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94edo: Difference between revisions

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== 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 well-rounded 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.


Its step size is close to that of [[144/143]], which is consistently represented in this tuning system.
Its step size is close to that of [[144/143]], which is consistently represented in this tuning system.


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.
=== As a tuning of other temperaments ===
94edo is the sum of [[41edo]] and [[53edo]], both of which are not only known for their approximation of [[Pythagorean tuning]], but also support a variety of [[Schismatic family|schismatic temperaments]], like [[Schismatic family#Cassandra|cassandra]] (which is itself a variety of [[Schismatic family#Garibaldi|garibaldi]]), tempering out [[32805/32768]], [[225/224]], and [[385/384]], and tempering together the [[81/80|syntonic]], [[Septimal comma|septimal]], and [[pythagorean comma]] into the same interval.


=== Significance of cassandra ===
94edo's fifth is the [[mediant]] of these two edos' fifths; it is ever so slightly sharp of just and only a hair 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 non-garibaldi schismatic notable edos in the patent val are [[118edo|118]], [[159edo|159]], [[171edo|171]], [[224edo|224]], and [[460edo|460]].
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 ===
The list of 23-limit commas it tempers out is huge (see below), 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]].


94edo is an excellent edo for [[Carlos Beta]] scale, since the difference between 1 step of Carlos Beta and 5 steps of 94edo is only 0.00314534 cents.
94edo is an excellent edo for [[Carlos Beta]] scale, since the difference between 1 step of Carlos Beta and 5 steps of 94edo is only 0.00314534 cents.
Line 19: Line 18:
=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|94|columns=11}}
{{Harmonics in equal|94|columns=11}}
=== Subsets and supersets ===
Since 94 factors into primes as {{nowrap| 2 × 47 }}, 94edo contains [[2edo]] and [[47edo]] as subset edos. It 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 dramatically improving on prime 3, as well as primes 11, 19, and 23 to a lesser degree.


