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


== 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} = {s2080, s4096, 35035/34992}'''
{| class="wikitable"
 
!311
* '''270 & 311''': Newt {S49, S55, S64, S65} = {s2080, s2401, s3025, s4096}; supported trivially by 41edo
!41
* '''94 & 270''': Gariwizmic {S11/S12, S64, S65, S99) = {s1716, <span data-darkreader-inline-color="">s2080, s4096, 35035/34992}; supported trivially by 94edo</span>
!53
* '''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>
!12e
* '''41g & 53''': Cassandra {S25*S26, S15, S64, S65} = {s225, s325, s352, s385}; supported trivially by 12e
!94
** '''270:''' {S49, S55, S64, S65, S99} = {s1001, s2401, s2080, s3025, s4096}
!270
** '''94:''' {S15, S11/S12, S64, S65, S99} = {s225, s325, s352, s385, s1716}
!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"
! colspan="2" |Newt
! colspan="2" |
! colspan="2" |Gariwizmic
!
! rowspan="3" |Ultimate r3
|-
!
! colspan="4" |Cassandra
! colspan="2" |Vulture
|- style="font-weight:bold;"
! 311
! 41
! 53
! 12e
! 94
! 270
! 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
|–
| –
|}
|}
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, 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.
A good and regular set of intervals I care about. Doesn't include all, but many things.
{| class="wikitable mw-collapsible mw-collapsed" data-darkreader-inline-color=""
{| class="wikitable mw-collapsible mw-collapsed" data-darkreader-inline-color=""
|+15-odd-limit ratios
|+15-odd-limit ratios
! colspan="4" |94edo
!Ratios
!Ratios
! colspan="4" |94edo
! colspan="4" |217edo
! colspan="4" |217edo
!Ratios
! colspan="4" |270edo
! colspan="4" |270edo
!Ratios
! colspan="4" |Ultimate r3
|-
|-
|[[16/15]]
| rowspan="2" |
| rowspan="2" |
| rowspan="3" |1
| rowspan="3" |1
| rowspan="2" |9
| rowspan="2" |9
| rowspan="2" |114.89
| rowspan="2" |114.89
|[[16/15]]
|
|
| rowspan="2" |2
| rowspan="2" |2
|20
|20
|110.6
|110.6
|[[16/15]]
|
|
| rowspan="2" |2
| rowspan="2" |2
|25
|25
|111.{{Overline|1}}
|111.{{Overline|1}}
|[[16/15]]
|
| rowspan="2" |8.23
|vSm2
|111.495
|-
|-
|[[15/14]]
|[[15/14]]
Line 59: Line 97:
|22
|22
|121.66
|121.66
|[[15/14]]
| rowspan="2" |2
| rowspan="2" |2
|27
|27
|120
|120
|[[15/14]]
| rowspan="2" |8.57
|^Sm2
|119.725
|-
|-
|[[14/13]]
| rowspan="2" |1
| rowspan="2" |1
|10
|10
|127.66
|127.66
|[[14/13]]
| rowspan="2" |2
| rowspan="2" |2
|23
|23
|127.19
|127.19
|[[14/13]]
| rowspan="2" |2
| rowspan="2" |2
|29
|29
|128.{{Overline|8}}
|128.{{Overline|8}}
|[[14/13]]
| rowspan="2" |9.96
|^Smm2
|128.295
|-
|-
|[[13/12]]
