Eufalesio: Updated Ultimate temp data (thanks Godtone!)

2026-05-13T15:49:04Z

Updated Ultimate temp data (thanks Godtone!)

← Older revision		Revision as of 15:49, 13 May 2026
Line 1:		Line 1:
	Data I deem important!		Data I deem important!

	== ~~Temp~~ properties of Ultimate edos ==		== Temperament properties of Ultimate edos (I care about) ==
	~~Organizing these edos by shared tempered out commas.~~		'''217 & 270 & 311: Ultimate {S49*S55, S64, S65} = {2080/2079, 4096/4095, 35035/34992}'''
	{\| class="wikitable"
	!311		* '''270 & 311''': Newt {S49, S55, S64, S65} = {2080/2079, 2401/2400, 3025/3024, 4096/4095}
	!41		* '''94 & 270''': Gariwizmic {S11/S12, S64, S65, S99) = {1716/1715, <span data-darkreader-inline-color="">2080/2079, 4096/4095, 35035/34992}</span>
	!53		* '''41 & 217''': Cotoneum {S21, S28<sup>2</sup>*S29, S64, S65} = {441/440, <span data-darkreader-inline-color="">2080/2079, 4096/4095, 10976/10935}</span>
	!12e		* '''41 & 53''': Cassandra {S25*S26, S15, S64, S65} = {225/224, 325/324, 352/351, 385/384}
	!94		** '''270:''' {S49, S55, S64, S65, S99} = {1001/1000, 2401/2400, 2080/2079, 3025/3024, 4096/4095}
	!270		** '''94:''' {S15, S11/S12, S64, S65, S99} = {225/224, 325/324, 352/351, 385/384, 1716/1715}
	!217		** '''12e:''' {S8, S9, S15, S64, S65} = {22/21, 50/49, 64/63, 65/63, 81/80}
	!Ultimate r3
			Which can implicitly be seen in this table:
			{\| class="wikitable" style="text-align:center; vertical-align:middle"
			\|- style="font-weight:bold;"
			! 311
			! 41
			! 53
			! 12e
			! 94
			! 270
			! 217
			! Ultimate r3
	\|-		\|-
	\| colspan="8" \|2080/2079		\| colspan="8" \| 2080/2079
	\|-		\|-
	\| colspan="8" \|4096/4095		\| colspan="8" \| 4096/4095
	\|-		\|-
	\| colspan="8" \|35035/34492		\| colspan="8" \| 35035/34492
	\|-		\|-
	\| colspan="2" \|2401/2400		\| colspan="2" \| 2401/2400
	\|676/675		\| 676/675
	\|81/80		\| 81/80
	\| colspan="2" \|1716/1715		\| colspan="2" \| 1716/1715
	\|441/440		\| 441/440
	\|–		\| –
	\|-		\|-
	\|625/624		\| 625/624
	\| colspan="4" \|385/384		\| colspan="4" \| 385/384
	\| colspan="2" \|1001/1000		\| colspan="2" \| 1001/1000
	\|–		\| –
	\|}		\|}


	== Table of Ultimate edos' intervals ==		== Table of Ultimate edos' intervals ==

Eufalesio: Moved all table dumps into this page

2026-05-11T23:56:48Z

Moved all table dumps into this page

New page

Data I deem important!

== Temp properties of Ultimate edos ==
Organizing these edos by shared tempered out commas.
{| class="wikitable"
!311
!41
!53
!12e
!94
!270
!217
!Ultimate r3
|-
| colspan="8" |2080/2079
|-
| colspan="8" |4096/4095
|-
| colspan="8" |35035/34492
|-
| colspan="2" |2401/2400
|676/675
|81/80
| colspan="2" |1716/1715
|441/440
|–
|-
|625/624
| colspan="4" |385/384
| colspan="2" |1001/1000
|–
|}