== Intervals ==
== Intervals ==
Line 31: Line 33:
! 13-limit
! 13-limit
! 23-limit
! 23-limit
![[Ups and downs notation|Ups and downs]]
! [[Ups and downs notation|Ups and downs]]
! Short-form [[SKULO interval names#WOFED interval names|WOFED]]
! Short-form [[SKULO interval names#WOFED interval names|WOFED]]
! Long-form WOFED
! Long-form WOFED
Line 38: Line 40:
|0
|0
|0
|0
|1/1
|[[1/1]]
|
|
|{{UDnote|step=0}}
|{{UDnote|step=0}}
Line 47: Line 49:
| 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]]
|{{UDnote|step=1}}
|{{UDnote|step=1}}
| L1, R1
| L1, R1
Line 56: Line 58:
| 2
| 2
| 25.532
| 25.532
| 81/80, 64/63, (50/49)
| [[531441/524288]], [[81/80]], [[64/63]], ([[50/49]])
|
|
|{{UDnote|step=2}}
|{{UDnote|step=2}}
Line 65: Line 67:
| 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]]
|{{UDnote|step=3}}
|{{UDnote|step=3}}
| O1, H1
| O1, H1
Line 74: Line 76:
| 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]])
|
|
|{{UDnote|step=4}}
|{{UDnote|step=4}}
Line 83: Line 85:
| 5
| 5
| 63.830
| 63.830
| 28/27, 729/704, 27/26, (25/24)
| [[28/27]], [[729/704]], [[27/26]], ([[25/24]])
|
|
|{{UDnote|step=5}}
|{{UDnote|step=5}}
Line 92: Line 94:
| 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]]
|{{UDnote|step=6}}
|{{UDnote|step=6}}
| lm2, oA1
| lm2, oA1
Line 101: Line 103:
| 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]]
|{{UDnote|step=7}}
|{{UDnote|step=7}}
| m2, kA1
| m2, kA1
Line 110: Line 112:
| 8
| 8
| 102.128
| 102.128
| 128/121, (35/33)
| [[128/121]], ([[35/33]])
| 17/16, 18/17
| [[17/16]], [[18/17]]
|{{UDnote|step=8}}
|{{UDnote|step=8}}
| Rm2, rA1
| Rm2, rA1
Line 119: Line 121:
| 9
| 9
| 114.894
| 114.894
| 16/15, (15/14)
| [[2187/2048]], [[16/15]], ([[15/14]])
|
|
|{{UDnote|step=9}}
|{{UDnote|step=9}}
Line 128: Line 130:
| 10
| 10
| 127.660
| 127.660
| 320/297, 189/176, (14/13)
| [[320/297]], [[189/176]], ([[14/13]])
|
|
|{{UDnote|step=10}}
|{{UDnote|step=10}}
Line 137: Line 139:
| 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]]
|{{UDnote|step=11}}
|{{UDnote|step=11}}
| n2, Tm2, SA1, (KKm2)
| n2, Tm2, SA1, (KKm2)
Line 146: Line 148:
| 12
| 12
| 153.191
| 153.191
| 12/11, (35/32)
| [[12/11]], ([[35/32]])
| 23/21
| [[23/21]]
|{{UDnote|step=12}}
|{{UDnote|step=12}}
| N2, tM2, HA1
| N2, tM2, HA1
Line 155: Line 157:
| 13
| 13
| 165.957
| 165.957
| 11/10
| [[11/10]]
|
|
|{{UDnote|step=13}}
|{{UDnote|step=13}}
Line 164: Line 166:
| 14
| 14
| 178.723
| 178.723
| 10/9
| [[10/9]]
| 21/19
| [[21/19]]
|{{UDnote|step=14}}
|{{UDnote|step=14}}
| kM2
| kM2
Line 173: Line 175:
| 15
| 15
| 191.489
| 191.489
| 121/108, (49/44, 39/35)
| [[121/108]], ([[49/44]], [[39/35]])
| 19/17
| [[19/17]]
|{{UDnote|step=15}}
|{{UDnote|step=15}}
| rM2
| rM2
Line 182: Line 184:
| 16
| 16
| 204.255
| 204.255
| 9/8
| [[9/8]]
|
|
|{{UDnote|step=16}}
|{{UDnote|step=16}}
Line 191: Line 193:
| 17
| 17
| 217.021
| 217.021
| 112/99, (25/22)
| [[112/99]], ([[25/22]])
| 17/15, 26/23
| [[17/15]], [[26/23]]
|{{UDnote|step=17}}
|{{UDnote|step=17}}
| LM2
| LM2
Line 200: Line 202:
| 18
| 18
| 229.787
| 229.787
| 8/7
| [[8/7]]
|
|
|{{UDnote|step=18}}
|{{UDnote|step=18}}
Line 209: Line 211:
| 19
| 19
| 242.553
| 242.553
| 15/13
| [[15/13]]
| 23/20, 38/33
| [[23/20]], [[38/33]]
|{{UDnote|step=19}}
|{{UDnote|step=19}}
| HM2
| HM2
Line 218: Line 220:
| 20
| 20
| 255.319
| 255.319
| 52/45
| [[52/45]]
| 22/19
| [[22/19]]
|{{UDnote|step=20}}
|{{UDnote|step=20}}
| hm3
| hm3
Line 227: Line 229:
| 21
| 21
| 268.085
| 268.085
| 7/6, (75/64)
| [[7/6]], ([[75/64]])
|
|
|{{UDnote|step=21}}
|{{UDnote|step=21}}
Line 236: Line 238:
| 22
| 22
| 280.851
| 280.851
| 33/28
| [[33/28]]
| 20/17, 27/23
| [[20/17]], [[27/23]]
|{{UDnote|step=22}}
|{{UDnote|step=22}}
| lm3
| lm3
Line 245: Line 247:
| 23
| 23
| 293.617
| 293.617
| 32/27, (25/21, 13/11)
| [[32/27]], ([[25/21]], [[13/11]])
| 19/16
| [[19/16]]
|{{UDnote|step=23}}
|{{UDnote|step=23}}
| m3
| m3
Line 254: Line 256:
| 24
| 24
| 306.383
| 306.383
| 144/121, (81/70)
| [[144/121]], ([[81/70]])
|
|
|{{UDnote|step=24}}
|{{UDnote|step=24}}
Line 263: Line 265:
| 25
| 25
| 319.149
| 319.149
| 6/5
| [[6/5]]
|
|
|{{UDnote|step=25}}
|{{UDnote|step=25}}
Line 272: Line 274:
| 26
| 26
| 331.915
| 331.915
| 40/33
| [[40/33]]
| 17/14, 23/19
| [[17/14]], [[23/19]]
|{{UDnote|step=26}}
|{{UDnote|step=26}}
| Om3
| Om3
Line 281: Line 283:
| 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]]
|{{UDnote|step=27}}
|{{UDnote|step=27}}
| n3, Tm3
| n3, Tm3
Line 290: Line 292:
| 28
| 28
| 357.447
| 357.447
| 27/22, 16/13, (100/81,49/40)
| [[27/22]], [[16/13]], ([[100/81]],[[49/40]])
|
|
|{{UDnote|step=28}}
|{{UDnote|step=28}}
Line 299: Line 301:
| 29
| 29
| 370.213
| 370.213
| 99/80, (26/21)
| [[99/80]], ([[26/21]])
| 21/17
| [[21/17]]
|{{UDnote|step=29}}
|{{UDnote|step=29}}
| oM3
| oM3
Line 308: Line 310:
| 30
| 30
| 382.979
| 382.979
| 5/4
| [[8192/6561]], [[5/4]]
|
|
|{{UDnote|step=30}}
|{{UDnote|step=30}}
Line 317: Line 319:
