57edo: Difference between revisions
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== Theory == | == Theory == | ||
57edo is an excellent tuning for the 2.5/3.7.11.13.17.19 [[just intonation subgroup]]. One way to describe 57edo is that it has a [[5-limit]] part consisting of three [[ring number|ring]]s of 19edo, plus a no-threes no-fives part which is much more accurate. | 57edo is an excellent tuning for the 2.5/3.7.11.13.17.19 [[just intonation subgroup]]. One way to describe 57edo is that it has a [[5-limit]] part consisting of three [[ring number|ring]]s of [[19edo]], plus a no-threes no-fives part which is much more accurate. | ||
Using the full prime-limit [[patent val]], the equal temperament tempers out [[81/80]], [[1029/1024]], and [[3125/3072]] in the 7-limit; and [[99/98]], [[385/384]], [[441/440]], and [[625/616]] in the [[11-limit]]. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate [[11/8]], which is 26\57. This gives the [[19-limit]] 46 & 57 temperament [[heinz]]. It can also be used to tune [[mothra]] as well as [[trismegistus]]. | Using the full prime-limit [[patent val]], the equal temperament tempers out [[81/80]], [[1029/1024]], and [[3125/3072]] in the 7-limit; and [[99/98]], [[385/384]], [[441/440]], and [[625/616]] in the [[11-limit]]. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate [[11/8]], which is 26\57. This gives the [[19-limit]] 46 & 57 temperament [[heinz]]. It can also be used to tune [[mothra]] as well as [[trismegistus]]. | ||
57edo is interesting in that it is a [[dual-fifth]] system where both fifths are somewhat plausible. The 57b val uses the alternative fifth of 715.789 cents. While not very accurate in the 5 and 7-limits (being even worse than 19edo), it does support some interesting temperaments like [[sixix]] and a near-perfect 1/2-comma [[archy]] (such that the diatonic minor seventh is almost exactly [[7/4]]). | |||
=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|57}} | {{Harmonics in equal|57}} | ||
{{Harmonics in equal|57|intervals=odd|columns=11|prec=2|start=12|collapsed=true|title=Approximation of odd harmonics in 57edo (continued)}} | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
57edo contains [[3edo]] and [[19edo]] as subsets. | 57edo contains [[3edo]] and [[19edo]] as subsets. Tripling 57edo yields [[171edo]], which corrects the 3rd and 5th harmonics. | ||
== Intervals == | == Intervals == | ||
{| class="wikitable center-1 right-2 center- | {| class="wikitable center-1 right-2 center-4 center-5" | ||
|- | |- | ||
! # | ! # | ||
! [[Cent]]s | ! [[Cent]]s | ||
! [[ | ! Approximate ratios* | ||
! [[ | ! [[Kite's ups and downs notation|Ups and downs notation]]<br>(Flat fifth 11\19) | ||
! [[Kite's ups and downs notation|Ups and downs notation]]<br>(Sharp fifth 34\57) | |||
|- | |- | ||
| 0 | | 0 | ||
| 0.00 | | 0.00 | ||
|[[1/1]] | |||
