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{{EDO intro|94}}
{{EDO intro|94}}


==Theory==
== Theory ==
94edo is a remarkable all-around utility tuning system, good from low [[prime limit]] to very high prime limit situations. It is the first edo to be [[consistent]] through the [[23-odd-limit]], and no other edo is so consistent until [[282edo|282]] and [[311edo|311]] make their appearance.
94edo is a remarkable all-around utility tuning system, good from low [[prime limit]] to very high prime limit situations. It is the first edo to be [[consistent]] through the [[23-odd-limit]], and no other edo is so consistent until [[282edo|282]] and [[311edo|311]] make their appearance.


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94edo can be thought of as two sets of [[47edo]] offset by one step of 94edo. It inherits from 47edo's good approximations of primes 5, 7, 13 and 17, while it dramatically improves on prime 3, as well as primes 11, 19 and 23 to a lesser degree.
94edo can be thought of as two sets of [[47edo]] offset by one step of 94edo. It inherits from 47edo's good approximations of primes 5, 7, 13 and 17, while it dramatically improves on prime 3, as well as primes 11, 19 and 23 to a lesser degree.


===Significance of cassandra===
=== Significance of cassandra ===
94edo can also be thought of as the "sum" of [[41edo]] and [[53edo]] (41 + 53 = 94), both of which are not only known for their approximation of [[Pythagorean tuning]], but also support a variety of [[Schismatic family|schismatic temperament]] known as [[Schismatic family#Cassandra|cassandra]] (which is itself a variety of [[Schismatic family#Garibaldi|garibaldi]]), tempering out [[32805/32768]], [[225/224]], and [[385/384]]. Therefore, 94edo's fifth is the [[mediant]] of these two edos' fifths; it is slightly sharp of just and less accurate than 53edo's fifth, but more accurate than 41edo's, and acts as a generator for a highly optimized and high-prime-limit form of cassandra. Few, if any, edos that support schismatic by [[Val|patent val]] have at least as high of a consistency limit as 94edo while also having a fifth that can stack to reach any interval in it.
94edo can also be thought of as the "sum" of [[41edo]] and [[53edo]] {{nowrap|(41 + 53 {{=}} 94)}}, both of which are not only known for their approximation of [[Pythagorean tuning]], but also support a variety of [[Schismatic family|schismatic temperament]] known as [[Schismatic family#Cassandra|cassandra]] (which is itself a variety of [[Schismatic family#Garibaldi|garibaldi]]), tempering out [[32805/32768]], [[225/224]], and [[385/384]]. Therefore, 94edo's fifth is the [[mediant]] of these two edos' fifths; it is slightly sharp of just and less accurate than 53edo's fifth, but more accurate than 41edo's, and acts as a generator for a highly optimized and high-prime-limit form of cassandra. Few, if any, edos that support schismatic by [[Val|patent val]] have at least as high of a consistency limit as 94edo while also having a fifth that can stack to reach any interval in it.


===Other temperament properties===
=== Other temperament properties ===
The list of 23-limit commas it tempers out is huge, and in lower prime limits, it also tempers out [[3125/3087]], [[4000/3969]], [[5120/5103]] and [[540/539]]. It provides the [[optimal patent val]] for gassormic, the rank-5 temperament tempering out [[275/273]] (despite one edostep being very close in size to this comma), and for a number of other temperaments, such as [[isis]].
The list of 23-limit commas it tempers out is huge, and in lower prime limits, it also tempers out [[3125/3087]], [[4000/3969]], [[5120/5103]] and [[540/539]]. It provides the [[optimal patent val]] for gassormic, the rank-5 temperament tempering out [[275/273]] (despite one edostep being very close in size to this comma), and for a number of other temperaments, such as [[isis]].


