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== Theory ==
== Theory ==
72edo approximates [[11-limit]] [[just intonation]] exceptionally well. It is [[consistent]] in the [[17-odd-limit]] and is the ninth [[zeta integral edo]]. It is the second edo (after [[58edo|58]]) to be [[consistency|distinctly consistent]] in the [[11-odd-limit]], the first edo to be [[consistency|consistent to distance 2]] in the 11-odd-limit, meaning every interval in the 11-odd-limit is approximated with less than 25% relative error (about 4 cents), and the first edo to be consistent in the 12- and 13-[[odd prime sum limit|odd-prime-sum-limit]].  
72edo approximates [[11-limit]] [[just intonation]] exceptionally well. It is the second edo (after [[58edo|58]]) to be [[consistent]] in the [[17-odd-limit]], and the second edo (also after 58) to be [[consistency|distinctly consistent]] in the [[11-odd-limit]], but it is the first edo to be [[consistency|consistent to distance 2]] in the 11-odd-limit, meaning every interval in the 11-odd-limit is approximated with less than 25% [[relative interval error|relative error]] (about 4 cents). It also has pretty good accuracy for the [[19-limit]], being almost consistent to the entire [[21-odd-limit]] with the only inconsistency occurring at [[19/13]] and its [[octave complement]]. It is the ninth [[zeta integral edo]].


The octave, fifth and fourth are the same size as they would be in 12edo, 72, 42 and 30 steps respectively, but the classic major third ([[5/4]]) measures 23 steps, not 24, and other [[5-limit]] major intervals are one step flat of 12edo while minor ones are one step sharp. The septimal minor seventh ([[7/4]]) is 58 steps, while the undecimal semiaugmented fourth ([[11/8]]) is 33.
The octave, fifth and fourth are the same size as they would be in 12edo, 72, 42 and 30 steps respectively, but the classic major third ([[5/4]]) measures 23 steps, not 24, and other [[5-limit]] major intervals are one step flat of 12edo while minor ones are one step sharp. The septimal minor seventh ([[7/4]]) is 58 steps, while the undecimal semiaugmented fourth ([[11/8]]) is 33.


The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 72edo could be treated as a 2.3.5.7.11.ϕ.17 temperament.
The [[octave reduction|octave reduced]] [[13/1|13th harmonic]] is mapped on 50\72, an interval inherited from [[36edo]] (25\36) that is a very close approximation to [[acoustic phi]], and the [[17/1|17th]] and [[19/1|19th harmonics]] come from 12edo.  