| {{UDnote|step=0}} | | {{UDnote|step=0}} | ||
| {{UDnote|fifth=34|step=0}} | | {{UDnote|fifth=34|step=0}} | ||
| Line 28: | Line 33: | ||
| 1 | | 1 | ||
| 21.05 | | 21.05 | ||
| | |||
| {{UDnote|step=1}} | | {{UDnote|step=1}} | ||
| {{UDnote|fifth=34|step=1}} | | {{UDnote|fifth=34|step=1}} | ||
| Line 33: | Line 39: | ||
| 2 | | 2 | ||
| 42.11 | | 42.11 | ||
| | |||
| {{UDnote|step=2}} | | {{UDnote|step=2}} | ||
| {{UDnote|fifth=34|step=2}} | | {{UDnote|fifth=34|step=2}} | ||
| Line 38: | Line 45: | ||
| 3 | | 3 | ||
| 63.16 | | 63.16 | ||
|[[29/28]] | |||
| {{UDnote|step=3}} | | {{UDnote|step=3}} | ||
| {{UDnote|fifth=34|step=3}} | | {{UDnote|fifth=34|step=3}} | ||
| Line 43: | Line 51: | ||
| 4 | | 4 | ||
| 84.21 | | 84.21 | ||
|[[20/19]], [[21/20]], [[22/21]] | |||
| {{UDnote|step=4}} | | {{UDnote|step=4}} | ||
| {{UDnote|fifth=34|step=4}} | | {{UDnote|fifth=34|step=4}} | ||
| Line 48: | Line 57: | ||
| 5 | | 5 | ||
| 105.26 | | 105.26 | ||
|[[17/16]], [[33/31]] | |||
| {{UDnote|step=5}} | | {{UDnote|step=5}} | ||
| {{UDnote|fifth=34|step=5}} | | {{UDnote|fifth=34|step=5}} | ||
| Line 53: | Line 63: | ||
| 6 | | 6 | ||
| 126.32 | | 126.32 | ||
|[[14/13]], ''[[16/15]]'' | |||
| {{UDnote|step=6}} | | {{UDnote|step=6}} | ||
| {{UDnote|fifth=34|step=6}} | | {{UDnote|fifth=34|step=6}} | ||
| Line 58: | Line 69: | ||
| 7 | | 7 | ||
| 147.37 | | 147.37 | ||
|[[12/11]] | |||
| {{UDnote|step=7}} | | {{UDnote|step=7}} | ||
| {{UDnote|fifth=34|step=7}} | | {{UDnote|fifth=34|step=7}} | ||
| Line 63: | Line 75: | ||
| 8 | | 8 | ||
| 168.42 | | 168.42 | ||
|[[11/10]], [[32/29]] | |||
| {{UDnote|step=8}} | | {{UDnote|step=8}} | ||
| {{UDnote|fifth=34|step=8}} | | {{UDnote|fifth=34|step=8}} | ||
| Line 68: | Line 81: | ||
| 9 | | 9 | ||
| 189.47 | | 189.47 | ||
|[[19/17]], [[29/26]],<br>[[10/9]], ''[[9/8]]'' | |||
| {{UDnote|step=9}} | | {{UDnote|step=9}} | ||
| {{UDnote|fifth=34|step=9}} | | {{UDnote|fifth=34|step=9}} | ||
| Line 73: | Line 87: | ||
| 10 | | 10 | ||
| 210.53 | | 210.53 | ||
|[[26/23]] | |||
| {{UDnote|step=10}} | | {{UDnote|step=10}} | ||
| {{UDnote|fifth=34|step=10}} | | {{UDnote|fifth=34|step=10}} | ||
| Line 78: | Line 93: | ||
| 11 | | 11 | ||
| 231.58 | | 231.58 | ||
|[[8/7]] | |||
| {{UDnote|step=11}} | | {{UDnote|step=11}} | ||
| {{UDnote|fifth=34|step=11}} | | {{UDnote|fifth=34|step=11}} | ||
| Line 83: | Line 99: | ||
| 12 | | 12 | ||
| 252.63 | | 252.63 | ||
|[[22/19]] | |||
| {{UDnote|step=12}} | | {{UDnote|step=12}} | ||
| {{UDnote|fifth=34|step=12}} | | {{UDnote|fifth=34|step=12}} | ||
| Line 88: | Line 105: | ||
| 13 | | 13 | ||
| 273.68 | | 273.68 | ||
|[[7/6]], [[34/29]] | |||
| {{UDnote|step=13}} | | {{UDnote|step=13}} | ||
| {{UDnote|fifth=34|step=13}} | | {{UDnote|fifth=34|step=13}} | ||
| Line 93: | Line 111: | ||
| 14 | | 14 | ||
| 294.74 | | 294.74 | ||
|[[19/16]] | |||
| {{UDnote|step=14}} | | {{UDnote|step=14}} | ||