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Assuming [[23-limit]] [[patent val]] {{val| 94 149 218 264 325 348 384 399 425 }}, here is a table of intervals as approximated by [[94edo]] steps, and their corresponding 13-limit well-ordered extended diatonic interval names. 'S/s' indicates alteration by the septimal comma, [[64/63]]; 'K/k' indicates alteration by the syntonic comma, [[81/80]]; 'U/u' by the undecimal quartertone, [[33/32]]; 'L/l' by pentacircle comma, [[896/891]]; 'O/o' by [[45/44]]; 'R/r' by the rastma, [[243/242]]; 'T/t' by the tridecimal quartertone, [[1053/1024]]; and finally, 'H/h', by [[40/39]]. Capital letters alter downward, lowercase alter upwards. Important 13-limit intervals approximated that are not associated with the extended diatonic interval names are added in brackets. Multiple alterations by 'K' down from augmented and major, or up from diminished and minor intervals are also added in brackets, along with their associated (5-limit) intervals.  
Assuming [[23-limit]] [[patent val]] {{val| 94 149 218 264 325 348 384 399 425 }}, here is a table of intervals as approximated by [[94edo]] steps, and their corresponding 13-limit well-ordered extended diatonic interval names. 'S/s' indicates alteration by the septimal comma, [[64/63]]; 'K/k' indicates alteration by the syntonic comma, [[81/80]]; 'U/u' by the undecimal quartertone, [[33/32]]; 'L/l' by pentacircle comma, [[896/891]]; 'O/o' by [[45/44]]; 'R/r' by the rastma, [[243/242]]; 'T/t' by the tridecimal quartertone, [[1053/1024]]; and finally, 'H/h', by [[40/39]]. Capital letters alter downward, lowercase alter upwards. Important 13-limit intervals approximated that are not associated with the extended diatonic interval names are added in brackets. Multiple alterations by 'K' down from augmented and major, or up from diminished and minor intervals are also added in brackets, along with their associated (5-limit) intervals.  
{| class="wikitable"
{| class="wikitable"
|+94edo [[SKULO interval names#WOFED interval names|WOFED interval names]]
|+ style="font-size: 105%;" | 94edo [[SKULO interval names#WOFED interval names|WOFED interval names]]
|-
|-
!Step
! Step
!Cents
! Cents
!13-limit
! 13-limit
!23-limit
! 23-limit
!Short-form WOFED
! Short-form WOFED
!Long-form WOFED
! Long-form WOFED
!Diatonic
! Diatonic
|-
|-
| 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
| 85/84
|L1, R1
| L1, R1
|large unison, rastma
| large unison, rastma
|
|  
|-
|-
| 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  
|
|  
|-
|-
|3
| 3
|38.298
| 38.298
|45/44, 40/39, (250/243, 49/48)
| 45/44, 40/39, (250/243, 49/48)
|46/45
| 46/45
|O1, H1
| O1, H1
|on unison, hyper unison
| on unison, hyper unison
|
|  
|-
|-
|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
|
|  
|-
|-
|5
| 5
|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)