72edo is the smallest multiple of 12edo that (just barely) has another diatonic fifth, 43\72, an extremely hard diatonic fifth suitable for a 5edo [[circulating temperament]].
72edo is the smallest multiple of 12edo that (just barely) has another diatonic fifth, 43\72, an extremely hard diatonic fifth suitable for a 5edo [[circulating temperament]].
Line 38: Line 38:
! Cents
! Cents
! Approximate ratios<ref group="note">As a 19-limit temperament, inconsistent intervals in ''italic''. For a table of intervals by prime limit, see [[Table of 72edo intervals]].</ref>
! Approximate ratios<ref group="note">As a 19-limit temperament, inconsistent intervals in ''italic''. For a table of intervals by prime limit, see [[Table of 72edo intervals]].</ref>
! [[Kite's ups and downs notation|Ups and downs notation]]
! colspan="2" |[[Kite's ups and downs notation|Ups and downs notation]]
([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>6</sup>A1 and d2)
|-
|-
| 0
| 0
| 0.0
| 0.0
| [[1/1]]
| [[1/1]]
|P1
| {{UDnote|step=0}}
| {{UDnote|step=0}}
|-
|-
Line 48: Line 50:
| 16.7
| 16.7
| [[81/80]], [[91/90]], [[99/98]], [[100/99]], [[105/104]]
| [[81/80]], [[91/90]], [[99/98]], [[100/99]], [[105/104]]
|^1
| {{UDnote|step=1}}
| {{UDnote|step=1}}
|-
|-
Line 53: Line 56:
| 33.3
| 33.3
| [[45/44]], [[49/48]], [[50/49]], [[55/54]], [[64/63]]
| [[45/44]], [[49/48]], [[50/49]], [[55/54]], [[64/63]]
|^^
| {{UDnote|step=2}}
| {{UDnote|step=2}}
|-
|-
Line 58: Line 62:
| 50.0
| 50.0
| [[33/32]], [[36/35]], [[40/39]]
| [[33/32]], [[36/35]], [[40/39]]
|^<sup>3</sup>1, v<sup>3</sup>m2
| {{UDnote|step=3}}
| {{UDnote|step=3}}
|-
|-
Line 63: Line 68:
| 66.7
| 66.7
| [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| [[25/24]], [[26/25]], [[27/26]], [[28/27]]
|vvm2
| {{UDnote|step=4}}
| {{UDnote|step=4}}
|-
|-
Line 68: Line 74:
| 83.3
| 83.3
| [[20/19]], [[21/20]], [[22/21]]
| [[20/19]], [[21/20]], [[22/21]]
|vm2
| {{UDnote|step=5}}
| {{UDnote|step=5}}
|-
|-
Line 73: Line 80:
| 100.0
| 100.0
| [[17/16]], [[18/17]], [[19/18]]
| [[17/16]], [[18/17]], [[19/18]]
|m2
| {{UDnote|step=6}}
| {{UDnote|step=6}}
|-
|-
Line 78: Line 86:
| 116.7
| 116.7
| [[15/14]], [[16/15]]
| [[15/14]], [[16/15]]
|^m2
| {{UDnote|step=7}}
| {{UDnote|step=7}}
|-
|-
Line 83: Line 92:
| 133.3
| 133.3
| [[13/12]], [[14/13]], [[27/25]]
| [[13/12]], [[14/13]], [[27/25]]
|^^m2, v~2
| {{UDnote|step=8}}
| {{UDnote|step=8}}
|-
|-
Line 88: Line 98:
| 150.0
| 150.0
| [[12/11]]
| [[12/11]]
|~2
| {{UDnote|step=9}}
| {{UDnote|step=9}}
|-
|-
| 10
| 10
| 166.7
| 166.7
| [[11/10]]
| [[11/10]], [[21/19]]
|^~2, vvM2
| {{UDnote|step=10}}
| {{UDnote|step=10}}
|-
|-
Line 98: Line 110:
| 183.3
| 183.3
| [[10/9]]
| [[10/9]]
|vM2
| {{UDnote|step=11}}
| {{UDnote|step=11}}
|-
|-
Line 103: Line 116:
| 200.0
| 200.0
| [[9/8]], [[19/17]]
| [[9/8]], [[19/17]]
|M2
| {{UDnote|step=12}}
| {{UDnote|step=12}}
|-
|-