| {{UDnote|fifth=34|step=14}} | | {{UDnote|fifth=34|step=14}} | ||
| Line 98: | Line 117: | ||
| 15 | | 15 | ||
| 315.79 | | 315.79 | ||
|[[6/5]] | |||
| {{UDnote|step=15}} | | {{UDnote|step=15}} | ||
| {{UDnote|fifth=34|step=15}} | | {{UDnote|fifth=34|step=15}} | ||
| Line 103: | Line 123: | ||
| 16 | | 16 | ||
| 336.84 | | 336.84 | ||
|[[17/14]], [[28/23]] | |||
| {{UDnote|step=16}} | | {{UDnote|step=16}} | ||
| {{UDnote|fifth=34|step=16}} | | {{UDnote|fifth=34|step=16}} | ||
| Line 108: | Line 129: | ||
| 17 | | 17 | ||
| 357.89 | | 357.89 | ||
|[[16/13]] | |||
| {{UDnote|step=17}} | | {{UDnote|step=17}} | ||
| {{UDnote|fifth=34|step=17}} | | {{UDnote|fifth=34|step=17}} | ||
| Line 113: | Line 135: | ||
| 18 | | 18 | ||
| 378.95 | | 378.95 | ||
|[[5/4]] | |||
| {{UDnote|step=18}} | | {{UDnote|step=18}} | ||
| {{UDnote|fifth=34|step=18}} | | {{UDnote|fifth=34|step=18}} | ||
| Line 118: | Line 141: | ||
| 19 | | 19 | ||
| 400.00 | | 400.00 | ||
|[[24/19]], [[29/23]] | |||
| {{UDnote|step=19}} | | {{UDnote|step=19}} | ||
| {{UDnote|fifth=34|step=19}} | | {{UDnote|fifth=34|step=19}} | ||
| Line 123: | Line 147: | ||
| 20 | | 20 | ||
| 421.05 | | 421.05 | ||
|[[14/11]], ''[[9/7]]'' | |||
| {{UDnote|step=20}} | | {{UDnote|step=20}} | ||
| {{UDnote|fifth=34|step=20}} | | {{UDnote|fifth=34|step=20}} | ||
| Line 128: | Line 153: | ||
| 21 | | 21 | ||
| 442.11 | | 442.11 | ||
|[[22/17]], [[31/24]] | |||
| {{UDnote|step=21}} | | {{UDnote|step=21}} | ||
| {{UDnote|fifth=34|step=21}} | | {{UDnote|fifth=34|step=21}} | ||
| Line 133: | Line 159: | ||
| 22 | | 22 | ||
| 463.16 | | 463.16 | ||
|[[17/13]], [[21/16]], [[38/29]] | |||
| {{UDnote|step=22}} | | {{UDnote|step=22}} | ||
| {{UDnote|fifth=34|step=22}} | | {{UDnote|fifth=34|step=22}} | ||
| Line 138: | Line 165: | ||
| 23 | | 23 | ||
| 484.21 | | 484.21 | ||
|[[33/25]] | |||
| {{UDnote|step=23}} | | {{UDnote|step=23}} | ||
| {{UDnote|fifth=34|step=23}} | | {{UDnote|fifth=34|step=23}} | ||
| Line 143: | Line 171: | ||
| 24 | | 24 | ||
| 505.26 | | 505.26 | ||
|[[4/3]] | |||
| {{UDnote|step=24}} | | {{UDnote|step=24}} | ||
| {{UDnote|fifth=34|step=24}} | | {{UDnote|fifth=34|step=24}} | ||
| Line 148: | Line 177: | ||
| 25 | | 25 | ||
| 526.32 | | 526.32 | ||
|[[19/14]], [[42/31]], [[23/17]] | |||
| {{UDnote|step=25}} | | {{UDnote|step=25}} | ||
| {{UDnote|fifth=34|step=25}} | | {{UDnote|fifth=34|step=25}} | ||
| Line 153: | Line 183: | ||
| 26 | | 26 | ||
| 547.37 | | 547.37 | ||
|[[11/8]], [[26/19]] | |||
| {{UDnote|step=26}} | | {{UDnote|step=26}} | ||
| {{UDnote|fifth=34|step=26}} | | {{UDnote|fifth=34|step=26}} | ||
| Line 158: | Line 189: | ||
| 27 | | 27 | ||
| 568.42 | | 568.42 | ||
|[[25/18]], [[32/23]] | |||
| {{UDnote|step=27}} | | {{UDnote|step=27}} | ||
| {{UDnote|fifth=34|step=27}} | | {{UDnote|fifth=34|step=27}} | ||
| Line 163: | Line 195: | ||