| sub minor second, unter augmented unison, tiny augmented unison, (classic augmented unison)
|dd3
| dd3
|-
|-
| 6
| 6
|76.596
| 76.596
|22/21, (648/625, 26/25)
| 22/21, (648/625, 26/25)
|23/22, 24/23
| 23/22, 24/23
|lm2, oA1
| lm2, oA1
|little minor second, off augmented unison
| little minor second, off augmented unison
|
|  
|-
|-
|7
| 7
|89.362
| 89.362
|256/243, 135/128, (21/20)
| 256/243, 135/128, (21/20)
|19/18, 20/19
| 19/18, 20/19
|m2, kA1
| m2, kA1
|minor second, komma-down augmented unison
| minor second, komma-down augmented unison
|m2
| m2
|-
|-
|8
| 8
|102.128
| 102.128
|128/121, (35/33)
| 128/121, (35/33)
|17/16, 18/17
| 17/16, 18/17
|Rm2, rA1
| Rm2, rA1
|rastmic minor second, rastmic augmented unison
| rastmic minor second, rastmic augmented unison
|
|  
|-
|-
|9
| 9
|114.894
| 114.894
|16/15, (15/14)
| 16/15, (15/14)
|
|  
|Km2, A1
| Km2, A1
|classic minor second, augmented unison
| classic minor second, augmented unison
|A1
| A1
|-
|-
|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
|
|  
|-
|-
|11
| 11
|140.426
| 140.426
|88/81, 13/12, 243/224, (27/25)
| 88/81, 13/12, 243/224, (27/25)
|25/23, 38/35
| 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)
|
|  
|-
|-
|12
| 12
|153.191
| 153.191
|12/11, (35/32)
| 12/11, (35/32)
|23/21
| 23/21
|N2, tM2, HA1
| N2, tM2, HA1
|greater netral second, tiny major second, hyper augmented unison
| greater netral second, tiny major second, hyper augmented unison
|ddd4
| ddd4
|-
|-
|13
| 13
| 165.957
| 165.957
|11/10
| 11/10
|
|  
|oM2
| oM2
|off major second
| off major second
|
|  
|-
|-
|14
| 14
|178.723
| 178.723
|10/9
| 10/9
|21/19
| 21/19
|kM2
| kM2
|komma-down major second
| komma-down major second
|d3
| d3
|-
|-
|15
| 15
| 191.489
| 191.489
|121/108, (49/44, 39/35)
| 121/108, (49/44, 39/35)
|19/17
| 19/17
|rM2
| rM2
|rastmic major second
| rastmic major second
|
|  
|-
|-
|16
| 16
|204.255
| 204.255
|9/8
| 9/8
|
|  
|M2
| M2
|major second
| major second
|M2
| M2
|-
|-
|17
| 17
|217.021
| 217.021
|112/99, (25/22)
| 112/99, (25/22)
|17/15, 26/23
| 17/15, 26/23
|LM2
| LM2
|large major second
| large major second
|
|  
|-
|-
|18
| 18
|229.787
| 229.787
|8/7
| 8/7
|
|  
|SM2
| SM2
|super major second
| super major second
|AA1
| AA1
|-
|-
|19
| 19
|242.553
| 242.553
|15/13
| 15/13
|23/20, 38/33
| 23/20, 38/33
|HM2
| HM2
|hyper major second
| hyper major second
|
|  
|-
|-
| 20
| 20
|255.319
| 255.319
|52/45
| 52/45
|22/19
| 22/19
|hm3
| hm3
|hypo minor third
| hypo minor third
|
|  
|-
|-
|21
| 21
|268.085
| 268.085
|7/6, (75/64)
| 7/6, (75/64)
|
|  
|sm3, (kkA2)
| sm3, (kkA2)
|sub minor third, (classic augmented second)
| sub minor third, (classic augmented second)
|dd4
| dd4
|-
|-
| 22
| 22
|280.851
| 280.851
|33/28
| 33/28
|20/17, 27/23
| 20/17, 27/23
|lm3
| lm3
|little minor third
| little minor third
|
|  
|-
|-
| 23
| 23
|293.617
| 293.617
|32/27, (25/21, 13/11)
| 32/27, (25/21, 13/11)
|19/16
| 19/16
