/322
| [{{val| 94 149 218 264 325 348 384 399 425 }}]
| +0.354
| 0.637
| 4.99
|}
94et is lower in relative error than any previous equal temperaments in the 23-limit, and the equal temperament that does better in this subgroup is 193.
=== Rank-2 temperaments ===
{| class="wikitable center-all right-3 left-5"
! Periods<br>per 8ve
! Generator
! Cents
! Associated<br>Ratio
! Temperament
|-
| 1
| 3\94
| 38.30
| 49/48
| [[Slender]]
|-
| 1
| 5\94
| 63.83
| 25/24
| [[Sycamore]] / [[betic]]
|-
| 1
| 11\94
| 140.43
| 243/224
| [[Tsaharuk]] / [[quanic]]
|-
| 1
| 13\94
| 165.96
| 11/10
| [[Tertiaschis]]
|-
| 1
| 19\94
| 242.55
| 147/128
| [[Septiquarter]]
|-
| 1
| 39\94
| 497.87
| 4/3
| [[Helmholtz]] / [[garibaldi]] / [[cassandra]]
|-
| 2
| 2\94
| 25.53
| 64/63
| [[Ketchup]]
|-
| 2
| 11\94
| 140.43
| 27/25
| [[Fifive]]
|-
| 2
| 30\94
| 382.98
| 5/4
| [[Wizard]] / [[gizzard]]
|-
| 2
| 34\94
| 434.04
| 9/7
| [[Pogo]] / [[supers]]
|-
| 2
| 43\94
| 548.94
| 11/8
| [[Kleischismic]]
|}
|}


Retrieved from "https://en.xen.wiki/w/94edo"