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Data I deem important!
Data I deem important! <small>Note on shorthand: sk = k/(k-1)</small>


== 13-limit Temperament properties of Ultimate edos (I care about) ==
== Temperament properties of Ultimate edos (I care about) ==
'''217 & 270 & 311: Ultimate {S49*S55, S64, S65} = {2080/2079, 4096/4095, 35035/34992}'''
'''217 & 270 & 311: Ultimate {S49*S55, S64, S65} = {s2080, s4096, 35035/34992}'''


* '''270 & 311''': Newt {S49, S55, S64, S65} = {2080/2079, 2401/2400, 3025/3024, 4096/4095}; supported trivially by 41edo
* '''270 & 311''': Newt {S49, S55, S64, S65} = {s2080, s2401, s3025, s4096}; supported trivially by 41edo
* '''94 & 270''': Gariwizmic {S11/S12, S64, S65, S99) = {1716/1715, <span data-darkreader-inline-color="">2080/2079, 4096/4095, 35035/34992}</span>
* '''94 & 270''': Gariwizmic {S11/S12, S64, S65, S99) = {s1716, <span data-darkreader-inline-color="">s2080, s4096, 35035/34992}; supported trivially by 94edo</span>
* '''41g & 217''': Cotoneum {S21, S28<sup>2</sup>*S29, S64, S65} = {441/440, <span data-darkreader-inline-color="">2080/2079, 4096/4095, 10976/10935}</span>
* '''41g & 217''': Cotoneum {S21, S28<sup>2</sup>*S29, S64, S65} = {s441, <span data-darkreader-inline-color="">s2080, s4096, 10976/10935}; supported trivially by 41edo</span>
* '''41g & 53''': Cassandra {S25*S26, S15, S64, S65} = {225/224, 325/324, 352/351, 385/384}; supported trivially by 12e
* '''41g & 53''': Cassandra {S25*S26, S15, S64, S65} = {s225, s325, s352, s385}; supported trivially by 12e
** '''270:''' {S49, S55, S64, S65, S99} = {1001/1000, 2401/2400, 2080/2079, 3025/3024, 4096/4095}
** '''270:''' {S49, S55, S64, S65, S99} = {s1001, s2401, s2080, s3025, s4096}
** '''94:''' {S15, S11/S12, S64, S65, S99} = {225/224, 325/324, 352/351, 385/384, 1716/1715}
** '''94:''' {S15, S11/S12, S64, S65, S99} = {s225, s325, s352, s385, s1716}
** '''12e:''' {S8, S9, S15, S64, S65} = {22/21, 50/49, 64/63, 65/63, 81/80}
** '''12e:''' {S8, S9, S15, S64, S65} = {22/21, 50/49, 64/63, 65/63, 81/80}


Line 32: Line 32:
! 217
! 217
|-
|-
| colspan="8" | 2080/2079
| colspan="8" | s2080
|-
|-
| colspan="8" | 4096/4095
| colspan="8" | s4096
|-
|-
| colspan="8" | 35035/34492
| colspan="8" | 35035/34492
|-
|-
| colspan="2" | 2401/2400
| colspan="2" | s2401
| 676/675
| s676
| 81/80
| s81
| colspan="2" | 1716/1715
| colspan="2" | s1716
| 441/440
| s441
| –
| –
|-
|-
| 625/624
| s625
| colspan="4" | 385/384
| colspan="4" | s385
| colspan="2" | 1001/1000
| colspan="2" | s1001
| –
| –
|}
|}
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Any other join of Ultimate edos is ommited because I either don't know or don't care.
Any other join of Ultimate edos is ommited because I either don't know or don't care.


Ultimate can be easily defined in 19-limit as {S35, S64, S65, S76, S77} = {1225/1224, 1540/1539, 1729/1728, 2080/2079, 4096/4095}.
Ultimate can be easily defined in 19-limit as {S35, S64, S65, S76, S77} = {1225/1224, 1540/1539, 1729/1728, s2080, s4096}.
 