|m3
| m3
|minor third
| minor third
|m3
| m3
|-
|-
|24
| 24
| 306.383
| 306.383
|144/121, (81/70)
| 144/121, (81/70)
|
|  
|Rm3
| Rm3
|rastmic minor third
| rastmic minor third
|
|  
|-
|-
|25
| 25
|319.149
| 319.149
|6/5
| 6/5
|
|  
|Km3
| Km3
|classic minor third
| classic minor third
|A2
| A2
|-
|-
|26
| 26
|331.915
| 331.915
|40/33
| 40/33
|17/14, 23/19
| 17/14, 23/19
|Om3
| Om3
|on minor third
| on minor third
|
|  
|-
|-
|27
| 27
|344.681
| 344.681
|11/9, 39/32, (243/200, 60/49)
| 11/9, 39/32, (243/200, 60/49)
|28/23
| 28/23
|n3, Tm3
| n3, Tm3
|lesser neutral third, tall minor third
| lesser neutral third, tall minor third
|AAA1
| AAA1
|-
|-
|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
| greater neutral third, tiny major third
|ddd5
| ddd5
|-
|-
|29
| 29
|370.213
| 370.213
|99/80, (26/21)
| 99/80, (26/21)
|21/17
| 21/17
|oM3
| oM3
|off major third
| off major third
|
|  
|-
|-
| 30
| 30
|382.979
| 382.979
|5/4
| 5/4
|
|  
|kM3
| kM3
|classic major third
| classic major third
|d4
| d4
|-
|-
|31
| 31
|395.745
| 395.745
|121/96, (34/27)
| 121/96, (34/27)
|
|  
|rM3
| rM3
|rastmic major third
| rastmic major third
|
|  
|-
|-
|32
| 32
| 408.511
| 408.511
|81/64, (33/26)
| 81/64, (33/26)
|19/15, 24/19
| 19/15, 24/19
|M3
| M3
|major third
| major third
|M3
| M3
|-
|-
|33
| 33
|421.277
| 421.277
|14/11
| 14/11
|23/18
| 23/18
|LM3
| LM3
|large major third
| large major third
|
|  
|-
|-
|34
| 34
|434.043
| 434.043
|9/7, (32/25)
| 9/7, (32/25)
|
|  
|SM3, (KKd4)
| SM3, (KKd4)
|super major third, (classic diminished fourth)
| super major third, (classic diminished fourth)
|AA2
| AA2
|-
|-
| 35
| 35
| 446.809
| 446.809
|135/104, (35/27)
| 135/104, (35/27)
|22/17
| 22/17
|HM3
| HM3
|hyper major third
| hyper major third
|ddd6
| ddd6
|-
|-
|36
| 36
|459.574
| 459.574
|13/10
| 13/10
|17/13, 30/23
| 17/13, 30/23
|h4
| h4
|hypo fourth
| hypo fourth
|
|  
|-
|-
|37
| 37
| 472.340
| 472.340
|21/16
| 21/16
|25/19, 46/35
| 25/19, 46/35
|s4
| s4
|sub fourth
| sub fourth
|dd5
| dd5
|-
|-
|38
| 38
|485.106
| 485.106
|297/224
| 297/224
|
|  
|l4
| l4
|little fourth
| little fourth
|
|  
|-
|-
| 39
| 39
|497.872
| 497.872
|4/3
| 4/3
|
|  
|P4
| P4
|perfect fourth
| perfect fourth
|P4
| P4
|-
|-
| 40
| 40
|510.638
| 510.638
|162/121, (35/26)
| 162/121, (35/26)
|
|  
|R4
| R4
|rastmic fourth
| rastmic fourth
|
|  
|-
|-
|41
| 41
|523.404
| 523.404
|27/20
| 27/20
|19/14, 23/17
| 19/14, 23/17
|K4
| K4
|komma-up fourth
| komma-up fourth
|A3
| A3
|-
|-
|42
| 42
|536.170
| 536.170
|15/11
| 15/11
|34/25
| 34/25
|O4
| O4
|on fourth
| on fourth
|
|  
|-
|-
|43
| 43
|548.936
| 548.936
|11/8
| 11/8
|26/19
| 26/19
|U4, T4
| U4, T4
|uber/undecimal fourth, tall fourth
| uber/undecimal fourth, tall fourth
|AAA2
| AAA2
|-
|-
|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)
| tiny augmented fourth, unter augmented fourth, (classic augmented fourth)
|dd6
