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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
| –
| –
|}
|}
Line 53: Line 53:
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 78: Line 87:
|25
|25
|111.{{Overline|1}}
|111.{{Overline|1}}
|[[16/15]]
|
| rowspan="2" |8.23
|vSm2
|111.495
|-
|-
|[[15/14]]
|[[15/14]]
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|27
|27
|120
|120
|[[15/14]]
| rowspan="2" |8.57
|^Sm2
|119.725
|-
|-
| rowspan="2" |1
| rowspan="2" |1
Line 99: Line 117:
|29
|29
|128.{{Overline|8}}
|128.{{Overline|8}}
|[[14/13]]
| rowspan="2" |9.96
|^Smm2
|128.295
|-
|-
| rowspan="2" |1
| rowspan="2" |1
Line 111: Line 133:
|31
|31
|137.{{Overline|7}}
|137.{{Overline|7}}
|[[13/12]]
| rowspan="2" |12.685
|vHm2
|138.255
|-
|-
| rowspan="2" |1
| rowspan="2" |1
Line 123: Line 149:
|34
|34
|151.{{Overline|1}}
|151.{{Overline|1}}
|[[12/11]]
| rowspan="2" |14.075
|hM2
|150.94
|-
|-
| rowspan="2" |1
| rowspan="2" |1
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|37
|37
|164.{{Overline|4}}
|164.{{Overline|4}}
|[[11/10]]
| rowspan="2" |16.8
|vsMM2
|165.015
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|41
|41
|182.{{Overline|2}}
|182.{{Overline|2}}
|[[10/9]]
| rowspan="2" |22.645
|^sM2
|181.815
|-
|-
| rowspan="2" |2
| rowspan="2" |2
Line 159: Line 197:
|46
|46
|204.{{Overline|4}}
|204.{{Overline|4}}
|[[9/8]]
| rowspan="2" |26.76
|M2
|204.46
|-
|-
| rowspan="2" |1
| rowspan="2" |1
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|52
|52
|231.{{Overline|1}}
|231.{{Overline|1}}
|[[8/7]]
| rowspan="2" |16.8
|SM2
|231.22
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|56
|56
|248.{{Overline|8}}
|248.{{Overline|8}}
|[[15/13]]
| rowspan="2" |18.53
|^^SMM2
|248.02
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|60
|60
|266.{{Overline|6}}
|266.{{Overline|6}}
|[[7/6]]
| rowspan="2" |22.645
|sm3
|266.55
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|65
|65
|288.{{Overline|8}}
|288.{{Overline|8}}
|[[13/11]]
| rowspan="2" |26.76
|vm3
|289.195
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|71
|71
|315.{{Overline|5}}
|315.{{Overline|5}}
|[[6/5]]
| rowspan="2" |30.875
|vSm3
|315.955
|-
|-
| rowspan="2" |1
| rowspan="2" |1
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|78
|78
|346.{{Overline|6}}
|346.{{Overline|6}}
|[[11/9]]
| rowspan="2" |12.685
|Hm3
|346.83
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|81
|81
|360.0
|360.0
|[[16/13]]
| rowspan="2" |26.76
|^hM3
|359.515
|-
|-
| rowspan="2" |3
| rowspan="2" |3
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|87
|87
|386.{{Overline|6}}
|386.{{Overline|6}}
|[[5/4]]
| rowspan="2" |31.215
|^sM3
|386.275
|-
|-
| rowspan="2" |1
| rowspan="2" |1
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|94
|94
|417.{{Overline|7}}
|417.{{Overline|7}}
|[[14/11]]
| rowspan="2" |18.19
|SmM3
|417.49
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|98
|98
|435.{{Overline|5}}
|435.{{Overline|5}}
|[[9/7]]
| rowspan="2" |18.53
|SM3
|435.68
|-
|-
| rowspan="2" |3
| rowspan="2" |3
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|102
|102
|453.{{Overline|3}}
|453.{{Overline|3}}
|[[13/10]]
| rowspan="2" |43.56
|vvHM3
|454.21
|-
|-
| rowspan="2" |3
| rowspan="2" |3
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|112
|112
|497.{{Overline|7}}
|497.{{Overline|7}}
|[[4/3]]
| rowspan="2" |39.445
|P4
|497.77
|-
|-
| rowspan="2" |1
| rowspan="2" |1
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|121
|121
|537.{{Overline|7}}
|537.{{Overline|7}}
|[[15/11]]
| rowspan="2" |14.075
|^SmP4
|537.215
|-
|-
| rowspan="2" |1
| rowspan="2" |1
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|124
|124
|551.{{Overline|1}}
|551.{{Overline|1}}
|[[11/8]]
| rowspan="2" |12.685
|HP4
|551.29
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|127
|127
|564.{{Overline|4}}
|564.{{Overline|4}}
|[[18/13]]
| rowspan="2" |18.53
|^hTT
|563.975
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|131
|131
|582.{{Overline|2}}
|582.{{Overline|2}}
|[[7/5]]
| rowspan="2" |34.99
|vsTT
|582.505
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|139
|139
|617.{{Overline|7}}
|617.{{Overline|7}}