== Table of Ultimate edos' intervals ==
A good and regular set of intervals I care about.
{| class="wikitable mw-collapsible mw-collapsed" data-darkreader-inline-color=""
|+15-odd-limit ratios
!Ratios
! colspan="4" |94edo
! colspan="4" |217edo
! colspan="4" |270edo
|-
|[[16/15]]
| rowspan="2" |
| rowspan="3" |1
| rowspan="2" |9
| rowspan="2" |114.89
|
| rowspan="2" |2
|20
|110.6
|
| rowspan="2" |2
|25
|111.{{Overline|1}}
|-
|[[15/14]]
| rowspan="2" |1
|22
|121.66
| rowspan="2" |2
|27
|120
|-
|[[14/13]]
| rowspan="2" |1
|10
|127.66
| rowspan="2" |2
|23
|127.19
| rowspan="2" |2
|29
|128.{{Overline|8}}
|-
|[[13/12]]
| rowspan="2" |1
|11
|140.43
| rowspan="2" |2
|25
|138.25
| rowspan="2" |3
|31
|137.{{Overline|7}}
|-
|[[12/11]]
| rowspan="2" |1
|12
|153.19
| rowspan="2" |3
|27
|149.31
| rowspan="2" |3
|34
|151.{{Overline|1}}
|-
|[[11/10]]
| rowspan="2" |1
|13
|165.96
| rowspan="2" |3
|30
|165.9
| rowspan="2" |4
|37
|164.{{Overline|4}}
|-
|[[10/9]]
| rowspan="2" |2
|14
|178.72
| rowspan="2" |4
|33
|182.49
| rowspan="2" |5
|41
|182.{{Overline|2}}
|-
|[[9/8]]
| rowspan="2" |2
|16
|204.26
| rowspan="2" |5
|37
|204.61
| rowspan="2" |6
|46
|204.{{Overline|4}}
|-
|[[8/7]]
| rowspan="2" |1
|18
|229.79
| rowspan="2" |3
|42
|232.26
| rowspan="2" |4
|52
|231.{{Overline|1}}
|-
|[[15/13]]
| rowspan="2" |2
|19
|242.55
| rowspan="2" |3
|45
|248.85
| rowspan="2" |4
|56
|248.{{Overline|8}}
|-
|[[7/6]]
| rowspan="2" |2
|21
|268.09
| rowspan="2" |4
|48
|265.44
| rowspan="2" |5
|60
|266.{{Overline|6}}
|-
|[[13/11]]
| rowspan="2" |2
|23
|293.62
| rowspan="2" |5
|52
|287.56
| rowspan="2" |6
|65
|288.{{Overline|8}}
|-
|[[6/5]]
| rowspan="2" |2
|25
|319.15
| rowspan="2" |6
|57
|315.21
| rowspan="2" |7
|71
|315.{{Overline|5}}
|-
|[[11/9]]
| rowspan="2" |1
|27
|344.68
| rowspan="2" |2
|63
|348.39
| rowspan="2" |4
|78
|346.{{Overline|6}}
|-
|[[16/13]]
| rowspan="2" |2
|28
|357.45
| rowspan="2" |5
|65
|359.45
| rowspan="2" |6
|81
|360.0
|-
|[[5/4]]
| rowspan="2" |3
|30
|382.98
| rowspan="2" |5
|70
|387.1
| rowspan="2" |7
|87
|386.{{Overline|6}}
|-
|[[14/11]]
| rowspan="2" |1
|33
|421.28
| rowspan="2" |4
|75
|414.75
| rowspan="2" |4
|94
|417.{{Overline|7}}
|-
|[[9/7]]
| rowspan="2" |2
|34
|434.04
| rowspan="2" |4
|79
|436.87
| rowspan="2" |4
|98
|435.{{Overline|5}}
|-
|[[13/10]]
| rowspan="2" |3
|36
|459.57
| rowspan="2" |8
|82
|453.46
| rowspan="2" |10
|102
|453.{{Overline|3}}
|-
|[[4/3]]
| rowspan="2" |3
|39
|497.87
| rowspan="2" |7
|90
|497.7
| rowspan="2" |9
|112
|497.{{Overline|7}}
|-
|[[15/11]]
| rowspan="2" |1
|42
|536.17
| rowspan="2" |3
|97
|536.41
| rowspan="2" |3
|121
|537.{{Overline|7}}
|-
|[[11/8]]
| rowspan="2" |1
|43
|548.94
| rowspan="2" |2
|100
|553.0
| rowspan="2" |3
|124
|551.{{Overline|1}}
|-
|[[18/13]]
| rowspan="2" |2
|44
|561.7
| rowspan="2" |3
|102
|564.06
| rowspan="2" |4
|127
|564.{{Overline|4}}
|-
|[[7/5]]
| rowspan="2" |2
|46
|587.23
| rowspan="2" |7
|105
|580.65
| rowspan="2" |8
|131
|582.{{Overline|2}}
|-
|[[10/7]]
| rowspan="2" |2
|48
|612.77
| rowspan="2" |3
|112
|619.35
| rowspan="2" |4
|139
|617.{{Overline|7}}
|-
|[[13/9]]
| rowspan="2" |1
|50
|638.3
| rowspan="2" |2
|115
|635.94
| rowspan="2" |3
|143
|635.{{Overline|5}}
|-
|[[16/11]]
| rowspan="2" |1
|51
|651.06
| rowspan="2" |3
|117
|647.0
| rowspan="2" |3
|146
|648.{{Overline|8}}
|-
|[[22/15]]
| rowspan="2" |3
|52
|663.83
| rowspan="2" |7
|120
|663.59
| rowspan="2" |9
|149
|662.{{Overline|2}}
|-
|[[3/2]]
| rowspan="2" |3
|55
|702.13
| rowspan="2" |8
|127
|702.3
| rowspan="2" |10
|158
|702.{{Overline|2}}
|-
|[[20/13]]
| rowspan="2" |2
|58
|740.43
| rowspan="2" |4
|135
|746.54
| rowspan="2" |4
|168
|746.{{Overline|6}}
|-
|[[14/9]]
| rowspan="2" |1
|60
|765.96
| rowspan="2" |4
|138
|763.13
| rowspan="2" |4
|172
|764.{{Overline|4}}
|-
|[[11/7]]
| rowspan="2" |3
|61
|778.72
| rowspan="2" |5
|142
|785.25
| rowspan="2" |5
|176
|782.{{Overline|2}}
|-
|[[8/5]]
| rowspan="2" |2
|64
|817.02
| rowspan="2" |5
|147
|812.9
| rowspan="2" |6
|183
|813.{{Overline|3}}
|-
|[[13/8]]
| rowspan="2" |1
|66
|842.55
| rowspan="2" |2
|152
|840.55
| rowspan="2" |3
|189
|840.0
|-
|[[18/11]]
| rowspan="2" |2
|67
|855.32
| rowspan="2" |6
|154
|851.61
| rowspan="2" |7
|192
|853.{{Overline|3}}
|-
|[[5/3]]
| rowspan="2" |2
|69
|880.85
| rowspan="2" |5
|160
|884.79
| rowspan="2" |6
|199
|884.{{Overline|4}}
|-
|[[22/13]]
| rowspan="2" |2
|71
|906.38
| rowspan="2" |5
|165
|912.44
| rowspan="2" |5
|205
|911.{{Overline|1}}
|-
|[[12/7]]
| rowspan="2" |2
|73
|931.91
| rowspan="2" |4
|169
|934.56
| rowspan="2" |4
|210
|933.{{Overline|3}}
|-
|[[26/15]]
| rowspan="2" |1
|75
|957.45
| rowspan="2" |4
|172
|951.15
| rowspan="2" |4
|214
|951.{{Overline|1}}
|-
|[[7/4]]
| rowspan="2" |2
|76
|970.21
| rowspan="2" |6
|175
|967.74
| rowspan="2" |6
|218
|968.{{Overline|8}}
|-
|[[16/9]]
| rowspan="2" |2
|78
|995.74
| rowspan="2" |5
|180
|995.39
| rowspan="2" |5
|224
|995.{{Overline|5}}
|-
|[[9/5]]
| rowspan="2" |1
|80
|1021.28
| rowspan="2" |4
|184
|1017.51
| rowspan="2" |4
|229
|1017.{{Overline|7}}
|-
|[[20/11]]
| rowspan="2" |1
|81
|1034.04
| rowspan="2" |4
|187
|1034.1
| rowspan="2" |4
|233
|1035.{{Overline|5}}
|-
|[[11/6]]
| rowspan="2" |1
|82
|1046.81
| rowspan="2" |3
|190
|1050.69
| rowspan="2" |3
|236
|1048.{{Overline|8}}
|-
|[[24/13]]
| rowspan="2" |1
|83
|1059.57
| rowspan="2" |2
|192
|1061.75
| rowspan="2" |2
|239
|1062.{{Overline|2}}
|-
|[[13/7]]
| rowspan="2" |1
|84
|1072.34
| rowspan="2" |2
|194
|1072.81
| rowspan="2" |2
|241
|1071.{{Overline|1}}
|-
|[[28/15]]
| rowspan="2" |0
| rowspan="2" |85
| rowspan="2" |1085.11
| rowspan="2" |2
|195
|1078.34
| rowspan="2" |2
|243
|1080.0
|-
|[[15/8]]
|
|
|197
|1089.4
|
|245
|1088.{{Overline|8}}
|}