Line 108: Line 122:
| 216.7
| 216.7
| [[17/15]], [[25/22]]
| [[17/15]], [[25/22]]
|^M2
| {{UDnote|step=13}}
| {{UDnote|step=13}}
|-
|-
Line 113: Line 128:
| 233.3
| 233.3
| [[8/7]]
| [[8/7]]
|^^M2
| {{UDnote|step=14}}
| {{UDnote|step=14}}
|-
|-
Line 118: Line 134:
| 250.0
| 250.0
| [[15/13]], [[22/19]]
| [[15/13]], [[22/19]]
|^<sup>3</sup>M2, v<sup>3</sup>m3
| {{UDnote|step=15}}
| {{UDnote|step=15}}
|-
|-
Line 123: Line 140:
| 266.7
| 266.7
| [[7/6]]
| [[7/6]]
|vvm3
| {{UDnote|step=16}}
| {{UDnote|step=16}}
|-
|-
Line 128: Line 146:
| 283.3
| 283.3
| [[13/11]], [[20/17]]
| [[13/11]], [[20/17]]
|vm3
| {{UDnote|step=17}}
| {{UDnote|step=17}}
|-
|-
Line 133: Line 152:
| 300.0
| 300.0
| [[19/16]], [[25/21]], [[32/27]]
| [[19/16]], [[25/21]], [[32/27]]
|m3
| {{UDnote|step=18}}
| {{UDnote|step=18}}
|-
|-
Line 138: Line 158:
| 316.7
| 316.7
| [[6/5]]
| [[6/5]]
|^m3
| {{UDnote|step=19}}
| {{UDnote|step=19}}
|-
|-
| 20
| 20
| 333.3
| 333.3
| [[17/14]], [[39/32]], [[40/33]]
| [[17/14]], ''[[39/32]]'', [[40/33]]
|^^m3, v~3
| {{UDnote|step=20}}
| {{UDnote|step=20}}
|-
|-
Line 148: Line 170:
| 350.0
| 350.0
| [[11/9]], [[27/22]]
| [[11/9]], [[27/22]]
|~3
| {{UDnote|step=21}}
| {{UDnote|step=21}}
|-
|-
Line 153: Line 176:
| 366.7
| 366.7
| [[16/13]], [[21/17]], [[26/21]]
| [[16/13]], [[21/17]], [[26/21]]
|^~3, vvM3
| {{UDnote|step=22}}
| {{UDnote|step=22}}
|-
|-
Line 158: Line 182:
| 383.3
| 383.3
| [[5/4]]
| [[5/4]]
|vM3
| {{UDnote|step=23}}
| {{UDnote|step=23}}
|-
|-
Line 163: Line 188:
| 400.0
| 400.0
| [[24/19]]
| [[24/19]]
|M3
| {{UDnote|step=24}}
| {{UDnote|step=24}}
|-
|-
Line 168: Line 194:
| 416.7
| 416.7
| [[14/11]], [[19/15]]
| [[14/11]], [[19/15]]
|^M3
| {{UDnote|step=25}}
| {{UDnote|step=25}}
|-
|-
Line 173: Line 200:
| 433.3
| 433.3
| [[9/7]]
| [[9/7]]
|^^M3
| {{UDnote|step=26}}
| {{UDnote|step=26}}
|-
|-
Line 178: Line 206:
| 450.0
| 450.0
| [[13/10]], [[22/17]]
| [[13/10]], [[22/17]]
|^<sup>3</sup>M3, v<sup>3</sup>4
| {{UDnote|step=27}}
| {{UDnote|step=27}}
|-
|-
Line 183: Line 212:
| 466.7
| 466.7
| [[17/13]], [[21/16]]
| [[17/13]], [[21/16]]
|vv4
| {{UDnote|step=28}}
| {{UDnote|step=28}}
|-
|-
Line 188: Line 218:
| 483.3
| 483.3
| [[33/25]]
| [[33/25]]
|v4
| {{UDnote|step=29}}
| {{UDnote|step=29}}
|-
|-
Line 193: Line 224:
| 500.0
| 500.0
| [[4/3]]
| [[4/3]]
|P4
| {{UDnote|step=30}}
| {{UDnote|step=30}}
|-
|-
Line 198: Line 230:
| 516.7
| 516.7
| [[27/20]]
| [[27/20]]
|^4
| {{UDnote|step=31}}
| {{UDnote|step=31}}
|-
|-
Line 203: Line 236:
| 533.3
| 533.3
| [[15/11]], [[19/14]], ''[[26/19]]''
| [[15/11]], [[19/14]], ''[[26/19]]''
|^^4, v~4
| {{UDnote|step=32}}
| {{UDnote|step=32}}
|-
|-
Line 208: Line 242:
| 550.0
| 550.0
| [[11/8]]
| [[11/8]]
|~4
| {{UDnote|step=33}}
| {{UDnote|step=33}}
|-
|-
Line 213: Line 248:
| 566.7
| 566.7
| [[18/13]], [[25/18]]
| [[18/13]], [[25/18]]
|^~4, vvA4
| {{UDnote|step=34}}
| {{UDnote|step=34}}
|-