Recommended tuning of Ultimate r3:
 
* Primes: '''1200, 1902.23, 2786.275''', 3368.78, 4151.29, 4440.485, ''4905.65'', 5097.425, ''5830.87''
* Generators: 1200, 702.23, 386.275
* (P8, P5, SP1, ^P1): 1200, 702.23, 26.76, 4.115
 
== Table of Ultimate edos' intervals ==
== Table of Ultimate edos' intervals ==
A good and regular set of intervals I care about. Doesn't include all, but many things.
A good and regular set of intervals I care about. Doesn't include all, but many things.
Line 63: Line 70:
!Ratios
!Ratios
! colspan="4" |270edo
! colspan="4" |270edo
!Ratios
! colspan="4" |Ultimate r3
|-
|-
| rowspan="2" |
| rowspan="2" |
Line 73: Line 82:
|20
|20
|110.6
|110.6
|[[16/15]]
|
| rowspan="2" |2
|25
|111.{{Overline|1}}
|[[16/15]]
|[[16/15]]
|
|
Line 83: Line 97:
|22
|22
|121.66
|121.66
|[[15/14]]
| rowspan="2" |2
|27
|120
|[[15/14]]
|[[15/14]]
| rowspan="2" |2
| rowspan="2" |2
Line 95: Line 113:
|23
|23
|127.19
|127.19
|[[14/13]]
| rowspan="2" |2
|29
|128.{{Overline|8}}
|[[14/13]]
|[[14/13]]
| rowspan="2" |2
| rowspan="2" |2
Line 107: Line 129:
|25
|25
|138.25
|138.25
|[[13/12]]
| rowspan="2" |3
|31
|137.{{Overline|7}}
|[[13/12]]
|[[13/12]]
| rowspan="2" |3
| rowspan="2" |3
Line 119: Line 145:
|27
|27
|149.31
|149.31
|[[12/11]]
| rowspan="2" |3
|34
|151.{{Overline|1}}
|[[12/11]]
|[[12/11]]
| rowspan="2" |3
| rowspan="2" |3
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|30
|30
|165.9
|165.9
|[[11/10]]
| rowspan="2" |4
|37
|164.{{Overline|4}}
|[[11/10]]
|[[11/10]]
| rowspan="2" |4
| rowspan="2" |4
Line 143: Line 177:
|33
|33
|182.49
|182.49
|[[10/9]]
| rowspan="2" |5
|41
|182.{{Overline|2}}
|[[10/9]]
|[[10/9]]
| rowspan="2" |5
| rowspan="2" |5
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|37
|37
|204.61
|204.61
|[[9/8]]
| rowspan="2" |6
|46
|204.{{Overline|4}}
|[[9/8]]
|[[9/8]]
| rowspan="2" |6
| rowspan="2" |6
Line 167: Line 209:
|42
|42
|232.26
|232.26
|[[8/7]]
| rowspan="2" |4
|52
|231.{{Overline|1}}
|[[8/7]]
|[[8/7]]
| rowspan="2" |4
| rowspan="2" |4
Line 179: Line 225:
|45
|45
|248.85
|248.85
|[[15/13]]
| rowspan="2" |4
|56
|248.{{Overline|8}}
|[[15/13]]
|[[15/13]]
| rowspan="2" |4
| rowspan="2" |4
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|48
|48
|265.44
|265.44
|[[7/6]]
| rowspan="2" |5
|60
|266.{{Overline|6}}
|[[7/6]]
|[[7/6]]
| rowspan="2" |5
| rowspan="2" |5
Line 203: Line 257:
|52
|52
|287.56
|287.56
|[[13/11]]
| rowspan="2" |6
|65
|288.{{Overline|8}}
|[[13/11]]
|[[13/11]]
| rowspan="2" |6
| rowspan="2" |6
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|57
|57
|315.21
|315.21
|[[6/5]]
| rowspan="2" |7
|71
|315.{{Overline|5}}
|[[6/5]]
|[[6/5]]
| rowspan="2" |7
| rowspan="2" |7
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|63
|63
|348.39
|348.39
|[[11/9]]