| 28 | | 28 | ||
| 589.47 | | 589.47 | ||
|[[31/22]] | |||
| {{UDnote|step=28}} | | {{UDnote|step=28}} | ||
| {{UDnote|fifth=34|step=28}} | | {{UDnote|fifth=34|step=28}} | ||
| Line 168: | Line 201: | ||
| 29 | | 29 | ||
| 610.53 | | 610.53 | ||
|[[44/31]] | |||
| {{UDnote|step=29}} | | {{UDnote|step=29}} | ||
| {{UDnote|fifth=34|step=29}} | | {{UDnote|fifth=34|step=29}} | ||
| Line 173: | Line 207: | ||
| 30 | | 30 | ||
| 631.58 | | 631.58 | ||
|[[23/16]] | |||
| {{UDnote|step=30}} | | {{UDnote|step=30}} | ||
| {{UDnote|fifth=34|step=30}} | | {{UDnote|fifth=34|step=30}} | ||
| Line 178: | Line 213: | ||
| 31 | | 31 | ||
| 652.63 | | 652.63 | ||
|[[16/11]], [[19/13]] | |||
| {{UDnote|step=31}} | | {{UDnote|step=31}} | ||
| {{UDnote|fifth=34|step=31}} | | {{UDnote|fifth=34|step=31}} | ||
| Line 183: | Line 219: | ||
| 32 | | 32 | ||
| 673.68 | | 673.68 | ||
|[[28/19]], [[31/21]], [[34/23]] | |||
| {{UDnote|step=32}} | | {{UDnote|step=32}} | ||
| {{UDnote|fifth=34|step=32}} | | {{UDnote|fifth=34|step=32}} | ||
| Line 188: | Line 225: | ||
| 33 | | 33 | ||
| 694.74 | | 694.74 | ||
|[[3/2]] | |||
| {{UDnote|step=33}} | | {{UDnote|step=33}} | ||
| {{UDnote|fifth=34|step=33}} | | {{UDnote|fifth=34|step=33}} | ||
| Line 193: | Line 231: | ||
| 34 | | 34 | ||
| 715.79 | | 715.79 | ||
|[[50/33]] | |||
| {{UDnote|step=34}} | | {{UDnote|step=34}} | ||
| {{UDnote|fifth=34|step=34}} | | {{UDnote|fifth=34|step=34}} | ||
| Line 198: | Line 237: | ||
| 35 | | 35 | ||
| 736.84 | | 736.84 | ||
|[[26/17]], [[32/21]], [[29/19]] | |||
| {{UDnote|step=35}} | | {{UDnote|step=35}} | ||
| {{UDnote|fifth=34|step=35}} | | {{UDnote|fifth=34|step=35}} | ||
| Line 203: | Line 243: | ||
| 36 | | 36 | ||
| 757.89 | | 757.89 | ||
|[[17/11]], [[31/20]] | |||
| {{UDnote|step=36}} | | {{UDnote|step=36}} | ||
| {{UDnote|fifth=34|step=36}} | | {{UDnote|fifth=34|step=36}} | ||
| Line 208: | Line 249: | ||
| 37 | | 37 | ||
| 778.95 | | 778.95 | ||
|[[11/7]], ''[[14/9]]'' | |||
| {{UDnote|step=37}} | | {{UDnote|step=37}} | ||
| {{UDnote|fifth=34|step=37}} | | {{UDnote|fifth=34|step=37}} | ||
| Line 213: | Line 255: | ||
| 38 | | 38 | ||
| 800.00 | | 800.00 | ||
|[[19/12]] | |||
| {{UDnote|step=38}} | | {{UDnote|step=38}} | ||
| {{UDnote|fifth=34|step=38}} | | {{UDnote|fifth=34|step=38}} | ||
| Line 218: | Line 261: | ||
| 39 | | 39 | ||
| 821.05 | | 821.05 | ||
|[[8/5]] | |||
| {{UDnote|step=39}} | | {{UDnote|step=39}} | ||
| {{UDnote|fifth=34|step=39}} | | {{UDnote|fifth=34|step=39}} | ||
| Line 223: | Line 267: | ||
| 40 | | 40 | ||
| 842.11 | | 842.11 | ||
|[[13/8]] | |||
| {{UDnote|step=40}} | | {{UDnote|step=40}} | ||
| {{UDnote|fifth=34|step=40}} | | {{UDnote|fifth=34|step=40}} | ||
| Line 228: | Line 273: | ||
| 41 | | 41 | ||
| 863.16 | | 863.16 | ||
|[[23/14]], [[28/17]], [[33/20]] | |||
| {{UDnote|step=41}} | | {{UDnote|step=41}} | ||