| 31
| 31
| 395.745
| 395.745
| 121/96, (34/27)
| [[121/96]], ([[34/27]])
|
|
|{{UDnote|step=31}}
|{{UDnote|step=31}}
Line 326: Line 328:
| 32
| 32
| 408.511
| 408.511
| 81/64, (33/26)
| [[81/64]], ([[33/26]])
| 19/15, 24/19
| [[19/15]], [[24/19]]
|{{UDnote|step=32}}
|{{UDnote|step=32}}
| M3
| M3
Line 335: Line 337:
| 33
| 33
| 421.277
| 421.277
| 14/11
| [[14/11]]
| 23/18
| [[23/18]]
|{{UDnote|step=33}}
|{{UDnote|step=33}}
| LM3
| LM3
Line 344: Line 346:
| 34
| 34
| 434.043
| 434.043
| 9/7, (32/25)
| [[9/7]], ([[32/25]])
|
|
|{{UDnote|step=34}}
|{{UDnote|step=34}}
Line 353: Line 355:
| 35
| 35
| 446.809
| 446.809
| 135/104, (35/27)
| [[135/104]], ([[35/27]])
| 22/17
| [[22/17]]
|{{UDnote|step=35}}
|{{UDnote|step=35}}
| HM3
| HM3
Line 362: Line 364:
| 36
| 36
| 459.574
| 459.574
| 13/10
| [[13/10]]
| 17/13, 30/23
| [[17/13]], [[30/23]]
|{{UDnote|step=36}}
|{{UDnote|step=36}}
| h4
| h4
Line 371: Line 373:
| 37
| 37
| 472.340
| 472.340
| 21/16
| [[21/16]]
| 25/19, 46/35
| [[25/19]], [[46/35]]
|{{UDnote|step=37}}
|{{UDnote|step=37}}
| s4
| s4
Line 380: Line 382:
| 38
| 38
| 485.106
| 485.106
| 297/224
| [[297/224]]
|
|
|{{UDnote|step=38}}
|{{UDnote|step=38}}
Line 389: Line 391:
| 39
| 39
| 497.872
| 497.872
| 4/3
| [[4/3]]
|
|
|{{UDnote|step=39}}
|{{UDnote|step=39}}
Line 398: Line 400:
| 40
| 40
| 510.638
| 510.638
| 162/121, (35/26)
| [[162/121]], ([[35/26]])
|
|
|{{UDnote|step=40}}
|{{UDnote|step=40}}
Line 407: Line 409:
| 41
| 41
| 523.404
| 523.404
| 27/20
| [[27/20]]
| 19/14, 23/17
| [[19/14]], [[23/17]]
|{{UDnote|step=41}}
|{{UDnote|step=41}}
| K4
| K4
Line 416: Line 418:
| 42
| 42
| 536.170
| 536.170
| 15/11
| [[15/11]]
| 34/25
| [[34/25]]
|{{UDnote|step=42}}
|{{UDnote|step=42}}
| O4
| O4
Line 425: Line 427:
| 43
| 43
| 548.936
| 548.936
| 11/8
| [[11/8]]
| 26/19
| [[26/19]]
|{{UDnote|step=43}}
|{{UDnote|step=43}}
| U4, T4
| U4, T4
Line 434: Line 436:
| 44
| 44
| 561.702
| 561.702
| 18/13, (25/18)
| [[18/13]], ([[25/18]])
|
|
|{{UDnote|step=44}}
|{{UDnote|step=44}}
Line 443: Line 445:
| 45
| 45
| 574.468
| 574.468
| 88/63
| [[88/63]]
| 32/23, 46/33
| [[32/23]], [[46/33]]
|{{UDnote|step=45}}
|{{UDnote|step=45}}
| ld5, oA4
| ld5, oA4
Line 452: Line 454:
| 46
| 46
| 587.234
| 587.234
| 45/32, (7/5)
| [[45/32]], ([[7/5]])
| 38/27
| [[38/27]]
|{{UDnote|step=46}}
|{{UDnote|step=46}}
| kA4
| kA4
Line 461: Line 463:
| 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]]
|{{UDnote|step=47}}
|{{UDnote|step=47}}
| rA4, Rd5
| rA4, Rd5
Line 470: Line 472:
| 48
| 48
| 612.766
| 612.766
| 64/45, (10/7)
| [[64/45]], ([[10/7]])
| 27/19
| [[27/19]]
|{{UDnote|step=48}}
|{{UDnote|step=48}}
| Kd5
| Kd5
Line 479: Line 481:
| 49
| 49
| 625.532
| 625.532
| 63/44
| [[63/44]]
| 23/16, 33/23
| [[23/16]], [[33/23]]
|{{UDnote|step=49}}
|{{UDnote|step=49}}
| LA4, Od5
| LA4, Od5
Line 488: Line 490:
| 50
| 50
| 638.298
| 638.298
| 13/9, (36/25)
| [[13/9]], ([[36/25]])
|
|
|{{UDnote|step=50}}
|{{UDnote|step=50}}
Line 497: Line 499:
| 51
| 51
| 651.064
| 651.064
| 16/11
| [[16/11]]
| 19/13
| [[19/13]]
|{{UDnote|step=51}}
|{{UDnote|step=51}}
| u5, t5
| u5, t5
Line 506: Line 508:
| 52
| 52
| 663.830
| 663.830
| 22/15
| [[22/15]]
| 25/17
| [[25/17]]
|{{UDnote|step=52}}
|{{UDnote|step=52}}
| o5
| o5
Line 515: Line 517:
| 53
| 53
| 676.596
| 676.596
| 40/27
| [[40/27]]
| 28/19, 34/23
| [[28/19]], [[34/23]]
|{{UDnote|step=53}}
|{{UDnote|step=53}}
| k5
| k5
Line 524: Line 526:
| 54
| 54
| 689.362
| 689.362
| 121/81, (52/35)
| [[121/81]], ([[52/35]])
|
|
|{{UDnote|step=54}}
|{{UDnote|step=54}}
Line 533: Line 535:
| 55
| 55
| 702.128
| 702.128
| 3/2
| [[3/2]]
|
|
|{{UDnote|step=55}}
|{{UDnote|step=55}}
Line 542: Line 544:
| 56
| 56
| 714.894
| 714.894
| 448/297
| [[448/297]]
|
|
|{{UDnote|step=56}}
|{{UDnote|step=56}}
Line 551: Line 553:
| 57
| 57
| 727.660
| 727.660
| 32/21
| [[32/21]]
| 38/25, 35/23
| [[38/25]], [[35/23]]
|{{UDnote|step=57}}
|{{UDnote|step=57}}
| S5
| S5
Line 560: Line 562:
| 58
| 58
| 740.426
| 740.426
| 20/13
| [[20/13]]
| 26/17, 23/15
| [[26/17]], [[23/15]]
|{{UDnote|step=58}}
|{{UDnote|step=58}}
| H5
| H5
Line 569: Line 571:
| 59
| 59
| 753.191
| 753.191
| 208/135
| [[208/135]]
| 17/11
| [[17/11]]
|{{UDnote|step=59}}
|{{UDnote|step=59}}
| hm6
| hm6
Line 578: Line 580:
| 60
| 60
| 765.957
| 765.957
| 14/9, (25/16)
| [[14/9]], ([[25/16]])
|
|
|{{UDnote|step=60}}
|{{UDnote|step=60}}
Line 587: Line 589:
| 61
| 61
| 778.723
| 778.723
| 11/7
| [[11/7]]
| 36/23
| [[36/23]]
|{{UDnote|step=61}}
|{{UDnote|step=61}}
| lm6
| lm6
Line 596: Line 598:
| 62
| 62
| 791.489
| 791.489
| 128/81
| [[128/81]]
| 19/12, 30/19
| [[19/12]], [[30/19]]
|{{UDnote|step=62}}
|{{UDnote|step=62}}
| m6
| m6
Line 605: Line 607:
| 63
| 63
| 804.255
| 804.255
| 192/121
| [[192/121]]
| 27/17
| [[27/17]]
|{{UDnote|step=63}}
|{{UDnote|step=63}}
| Rm6
| Rm6
Line 614: Line 616:
| 64
| 64
| 817.021
| 817.021
| 8/5
| [[8/5]]
|
|
|{{UDnote|step=64}}
|{{UDnote|step=64}}
Line 623: Line 625:
| 65
| 65
| 829.787
| 829.787
| 160/99, (21/13)
| [[160/99]], ([[21/13]])
| 34/21
| [[34/21]]
|{{UDnote|step=65}}
|{{UDnote|step=65}}
| Om6
| Om6
Line 632: Line 634:
| 66
| 66
| 842.553
| 842.553
| 44/27, 13/8, (81/50, 80/49)
| [[44/27]], [[13/8]], ([[81/50]], [[80/49]])
|
|
|{{UDnote|step=66}}
|{{UDnote|step=66}}
Line 641: Line 643:
| 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]]
|{{UDnote|step=67}}
|{{UDnote|step=67}}
| N6, tM6
| N6, tM6
Line 650: Line 652:
| 68
| 68
| 868.085
| 868.085
| 33/20
| [[33/20]]
| 28/17, 38/23
| [[28/17]], [[38/23]]
|{{UDnote|step=68}}
|{{UDnote|step=68}}
| oM6
| oM6
Line 659: Line 661:
| 69
| 69
| 880.851
| 880.851
| 5/3
| [[5/3]]
|
|
|{{UDnote|step=69}}
|{{UDnote|step=69}}
Line 668: Line 670:
| 70
| 70
| 893.617
| 893.617
| 121/72
| [[121/72]]
|
|
|{{UDnote|step=70}}
|{{UDnote|step=70}}
Line 677: Line 679:
| 71
| 71
| 906.383
| 906.383
| 27/16, (42/35, 22/13)
| [[27/16]], ([[42/35]], [[22/13]])
| 32/19
| [[32/19]]
|{{UDnote|step=71}}
|{{UDnote|step=71}}
| M6
| M6
Line 686: Line 688:
| 72
| 72
| 919.149
| 919.149
| 56/33
| [[56/33]]
| 17/10, 46/27
| [[17/10]], [[46/27]]
|{{UDnote|step=72}}
|{{UDnote|step=72}}
| LM6
| LM6
Line 695: Line 697:
| 73
| 73
| 931.915
| 931.915
| 12/7, (128/75)
| [[12/7]], ([[128/75]])
|
|
|{{UDnote|step=73}}
|{{UDnote|step=73}}
Line 704: Line 706:
| 74
| 74
| 944.681
| 944.681
| 45/26
| [[45/26]]
| 19/11
| [[19/11]]
|{{UDnote|step=74}}
|{{UDnote|step=74}}
| HM6
| HM6
Line 713: Line 715:
| 75
| 75
| 957.447
| 957.447
| 26/15
| [[26/15]]
| 40/23, 33/19
| [[40/23]], [[33/19]]
|{{UDnote|step=75}}
|{{UDnote|step=75}}
| hm7
| hm7
Line 722: Line 724:
| 76
| 76
| 970.213
| 970.213
| 7/4
| [[7/4]]
|
|
|{{UDnote|step=76}}
|{{UDnote|step=76}}
Line 731: Line 733:
| 77
| 77
| 982.979
| 982.979
| 99/56, (44/25)
| [[99/56]], ([[44/25]])
| 30/17, 23/13
| [[30/17]], [[23/13]]
|{{UDnote|step=77}}
|{{UDnote|step=77}}
| lm7
| lm7
Line 740: Line 742:
| 78
| 78
| 995.745
| 995.745
| 16/9
| [[16/9]]
|
|
|{{UDnote|step=78}}
|{{UDnote|step=78}}
Line 749: Line 751:
| 79
| 79
| 1008.511
| 1008.511
| 216/121
| [[216/121]]
| 34/19
| [[34/19]]
|{{UDnote|step=79}}
|{{UDnote|step=79}}
| Rm7
| Rm7
Line 758: Line 760:
| 80
| 80
| 1021.277
| 1021.277
| 9/5
| [[9/5]]
| 38/21
| [[38/21]]
|{{UDnote|step=80}}
|{{UDnote|step=80}}
| Km7
| Km7
Line 767: Line 769:
| 81
| 81
| 1034.043
| 1034.043
| 20/11
| [[20/11]]
|
|
|{{UDnote|step=81}}
|{{UDnote|step=81}}
Line 776: Line 778:
| 82
| 82
| 1046.809
| 1046.809
| 11/6, (64/35)
| [[11/6]], ([[64/35]])
| 42/23
| [[42/23]]
|{{UDnote|step=82}}
|{{UDnote|step=82}}
| n7, Tm7, hd8
| n7, Tm7, hd8
Line 785: Line 787:
| 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]]
|{{UDnote|step=83}}
|{{UDnote|step=83}}
| N7, tM7, sd8, (kkM7)
| N7, tM7, sd8, (kkM7)
Line 794: Line 796:
| 84
| 84
| 1072.340
| 1072.340
| 297/160, 144/91, (13/7)
| [[297/160]], [[144/91]], ([[13/7]])
|
|
|{{UDnote|step=84}}
|{{UDnote|step=84}}
Line 803: Line 805:
| 85
| 85
| 1085.106
| 1085.106
| 15/8, (28/15)
| [[15/8]], ([[28/15]])
|
|
|{{UDnote|step=85}}
|{{UDnote|step=85}}
Line 812: Line 814:
| 86
| 86
| 1097.872
| 1097.872
| 121/64
| [[121/64]]
| 32/17, 17/9
| [[32/17]], [[17/9]]
|{{UDnote|step=86}}
|{{UDnote|step=86}}
| rM7, Rd8
| rM7, Rd8
Line 821: Line 823:
| 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]]
|{{UDnote|step=87}}
|{{UDnote|step=87}}
| M7, Kd8
| M7, Kd8
Line 830: Line 832:
| 88
| 88
| 1123.404
| 1123.404
| 21/11, (25/13)
| [[21/11]], ([[25/13]])
| 44/23, 23/12
| [[44/23]], [[23/12]]
|{{UDnote|step=88}}
|{{UDnote|step=88}}
| LM7, Od8
| LM7, Od8
Line 839: Line 841:
| 89
| 89
| 1136.170
| 1136.170
| 27/14, 52/27, (48/25)
| [[27/14]], [[52/27]], ([[48/25]])
|
|
|{{UDnote|step=89}}
|{{UDnote|step=89}}
Line 848: Line 850:
| 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]]
|{{UDnote|step=90}}
|{{UDnote|step=90}}
| u8, t8, HM7
| u8, t8, HM7
Line 857: Line 859:
| 91
| 91
| 1161.702
| 1161.702
| 88/45, 39/20
| [[88/45]], [[39/20]]
| 45/23
| [[45/23]]
|{{UDnote|step=91}}
|{{UDnote|step=91}}
| o8, h8
| o8, h8
Line 866: Line 868:
| 92
| 92
| 1174.468
| 1174.468
| 160/81, 63/32, (49/25)
| [[160/81]], [[63/32]], ([[49/25]])
|
|
|{{UDnote|step=92}}
|{{UDnote|step=92}}
Line 875: Line 877:
| 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]])
|
|
|{{UDnote|step=93}}
|{{UDnote|step=93}}
Line 884: Line 886:
| 94
| 94
| 1200.000
| 1200.000
| 2/1
| [[2/1]]
|
|
|{{UDnote|step=94}}
|{{UDnote|step=94}}
Line 894: Line 896:
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.
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.
The perfect fifth has three, or perhaps even five, functional options, each differing by one step. 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.
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.
Line 902: Line 904:
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.
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.