| rowspan="2" |4
|78
|346.{{Overline|6}}
|[[11/9]]
|[[11/9]]
| rowspan="2" |4
| rowspan="2" |4
Line 239: Line 305:
|65
|65
|359.45
|359.45
|[[16/13]]
| rowspan="2" |6
|81
|360.0
|[[16/13]]
|[[16/13]]
| rowspan="2" |6
| rowspan="2" |6
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|70
|70
|387.1
|387.1
|[[5/4]]
| rowspan="2" |7
|87
|386.{{Overline|6}}
|[[5/4]]
|[[5/4]]
| rowspan="2" |7
| rowspan="2" |7
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|75
|75
|414.75
|414.75
|[[14/11]]
| rowspan="2" |4
|94
|417.{{Overline|7}}
|[[14/11]]
|[[14/11]]
| rowspan="2" |4
| rowspan="2" |4
Line 275: Line 353:
|79
|79
|436.87
|436.87
|[[9/7]]
| rowspan="2" |4
|98
|435.{{Overline|5}}
|[[9/7]]
|[[9/7]]
| rowspan="2" |4
| rowspan="2" |4
Line 287: Line 369:
|82
|82
|453.46
|453.46
|[[13/10]]
| rowspan="2" |10
|102
|453.{{Overline|3}}
|[[13/10]]
|[[13/10]]
| rowspan="2" |10
| rowspan="2" |10
Line 299: Line 385:
|90
|90
|497.7
|497.7
|[[4/3]]
| rowspan="2" |9
|112
|497.{{Overline|7}}
|[[4/3]]
|[[4/3]]
| rowspan="2" |9
| rowspan="2" |9
Line 311: Line 401:
|97
|97
|536.41
|536.41
|[[15/11]]
| rowspan="2" |3
|121
|537.{{Overline|7}}
|[[15/11]]
|[[15/11]]
| rowspan="2" |3
| rowspan="2" |3
Line 323: Line 417:
|100
|100
|553.0
|553.0
|[[11/8]]
| rowspan="2" |3
|124
|551.{{Overline|1}}
|[[11/8]]
|[[11/8]]
| rowspan="2" |3
| rowspan="2" |3
Line 335: Line 433:
|102
|102
|564.06
|564.06
|[[18/13]]
| rowspan="2" |4
|127
|564.{{Overline|4}}
|[[18/13]]
|[[18/13]]
| rowspan="2" |4
| rowspan="2" |4
Line 347: Line 449:
|105
|105
|580.65
|580.65
|[[7/5]]
| rowspan="2" |8
|131
|582.{{Overline|2}}
|[[7/5]]
|[[7/5]]
| rowspan="2" |8
| rowspan="2" |8
Line 359: Line 465:
|112
|112
|619.35
|619.35
|[[10/7]]
| rowspan="2" |4
|139
|617.{{Overline|7}}
|[[10/7]]
|[[10/7]]
| rowspan="2" |4
| rowspan="2" |4
Line 371: Line 481:
|115
|115
|635.94
|635.94
|[[13/9]]
| rowspan="2" |3
|143
|635.{{Overline|5}}
|[[13/9]]
|[[13/9]]
| rowspan="2" |3
| rowspan="2" |3
Line 383: Line 497:
|117
|117
|647.0
|647.0
|[[16/11]]
| rowspan="2" |3
|146
|648.{{Overline|8}}
|[[16/11]]
|[[16/11]]
| rowspan="2" |3
| rowspan="2" |3
Line 395: Line 513:
|120
|120
|663.59
|663.59
|[[22/15]]
| rowspan="2" |9
|149
|662.{{Overline|2}}
|[[22/15]]
|[[22/15]]
| rowspan="2" |9
| rowspan="2" |9
Line 407: Line 529:
|127
|127
|702.3
|702.3
|[[3/2]]
| rowspan="2" |10
|158
|702.{{Overline|2}}
|[[3/2]]
|[[3/2]]
| rowspan="2" |10
| rowspan="2" |10
Line 419: Line 545:
|135
|135
|746.54
|746.54
|[[20/13]]
| rowspan="2" |4
|168
|746.{{Overline|6}}
|[[20/13]]
|[[20/13]]
| rowspan="2" |4
| rowspan="2" |4
Line 431: Line 561:
|138
|138
|763.13
|763.13
|[[14/9]]
| rowspan="2" |4
|172
|764.{{Overline|4}}
|[[14/9]]
|[[14/9]]
| rowspan="2" |4
| rowspan="2" |4
Line 443: Line 577:
|142