| dd6
|-
|-
|45
| 45
|574.468
| 574.468
|88/63
| 88/63
|32/23, 46/33
| 32/23, 46/33
|ld5, oA4
| ld5, oA4
|little diminished fifth, off augmented fourth
| little diminished fifth, off augmented fourth
|
|  
|-
|-
| 46
| 46
|587.234
| 587.234
|45/32, (7/5)
| 45/32, (7/5)
|38/27
| 38/27
|kA4
| kA4
|komma-down augmented fourth
| komma-down augmented fourth
|d5
| d5
|-
|-
| 47
| 47
|600.000
| 600.000
|363/256, 512/363, (99/70)
| 363/256, 512/363, (99/70)
|17/12, 24/17
| 17/12, 24/17
|rA4, Rd5
| rA4, Rd5
|rastmic augmented fourth, rastmic diminished fifth
| rastmic augmented fourth, rastmic diminished fifth
|
|  
|-
|-
|48
| 48
|612.766
| 612.766
|64/45, (10/7)
| 64/45, (10/7)
|27/19
| 27/19
|Kd5
| Kd5
|komma-up diminished fifth
| komma-up diminished fifth
|A4
| A4
|-
|-
|49
| 49
|625.532
| 625.532
|63/44
| 63/44
|23/16, 33/23
| 23/16, 33/23
|LA4, Od5
| LA4, Od5
|large augmented fourth, off diminished fifth
| large augmented fourth, off diminished fifth
|
|  
|-
|-
| 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)
| tall diminished fifth, uber diminished fifth, (classic diminished fifth)
|AA3
| AA3
|-
|-
|51
| 51
|651.064
| 651.064
|16/11
| 16/11
|19/13
| 19/13
|u5, t5
| u5, t5
|unter/undecimal fifth, tiny fifth
| unter/undecimal fifth, tiny fifth
|ddd7
| ddd7
|-
|-
| 52
| 52
|663.830
| 663.830
|22/15
| 22/15
|25/17
| 25/17
|o5
| o5
|off fifth
| off fifth
|
|  
|-
|-
|53
| 53
|676.596
| 676.596
|40/27
| 40/27
|28/19, 34/23
| 28/19, 34/23
|k5
| k5
|komma-down fifth
| komma-down fifth
|d6
| d6
|-
|-
|54
| 54
| 689.362
| 689.362
|121/81, (52/35)
| 121/81, (52/35)
|
|  
|r5
| r5
|rastmic fifth
| rastmic fifth
|
|  
|-
|-
|55
| 55
|702.128
| 702.128
|3/2
| 3/2
|
|  
|P5
| P5
|perfect fifth
| perfect fifth
|P5
| P5
|-
|-
|56
| 56
|714.894
| 714.894
|448/297
| 448/297
|
|  
|L5
| L5
|large fifth
| large fifth
|
|  
|-
|-
|57
| 57
| 727.660
| 727.660
|32/21
| 32/21
|38/25, 35/23
| 38/25, 35/23
|S5
| S5
|super fifth
| super fifth
|AA4
| AA4
|-
|-
|58
| 58
|740.426
| 740.426
|20/13
| 20/13
|26/17, 23/15
| 26/17, 23/15
|H5
| H5
|hyper fifth
| hyper fifth
|
|  
|-
|-
|59
| 59
|753.191
| 753.191
|208/135
| 208/135
|17/11
| 17/11
|hm6
| hm6
|hypo minor sixth
| hypo minor sixth
|AAA3
| AAA3
|-
|-
|60
| 60
|765.957
| 765.957
|14/9, (128/75)
| 14/9, (128/75)
|
|  
|sm6, (kkA5)
| sm6, (kkA5)
|sub minor sixth, (classic augmented fifth)
| sub minor sixth, (classic augmented fifth)
|dd7
| dd7
|-
|-
| 61
| 61
|778.723
| 778.723
|11/7
| 11/7
|36/23
| 36/23
|lm6
| lm6
|little minor sixth
| little minor sixth
|
|  
|-
|-
|62
| 62
|791.489
| 791.489
|128/81
| 128/81
|19/12, 30/19
| 19/12, 30/19
|m6
| m6
|minor sixth
| minor sixth
|m6
| m6
|-
|-
|63
| 63
|804.255
| 804.255
|192/121
| 192/121
|27/17
| 27/17
|Rm6
| Rm6
|rastmic minor sixth
| rastmic minor sixth
|
|  
|-
|-
|64
| 64
|817.021
| 817.021
|8/5
| 8/5
|
|  
|Km6
| Km6
|classic minor sixth
| classic minor sixth