== Approximation to JI ==
== Notation ==
=== Zeta peak index ===
=== Ups and downs notation ===
{{ZPI
94edo can be written using [[Kite's ups and downs notation]]. Note that quudsharp (quadruple-down sharp) is equivalent to quip (quintuple-up) and that quupflat (quadruple-up flat) is equivalent to quid (quintuple-down):
| zpi = 532
{{Ups and downs sharpness}}
| steps = 93.9836761074943
 
| step size = 12.7681747480009
=== Sagittal ===
| tempered height = 8.806201
94edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal_notation#Athenian|Athenian set]], with the apotome equal to 9 edosteps and the limma to 7 edosteps.
| pure height = 8.585151
{| class="wikitable" style="text-align: center;"
| integral = 1.394050
! colspan="2" |Steps
| gap = 17.832744
!'''0'''
| octave = 1200.20842631208
! 1
| consistent = 24
! 2
| distinct = 15
! 3
}}
! 4
! 5
! 6
! 7
! 8
! '''9'''
|-
! rowspan="2" |Symbol
!Evo
| rowspan="2" |<big>{{sagittal||//|}}</big>
| rowspan="2" |<big>{{sagittal|~|(}}</big>
| rowspan="2" |<big>{{sagittal|/|}}</big>
| rowspan="2" |<big>{{sagittal|(|(}}</big>
| rowspan="2" |<big>{{sagittal|/|\}}</big>
| rowspan="2" |<big>{{sagittal|(|)}}</big>
|{{sagittal|(!(}}{{sagittal|#}}
|{{sagittal|\!}}{{sagittal|#}}
|{{sagittal|~!(}}{{sagittal|#}}
|{{sagittal|#}}
|-
!Revo
|<big>{{sagittal|~||(}}</big>
|<big>{{sagittal|||\}}</big>
|<big>{{sagittal|(||(}}</big>
|<big>{{sagittal|/||\}}</big>
|}
The following enharmonics from the Athenian set are present (comma tempered out):
 