| rowspan="2" |1
| rowspan="2" |1
|11
|11
|140.43
|140.43
|[[13/12]]
| rowspan="2" |2
| rowspan="2" |2
|25
|25
|138.25
|138.25
|[[13/12]]
| rowspan="2" |3
| rowspan="2" |3
|31
|31
|137.{{Overline|7}}
|137.{{Overline|7}}
|[[13/12]]
| rowspan="2" |12.685
|vHm2
|138.255
|-
|-
|[[12/11]]
| rowspan="2" |1
| rowspan="2" |1
|12
|12
|153.19
|153.19
|[[12/11]]
| rowspan="2" |3
| rowspan="2" |3
|27
|27
|149.31
|149.31
|[[12/11]]
| rowspan="2" |3
| rowspan="2" |3
|34
|34
|151.{{Overline|1}}
|151.{{Overline|1}}
|[[12/11]]
| rowspan="2" |14.075
|hM2
|150.94
|-
|-
|[[11/10]]
| rowspan="2" |1
| rowspan="2" |1
|13
|13
|165.96
|165.96
|[[11/10]]
| rowspan="2" |3
| rowspan="2" |3
|30
|30
|165.9
|165.9
|[[11/10]]
| rowspan="2" |4
| rowspan="2" |4
|37
|37
|164.{{Overline|4}}
|164.{{Overline|4}}
|[[11/10]]
| rowspan="2" |16.8
|vsMM2
|165.015
|-
|-
|[[10/9]]
| rowspan="2" |2
| rowspan="2" |2
|14
|14
|178.72
|178.72
|[[10/9]]
| rowspan="2" |4
| rowspan="2" |4
|33
|33
|182.49
|182.49
|[[10/9]]
| rowspan="2" |5
| rowspan="2" |5
|41
|41
|182.{{Overline|2}}
|182.{{Overline|2}}
|[[10/9]]
| rowspan="2" |22.645
|^sM2
|181.815
|-
|-
|[[9/8]]
| rowspan="2" |2
| rowspan="2" |2
|16
|16
|204.26
|204.26
|[[9/8]]
| rowspan="2" |5
| rowspan="2" |5
|37
|37
|204.61
|204.61
|[[9/8]]
| rowspan="2" |6
| rowspan="2" |6
|46
|46
|204.{{Overline|4}}
|204.{{Overline|4}}
|[[9/8]]
| rowspan="2" |26.76
|M2
|204.46
|-
|-
|[[8/7]]
| rowspan="2" |1
| rowspan="2" |1
|18
|18
|229.79
|229.79
|[[8/7]]
| rowspan="2" |3
| rowspan="2" |3
|42
|42
|232.26
|232.26
|[[8/7]]
| rowspan="2" |4
| rowspan="2" |4
|52
|52
|231.{{Overline|1}}
|231.{{Overline|1}}
|[[8/7]]
| rowspan="2" |16.8
|SM2
|231.22
|-
|-
|[[15/13]]
| rowspan="2" |2
| rowspan="2" |2
|19
|19
|242.55
|242.55
|[[15/13]]
| rowspan="2" |3
| rowspan="2" |3
|45
|45
|248.85
|248.85
|[[15/13]]
| rowspan="2" |4
| rowspan="2" |4
|56
|56
|248.{{Overline|8}}
|248.{{Overline|8}}
|[[15/13]]
| rowspan="2" |18.53
|^^SMM2
|248.02
|-
|-
|[[7/6]]
| rowspan="2" |2
| rowspan="2" |2
|21
|21
|268.09
|268.09
|[[7/6]]
| rowspan="2" |4
| rowspan="2" |4
|48
|48
|265.44
|265.44
|[[7/6]]
| rowspan="2" |5
| rowspan="2" |5
|60
|60
|266.{{Overline|6}}
|266.{{Overline|6}}
|[[7/6]]
| rowspan="2" |22.645
|sm3
|266.55
|-
|-
|[[13/11]]
| rowspan="2" |2
| rowspan="2" |2
|23
|23
|293.62
|293.62
|[[13/11]]
| rowspan="2" |5
| rowspan="2" |5
|52
|52
|287.56
|287.56
|[[13/11]]
| rowspan="2" |6
| rowspan="2" |6
|65
|65
|288.{{Overline|8}}
|288.{{Overline|8}}
|[[13/11]]
| rowspan="2" |26.76
|vm3
|289.195
|-
|-
|[[6/5]]
| rowspan="2" |2
| rowspan="2" |2
|25
|25
|319.15
|319.15