|A5
| A5
|-
|-
|65
| 65
|829.787
| 829.787
|160/99, (21/13)
| 160/99, (21/13)
|34/21
| 34/21
|Om6
| Om6
|on minor sixth
| on minor sixth
|
|  
|-
|-
|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
| less neutral sixth, tall minor sixth
|AAA4
| AAA4
|-
|-
|67
| 67
| 855.319
| 855.319
|18/11, 64/39, (400/243, 49/30)
| 18/11, 64/39, (400/243, 49/30)
|23/14
| 23/14
|N6, tM6
| N6, tM6
|greater neutral sixth, tiny minor sixth
| greater neutral sixth, tiny minor sixth
|ddd8
| ddd8
|-
|-
|68
| 68
| 868.085
| 868.085
|33/20
| 33/20
|28/17, 38/23
| 28/17, 38/23
|oM6
| oM6
|off major sixth
| off major sixth
|
|  
|-
|-
|69
| 69
|880.851
| 880.851
|5/3
| 5/3
|
|  
|kM6
| kM6
|classic major sixth
| classic major sixth
|d7
| d7
|-
|-
|70
| 70
|893.617
| 893.617
|121/72
| 121/72
|
|  
|rM6
| rM6
|rastmic major sixth
| rastmic major sixth
|
|  
|-
|-
|71
| 71
|906.383
| 906.383
|27/16, (42/35, 22/13)
| 27/16, (42/35, 22/13)
|32/19
| 32/19
|M6
| M6
|major sixth
| major sixth
|M6
| M6
|-
|-
|72
| 72
|919.149
| 919.149
|56/33
| 56/33
|17/10, 46/27
| 17/10, 46/27
|LM6
| LM6
|large major sixth
| large major sixth
|
|  
|-
|-
|73
| 73
|931.915
| 931.915
|12/7, 128/75
| 12/7, 128/75
|
|  
|SM6, (KKd7)
| SM6, (KKd7)
|super major sixth (classic diminished seventh)
| super major sixth (classic diminished seventh)
|AA5
| AA5
|-
|-
|74
| 74
|944.681
| 944.681
|45/26
| 45/26
|19/11
| 19/11
|HM6
| HM6
|hyper major sixth
| hyper major sixth
|
|  
|-
|-
|75
| 75
|957.447
| 957.447
|26/15
| 26/15
|40/23, 33/19
| 40/23, 33/19
|hm7
| hm7
|hypo minor seventh
| hypo minor seventh
|
|  
|-
|-
|76
| 76
|970.213
| 970.213
|7/4
| 7/4
|
|  
|sm7
| sm7
|sub minor seventh
| sub minor seventh
|dd8
| dd8
|-
|-
|77
| 77
|982.979
| 982.979
|99/56, (44/25)
| 99/56, (44/25)
|30/17, 23/13
| 30/17, 23/13
|lm7
| lm7
|little minor seventh
| little minor seventh
|
|  
|-
|-
|78
| 78
|995.745
| 995.745
|16/9
| 16/9
|
|  
|m7
| m7
|minor seventh
| minor seventh
|m7
| m7
|-
|-
| 79
| 79
|1008.511
| 1008.511
|216/121
| 216/121
|34/19
| 34/19
|Rm7
| Rm7
|rastmic minor seventh
| rastmic minor seventh
|
|  
|-
|-
|80
| 80
|1021.277
| 1021.277
|9/5
| 9/5
|38/21
| 38/21
|Km7
| Km7
|classic minor seventh
| classic minor seventh
|A6
| A6
|-
|-
|81
| 81
|1034.043
| 1034.043
|20/11
| 20/11
|
|  
|Om7
| Om7
|on minor seventh
| on minor seventh
|
|  
|-
|-
|82
| 82
| 1046.809
| 1046.809
|11/6, (64/35)
| 11/6, (64/35)
|42/23
| 42/23
|n7, Tm7, hd8
| n7, Tm7, hd8
|less neutral seventh, tall minor seventh, hypo diminished octave
| less neutral seventh, tall minor seventh, hypo diminished octave
|AAA5
| AAA5
|-
|-
|83
| 83
|1059.574
| 1059.574
|81/44, 24/13, (50/27)
| 81/44, 24/13, (50/27)
|46/25, 35/19
| 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)
|
|  
|-
|-
|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
|
|  
|-
|-
|85
| 85
|1085.106
| 1085.106
|15/8, (28/15)
| 15/8, (28/15)
|
|  