* {{sagittal|//|}} = {{Sagittal|/|)}} = {{Sagittal|/|\}} ([[325/324]], [[352/351]])
* {{sagittal|/|}} = {{sagittal||)}} = {{sagittal||\}} ([[225/224]], [[2200/2187]])
* {{sagittal|)|(}} = {{sagittal|~|(}} ([[3680721/3670016]])
* {{sagittal|(|}} = {{sagittal|(|(}} ([[5120/5103]])
* {{sagittal||(}} = {{sagittal||//|}} ([[5120/5103]])
 
See [[Sagittal notation#Revo|apotome complements]] for equivalent accidental pairs.
 
The JI chord 16:17:18:19:20:21:22:23:24:25:26:27:28:30 from D would be written D{{sagittal||//|}}:E{{sagittal|(!!(}}:E{{sagittal||//|}}:F{{sagittal||//|}}:F{{sagittal|||\}}:G{{sagittal|\!}}:G{{sagittal|/|\}}:G{{sagittal|~|||(}}:A{{sagittal||//|}}:A{{sagittal|(|)}}:B{{sagittal|(!)}}:B{{sagittal||//|}}:C{{sagittal|\!}}:C{{sagittal|||\}}. Music that doesn't modulate much in the 2.3.5.7.11.13.19 subgroup can be notated by only using {{sagittal|/|}} {{sagittal|/|\}} / {{sagittal|\!}} {{sagittal|\!/}} and their apotome complements; where naturals are used for 3 and 19, {{sagittal|/|}} / {{sagittal|\!}} for 5 and 7, and {{sagittal|/|\}} / {{sagittal|\!/}} for 11 and 13.


== Regular temperament properties ==
== Regular temperament properties ==
Line 930: Line 968:
|-
|-
| 2.3
| 2.3
| {{monzo| 149 -94 }}
| {{Monzo| 149 -94 }}
| {{mapping| 94 149 }}
| {{Mapping| 94 149 }}
| −0.054
| −0.054
| 0.054
| 0.054
Line 938: Line 976:
| 2.3.5
| 2.3.5
| 32805/32768, 9765625/9565938
| 32805/32768, 9765625/9565938
| {{mapping| 94 149 218 }}
| {{Mapping| 94 149 218 }}
| +0.442
| +0.442
| 0.704
| 0.704
Line 945: Line 983:
| 2.3.5.7
| 2.3.5.7
| 225/224, 3125/3087, 118098/117649
| 225/224, 3125/3087, 118098/117649
| {{mapping| 94 149 218 264 }}
| {{Mapping| 94 149 218 264 }}
| +0.208
| +0.208
| 0.732
| 0.732
Line 952: Line 990:
| 2.3.5.7.11
| 2.3.5.7.11
| 225/224, 385/384, 1331/1323, 2200/2187
| 225/224, 385/384, 1331/1323, 2200/2187
| {{mapping| 94 149 218 264 325 }}
| {{Mapping| 94 149 218 264 325 }}
| +0.304
| +0.304
| 0.683
| 0.683
Line 959: Line 997:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 225/224, 275/273, 325/324, 385/384, 1331/1323
| 225/224, 275/273, 325/324, 385/384, 1331/1323
| {{mapping| 94 149 218 264 325 348 }}
| {{Mapping| 94 149 218 264 325 348 }}
| +0.162
| +0.162
| 0.699
| 0.699
Line 966: Line 1,004:
| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 170/169, 225/224, 275/273, 289/288, 325/324, 385/384
| 170/169, 225/224, 275/273, 289/288, 325/324, 385/384
| {{mapping| 94 149 218 264 325 348 384 }}
| {{Mapping| 94 149 218 264 325 348 384 }}
| +0.238
| +0.238
| 0.674
| 0.674
Line 973: Line 1,011:
| 2.3.5.7.11.13.17.19
| 2.3.5.7.11.13.17.19
| 170/169, 190/189, 225/224, 275/273, 289/288, 325/324, 385/384
| 170/169, 190/189, 225/224, 275/273, 289/288, 325/324, 385/384
| {{mapping| 94 149 218 264 325 348 384 399 }}
| {{Mapping| 94 149 218 264 325 348 384 399 }}
| +0.323
| +0.323
| 0.669
| 0.669
Line 980: Line 1,018:
| 2.3.5.7.11.13.17.19.23
| 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
| 170/169, 190/189, 209/208, 225/224, 275/273, 289/288, 300/299, 323/322
| {{mapping| 94 149 218 264 325 348 384 399 425 }}
| {{Mapping| 94 149 218 264 325 348 384 399 425 }}
| +0.354
| +0.354
| 0.637
| 0.637
Line 1,008: Line 1,046:
| 25/24
| 25/24
| [[Betic]]
| [[Betic]]
|-
| 1
| 7\94
| 89.36
| 21/20
| [[Slithy]]
|-
|-
| 1
| 1
| 11\94
| 11\94
| 140.43
| 140.43
| 243/224
| 13/12
| [[Tsaharuk]] / [[quanic]]
| [[Tsaharuk]] / [[quanic]]
|-
|-
Line 1,026: Line 1,070:
| 147/128
| 147/128
| [[Septiquarter]]
| [[Septiquarter]]
|-
| 1
| 25\94
| 319.15
| 6/5
| [[Dhaivatic]]
|-
|-
| 1
| 1
Line 1,063: Line 1,113:
| [[Kleischismic]]
| [[Kleischismic]]
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct


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.
Temperaments to which 94et can be detempered:
* [[Satin]] ({{nowrap| 94 & 217 }})
* [[Gariwizmic]] ({{nowrap| 94 & 176 }})
* {{nowrap| 94 & 422 }}


* {{nowrap|46 &amp; 94}} {{multival| 8 30 -18 -4 -28 8 -24 2 … }}
=== Commas ===
* {{nowrap|68 &amp; 94}} {{multival| 20 28 2 -10 24 20 34 52 … }}
94et [[tempering out|tempers out]] the following [[comma]]s using its 23-limit patent [[val]], {{val| 94 149 218 264 325 348 384 399 425 }}.
* {{nowrap|53 &amp; 94}} {{multival| 1 -8 -14 23 20 -46 -3 -35 … }} (one garibaldi)
* {{nowrap|41 &amp; 94}} {{multival| 1 -8 -14 23 20 48 -3 -35 … }} (another garibaldi, only differing in the mappings of 17 and 23)
* {{nowrap|135 &amp; 94}} {{multival| 1 -8 -14 23 20 48 -3 59 … }} (another garibaldi)
* {{nowrap|130 &amp; 94}} {{multival| 6 -48 10 -50 26 6 -18 -22 … }} (a pogo extension)
* {{nowrap|58 &amp; 94}} {{multival| 6 46 10 44 26 6 -18 -22 … }} (a supers extension)
* {{nowrap|50 &amp; 94}} {{multival| 24 -4 40 -12 10 24 22 6 … }}
* {{nowrap|72 &amp; 94}} {{multival| 12 -2 20 -6 52 12 -36 -44 … }} (a gizzard extension)
* {{nowrap|80 &amp; 94}} {{multival| 18 44 30 38 -16 18 40 28 … }}
* 94 solo {{multival| 12 -2 20 -6 -42 12 -36 -44 … }} (a rank one temperament!)


Temperaments to which 94et can be detempered:
{| class="commatable wikitable center-1 center-2 right-3 center-6"
 