|[[6/5]]
| rowspan="2" |6
| rowspan="2" |6
|57
|57
|315.21
|315.21
|[[6/5]]
| rowspan="2" |7
| rowspan="2" |7
|71
|71
|315.{{Overline|5}}
|315.{{Overline|5}}
|[[6/5]]
| rowspan="2" |30.875
|vSm3
|315.955
|-
|-
|[[11/9]]
| rowspan="2" |1
| rowspan="2" |1
|27
|27
|344.68
|344.68
|[[11/9]]
| rowspan="2" |2
| rowspan="2" |2
|63
|63
|348.39
|348.39
|[[11/9]]
| rowspan="2" |4
| rowspan="2" |4
|78
|78
|346.{{Overline|6}}
|346.{{Overline|6}}
|[[11/9]]
| rowspan="2" |12.685
|Hm3
|346.83
|-
|-
|[[16/13]]
| rowspan="2" |2
| rowspan="2" |2
|28
|28
|357.45
|357.45
|[[16/13]]
| rowspan="2" |5
| rowspan="2" |5
|65
|65
|359.45
|359.45
|[[16/13]]
| rowspan="2" |6
| rowspan="2" |6
|81
|81
|360.0
|360.0
|[[16/13]]
| rowspan="2" |26.76
|^hM3
|359.515
|-
|-
|[[5/4]]
| rowspan="2" |3
| rowspan="2" |3
|30
|30
|382.98
|382.98
|[[5/4]]
| rowspan="2" |5
| rowspan="2" |5
|70
|70
|387.1
|387.1
|[[5/4]]
| rowspan="2" |7
| rowspan="2" |7
|87
|87
|386.{{Overline|6}}
|386.{{Overline|6}}
|[[5/4]]
| rowspan="2" |31.215
|^sM3
|386.275
|-
|-
|[[14/11]]
| rowspan="2" |1
| rowspan="2" |1
|33
|33
|421.28
|421.28
|[[14/11]]
| rowspan="2" |4
| rowspan="2" |4
|75
|75
|414.75
|414.75
|[[14/11]]
| rowspan="2" |4
| rowspan="2" |4
|94
|94
|417.{{Overline|7}}
|417.{{Overline|7}}
|[[14/11]]
| rowspan="2" |18.19
|SmM3
|417.49
|-
|-
|[[9/7]]
| rowspan="2" |2
| rowspan="2" |2
|34
|34
|434.04
|434.04
|[[9/7]]
| rowspan="2" |4
| rowspan="2" |4
|79
|79
|436.87
|436.87
|[[9/7]]
| rowspan="2" |4
| rowspan="2" |4
|98
|98
|435.{{Overline|5}}
|435.{{Overline|5}}
|[[9/7]]
| rowspan="2" |18.53
|SM3
|435.68
|-
|-
|[[13/10]]
| rowspan="2" |3
| rowspan="2" |3
|36
|36
|459.57
|459.57
|[[13/10]]
| rowspan="2" |8
| rowspan="2" |8
|82
|82
|453.46
|453.46
|[[13/10]]
| rowspan="2" |10
| rowspan="2" |10
|102
|102
|453.{{Overline|3}}
|453.{{Overline|3}}
|[[13/10]]
| rowspan="2" |43.56
|vvHM3
|454.21
|-
|-
|[[4/3]]
| rowspan="2" |3
| rowspan="2" |3
|39
|39
|497.87
|497.87
|[[4/3]]
| rowspan="2" |7
| rowspan="2" |7
|90
|90
|497.7
|497.7
|[[4/3]]
| rowspan="2" |9
| rowspan="2" |9
|112
|112
|497.{{Overline|7}}
|497.{{Overline|7}}
|[[4/3]]
| rowspan="2" |39.445
|P4
|497.77
|-
|-
|[[15/11]]
| rowspan="2" |1
| rowspan="2" |1
|42
|42
|536.17
|536.17
|[[15/11]]
| rowspan="2" |3
| rowspan="2" |3
|97
|97
|536.41
|536.41
|[[15/11]]
| rowspan="2" |3
| rowspan="2" |3
|121
|121
|537.{{Overline|7}}
|537.{{Overline|7}}
|[[15/11]]
| rowspan="2" |14.075
|^SmP4
|537.215
|-
|-
|[[11/8]]
| rowspan="2" |1
| rowspan="2" |1
|43
|43
|548.94
|548.94
|[[11/8]]
| rowspan="2" |2
| rowspan="2" |2
|100
|100
|553.0
|553.0
|[[11/8]]