|kM7, d8
| kM7, d8
|classic major seventh, diminished octave
| classic major seventh, diminished octave
|d8
| d8
|-
|-
|86
| 86
|1097.872
| 1097.872
|121/64
| 121/64
|32/17, 17/9
| 32/17, 17/9
|rM7, Rd8
| rM7, Rd8
|rastmic major seventh, rastmic diminished octave
| rastmic major seventh, rastmic diminished octave
|
|  
|-
|-
|87
| 87
|1110.638
| 1110.638
|243/128, 256/135, (40/21)
| 243/128, 256/135, (40/21)
|36/19, 19/10
| 36/19, 19/10
|M7, Kd8
| M7, Kd8
|major seventh, komma-up diminished octave
| major seventh, komma-up diminished octave
|M7
| M7
|-
|-
|88
| 88
|1123.404
| 1123.404
|21/11, (25/13)
| 21/11, (25/13)
|44/23, 23/12
| 44/23, 23/12
|LM7, Od8
| LM7, Od8
|large major seventh, on diminished octave
| large major seventh, on diminished octave
|
|  
|-
|-
|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)
| super major seventh, tall diminished octave, unter diminished octave, (classic diminished octave)
|AA6
| AA6
|-
|-
|90
| 90
|1148.936
| 1148.936
|64/33, (35/18, 68/35, 33/17)
| 64/33, (35/18, 68/35, 33/17)
|33/17
| 33/17
|u8, t8, HM7
| u8, t8, HM7
|unter octave, tiny octave, hyper major seventh
| unter octave, tiny octave, hyper major seventh
|
|  
|-
|-
|91
| 91
| 1161.702
| 1161.702
|88/45, 39/20
| 88/45, 39/20
|45/23
| 45/23
|o8, h8
| o8, h8
|off octave, hypo octave
| off octave, hypo octave
|
|  
|-
|-
|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
|
|  
|-
|-
|93
| 93
|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
|
|  
|-
|-
|94
| 94
|1200.000
| 1200.000
|2/1
| 2/1
|
|  
|P8
| P8
|perfect octave
| perfect octave
|P8
| P8
|}
|}


Line 799: Line 799:


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! 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
| 2.3
| {{monzo| 149 -94 }}
| {{monzo| 149 -94 }}
| {{mapping| 94 149 }}
| {{mapping| 94 149 }}
| -0.054
| &minus;0.054
| 0.054
| 0.054
| 0.43
| 0.43
Line 864: Line 856:
| 0.637
| 0.637
| 4.99
| 4.99
|}
{{comma basis end}}
* 94et is lower in relative error than any previous equal temperaments in the 23-limit, and the next equal temperament that does better in this subgroup is [[190edo|190g]].  
* 94et is lower in relative error than any previous equal temperaments in the 23-limit, and the next equal temperament that does better in this subgroup is [[190edo|190g]].  


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all right-3 left-5"
{{rank-2 begin}}
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperament
|-
|-
| 1
| 1
Line 940: Line 927:
| 11/8
| 11/8
| [[Kleischismic]]
| [[Kleischismic]]
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}


Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for [[garibaldi temperament]], shows us how to extend it to the 23-limit.
Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for [[garibaldi temperament]], shows us how to extend it to the 23-limit.
Retrieved from "https://en.xen.wiki/w/94edo"