| {{UDnote|fifth=34|step=41}} | | {{UDnote|fifth=34|step=41}} | ||
| Line 233: | Line 279: | ||
| 42 | | 42 | ||
| 884.21 | | 884.21 | ||
|[[5/3]] | |||
| {{UDnote|step=42}} | | {{UDnote|step=42}} | ||
| {{UDnote|fifth=34|step=42}} | | {{UDnote|fifth=34|step=42}} | ||
| Line 238: | Line 285: | ||
| 43 | | 43 | ||
| 905.26 | | 905.26 | ||
|[[32/19]] | |||
| {{UDnote|step=43}} | | {{UDnote|step=43}} | ||
| {{UDnote|fifth=34|step=43}} | | {{UDnote|fifth=34|step=43}} | ||
| Line 243: | Line 291: | ||
| 44 | | 44 | ||
| 926.32 | | 926.32 | ||
|[[12/7]], [[29/17]] | |||
| {{UDnote|step=44}} | | {{UDnote|step=44}} | ||
| {{UDnote|fifth=34|step=44}} | | {{UDnote|fifth=34|step=44}} | ||
| Line 248: | Line 297: | ||
| 45 | | 45 | ||
| 947.37 | | 947.37 | ||
|[[19/11]] | |||
| {{UDnote|step=45}} | | {{UDnote|step=45}} | ||
| {{UDnote|fifth=34|step=45}} | | {{UDnote|fifth=34|step=45}} | ||
| Line 253: | Line 303: | ||
| 46 | | 46 | ||
| 968.42 | | 968.42 | ||
|[[7/4]] | |||
| {{UDnote|step=46}} | | {{UDnote|step=46}} | ||
| {{UDnote|fifth=34|step=46}} | | {{UDnote|fifth=34|step=46}} | ||
| Line 258: | Line 309: | ||
| 47 | | 47 | ||
| 989.47 | | 989.47 | ||
|[[23/13]] | |||
| {{UDnote|step=47}} | | {{UDnote|step=47}} | ||
| {{UDnote|fifth=34|step=47}} | | {{UDnote|fifth=34|step=47}} | ||
| Line 263: | Line 315: | ||
| 48 | | 48 | ||
| 1010.53 | | 1010.53 | ||
|[[34/19]], [[52/29]],<br>[[9/5]], ''[[16/9]]'' | |||
| {{UDnote|step=48}} | | {{UDnote|step=48}} | ||
| {{UDnote|fifth=34|step=48}} | | {{UDnote|fifth=34|step=48}} | ||
| Line 268: | Line 321: | ||
| 49 | | 49 | ||
| 1031.58 | | 1031.58 | ||
|[[20/11]], [[29/16]] | |||
| {{UDnote|step=49}} | | {{UDnote|step=49}} | ||
| {{UDnote|fifth=34|step=49}} | | {{UDnote|fifth=34|step=49}} | ||
| Line 273: | Line 327: | ||
| 50 | | 50 | ||
| 1052.63 | | 1052.63 | ||
|[[11/6]] | |||
| {{UDnote|step=50}} | | {{UDnote|step=50}} | ||
| {{UDnote|fifth=34|step=50}} | | {{UDnote|fifth=34|step=50}} | ||
| Line 278: | Line 333: | ||
| 51 | | 51 | ||
| 1073.68 | | 1073.68 | ||
|[[13/7]], ''[[15/8]]'' | |||
| {{UDnote|step=51}} | | {{UDnote|step=51}} | ||
| {{UDnote|fifth=34|step=51}} | | {{UDnote|fifth=34|step=51}} | ||
| Line 283: | Line 339: | ||
| 52 | | 52 | ||
| 1094.74 | | 1094.74 | ||
|[[32/17]] | |||
| {{UDnote|step=52}} | | {{UDnote|step=52}} | ||
| {{UDnote|fifth=34|step=52}} | | {{UDnote|fifth=34|step=52}} | ||
| Line 288: | Line 345: | ||
| 53 | | 53 | ||
| 1115.79 | | 1115.79 | ||
|[[19/10]], [[21/11]] | |||
| {{UDnote|step=53}} | | {{UDnote|step=53}} | ||
| {{UDnote|fifth=34|step=53}} | | {{UDnote|fifth=34|step=53}} | ||
| Line 293: | Line 351: | ||
| 54 | | 54 | ||
| 1136.84 | | 1136.84 | ||
|[[56/29]] | |||
| {{UDnote|step=54}} | | {{UDnote|step=54}} | ||
| {{UDnote|fifth=34|step=54}} | | {{UDnote|fifth=34|step=54}} | ||
| Line 298: | Line 357: | ||
| 55 | | 55 | ||
| 1157.89 | | 1157.89 | ||