| rowspan="2" |3
| rowspan="2" |3
|124
|124
|551.{{Overline|1}}
|551.{{Overline|1}}
|[[11/8]]
| rowspan="2" |12.685
|HP4
|551.29
|-
|-
|[[18/13]]
| rowspan="2" |2
| rowspan="2" |2
|44
|44
|561.7
|561.7
|[[18/13]]
| rowspan="2" |3
| rowspan="2" |3
|102
|102
|564.06
|564.06
|[[18/13]]
| rowspan="2" |4
| rowspan="2" |4
|127
|127
|564.{{Overline|4}}
|564.{{Overline|4}}
|[[18/13]]
| rowspan="2" |18.53
|^hTT
|563.975
|-
|-
|[[7/5]]
| rowspan="2" |2
| rowspan="2" |2
|46
|46
|587.23
|587.23
|[[7/5]]
| rowspan="2" |7
| rowspan="2" |7
|105
|105
|580.65
|580.65
|[[7/5]]
| rowspan="2" |8
| rowspan="2" |8
|131
|131
|582.{{Overline|2}}
|582.{{Overline|2}}
|[[7/5]]
| rowspan="2" |34.99
|vsTT
|582.505
|-
|-
|[[10/7]]
| rowspan="2" |2
| rowspan="2" |2
|48
|48
|612.77
|612.77
|[[10/7]]
| rowspan="2" |3
| rowspan="2" |3
|112
|112
|619.35
|619.35
|[[10/7]]
| rowspan="2" |4
| rowspan="2" |4
|139
|139
|617.{{Overline|7}}
|617.{{Overline|7}}
|[[10/7]]
| rowspan="2" |18.53
|vTT
|617.495
|-
|-
|[[13/9]]
| rowspan="2" |1
| rowspan="2" |1
|50
|50
|638.3
|638.3
|[[13/9]]
| rowspan="2" |2
| rowspan="2" |2
|115
|115
|635.94
|635.94
|[[13/9]]
| rowspan="2" |3
| rowspan="2" |3
|143
|143
|635.{{Overline|5}}
|635.{{Overline|5}}
|[[13/9]]
| rowspan="2" |12.685
|^STT
|636.025
|-
|-
|[[16/11]]
| rowspan="2" |1
| rowspan="2" |1
|51
|51
|651.06
|651.06
|[[16/11]]
| rowspan="2" |3
| rowspan="2" |3
|117
|117
|647.0
|647.0
|[[16/11]]
| rowspan="2" |3
| rowspan="2" |3
|146
|146
|648.{{Overline|8}}
|648.{{Overline|8}}
|[[16/11]]
| rowspan="2" |14.075
|hP5
|648.71
|-
|-
|[[22/15]]
| rowspan="2" |3
| rowspan="2" |3
|52
|52
|663.83
|663.83
|[[22/15]]
| rowspan="2" |7
| rowspan="2" |7
|120
|120
|663.59
|663.59
|[[22/15]]
| rowspan="2" |9
| rowspan="2" |9
|149
|149
|662.{{Overline|2}}
|662.{{Overline|2}}
|[[22/15]]
| rowspan="2" |39.445
|vsMP5
|662.785
|-
|-
|[[3/2]]
| rowspan="2" |3
| rowspan="2" |3
|55
|55
|702.13
|702.13
|[[3/2]]
| rowspan="2" |8
| rowspan="2" |8
|127
|127
|702.3
|702.3
|[[3/2]]
| rowspan="2" |10
| rowspan="2" |10
|158
|158
|702.{{Overline|2}}
|702.{{Overline|2}}
|[[3/2]]
| rowspan="2" |43.56
|P5
|702.23
|-
|-
|[[20/13]]
| rowspan="2" |2
| rowspan="2" |2
|58
|58
|740.43
|740.43
|[[20/13]]
| rowspan="2" |4
| rowspan="2" |4
|135
|135
|746.54
|746.54
|[[20/13]]
| rowspan="2" |4
| rowspan="2" |4
|168
|168
|746.{{Overline|6}}
|746.{{Overline|6}}
|[[20/13]]
| rowspan="2" |18.53
|^^hm6
|745.79
|-
|-
|[[14/9]]
| rowspan="2" |1
| rowspan="2" |1
|60
|60
|765.96
|765.96
|[[14/9]]
| rowspan="2" |4
| rowspan="2" |4
|138
|138
|763.13
|763.13
|[[14/9]]
| rowspan="2" |4