|-
Line 218: Line 254:
| 583.3
| 583.3
| [[7/5]]
| [[7/5]]
|vA4, vd5
| {{UDnote|step=35}}
| {{UDnote|step=35}}
|-
|-
Line 223: Line 260:
| 600.0
| 600.0
| [[17/12]], [[24/17]]
| [[17/12]], [[24/17]]
|A4, d5
| {{UDnote|step=36}}
| {{UDnote|step=36}}
|-
|-
Line 228: Line 266:
| 616.7
| 616.7
| [[10/7]]
| [[10/7]]
|^A4, ^d5
| {{UDnote|step=37}}
| {{UDnote|step=37}}
|-
|-
Line 233: Line 272:
| 633.3
| 633.3
| [[13/9]], [[36/25]]
| [[13/9]], [[36/25]]
|v~5, ^^d5
| {{UDnote|step=38}}
| {{UDnote|step=38}}
|-
|-
Line 238: Line 278:
| 650.0
| 650.0
| [[16/11]]
| [[16/11]]
|~5
| {{UDnote|step=39}}
| {{UDnote|step=39}}
|-
|-
Line 243: Line 284:
| 666.7
| 666.7
| ''[[19/13]]'', [[22/15]], [[28/19]]
| ''[[19/13]]'', [[22/15]], [[28/19]]
|vv5, ^~5
| {{UDnote|step=40}}
| {{UDnote|step=40}}
|-
|-
Line 248: Line 290:
| 683.3
| 683.3
| [[40/27]]
| [[40/27]]
|v5
| {{UDnote|step=41}}
| {{UDnote|step=41}}
|-
|-
Line 253: Line 296:
| 700.0
| 700.0
| [[3/2]]
| [[3/2]]
|P5
| {{UDnote|step=42}}
| {{UDnote|step=42}}
|-
|-
Line 258: Line 302:
| 716.7
| 716.7
| [[50/33]]
| [[50/33]]
|^5
| {{UDnote|step=43}}
| {{UDnote|step=43}}
|-
|-
Line 263: Line 308:
| 733.3
| 733.3
| [[26/17]], [[32/21]]
| [[26/17]], [[32/21]]
|^^5
| {{UDnote|step=44}}
| {{UDnote|step=44}}
|-
|-
Line 268: Line 314:
| 750.0
| 750.0
| [[17/11]], [[20/13]]
| [[17/11]], [[20/13]]
|^<sup>3</sup>5, v<sup>3</sup>m6
| {{UDnote|step=45}}
| {{UDnote|step=45}}
|-
|-
Line 273: Line 320:
| 766.7
| 766.7
| [[14/9]]
| [[14/9]]
|vvm6
| {{UDnote|step=46}}
| {{UDnote|step=46}}
|-
|-
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| 783.3
| 783.3
| [[11/7]], [[30/19]]
| [[11/7]], [[30/19]]
|vm6
| {{UDnote|step=47}}
| {{UDnote|step=47}}
|-
|-
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| 800.0
| 800.0
| [[19/12]]
| [[19/12]]
|m6
| {{UDnote|step=48}}
| {{UDnote|step=48}}
|-
|-
Line 288: Line 338:
| 816.7
| 816.7
| [[8/5]]
| [[8/5]]
|^m6
| {{UDnote|step=49}}
| {{UDnote|step=49}}
|-
|-
Line 293: Line 344:
| 833.3
| 833.3
| [[13/8]], [[21/13]], [[34/21]]
| [[13/8]], [[21/13]], [[34/21]]
|^^m6, v~6
| {{UDnote|step=50}}
| {{UDnote|step=50}}
|-
|-
Line 298: Line 350:
| 850.0
| 850.0
| [[18/11]], [[44/27]]
| [[18/11]], [[44/27]]
|~6
| {{UDnote|step=51}}
| {{UDnote|step=51}}
|-
|-
| 52
| 52
| 866.7
| 866.7
| [[28/17]], [[33/20]], [[64/39]]
| [[28/17]], [[33/20]], ''[[64/39]]''
|^~6, vvM6
| {{UDnote|step=52}}
| {{UDnote|step=52}}
|-
|-
Line 308: Line 362:
| 883.3
| 883.3
| [[5/3]]
| [[5/3]]
|vM6
| {{UDnote|step=53}}
| {{UDnote|step=53}}
|-
|-
Line 313: Line 368:
| 900.0
| 900.0
| [[27/16]], [[32/19]], [[42/25]]
| [[27/16]], [[32/19]], [[42/25]]
|M6
| {{UDnote|step=54}}
| {{UDnote|step=54}}
|-
|-
Line 318: Line 374:
| 916.7
| 916.7
| [[17/10]], [[22/13]]
| [[17/10]], [[22/13]]
|^M6
| {{UDnote|step=55}}
| {{UDnote|step=55}}
|-
|-
Line 323: Line 380:
| 933.3
| 933.3
| [[12/7]]
| [[12/7]]
|^^M6