== Table of 270edo's yazalatha 225-odd-limit ==
Almost consistent to distance 2. Covers almost the entire gamut in almost pure 13-limit glory. Incredible.
{| class="wikitable mw-collapsible mw-collapsed" data-darkreader-inline-color=""
|+270edo yazalatha 225-odd-limit
|1
|4.{{overline|4}}
|[[540/539]], [[441/440]], [[5120/5103]], [[385/384]], [[352/351]]
|-
!Tredeks
!Cents
!Ratio
|-
|2
|8.{{overline|8}}
|[[225/224]], [[196/195]], [[176/175]], [[169/168]]
|-
|3
|13.{{overline|3}}
|[[144/143]], [[126/125]], [[121/120]]
|-
|4
|17.{{overline|7}}
|[[105/104]], [[100/99]], [[99/98]], [[91/90]]
|-
|5
|22.{{overline|2}}
|[[81/80]], [[78/77]]
|-
|6
|26.{{overline|6}}
|[[66/65]], [[65/64]], [[64/63]]
|-
|7
|31.{{overline|1}}
|[[56/55]], [[55/54]]
|-
|8
|35.{{overline|5}}
|[[50/49]], [[49/48]], [[143/140]]
|-
|9
|40.0
|[[45/44]], [[128/125]], [[169/165]]
|-
|10
|44.{{overline|4}}
|[[40/39]], [[77/75]]
|-
|11
|48.{{overline|8}}
|[[147/143]], [[36/35]]
|-
|12
|53.{{overline|3}}
|[[33/32]], [[65/63]]
|-
|13
|57.{{overline|7}}
|[[125/121]], [[91/88]], [[121/117]]
|-
|14
|62.{{overline|2}}
|[[175/169]], [[28/27]]
|-
|15
|66.{{overline|6}}
|[[27/26]], [[80/77]], [[26/25]]
|-
|16
|71.{{overline|1}}
|[[126/121]], [[176/169]], [[25/24]], [[169/162]]
|-
|17
|75.{{overline|5}}
|[[117/112]]
|-
|18
|80.0
|[[22/21]]
|-
|19
|84.{{overline|4}}
|[[150/143]], [[21/20]], [[104/99]]
|-
|20
|88.{{overline|8}}
|[[81/77]]
|-
|21
|93.{{overline|3}}
|[[135/128]], [[96/91]], [[132/125]], [[169/160]]
|-
|22
|97.{{overline|7}}
|[[55/52]], [[128/121]], [[200/189]], [[143/135]]
|-
|23
|102.{{overline|2}}
|[[35/33]], [[52/49]]
|-
|24
|106.{{overline|6}}
|[[117/110]]
|-
|25
|111.{{overline|1}}
|[[180/169]], [[16/15]]
|-
|26
|115.{{overline|5}}
|[[125/117]], [[77/72]]
|-
|27
|120.0
|[[15/14]]
|-
|28
|124.{{overline|4}}
|[[189/176]], [[130/121]], [[242/225]]
|-
|29
|128.{{overline|8}}
|[[14/13]]
|-
|30
|133.{{overline|3}}
|[[27/25]], [[175/162]], [[121/112]]
|-
|31
|137.{{overline|7}}
|[[225/208]], [[13/12]]
|-
|32
|142.{{overline|2}}
|[[88/81]]
|-
|33
|146.{{overline|6}}
|[[99/91]], [[160/147]], [[49/45]]
|-
|34
|151.{{overline|1}}
|[[12/11]]
|-
|35
|155.{{overline|5}}
|[[35/32]], [[128/117]]
|-
|36
|160.0
|[[192/175]], [[169/154]]
|-
|37
|164.{{overline|4}}
|[[100/91]], [[11/10]], [[208/189]]
|-
|38
|168.{{overline|8}}
|[[54/49]], [[182/165]]
|-
|39
|173.{{overline|3}}
|
|-
|40
|177.{{overline|7}}
|[[72/65]], [[195/176]]
|-
|41
|182.{{overline|2}}
|[[10/9]]
|-
|42
|186.{{overline|6}}
|[[49/44]], [[39/35]]
|-
|43
|191.{{overline|1}}
|[[135/121]], [[125/112]], [[143/128]]
|-
|44
|195.{{overline|5}}
|[[189/169]], [[160/143]], [[28/25]], [[121/108]]
|-
|45
|200.0
|[[175/156]], [[55/49]], [[91/81]]
|-
|46
|204.{{overline|4}}
|[[9/8]], [[169/150]]
|-
|47
|208.{{overline|8}}
|[[44/39]]
|-
|48
|213.{{overline|3}}
|[[147/130]], [[112/99]], [[198/175]]
|-
|49
|217.{{overline|7}}
|[[162/143]], [[143/126]]
|-
|50
|222.{{overline|2}}
|[[192/169]], [[25/22]], [[91/80]], [[256/225]]
|-
|51
|226.{{overline|6}}
|[[154/135]]
|-
|52
|231.{{overline|1}}
|[[8/7]], [[143/125]]
|-
|53
|235.{{overline|5}}
|[[63/55]], [[55/48]]
|-
|54
|240.0
|[[225/196]], [[147/128]], [[224/195]], [[169/147]]
|-
|55
|244.{{overline|4}}
|[[144/125]], [[121/105]]
|-
|56
|248.{{overline|8}}
|[[15/13]], [[52/45]]
|-
|57
|253.{{overline|3}}
|[[140/121]], [[81/70]], [[125/108]]
|-
|58
|257.{{overline|7}}
|[[196/169]], [[65/56]]
|-
|59
|262.{{overline|2}}
|[[121/104]], [[64/55]], [[220/189]]
|-
|60
|266.{{overline|6}}
|[[7/6]]
|-
|61
|271.{{overline|1}}
|[[90/77]], [[117/100]]
|-
|62
|275.{{overline|5}}
|[[198/169]], [[75/64]], [[88/75]], [[169/144]]
|-
|63
|280.0
|[[168/143]], [[147/125]]
|-
|64
|284.{{overline|4}}
|[[33/28]]