| rowspan="2" |4
|172
|172
|764.{{Overline|4}}
|764.{{Overline|4}}
|[[14/9]]
| rowspan="2" |18.19
|sm6
|764.32
|-
|-
|[[11/7]]
| rowspan="2" |3
| rowspan="2" |3
|61
|61
|778.72
|778.72
|[[11/7]]
| rowspan="2" |5
| rowspan="2" |5
|142
|142
|785.25
|785.25
|[[11/7]]
| rowspan="2" |5
| rowspan="2" |5
|176
|176
|782.{{Overline|2}}
|782.{{Overline|2}}
|[[11/7]]
| rowspan="2" |31.215
|sMm6
|782.51
|-
|-
|[[8/5]]
| rowspan="2" |2
| rowspan="2" |2
|64
|64
|817.02
|817.02
|[[8/5]]
| rowspan="2" |5
| rowspan="2" |5
|147
|147
|812.9
|812.9
|[[8/5]]
| rowspan="2" |6
| rowspan="2" |6
|183
|183
|813.{{Overline|3}}
|813.{{Overline|3}}
|[[8/5]]
| rowspan="2" |26.76
|vSm6
|813.725
|-
|-
|[[13/8]]
| rowspan="2" |1
| rowspan="2" |1
|66
|66
|842.55
|842.55
|[[13/8]]
| rowspan="2" |2
| rowspan="2" |2
|152
|152
|840.55
|840.55
|[[13/8]]
| rowspan="2" |3
| rowspan="2" |3
|189
|189
|840.0
|840.0
|[[13/8]]
| rowspan="2" |12.685
|vHm6
|840.485
|-
|-
|[[18/11]]
| rowspan="2" |2
| rowspan="2" |2
|67
|67
|855.32
|855.32
|[[18/11]]
| rowspan="2" |6
| rowspan="2" |6
|154
|154
|851.61
|851.61
|[[18/11]]
| rowspan="2" |7
| rowspan="2" |7
|192
|192
|853.{{Overline|3}}
|853.{{Overline|3}}
|[[18/11]]
| rowspan="2" |30.875
|hM6
|853.17
|-
|-
|[[5/3]]
| rowspan="2" |2
| rowspan="2" |2
|69
|69
|880.85
|880.85
|[[5/3]]
| rowspan="2" |5
| rowspan="2" |5
|160
|160
|884.79
|884.79
|[[5/3]]
| rowspan="2" |6
| rowspan="2" |6
|199
|199
|884.{{Overline|4}}
|884.{{Overline|4}}
|[[5/3]]
| rowspan="2" |26.76
|^sm6
|884.045
|-
|-
|[[22/13]]
| rowspan="2" |2
| rowspan="2" |2
|71
|71
|906.38
|906.38
|[[22/13]]
| rowspan="2" |5
| rowspan="2" |5
|165
|165
|912.44
|912.44
|[[22/13]]
| rowspan="2" |5
| rowspan="2" |5
|205
|205
|911.{{Overline|1}}
|911.{{Overline|1}}
|[[22/13]]
| rowspan="2" |22.645
|^M6
|910.805
|-
|-
|[[12/7]]
| rowspan="2" |2
| rowspan="2" |2
|73
|73
|931.91
|931.91
|[[12/7]]
| rowspan="2" |4
| rowspan="2" |4
|169
|169
|934.56
|934.56
|[[12/7]]
| rowspan="2" |4
| rowspan="2" |4
|210
|210
|933.{{Overline|3}}
|933.{{Overline|3}}
|[[12/7]]
| rowspan="2" |18.53
|SM6
|933.45
|-
|-
|[[26/15]]
| rowspan="2" |1
| rowspan="2" |1
|75
|75
|957.45
|957.45
|[[26/15]]
| rowspan="2" |4
| rowspan="2" |4
|172
|172
|951.15
|951.15
|[[26/15]]
| rowspan="2" |4
| rowspan="2" |4
|214
|214
|951.{{Overline|1}}
|951.{{Overline|1}}
|[[26/15]]
| rowspan="2" |16.8
|vvsmm7
|951.98
|-
|-
|[[7/4]]
| rowspan="2" |2
| rowspan="2" |2
|76
|76
|970.21
|970.21
|[[7/4]]
| rowspan="2" |6
| rowspan="2" |6
|175
|175
|967.74
|967.74
|[[7/4]]
| rowspan="2" |6
| rowspan="2" |6
|218
|218
|968.{{Overline|8}}