| {{UDnote|step=56}}
| {{UDnote|step=56}}
|-
|-
Line 328: Line 386:
| 950.0
| 950.0
| [[19/11]], [[26/15]]
| [[19/11]], [[26/15]]
|^<sup>3</sup>M6, v<sup>3</sup>m7
| {{UDnote|step=57}}
| {{UDnote|step=57}}
|-
|-
Line 333: Line 392:
| 966.7
| 966.7
| [[7/4]]
| [[7/4]]
|vvm7
| {{UDnote|step=58}}
| {{UDnote|step=58}}
|-
|-
Line 338: Line 398:
| 983.3
| 983.3
| [[30/17]], [[44/25]]
| [[30/17]], [[44/25]]
|vm7
| {{UDnote|step=59}}
| {{UDnote|step=59}}
|-
|-
Line 343: Line 404:
| 1000.0
| 1000.0
| [[16/9]], [[34/19]]
| [[16/9]], [[34/19]]
|m7
| {{UDnote|step=60}}
| {{UDnote|step=60}}
|-
|-
Line 348: Line 410:
| 1016.7
| 1016.7
| [[9/5]]
| [[9/5]]
|^m7
| {{UDnote|step=61}}
| {{UDnote|step=61}}
|-
|-
| 62
| 62
| 1033.3
| 1033.3
| [[20/11]]
| [[20/11]], [[38/21]]
|^^m7, v~7
| {{UDnote|step=62}}
| {{UDnote|step=62}}
|-
|-
Line 358: Line 422:
| 1050.0
| 1050.0
| [[11/6]]
| [[11/6]]
|~7
| {{UDnote|step=63}}
| {{UDnote|step=63}}
|-
|-
Line 363: Line 428:
| 1066.7
| 1066.7
| [[13/7]], [[24/13]], [[50/27]]
| [[13/7]], [[24/13]], [[50/27]]
|^~7, vvM7
| {{UDnote|step=64}}
| {{UDnote|step=64}}
|-
|-
Line 368: Line 434:
| 1083.3
| 1083.3
| [[15/8]], [[28/15]]
| [[15/8]], [[28/15]]
|vM7
| {{UDnote|step=65}}
| {{UDnote|step=65}}
|-
|-
Line 373: Line 440:
| 1100.0
| 1100.0
| [[17/9]], [[32/17]], [[36/19]]
| [[17/9]], [[32/17]], [[36/19]]
|M7
| {{UDnote|step=66}}
| {{UDnote|step=66}}
|-
|-
Line 378: Line 446:
| 1116.7
| 1116.7
| [[19/10]], [[21/11]], [[40/21]]
| [[19/10]], [[21/11]], [[40/21]]
|^M7
| {{UDnote|step=67}}
| {{UDnote|step=67}}
|-
|-
Line 383: Line 452:
| 1133.3
| 1133.3
| [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| [[25/13]], [[27/14]], [[48/25]], [[52/27]]
|^^M7
| {{UDnote|step=68}}
| {{UDnote|step=68}}
|-
|-
Line 388: Line 458:
| 1150.0
| 1150.0
| [[35/18]], [[39/20]], [[64/33]]
| [[35/18]], [[39/20]], [[64/33]]
|^<sup>3</sup>M7, v<sup>3</sup>8
| {{UDnote|step=69}}
| {{UDnote|step=69}}
|-
|-
Line 393: Line 464:
| 1166.7
| 1166.7
| [[49/25]], [[55/28]], [[63/32]], [[88/45]], [[96/49]]
| [[49/25]], [[55/28]], [[63/32]], [[88/45]], [[96/49]]
|vv8
| {{UDnote|step=70}}
| {{UDnote|step=70}}
|-
|-
Line 398: Line 470:
| 1183.3
| 1183.3
| [[99/50]], [[160/81]], [[180/91]], [[196/99]], [[208/105]]
| [[99/50]], [[160/81]], [[180/91]], [[196/99]], [[208/105]]
|v8
| {{UDnote|step=71}}
| {{UDnote|step=71}}
|-
|-
Line 403: Line 476:
| 1200.0
| 1200.0
| [[2/1]]
| [[2/1]]
|P8
| {{UDnote|step=72}}
| {{UDnote|step=72}}
|}
|}
Line 409: Line 483:
=== Proposed interval names and solfèges ===
=== Proposed interval names and solfèges ===
{| class="wikitable center-all right-2 left-4 left-7 mw-collapsible mw-collapsed"
{| class="wikitable center-all right-2 left-4 left-7 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
|+ style="font-size: 105%; white-space: nowrap;" | Table of proposed interval names and solfèges
|-
|-
! #
! #
Line 1,285: Line 1,359:


== Notation ==
== Notation ==
=== Ups and downs notation ===
=== Stein–Zimmermann–Gould notation ===
72edo can be notated with ups and downs, spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.
[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
{{Sharpness-sharp6-szg}}
 
If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:
{{Sharpness-sharp6-qt-szg}}
 
=== Kite's ups and downs notation ===
72edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.
{{Ups and downs sharpness}}
{{Ups and downs sharpness}}


Half-sharps and half-flats can be used to avoid triple arrows:
Half-sharps and half-flats can be used to avoid triple arrows:
{{Ups and downs sharpness|72|true}}
{{Ups and downs sharpness|72|true}}
[[Alternative symbols for ups and downs notation#Sharp-6| Alternative ups and downs]] have sharps and flats with arrows borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp6}}
If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:
{{Sharpness-sharp6-qt}}


=== Sagittal notation ===
=== Sagittal notation ===
Line 1,326: Line 1,401:


=== Zeta properties ===
=== Zeta properties ===
72edo is the ninth [[zeta integral edo]], as well as being a peak and gap edo, and the maximum value of the [[the Riemann zeta function and tuning#The Z function|Z function]] in the region near 72 occurs at 71.9506, giving an octave of 1200.824 cents, the stretched octaves of the zeta tuning. Below is a plot of Z in the region around 72.
72edo is the ninth [[zeta integral edo]], as well as being a peak and gap edo, and the maximum value of the [[Z function]] in the region near 72 occurs at 71.9506, giving an octave of 1200.824 cents, the stretched octaves of the zeta tuning. Below is a plot of Z in the region around 72.