|-
|65
|288.{{overline|8}}
|[[189/160]], [[13/11]]
|-
|66
|293.{{overline|3}}
|[[200/169]], [[77/65]], [[32/27]]
|-
|67
|297.{{overline|7}}
|[[108/91]], [[196/165]], [[208/175]]
|-
|68
|302.{{overline|2}}
|[[144/121]], [[25/21]], [[143/120]]
|-
|69
|306.{{overline|6}}
|[[105/88]], [[117/98]]
|-
|70
|311.{{overline|1}}
|[[140/117]], [[176/147]]
|-
|71
|315.{{overline|5}}
|[[6/5]]
|-
|72
|320.0
|[[125/104]], [[77/64]], [[65/54]]
|-
|73
|324.{{overline|4}}
|[[135/112]], [[169/140]]
|-
|74
|328.{{overline|8}}
|[[110/91]], [[98/81]], [[121/100]]
|-
|75
|333.{{overline|3}}
|[[63/52]], [[40/33]], [[91/75]]
|-
|76
|337.{{overline|7}}
|[[147/121]], [[175/144]]
|-
|77
|342.{{overline|2}}
|[[39/32]], [[128/105]]
|-
|78
|346.{{overline|6}}
|[[11/9]]
|-
|79
|351.{{overline|1}}
|[[175/143]], [[60/49]], [[49/40]]
|-
|80
|355.{{overline|5}}
|[[27/22]]
|-
|81
|360.0
|[[16/13]], [[154/125]]
|-
|82
|364.{{overline|4}}
|[[216/175]], [[100/81]], [[121/98]]
|-
|83
|368.{{overline|8}}
|[[225/182]], [[99/80]], [[26/21]]
|-
|84
|373.{{overline|3}}
|[[150/121]], [[242/195]]
|-
|85
|377.{{overline|7}}
|[[210/169]], [[56/45]]
|-
|86
|382.{{overline|2}}
|[[81/65]], [[96/77]], [[156/125]]
|-
|87
|386.{{overline|6}}
|[[5/4]], [[169/135]]
|-
|89
|391.{{overline|1}}
|[[49/39]], [[44/35]]
|-
|90
|395.{{overline|5}}
|[[180/143]], [[63/50]], [[121/96]], [[208/165]]
|-
|91
|400.0
|[[125/99]], [[91/72]]
|-
|92
|404.{{overline|4}}
|[[81/64]], [[195/154]]
|-
|93
|408.{{overline|8}}
|[[33/26]], [[80/63]], [[286/225]]
|-
|94
|413.{{overline|3}}
|[[14/11]]
|-
|95
|417.{{overline|7}}
|[[125/98]], [[143/112]]
|-
|96
|422.{{overline|2}}
|[[216/169]], [[225/176]], [[32/25]], [[169/132]], [[242/189]]
|-
|97
|426.{{overline|6}}
|[[50/39]], [[77/60]], [[104/81]]
|-
|98
|431.{{overline|1}}
|[[9/7]]
|-
|99
|435.{{overline|5}}
|[[165/128]], [[156/121]]
|-
|100
|440.0
|[[84/65]], [[128/99]]
|-
|101
|444.{{overline|4}}
|[[162/125]], [[35/27]]
|-
|102
|448.{{overline|8}}
|[[135/104]], [[100/77]], [[13/10]]
|-
|103
|453.{{overline|3}}
|[[220/169]], [[125/96]], [[176/135]]
|-
|104
|457.{{overline|7}}
|[[64/49]], [[98/75]]
|-
|105
|462.{{overline|2}}
|[[72/55]], [[55/42]]
|-
|106
|466.{{overline|6}}
|[[21/16]], [[256/195]], [[130/99]]
|-
|107
|471.{{overline|1}}
|[[154/117]]
|-
|108
|475.{{overline|5}}
|[[120/91]], [[33/25]], [[169/128]]
|-
|109
|480.0
|[[189/143]], [[160/121]], [[250/189]], [[143/108]]
|-
|110
|484.{{overline|4}}
|[[224/169]], [[175/132]], [[65/49]]
|-
|111
|488.{{overline|8}}
|[[117/88]], [[121/91]]
|-
|112
|493.{{overline|3}}
|*[[225/169]]*, [[4/3]]
|-
|113
|497.{{overline|7}}
|[[147/110]], [[234/175]]
|-
|114
|502.{{overline|2}}
|[[162/121]], [[75/56]], [[169/126]]
|-
|115
|506.{{overline|6}}
|[[192/143]], [[168/125]], [[121/90]]
|-
|116
|511.{{overline|1}}
|[[35/26]], [[66/49]], [[182/135]]
|-
|117
|515.{{overline|5}}
|[[27/20]], [[104/77]], [[169/125]]
|-
|118
|520.0
|[[88/65]], [[65/48]], [[256/189]]
|-
|119
|524.{{overline|4}}
|[[224/165]], [[110/81]]
|-
|120
|528.{{overline|8}}
|[[200/147]], [[49/36]], [[143/105]]
|-
|121
|533.{{overline|3}}
|[[15/11]]
|-
|122
|537.{{overline|7}}
|[[175/128]], [[160/117]], [[308/225]]
|-
|123
|542.{{overline|2}}
|[[196/143]], [[48/35]]
|-
|124
|546.{{overline|6}}
|[[125/91]], [[11/8]], [[260/189]]
|-
|125
|551.{{overline|1}}
|[[135/98]], [[91/66]]
|-
|126
|555.{{overline|5}}
|[[112/81]], [[242/175]]
|-
|127
|560.0
|[[18/13]], [[104/75]]
|-
|128
|564.{{overline|4}}
|[[168/121]], [[25/18]]
|-
|129
|568.{{overline|8}}
|[[39/28]]
|-
|130
|573.{{overline|3}}
|[[169/121]], [[88/63]]
|-
|131
|577.{{overline|7}}
|[[200/143]], [[7/5]]
|-
|132
|582.{{overline|2}}
|[[108/77]]
|-
|133
|586.{{overline|6}}
|[[45/32]], [[128/91]], [[176/125]], [[169/120]]