|968.{{Overline|8}}
|[[7/4]]
| rowspan="2" |26.76
|sm7
|968.78
|-
|-
|[[16/9]]
| rowspan="2" |2
| rowspan="2" |2
|78
|78
|995.74
|995.74
|[[16/9]]
| rowspan="2" |5
| rowspan="2" |5
|180
|180
|995.39
|995.39
|[[16/9]]
| rowspan="2" |5
| rowspan="2" |5
|224
|224
|995.{{Overline|5}}
|995.{{Overline|5}}
|[[16/9]]
| rowspan="2" |22.645
|m7
|995.54
|-
|-
|[[9/5]]
| rowspan="2" |1
| rowspan="2" |1
|80
|80
|1021.28
|1021.28
|[[9/5]]
| rowspan="2" |4
| rowspan="2" |4
|184
|184
|1017.51
|1017.51
|[[9/5]]
| rowspan="2" |4
| rowspan="2" |4
|229
|229
|1017.{{Overline|7}}
|1017.{{Overline|7}}
|[[9/5]]
| rowspan="2" |16.8
|vSm7
|1018.185
|-
|-
|[[20/11]]
| rowspan="2" |1
| rowspan="2" |1
|81
|81
|1034.04
|1034.04
|[[20/11]]
| rowspan="2" |4
| rowspan="2" |4
|187
|187
|1034.1
|1034.1
|[[20/11]]
| rowspan="2" |4
| rowspan="2" |4
|233
|233
|1035.{{Overline|5}}
|1035.{{Overline|5}}
|[[20/11]]
| rowspan="2" |14.075
|^Smm7
|1034.985
|-
|-
|[[11/6]]
| rowspan="2" |1
| rowspan="2" |1
|82
|82
|1046.81
|1046.81
|[[11/6]]
| rowspan="2" |3
| rowspan="2" |3
|190
|190
|1050.69
|1050.69
|[[11/6]]
| rowspan="2" |3
| rowspan="2" |3
|236
|236
|1048.{{Overline|8}}
|1048.{{Overline|8}}
|[[11/6]]
| rowspan="2" |12.685
|Hm7
|1049.06
|-
|-
|[[24/13]]
| rowspan="2" |1
| rowspan="2" |1
|83
|83
|1059.57
|1059.57
|[[24/13]]
| rowspan="2" |2
| rowspan="2" |2
|192
|192
|1061.75
|1061.75
|[[24/13]]
| rowspan="2" |2
| rowspan="2" |2
|239
|239
|1062.{{Overline|2}}
|1062.{{Overline|2}}
|[[24/13]]
| rowspan="2" |9.96
|^hM7
|1061.745
|-
|-
|[[13/7]]
| rowspan="2" |1
| rowspan="2" |1
|84
|84
|1072.34
|1072.34
|[[13/7]]
| rowspan="2" |2
| rowspan="2" |2
|194
|194
|1072.81
|1072.81
|[[13/7]]
| rowspan="2" |2
| rowspan="2" |2
|241
|241
|1071.{{Overline|1}}
|1071.{{Overline|1}}
|[[13/7]]
| rowspan="2" |8.57
|vsMM7
|1071.705
|-
|-
|[[28/15]]
| rowspan="2" |0
| rowspan="2" |0
| rowspan="2" |85
| rowspan="2" |85
| rowspan="2" |1085.11
| rowspan="2" |1085.11
|[[28/15]]
| rowspan="2" |2
| rowspan="2" |2
|195
|195
|1078.34
|1078.34
|[[28/15]]
| rowspan="2" |2
| rowspan="2" |2
|243
|243
|1080.0
|1080.0
|[[28/15]]
| rowspan="2" |8.23
|vsM7
|1080.275
|-
|-
|
|[[15/8]]
|[[15/8]]
|
|
|
|197
|197
|1089.4
|1089.4
|[[15/8]]
|
|
|245
|245
|1088.{{Overline|8}}
|1088.{{Overline|8}}
|[[15/8]]
|
|^sM7
|1088.505
|}
|}


== Table of 270edo's yazalatha 225-odd-limit ==
== 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.
Almost consistent to distance 2. Covers the whole gamut except 4 edostep-classes in almost pure 13-limit glory, only inconsistency is (15/13)<sup>2</sup> which is ~4/3 here. Incredible.