| | |||
| {{UDnote|step=55}} | | {{UDnote|step=55}} | ||
| {{UDnote|fifth=34|step=55}} | | {{UDnote|fifth=34|step=55}} | ||
| Line 303: | Line 363: | ||
| 56 | | 56 | ||
| 1178.95 | | 1178.95 | ||
| | |||
| {{UDnote|step=56}} | | {{UDnote|step=56}} | ||
| {{UDnote|fifth=34|step=56}} | | {{UDnote|fifth=34|step=56}} | ||
| Line 308: | Line 369: | ||
| 57 | | 57 | ||
| 1200.00 | | 1200.00 | ||
|[[2/1]] | |||
| {{UDnote|step=57}} | | {{UDnote|step=57}} | ||
| {{UDnote|fifth=34|step=57}} | | {{UDnote|fifth=34|step=57}} | ||
|} | |} | ||
<nowiki>*</nowiki> As a 2.3.5.7.11.13.17.19.23.29.31-subgroup temperament, in ''italics'' if inconsistent | |||
== Notation == | == Notation == | ||
=== | === Stein–Zimmermann–Gould notation === | ||
57edo can be notated using [[Stein–Zimmermann–Gould notation]]: | |||
{{ | {{Sharpness-sharp3-szg}} | ||
Here, a sharp raises by three steps, and a flat lowers by three steps, so arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, some notes may be best spelled with double arrows. | Here, a sharp raises by three steps, and a flat lowers by three steps, so arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, some notes may be best spelled with double arrows. | ||
=== Kite's ups and downs notation === | |||
Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud. | |||
{{Ups and downs sharpness}} | |||
=== Sagittal notation === | === Sagittal notation === | ||
This notation uses the same sagittal sequence as | This notation uses the same sagittal sequence as edos [[50edo #Sagittal notation|50]], [[64edo #Sagittal notation|64]], and [[71edo #Sagittal notation|71b]], and is a superset of the notation for [[19edo #Sagittal notation|19edo]]. | ||
==== Evo flavor ==== | ==== Evo flavor ==== | ||
| Line 344: | Line 409: | ||
</imagemap> | </imagemap> | ||
In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this | In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this edo. | ||
== Scales == | == Scales == | ||
| Line 360: | Line 425: | ||
== Music == | == Music == | ||
; [[Bryan Deister]] | ; [[Bryan Deister]] | ||
* [https://www.youtube.com/watch?v=4NZvSgS3ryY ''57edo improv''] (2025) | * [https://www.youtube.com/watch?v=4NZvSgS3ryY ''57edo improv''] (2025-05-12) | ||
* ''Prelude in 57edo'' (2025) (Uses different temperaments in different sections) | |||
** [https://www.youtube.com/shorts/FylRB5MGBz4 ''Part 1 (short clip)''] (Lumatone view using [[5L 2s|diatonic]] sharp fifth + [[mothra]] flat fifth mapping) | |||
** [https://www.youtube.com/shorts/yVv0s8t--pg ''Part 2 (short clip)''] (Lumatone view using [[lithium]] mapping) | |||
** [https://www.youtube.com/watch?v=RH2QkHqVb2c ''Whole composition''] (but no view of Lumatone) | |||
* [https://www.youtube.com/shorts/MTMRlRxRbjQ ''57edo groove''] (2025) | |||
* [https://www.youtube.com/shorts/TrgdgDduDIk ''57edo improv''] (2026-09-27) | |||