! [[Harmonic limit|Prime<br>limit]]
* [[Satin]] ({{nowrap|94 & 311}}) {{multival| 3 70 -42 69 -34 50 85 83 … }}
! [[Ratio]]<ref>Ratios with more than 8 digits are presented by placeholders with informative hints</ref>
* {{nowrap|94 & 422}} {{multival| 8 124 -18 90 -28 102 164 96 … }}
! [[Cents]]
! [[Monzo]]
! colspan="2" | [[Kite's color notation|Color name]]
! Name(s)
|-
| 3
| <abbr title="36893488147419103232/36472996377170786403">(90 digits)</abbr>
| 16.22
| {{Monzo| 149 -94 }}
| Wa-94
| 94-edo
| [[94-comma]]
|-
| 5
| [[32805/32768|(10 digits)]]
| 1.95
| {{Monzo| -15 8 1 }}
| Layo
| Ly
| [[Schisma]]
|-
| 7
| [[3125/3087]]
| 21.18
| {{Monzo| 0 -2 5 -3 }}
| Triru-aquinyo
| r<sup>3</sup>y<sup>5</sup>
| Gariboh comma
|-
| 7
| [[4000/3969]]
| 13.47
| {{Monzo| 5 -4 3 -2 }}
| Rurutriyo
| rry<sup>3</sup>
| Octagar comma
|-
| 7
| [[225/224]]
| 7.71
| {{monzo| -5 2 2 -1 }}
| Ruyoyo
| ryy
| Marvel comma
|-
| 7
| <abbr title="36893488147419103232/36472996377170786403">(12 digits)</abbr>
| 6.59
| {{monzo| 1 10 0 -6 }}
| Latribiru
| L6r
| Stearnsma
|-
| 7
| [[5120/5103]]
| 5.76
| {{monzo| 10 -6 1 -1 }}
| Saruyo
| sry
| Hemifamity comma
|-
| 7
| [[33554432/33480783|(16 digits)]]
| 3.80
| {{Monzo| 25 -14 0 -1 }}
| Sasaru
| ssr
| [[Garischisma]]
|-
| 11
| [[385/384]]
| 4.50
| {{Monzo| -7 -1 1 1 1 }}
| Lozoyo
| 1ozg
| Keenanisma
|-
| 11
| [[540/539]]
| 3.21
| {{Monzo| 2 3 1 -2 -1 }}
| Lururuyo
| 1urry
| Swetisma
|-
| 11
| [[9801/9800]]
| 0.17
| {{Monzo| -3 4 -2 -2 2 }}
| Bilorugu
| 1oorrgg-2
| Kalisma
|-
| 13
| [[275/273]]
| 12.64
| {{Monzo| 0 -1 2 -1 1 -1 }}
| Thuloruyoyo
| 3u1oryy
| Gassorma
|-
| 13
| [[640/637]]
| 8.13
| {{Monzo| 7 0 1 -2 0 -1 }}
| Thururuyo
| 3urry
| Huntma
|-
| 13
| [[1188/1183]]
| 7.30
| {{Monzo| 2 3 0 -1 1 -2 }}
| Thuthuloru
| 3uu1or
| Kestrel comma
|-
| 13
| [[325/324]]
| 5.34
| {{Monzo| -2 -4 2 0 0 1 }}
| Thoyoyo
| 3oyy
| Marveltwin comma
|-
| 13
| [[352/351]]
| 4.93
| {{Monzo| 5 -3 0 0 1 -1 }}
| Thulo
| 3u1o
| Major minthma
|-
| 13
| [[847/845]]
| 4.09
| {{Monzo| 0 0 -1 1 2 -2 }}
| Thuthulolozogu
| 3uu1oozg
| Cuthbert comma
|-
| 13
| [[729/728]]
| 2.38
| {{Monzo| -3 6 0 -1 0 -1 }}
| Lathuru
| L3ur
| Squbema
|-
| 13
| [[2080/2079]]
| 0.83
| {{Monzo| 5 -3 1 -1 -1 1 }}
| Tholuruyo
| 3o1ury
| Ibnsinma, sinaisma
|-
| 13
| [[4096/4095]]
| 0.42
| {{Monzo| 12 -2 -1 -1 0 -1 }}
| Sathurugu
| s3urg
| Minisma
|-
| 13
| [[4225/4224]]
| 0.41
| {{Monzo| -7 -1 2 0 -1 2 }}
| Thotholuyoyo
| 3oo1uyy
| Leprechaun comma
|-
| 17
| [[289/288]]
| 6.00
| {{Monzo| 5 -2 0 0 0 0 2 }}
| Soso
| 17oo
| Semitonisma
|-
| 17
| [[715/714]]
| 2.42
| {{Monzo| -1 -1 1 -1 1 1 -1 }}
| Sutholoruyo
| 17u3o1ory
| Septendecimal bridge comma
|-
| 19
| [[361/360]]
| 4.80
| {{Monzo| -3 -2 -1 0 0 0 0 2 }}
| Nonogu
| 19oog2
| Go comma
|-
| 19
| [[513/512]]
| 3.38
| {{Monzo| -9 3 0 0 0 0 0 1 }}
| Lano
| L19o
| Boethius' comma
|-
| 19
| [[1216/1215]]
| 1.42
| {{Monzo| 6 -5 -1 0 0 0 0 1 }}
| Sanogu
| s19og
| Eratosthenes' comma
|-
| 19
| [[11859211/11859210|(16 digits)]]
| 0.00
| {{Monzo| -1 -4 -1 1 -4 1 0 4 }}
| <small>Quadno-athoquadlu-azogu</small>
| <small>9o<sup>4</sup>3o1u<sup>4</sup>zg</small>
| Tredekisma
|-
| 23
| [[300/299]]
| 5.78
| {{Monzo| 2 1 2 0 0 -1 0 0 -1 }}
| Twethuthuyoyo
| 23u3uyy
| Major naiadvicema
|-
| 23
| [[323/322]]
| 5.37
| {{Monzo| -1 0 0 -1 0 0 1 1 -1 }}
| Twethunosoru
| 23u19o17or
| Major semivicema
|-
| 23
| [[391/390]]
| 4.43
| {{Monzo| -1 -1 -1 0 0 -1 1 0 1 }}
| Twethosothugu
| 23o17o3ug
| Minor naiadvicema
|-
| 23
| [[460/459]]
| 3.77
| {{Monzo| 2 -3 1 0 0 0 -1 0 1 }}
| Twethosuyo
| 23o17uy
| Scanisma, vicewolf comma
|-
| 23
| [[484/483]]
| 3.58
| {{Monzo| 2 -1 0 -1 2 0 0 0 -1 }}
| Twethuloloru
| 23u1oor
| Pittsburghisma
|}


== Scales ==
== Scales ==
Line 1,089: Line 1,393:
* [[Garibaldi12]]
* [[Garibaldi12]]
* [[Garibaldi17]]
* [[Garibaldi17]]
* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic|Gutierrez-Lambeth quasi-subharmonic pentatonic]]
* [[Overtone scale#Over-3 scales|Mode 12]]: 11 10 9 9 8 8 7 7 7 6 6 6


== Instruments ==
== Instruments ==
Line 1,100: Line 1,406:
; [[Bryan Deister]]
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/Zx4xbJhXmgc ''microtonal improvisation in 94edo''] (2025)
* [https://www.youtube.com/shorts/Zx4xbJhXmgc ''microtonal improvisation in 94edo''] (2025)
* [https://www.youtube.com/shorts/HMD8QFpB2-U ''94edo improv''] (2025)
* [https://www.youtube.com/watch?v=KrPQ_tPsvzQ ''Waltz in 94edo''] (2025)
* [https://www.youtube.com/shorts/KJ5dbF4aH2A ''Twinleaf Town - Pokémon Diamond and Pearl (microtonal cover in 94edo)''] (2026)
; [[Eufalesio]]
* [https://soundcloud.com/eufalesio/expanding-my-horizons?in=eufalesio/sets/microtonal-stuff "Expanding my Horizons"] from [https://soundcloud.com/eufalesio/sets/microtonal-stuff ''Microtonal stuff''] (2022)


; [[Cam Taylor]]
; [[Cam Taylor]]
Retrieved from "https://en.xen.wiki/w/94edo"