{| class="wikitable mw-collapsible mw-collapsed" data-darkreader-inline-color=""
{| class="wikitable mw-collapsible mw-collapsed" data-darkreader-inline-color=""
|+270edo yazalatha 225-odd-limit
|+270edo yazalatha 225-odd-limit
|1
|4.{{overline|4}}
|[[540/539]], [[441/440]], [[5120/5103]], [[385/384]], [[352/351]]
|-
|-
!Tredeks
!Tredeks
!Cents
!Cents
!Ratio
!Ratios
|-
|1
|4.{{overline|4}}
|–
|-
|-
|2
|2
Line 730: Line 1,004:
|39
|39
|173.{{overline|3}}
|173.{{overline|3}}
|
|–
|-
|-
|40
|40
Line 1,490: Line 1,764:
|231
|231
|1026.{{overline|6}}
|1026.{{overline|6}}
|
|–
|-
|-
|232
|232
Line 1,642: Line 1,916:
|269
|269
|1186.{{overline|6}}
|1186.{{overline|6}}
|
|–
|-
|-
|270
|270
Line 1,650: Line 1,924:


== Table of prime-generated MOS scales ==
== Table of prime-generated MOS scales ==
<span data-darkreader-inline-color="">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.</span>
<span data-darkreader-inline-color="">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 good. '''I''' wouldn't use most of them, but they are good. If the hyperlink is in italics it means that it is a multiple that whose prime is convergent, but no longer telic.</span>


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. Luckily its triple, 111edo, is very solid. Also 10edo, which basically reaches near-perfection on p13 and 15/14, for which 270edo is one of the best detempers.
{| class="wikitable mw-collapsible mw-collapsed" 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'''
Line 1,666: Line 1,940:
!'''23'''
!'''23'''
|-
|-
|eva
|Eve
| colspan="7" |<small>1L 1s</small>
| colspan="7" |<small>1L 1s</small>
| colspan="3" |'''<small>1L 1s</small>'''
| colspan="3" |'''<small>1L 1s</small>'''
Line 1,672: Line 1,946:
|1st filial scale
|1st filial scale
| colspan="5" |<small>1L 2s</small>
| colspan="5" |<small>1L 2s</small>
| colspan="2" |<small>'''[[3edo|1L 2s]]'''</small>
| colspan="2" |<small>'''1L 2s'''</small>
| colspan="3" |<small>2L 1s</small>
| colspan="3" |<small>2L 1s</small>
|-
|-
|2nd filial scale
|2nd filial scale
| colspan="4" |<small>1L 3s</small>
| colspan="4" |<small>1L 3s</small>
|'''<small>[[4edo|1L 3s]]</small>'''
|'''<small>1L 3s</small>'''
| colspan="2" |<small>3L 1s</small>
| colspan="2" |<small>3L 1s</small>
|'''<small>[[5edo|2L 3s]]</small>'''
|'''<small>[[5edo|2L 3s]]</small>'''
Line 1,695: Line 1,969:
|<small>5L 1s</small>
|<small>5L 1s</small>
|<small>4L 5s</small>
|<small>4L 5s</small>
|'''<small>[[10edo|7L 3s]]</small>'''
|'''<small>[[270edo|''7L 3s'']]</small>'''
|<small>[[10edo|3L 7s]]</small>
|<small>[[10edo|3L 7s]]</small>
|'''<small>[[12edo|5L 7s]]</small>'''
|'''<small>[[12edo|5L 7s]]</small>'''
Line 1,718: Line 1,992:
|<small>3L 13s</small>
|<small>3L 13s</small>
|<small>12L 17s</small>
|<small>12L 17s</small>
|'''<small>11L 2s</small>'''
|'''<small>[[130edo|''11L 2s'']]</small>'''
|<small>2L 11s</small>
|<small>2L 11s</small>
|-
|-
Line 1,740: Line 2,014:
|<small>3L 19s</small>
|<small>3L 19s</small>
|'''<small>[[53edo|41L 12s]]</small>'''
|'''<small>[[53edo|41L 12s]]</small>'''
|'''<small>24L 13s</small>'''
|'''<small>[[111edo|24L 13s]]</small>'''
|<small>2L 15s</small>
|<small>2L 15s</small>
|-
|-
Line 1,786: Line 2,060:
|<small>[[41edo|4L 37s]]</small>
|<small>[[41edo|4L 37s]]</small>
|<small>10L 77s</small>
|<small>10L 77s</small>
|'''<small>28L 31s</small>'''
|'''<small>[[118edo|''28L 31s'']]</small>'''
|<small>53L 200s</small>
|<small>53L 200s</small>
|<small>37L 135s</small>
|<small>37L 135s</small>
Retrieved from "https://en.xen.wiki/w/User:Eufalesio/Important_Tables"