|[[10/7]]
| rowspan="2" |18.53
|vTT
|617.495
|-
|-
| rowspan="2" |1
| rowspan="2" |1
Line 375: Line 485:
|143
|143
|635.{{Overline|5}}
|635.{{Overline|5}}
|[[13/9]]
| rowspan="2" |12.685
|^STT
|636.025
|-
|-
| rowspan="2" |1
| rowspan="2" |1
Line 387: Line 501:
|146
|146
|648.{{Overline|8}}
|648.{{Overline|8}}
|[[16/11]]
| rowspan="2" |14.075
|hP5
|648.71
|-
|-
| rowspan="2" |3
| rowspan="2" |3
Line 399: Line 517:
|149
|149
|662.{{Overline|2}}
|662.{{Overline|2}}
|[[22/15]]
| rowspan="2" |39.445
|vsMP5
|662.785
|-
|-
| rowspan="2" |3
| rowspan="2" |3
Line 411: Line 533:
|158
|158
|702.{{Overline|2}}
|702.{{Overline|2}}
|[[3/2]]
| rowspan="2" |43.56
|P5
|702.23
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|168
|168
|746.{{Overline|6}}
|746.{{Overline|6}}
|[[20/13]]
| rowspan="2" |18.53
|^^hm6
|745.79
|-
|-
| rowspan="2" |1
| rowspan="2" |1
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|172
|172
|764.{{Overline|4}}
|764.{{Overline|4}}
|[[14/9]]
| rowspan="2" |18.19
|sm6
|764.32
|-
|-
| rowspan="2" |3
| rowspan="2" |3
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|176
|176
|782.{{Overline|2}}
|782.{{Overline|2}}
|[[11/7]]
| rowspan="2" |31.215
|sMm6
|782.51
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|183
|183
|813.{{Overline|3}}
|813.{{Overline|3}}
|[[8/5]]
| rowspan="2" |26.76
|vSm6
|813.725
|-
|-
| rowspan="2" |1
| rowspan="2" |1
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|189
|189
|840.0
|840.0
|[[13/8]]
| rowspan="2" |12.685
|vHm6
|840.485
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|192
|192
|853.{{Overline|3}}
|853.{{Overline|3}}
|[[18/11]]
| rowspan="2" |30.875
|hM6
|853.17
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|199
|199
|884.{{Overline|4}}
|884.{{Overline|4}}
|[[5/3]]
| rowspan="2" |26.76
|^sm6
|884.045
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|205
|205
|911.{{Overline|1}}
|911.{{Overline|1}}
|[[22/13]]
| rowspan="2" |22.645
|^M6
|910.805
|-
|-
| rowspan="2" |2
| rowspan="2" |2
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|210
|210
|933.{{Overline|3}}
|933.{{Overline|3}}
|[[12/7]]
| rowspan="2" |18.53
|SM6
|933.45
|-
|-
| rowspan="2" |1
| rowspan="2" |1
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|214
|214
|951.{{Overline|1}}
|951.{{Overline|1}}
|[[26/15]]
| rowspan="2" |16.8
|vvsmm7
|951.98
|-
|-
| rowspan="2" |2
| rowspan="2" |2
Line 543: Line 709:
|218
|218
|968.{{Overline|8}}
|968.{{Overline|8}}
|[[7/4]]
| rowspan="2" |26.76
|sm7
|968.78
|-
|-
| rowspan="2" |2
| rowspan="2" |2
Line 555: Line 725:
|224
|224
|995.{{Overline|5}}
|995.{{Overline|5}}
|[[16/9]]
| rowspan="2" |22.645
|m7
|995.54
|-
|-
| rowspan="2" |1
| rowspan="2" |1
Line 567: Line 741:
|229
|229
|1017.{{Overline|7}}
|1017.{{Overline|7}}
|[[9/5]]
| rowspan="2" |16.8
|vSm7
|1018.185
|-
|-
| rowspan="2" |1
| rowspan="2" |1
Line 579: Line 757:
|233
|233
|1035.{{Overline|5}}
|1035.{{Overline|5}}
|[[20/11]]
| rowspan="2" |14.075
|^Smm7
|1034.985
|-
|-
| rowspan="2" |1
| rowspan="2" |1
Line 591: Line 773:
|236
|236
|1048.{{Overline|8}}
|1048.{{Overline|8}}
|[[11/6]]
| rowspan="2" |12.685
|Hm7
|1049.06
|-
|-
| rowspan="2" |1
| rowspan="2" |1
Line 603: Line 789:
|239
|239
|1062.{{Overline|2}}
|1062.{{Overline|2}}
|[[24/13]]
| rowspan="2" |9.96
|^hM7
|1061.745
|-
|-
| rowspan="2" |1
| rowspan="2" |1
Line 615: Line 805:
|241
|241
|1071.{{Overline|1}}
|1071.{{Overline|1}}
|[[13/7]]
| rowspan="2" |8.57
|vsMM7
|1071.705
|-
|-
| rowspan="2" |0
| rowspan="2" |0
Line 627: Line 821:
|243
|243
|1080.0
|1080.0
|[[28/15]]
| rowspan="2" |8.23
|vsM7
|1080.275
|-
|-
|
|
Line 637: Line 835:
|245
|245
|1088.{{Overline|8}}
|1088.{{Overline|8}}
|[[15/8]]
|
|^sM7
|1088.505
|}
|}


Line 1,722: 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. Luckily its triple, 111edo, is quite decent.
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 1,738: 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 1,744: 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 1,767: 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 1,790: 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 1,858: 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"