|-
|134
|591.{{overline|1}}
|[[55/39]]
|-
|135
|595.{{overline|5}}
|[[147/104]], [[140/99]], [[99/70]], [[208/147]]
|-
|136
|600.0
|[[78/55]]
|-
|137
|604.{{overline|4}}
|[[240/169]], [[125/88]], [[91/64]], [[64/45]]
|-
|138
|608.{{overline|8}}
|[[77/54]]
|-
|139
|613.{{overline|3}}
|[[10/7]], [[143/100]]
|-
|140
|617.{{overline|7}}
|[[63/44]], [[242/169]]
|-
|141
|622.{{overline|2}}
|[[56/39]]
|-
|142
|626.{{overline|6}}
|[[36/25]], [[121/84]]
|-
|143
|631.{{overline|1}}
|[[75/52]], [[13/9]]
|-
|144
|635.{{overline|5}}
|[[175/121]], [[81/56]]
|-
|145
|640.0
|[[132/91]], [[196/135]]
|-
|146
|644.{{overline|4}}
|[[189/130]], [[16/11]], [[182/125]]
|-
|147
|648.{{overline|8}}
|[[35/24]], [[143/98]]
|-
|148
|653.{{overline|3}}
|[[225/154]], [[117/80]], [[256/175]]
|-
|149
|657.{{overline|7}}
|[[22/15]]
|-
|150
|662.{{overline|2}}
|[[210/143]], [[72/49]], [[147/100]]
|-
|151
|666.{{overline|6}}
|[[81/55]], [[165/112]]
|-
|152
|671.{{overline|1}}
|[[189/128]], [[96/65]], [[65/44]]
|-
|153
|675.{{overline|5}}
|[[250/169]], [[77/52]], [[40/27]]
|-
|154
|680.0
|[[135/91]], [[49/33]], [[52/35]]
|-
|155
|684.{{overline|4}}
|[[180/121]], [[125/84]], [[143/96]]
|-
|156
|688.{{overline|8}}
|[[252/169]], [[112/75]], [[121/81]]
|-
|157
|693.{{overline|3}}
|[[175/117]], [[220/147]]
|-
|158
|697.{{overline|7}}
|[[3/2]], *[[338/225]]*
|-
|159
|702.{{overline|2}}
|[[182/121]], [[176/117]]
|-
|160
|706.{{overline|6}}
|[[98/65]], [[264/175]], [[169/112]]
|-
|161
|711.{{overline|1}}
|[[216/143]], [[189/125]], [[121/80]], [[286/189]]
|-
|162
|715.{{overline|5}}
|[[256/169]], [[50/33]], [[91/60]]
|-
|163
|720.0
|[[117/77]]
|-
|164
|724.{{overline|4}}
|[[99/65]], [[195/128]], [[32/21]]
|-
|165
|728.{{overline|8}}
|[[84/55]], [[55/36]]
|-
|166
|733.{{overline|3}}
|[[75/49]], [[49/32]]
|-
|167
|737.{{overline|7}}
|[[135/88]], [[192/125]], [[169/110]]
|-
|168
|742.{{overline|2}}
|[[20/13]], [[77/50]], [[208/135]]
|-
|169
|746.{{overline|6}}
|[[54/35]], [[125/81]]
|-
|170
|751.{{overline|1}}
|[[99/64]], [[65/42]]
|-
|171
|755.{{overline|5}}
|[[121/78]], [[256/165]]
|-
|172
|760.0
|[[14/9]]
|-
|173
|764.{{overline|4}}
|[[81/52]], [[120/77]], [[39/25]]
|-
|174
|768.{{overline|8}}
|[[189/121]], [[264/169]], [[25/16]], [[352/225]], [[169/108]]
|-
|175
|773.{{overline|3}}
|[[224/143]], [[196/125]]
|-
|176
|777.{{overline|7}}
|[[11/7]]
|-
|177
|782.{{overline|2}}
|[[225/143]], [[63/40]], [[52/33]]
|-
|178
|786.{{overline|6}}
|[[308/195]], [[128/81]]
|-
|179
|791.{{overline|1}}
|[[144/91]], [[198/125]]
|-
|180
|795.{{overline|5}}
|[[165/104]], [[192/121]], [[100/63]], [[143/90]]
|-
|181
|800.0
|[[35/22]], [[78/49]]
|-
|183
|804.{{overline|4}}
|[[270/169]], [[8/5]]
|-
|184
|808.{{overline|8}}
|[[125/78]], [[77/48]], [[130/81]]
|-
|185
|813.{{overline|3}}
|[[45/28]], [[169/105]]
|-
|186
|817.{{overline|7}}
|[[195/121]], [[121/75]]
|-
|187
|822.{{overline|2}}
|[[21/13]], [[160/99]], [[364/225]]
|-
|188
|826.{{overline|6}}
|[[196/121]], [[81/50]], [[175/108]]
|-
|189
|831.{{overline|1}}
|[[125/77]], [[13/8]]
|-
|190
|835.{{overline|5}}
|[[44/27]]
|-
|191
|840.0
|[[80/49]], [[49/30]], [[286/175]]
|-
|192
|844.{{overline|4}}
|[[18/11]]
|-
|193
|848.{{overline|8}}
|[[105/64]], [[64/39]]
|-
|194
|853.{{overline|3}}
|[[288/175]], [[242/147]]
|-
|195
|857.{{overline|7}}
|[[150/91]], [[33/20]], [[104/63]]
|-
|196
|862.{{overline|2}}
|[[200/121]], [[81/49]], [[91/55]]
|-
|197
|866.{{overline|6}}
|[[280/169]], [[224/135]]
|-
|198
|871.{{overline|1}}
|[[108/65]], [[128/77]], [[208/125]]
|-
|199
|875.{{overline|5}}
|[[5/3]]
|-
|200
|880.0
|[[147/88]], [[117/70]]
|-
|201
|884.{{overline|4}}
|[[196/117]], [[176/105]]
|-
|202
|888.{{overline|8}}
|[[240/143]], [[42/25]], [[121/72]]