[[File:plot72.png|alt=plot72.png|plot72.png]]
[[File:plot72.png|alt=plot72.png|plot72.png]]
Line 1,669: Line 1,744:
| 516.7
| 516.7
| 27/20
| 27/20
| [[Marvo]] / [[zarvo]]
| [[Gravity]] / [[marvo]] / [[zarvo]]
|-
|-
| 1
| 1
Line 1,741: Line 1,816:
| 316.7<br>(50.0)
| 316.7<br>(50.0)
| 6/5<br>(36/35)
| 6/5<br>(36/35)
| [[Ennealimmal]] / ennealimnic
| [[Ennealimmal]] / ennealimnic / ennealiminal
|-
|-
| 9
| 9
Line 1,773: Line 1,848:
| [[Gamelstearn]]
| [[Gamelstearn]]
|}
|}
<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


== Octave stretch or compression ==
== Octave stretch or compression ==
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== Music ==
== Music ==
; [[Tolgahan Çoğulu]]
* [https://www.youtube.com/watch?v=BItT4f8MOiI ''Ne ağlarsın benim zülfü siyahım''] (from the UnTwelving 2026 convention) – transcription by [[Stephen Weigel]]
; [[Bryan Deister]]
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/VwVp3RVao_k ''microtonal improvisation in 72edo''] (2025)
* [https://www.youtube.com/shorts/VwVp3RVao_k ''microtonal improvisation in 72edo''] (2025)
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; [[Jake Freivald]]
; [[Jake Freivald]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lazy%20Sunday.mp3 ''Lazy Sunday'']{{dead link}} in the [[lazysunday]] scale
* [https://web.archive.org/web/20201127014336/http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lazy%20Sunday.mp3 ''Lazy Sunday''] in the [[lazysunday]] scale


{{Wikipedia|In vain (Haas)}}
{{Wikipedia|In vain (Haas)}}
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; [[Claudi Meneghin]]
; [[Claudi Meneghin]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-72-edo.mp3 ''Twinkle canon – 72 edo'']{{dead link}}
* [https://web.archive.org/web/20201127015744/http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-72-edo.mp3 ''Twinkle canon – 72 edo'']
* [https://www.youtube.com/watch?v=zR0NDgh4944 ''The Miracle Canon'', 3-in-1 on a Ground]
* [https://www.youtube.com/watch?v=zR0NDgh4944 ''The Miracle Canon'', 3-in-1 on a Ground]
* [https://www.youtube.com/watch?v=w6Bckog1eOM ''Sicilienne in Miracle'']
* [https://www.youtube.com/watch?v=w6Bckog1eOM ''Sicilienne in Miracle'']
* [https://www.youtube.com/watch?v=QKeZLtFHfNU ''Arietta with 5 Variations'', for Organ] (2024)
* [https://www.youtube.com/watch?v=QKeZLtFHfNU ''Arietta with 5 Variations'', for Organ] (2024)
; [https://www.youtube.com/@Mintsoda_15/videos Mintsoda_15]
* [https://www.youtube.com/watch?v=eA8S746K9_A ''Quarter-tone Impromptu-72 TET''] (2022)


; [[Prent Rodgers]]
; [[Prent Rodgers]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/drum12a-c-t9.mp3 ''June Gloom #9'']{{dead link}}
* [https://web.archive.org/web/20201127012907/http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/drum12a-c-t9.mp3 ''June Gloom #9'']


; [[Gene Ward Smith]]
; [[Gene Ward Smith]]
* [https://www.archive.org/details/Kotekant ''Kotekant''] [https://www.archive.org/download/Kotekant/kotekant.mp3 play] (2010)
* [https://www.archive.org/details/Kotekant ''Kotekant''] [https://www.archive.org/download/Kotekant/kotekant.mp3 play] (2010)


;[[Ivan Wyschnegradsky]]
; [[Ivan Wyschnegradsky]]
* [https://www.youtube.com/watch?v=RCcJHCkYQ6U ''Arc-en-ciel, for 6 pianos in twelfth tones, Op. 37''] (1956)
* [https://www.youtube.com/watch?v=RCcJHCkYQ6U ''Arc-en-ciel, for 6 pianos in twelfth tones, Op. 37''] (1956)


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