|142
|785.25
|785.25
|[[11/7]]
| rowspan="2" |5
|176
|782.{{Overline|2}}
|[[11/7]]
|[[11/7]]
| rowspan="2" |5
| rowspan="2" |5
Line 455: Line 593:
|147
|147
|812.9
|812.9
|[[8/5]]
| rowspan="2" |6
|183
|813.{{Overline|3}}
|[[8/5]]
|[[8/5]]
| rowspan="2" |6
| rowspan="2" |6
Line 467: Line 609:
|152
|152
|840.55
|840.55
|[[13/8]]
| rowspan="2" |3
|189
|840.0
|[[13/8]]
|[[13/8]]
| rowspan="2" |3
| rowspan="2" |3
Line 479: Line 625:
|154
|154
|851.61
|851.61
|[[18/11]]
| rowspan="2" |7
|192
|853.{{Overline|3}}
|[[18/11]]
|[[18/11]]
| rowspan="2" |7
| rowspan="2" |7
Line 491: Line 641:
|160
|160
|884.79
|884.79
|[[5/3]]
| rowspan="2" |6
|199
|884.{{Overline|4}}
|[[5/3]]
|[[5/3]]
| rowspan="2" |6
| rowspan="2" |6
Line 503: Line 657:
|165
|165
|912.44
|912.44
|[[22/13]]
| rowspan="2" |5
|205
|911.{{Overline|1}}
|[[22/13]]
|[[22/13]]
| rowspan="2" |5
| rowspan="2" |5
Line 515: Line 673:
|169
|169
|934.56
|934.56
|[[12/7]]
| rowspan="2" |4
|210
|933.{{Overline|3}}
|[[12/7]]
|[[12/7]]
| rowspan="2" |4
| rowspan="2" |4
Line 527: Line 689:
|172
|172
|951.15
|951.15
|[[26/15]]
| rowspan="2" |4
|214
|951.{{Overline|1}}
|[[26/15]]
|[[26/15]]
| rowspan="2" |4
| rowspan="2" |4
Line 539: Line 705:
|175
|175
|967.74
|967.74
|[[7/4]]
| rowspan="2" |6
|218
|968.{{Overline|8}}
|[[7/4]]
|[[7/4]]
| rowspan="2" |6
| rowspan="2" |6
Line 551: Line 721:
|180
|180
|995.39
|995.39
|[[16/9]]
| rowspan="2" |5
|224
|995.{{Overline|5}}
|[[16/9]]
|[[16/9]]
| rowspan="2" |5
| rowspan="2" |5
Line 563: Line 737:
|184
|184
|1017.51
|1017.51
|[[9/5]]
| rowspan="2" |4
|229
|1017.{{Overline|7}}
|[[9/5]]
|[[9/5]]
| rowspan="2" |4
| rowspan="2" |4
Line 575: Line 753:
|187
|187
|1034.1
|1034.1
|[[20/11]]
| rowspan="2" |4
|233
|1035.{{Overline|5}}
|[[20/11]]
|[[20/11]]
| rowspan="2" |4
| rowspan="2" |4
Line 587: Line 769:
|190
|190
|1050.69
|1050.69
|[[11/6]]
| rowspan="2" |3
|236
|1048.{{Overline|8}}
|[[11/6]]
|[[11/6]]
| rowspan="2" |3
| rowspan="2" |3
Line 599: Line 785:
|192
|192
|1061.75
|1061.75
|[[24/13]]
| rowspan="2" |2
|239
|1062.{{Overline|2}}
|[[24/13]]
|[[24/13]]
| rowspan="2" |2
| rowspan="2" |2
Line 611: Line 801:
|194
|194
|1072.81
|1072.81
|[[13/7]]
| rowspan="2" |2
|241
|1071.{{Overline|1}}
|[[13/7]]
|[[13/7]]
| rowspan="2" |2
| rowspan="2" |2
Line 623: Line 817:
|195
|195
|1078.34
|1078.34
|[[28/15]]
| rowspan="2" |2
|243
|1080.0
|[[28/15]]
|[[28/15]]
| rowspan="2" |2
| rowspan="2" |2
Line 633: Line 831:
|197
|197
|1089.4
|1089.4
|[[15/8]]
|
|245
|1088.{{Overline|8}}
|[[15/8]]
|[[15/8]]
|
|
Line 654: Line 856:
|2
|2
|8.{{overline|8}}
|8.{{overline|8}}
|[[225/224]], [[196/195]], [[176/175]], [[169/168]]
|[[225/224|s225]], [[196/195]], [[176/175]], [[169/168]]
|-
|-
|3
|3
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