|-
|203
|893.{{overline|3}}
|[[175/104]], [[165/98]], [[91/54]]
|-
|204
|897.{{overline|7}}
|[[27/16]], [[130/77]], [[169/100]]
|-
|205
|902.{{overline|2}}
|[[22/13]], [[320/189]]
|-
|206
|906.{{overline|6}}
|[[56/33]]
|-
|207
|911.{{overline|1}}
|[[250/147]], [[143/84]]
|-
|208
|915.{{overline|5}}
|[[288/169]], [[75/44]], [[128/75]], [[169/99]]
|-
|209
|920.0
|[[200/117]], [[77/45]]
|-
|210
|924.{{overline|4}}
|[[12/7]]
|-
|211
|928.{{overline|8}}
|[[189/110]], [[55/32]], [[208/121]]
|-
|212
|933.{{overline|3}}
|[[112/65]], [[169/98]]
|-
|213
|937.{{overline|7}}
|[[216/125]], [[140/81]], [[121/70]]
|-
|214
|942.{{overline|2}}
|[[45/26]], [[26/15]]
|-
|215
|946.{{overline|6}}
|[[210/121]], [[125/72]]
|-
|216
|951.{{overline|1}}
|[[294/169]], [[195/112]], [[256/147]], [[392/225]]
|-
|217
|955.{{overline|5}}
|[[96/55]], [[110/63]]
|-
|218
|960.0
|[[250/143]], [[7/4]]
|-
|219
|964.{{overline|4}}
|[[135/77]]
|-
|220
|968.{{overline|8}}
|[[225/128]], [[160/91]], [[44/25]], [[169/96]]
|-
|221
|973.{{overline|3}}
|[[252/143]], [[143/81]]
|-
|222
|977.{{overline|7}}
|[[175/99]], [[99/56]], [[260/147]]
|-
|223
|982.{{overline|2}}
|[[39/22]]
|-
|224
|986.{{overline|6}}
|[[300/169]], [[16/9]]
|-
|225
|991.{{overline|1}}
|[[162/91]], [[98/55]], [[312/175]]
|-
|226
|995.{{overline|5}}
|[[216/121]], [[25/14]], [[143/80]], [[338/189]]
|-
|227
|1000.0
|[[256/143]], [[224/125]], [[242/135]]
|-
|228
|1004.{{overline|4}}
|[[70/39]], [[88/49]]
|-
|229
|1008.{{overline|8}}
|[[9/5]]
|-
|230
|1013.{{overline|3}}
|[[352/195]], [[65/36]]
|-
|231
|1026.{{overline|6}}
|
|-
|232
|1022.{{overline|2}}
|[[165/91]], [[49/27]]
|-
|233
|1026.{{overline|6}}
|[[189/104]], [[20/11]], [[91/50]]
|-
|234
|1031.{{overline|1}}
|[[308/169]], [[175/96]]
|-
|235
|1035.{{overline|5}}
|[[117/64]], [[64/35]]
|-
|236
|1040.0
|[[11/6]]
|-
|237
|1044.{{overline|4}}
|[[90/49]], [[147/80]], [[182/99]]
|-
|238
|1048.{{overline|8}}
|[[81/44]]
|-
|239
|1053.{{overline|3}}
|[[24/13]], [[416/225]]
|-
|240
|1057.{{overline|7}}
|[[224/121]], [[324/175]], [[50/27]]
|-
|241
|1062.{{overline|2}}
|[[13/7]]
|-
|242
|1066.{{overline|6}}
|[[225/121]], [[121/65]], [[352/189]]
|-
|243
|1071.{{overline|1}}
|[[28/15]]
|-
|244
|1075.{{overline|5}}
|[[144/77]], [[234/125]]
|-
|245
|1080.0
|[[15/8]], [[169/90]]
|-
|246
|1084.{{overline|4}}
|[[220/117]]
|-
|247
|1088.{{overline|8}}
|[[49/26]], [[66/35]]
|-
|248
|1093.{{overline|3}}
|[[270/143]], [[189/100]], [[121/64]], [[104/55]]
|-
|249
|1097.{{overline|7}}
|[[320/169]], [[125/66]], [[91/48]], [[256/135]]
|-
|250
|1102.{{overline|2}}
|[[154/81]]
|-
|251
|1106.{{overline|6}}
|[[99/52]], [[40/21]], [[143/75]]
|-
|252
|1111.{{overline|1}}
|[[21/11]]
|-
|253
|1115.{{overline|5}}
|[[224/117]]
|-
|254
|1120.0
|[[324/169]], [[48/25]], [[169/88]], [[121/63]]
|-
|255
|1124.{{overline|4}}
|[[25/13]], [[77/40]], [[52/27]]
|-
|256
|1128.{{overline|8}}
|[[27/14]], [[338/175]]
|-
|257
|1133.{{overline|3}}
|[[234/121]], [[176/91]], [[242/125]]
|-
|258
|1137.{{overline|7}}
|[[126/65]], [[64/33]]
|-
|259
|1142.{{overline|2}}
|[[35/18]], [[286/147]]
|-
|260
|1146.{{overline|6}}
|[[150/77]], [[39/20]]
|-
|261
|1151.{{overline|1}}
|[[330/169]], [[125/64]], [[88/45]]
|-
|262
|1155.{{overline|5}}
|[[280/143]], [[96/49]], [[49/25]]
|-
|263
|1160.0
|[[108/55]], [[55/28]]
|-
|264
|1164.{{overline|4}}
|[[63/32]], [[128/65]], [[65/33]]
|-
|265
|1168.{{overline|8}}
|[[77/39]], [[160/81]]
|-
|266
|1173.{{overline|3}}
|[[180/91]], [[196/99]], [[99/50]], [[208/105]]
|-
|267
|1177.{{overline|7}}
|[[240/121]], [[125/63]], [[143/72]]
|-
|268
|1182.{{overline|2}}
|[[336/169]], [[175/88]], [[195/98]], [[448/225]]
|-
|269
|1186.{{overline|6}}
|
|-
|270
|1191.{{overline|1}}
|[[2/1]]
|}

