User:Eufalesio/Important Tables: Difference between revisions

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'''217 & 270 & 311: Ultimate {S49*S55, S64, S65} = {2080/2079, 4096/4095, 35035/34992}'''
'''217 & 270 & 311: Ultimate {S49*S55, S64, S65} = {2080/2079, 4096/4095, 35035/34992}'''


* '''270 & 311''': Newt {S49, S55, S64, S65} = {2080/2079, 2401/2400, 3025/3024, 4096/4095}
* '''270 & 311''': Newt {S49, S55, S64, S65} = {2080/2079, 2401/2400, 3025/3024, 4096/4095}; 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) = {1716/1715, <span data-darkreader-inline-color="">2080/2079, 4096/4095, 35035/34992}</span>
* '''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>
* '''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>
* '''41 & 53''': Cassandra {S25*S26, S15, S64, S65} = {225/224, 325/324, 352/351, 385/384}
* '''41 & 53''': Cassandra {S25*S26, S15, S64, S65} = {225/224, 325/324, 352/351, 385/384}; 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} = {1001/1000, 2401/2400, 2080/2079, 3025/3024, 4096/4095}
** '''94:''' {S15, S11/S12, S64, S65, S99} = {225/224, 325/324, 352/351, 385/384, 1716/1715}
** '''94:''' {S15, S11/S12, S64, S65, S99} = {225/224, 325/324, 352/351, 385/384, 1716/1715}
Line 43: Line 43:
|}
|}


Special thanks to [[Godtone]] for helping me make sense of all these temp properties and and helping me format them in a correct way.
Any other join of Ultimate edos is ommited because I either don't know or don't care.
== 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
|-
|-
|[[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
Line 71: Line 73:
|22
|22
|121.66
|121.66
|[[15/14]]
| rowspan="2" |2
| rowspan="2" |2
|27
|27
|120
|120
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
|[[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}}
|-
|-
| rowspan="2" |0
| rowspan="2" |85
| rowspan="2" |1085.11
|[[28/15]]
|[[28/15]]
| rowspan="2" |0
| rowspan="2" |2
| rowspan="2" |85
|195
| rowspan="2" |1085.11
|1078.34
| rowspan="2" |2
|[[28/15]]
|195
| rowspan="2" |2
|1078.34
|243
| rowspan="2" |2
|1080.0
|243
|-
|1080.0
|
|[[15/8]]
|
|197
|1089.4
|[[15/8]]
|
|245
|1088.{{Overline|8}}
|}
 
== Table of 270edo's yazalatha 225-odd-limit ==
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=""
|+270edo yazalatha 225-odd-limit
|-
!Tredeks
!Cents
!Ratios
|-
|-
|[[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
|1
|4.{{overline|4}}
|4.{{overline|4}}
|[[540/539]], [[441/440]], [[5120/5103]], [[385/384]], [[352/351]]
|
|-
!Tredeks
!Cents
!Ratio
|-
|-
|2
|2
Line 742: Line 792:
|39
|39
|173.{{overline|3}}
|173.{{overline|3}}
|
|
|-
|-
|40
|40
Line 1,502: Line 1,552:
|231
|231
|1026.{{overline|6}}
|1026.{{overline|6}}
|
|
|-
|-
|232
|232
Line 1,654: Line 1,704:
|269
|269
|1186.{{overline|6}}
|1186.{{overline|6}}
|
|
|-
|-
|270
|270