== Table of prime-generated MOS scales ==
Bolded has an equalized tuning with a telic convergent. Ending sequence at the biggest telic convergent below a thousand. The reason for doing this is that MOSes with record low softness have equalized tunings with convergent primes. MOSes with a hyperlink represent equalized tunings I deem notable.

Also note how p3 has the the shortest length out of all the primes. Shoutout to p11, it manages to build some good scales up until 37edo, on which it basically hits a dead end.
{| class="wikitable" data-darkreader-inline-color="" style="text-align: center;"
!'''Generation \ Prime'''
!31
!'''17'''
!29
!'''7'''
!'''19'''
!'''13'''
!'''5'''
!'''3'''
!'''11'''
!'''23'''
|-
|eva
| colspan="7" |1L 1s
| colspan="3" |'''1L 1s'''
|-
|1st filial scale
| colspan="5" |1L 2s
| colspan="2" |'''[[3edo|1L 2s]]'''
| colspan="3" |2L 1s
|-
|2nd filial scale
| colspan="4" |1L 3s
|'''[[4edo|1L 3s]]'''
| colspan="2" |3L 1s
|'''[[5edo|2L 3s]]'''
| colspan="2" |2L 3s
|-
|3rd filial scale
| colspan="3" |1L 4s
|'''[[5edo|1L 4s]]'''
|4L 1s
|'''[[7edo|3L 4s]]'''
|[[7edo|3L 4s]]
|[[7edo|5L 2s]]
| colspan="2" |2L 5s
|-
|4th filial scale
| colspan="3" |1L 5s
|5L 1s
|4L 5s
|'''[[10edo|7L 3s]]'''
|[[10edo|3L 7s]]
|'''[[12edo|5L 7s]]'''
| colspan="2" |2L 7s
|-
|5th filial scale
| colspan="2" |1L 6s
|'''[[7edo|1L 6s]]'''
|5L 6s
|4L 9s
|10L 7s
|3L 10s
|12L 5s
| colspan="2" |2L 9s
|-
|6th filial scale
| colspan="2" |1L 7s
|7L 1s
|5L 11s
|4L 13s
|10L 17s
|3L 13s
|12L 17s
|'''11L 2s'''
|2L 11s
|-
|7th filial scale
| colspan="2" |1L 8s
|7L 8s
|5L 16s
|4L 17s
|10L 27s
|3L 16s
|'''[[41edo|12L 29s]]'''
|[[24edo|13L 11s]]
|2L 13s
|-
|8th filial scale
| colspan="2" |1L 9s
|7L 15s
|'''5L 21s'''
|4L 21s
|10L 37s
|3L 19s
|'''[[53edo|41L 12s]]'''
|'''24L 13s'''
|2L 15s
|-
|9th filial scale
|1L 10s
|'''1L 10s'''
|7L 22s
|26L 5s
|4L 25s
|10L 47s
|3L 22s
|[[94edo|53L 41s]]
|37L 24s
|2L 17s
|-
|10th filial scale
|1L 11s
|[[12edo|11L 1s]]
|7L 29s
|26L 31s
|4L 29s
|10L 57s
|'''3L 25s'''
|53L 94s
|37L 61s
|'''2L 19s'''
|-
|11st filial scale
|1L 12s
|'''11L 12s'''
|7L 36s
|26L 57s
|4L 33s
|10L 67s
|28L 3s
|53L 147s
|37L 98s
|21L 2s
|-
|12nd filial scale
|1L 13s
|23L 34s
|7L 43s
|26L 57s
|[[41edo|4L 37s]]
|10L 77s
|'''28L 31s'''
|53L 200s
|37L 135s
|21L 23s
|-
|13rd filial scale
|1L 14s
|'''[[80edo|23L 57s]]'''
|7L 50s
|26L 83s
|4L 41s
|10L 87s
|59L 28s
|'''53L 253s'''
|37L 172s
|21L 44s
|-
|14th filial scale
|1L 15s
|80L 23s
|7L 57s
|'''26L 83s'''
|4L 45s
|10L 97s
|'''59L 87s'''
|306L 53s
|37L 209s
|21L 65s
|-
|15th filial scale
|1L 16s
|80L 103s
|7L 64s
|109L 26s
|[[53edo|4L 49s]]
|10L 107s
|146L 59s
|'''[[665edo|306L 359s]]'''
|37L 246s
|21L 86s
|-
|16th filial scale
|1L 17s
|80L 183s
|7L 71s
|109L 135s
|4L 53s
|10L 117s
|146L 205s
|
|37L 283s
|21L 107s
|-
|17th filial scale
|1L 18s
|'''263L 80s'''
|7L 78s
|109L 244s
|4L 57s
|10L 127s
|146L 351s
|
|37L 320s
|21L 128s
|-
|18th filial scale
|1L 19s
|
|7L 85s
|109L 353s
|4L 61s
|10L 137s
|'''146L 497s'''
|
|37L 357s
|21L 149s
|-
|19th filial scale
|1L 20s
|
|7L 92s
|'''109L 462s'''
|4L 65s
|10L 147s
|
|
|37L 394s
|'''21L 170s'''
|-
|20th filial scale
|'''21L 1s'''
|
|7L 99s
|
|4L 69s
|10L 157s
|
|
|37L 431s
|
|-
|21st filial scale
|22L 21s
|
|7L 106s
|
|4L 73s
|10L 167s
|
|
|37L 468s
|
|-
|22nd filial scale
|22L 43s
|
|7L 113s
|
|4L 77s
|10L 177s
|
|
|37L 505s
|
|-
|23rd filial scale
|22L 65s
|
|7L 120s
|
|4L 81s
|10L 187s
|
|
|37L 542s
|
|-
|24th filial scale
|'''22L 87s'''
|
|7L 127s
|
|4L 85s
|10L 197s
|
|
|37L 579s
|
|-
|25th filial scale
|'''22L 109s'''
|
|7L 134s
|
|4L 89s
|[[217edo|10L 207s]]
|
|
|37L 616s
|
|-
|26th filial scale
|
|
|7L 141s
|
|4L 93s
|'''10L 217s'''
|
|
|37L 653s
|
|-
|27th filial scale
|
|
|7L 148s
|
|4L 97s
|
|
|
|37L 690s
|
|-
|28th filial scale
|
|
|7L 155s
|
|4L 101s
|
|
|
|37L 727s
|
|-
|29th filial scale
|
|
|'''7L 162s'''
|
|4L 105s
|
|
|
|37L 764s
|
|-
|30th filial scale
|
|
|169L 7s
|
|4L 109s
|
|
|
|37L 801s
|
|-
|31st filial scale
|
|
|169L 176s
|
|''4L 113s''
|
|
|
|37L 838s
|
|-
|32nd filial scale
|
|
|169L 345s
|
|'''117L 4s'''
|
|
|
|37L 875s
|
|-
|33rd filial scale
|
|
|'''169L 514s'''
|
|
|
|
|
|37L 912s
|
|-
|34th filial scale
|
|
|'''852L 169s'''
|
|
|
|
|
|'''37L 949s'''
|
|}

User:Eufalesio/Important Tables - Revision history

Eufalesio at 18:42, 17 May 2026

Eufalesio: Acknowledgements to osmium/Godtone

Eufalesio: Updated Ultimate temp data (thanks Godtone!)

Eufalesio: Hotfixes!

Eufalesio: Moved all table dumps into this page

← Older revision		Revision as of 18:04, 17 May 2026
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	\|}		\|}

			Special thanks to [[Godtone]] for helping me make sense of all these temp properties and and helping me format them in a correct way.
	== Table of Ultimate edos' intervals ==		== Table of Ultimate edos' intervals ==
	A good and regular set of intervals I care about.		A good and regular set of intervals I care about.

← Older revision		Revision as of 23:57, 11 May 2026
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	Also note how p3 has the the shortest length out of all the primes. Shoutout to p11, it manages to build some good scales up until 37edo, on which it basically hits a dead end.		Also note how p3 has the the shortest length out of all the primes. Shoutout to p11, it manages to build some good scales up until 37edo, on which it basically hits a dead end.
	{\| class="wikitable" data-darkreader-inline-color="" style="text-align: center;"		{\| class="wikitable mw-collapsible mw-collapsed" data-darkreader-inline-color="" style="text-align: center;"
	!'''Generation \ Prime'''		!'''Generation \ Prime'''
	!31		!31