@@ Line 1: / Line 1: @@
 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}; supported trivially by 41edo
-!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}; supported trivially by 12e
-!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
-|–
+| –
 |}
+Any other join of Ultimate edos is ommited because I either don't know or don't care.
 == 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=""
 |+15-odd-limit ratios
+! colspan="4" |94edo
 !Ratios
-! colspan="4" |94edo
 ! colspan="4" |217edo
+!Ratios
 ! colspan="4" |270edo
 |-
-|[[16/15]]
 | rowspan="2" |
 | rowspan="3" |1
 | rowspan="2" |9
 | rowspan="2" |114.89
+|[[16/15]]
 |
 | rowspan="2" |2
 |20
 |110.6
+|[[16/15]]
 |
 | rowspan="2" |2
@@ Line 59: / Line 73: @@
 |22
 |121.66
+|[[15/14]]
 | rowspan="2" |2
 |27
 |120
 |-
-|[[14/13]]
 | rowspan="2" |1
 |10
 |127.66
+|[[14/13]]
 | rowspan="2" |2
 |23
 |127.19
+|[[14/13]]
 | rowspan="2" |2
 |29
 |128.{{Overline|8}}
 |-
-|[[13/12]]
 | rowspan="2" |1
 |11
 |140.43
+|[[13/12]]
 | rowspan="2" |2
 |25
 |138.25
+|[[13/12]]
 | rowspan="2" |3
 |31
 |137.{{Overline|7}}
 |-
-|[[12/11]]
 | rowspan="2" |1
 |12
 |153.19
+|[[12/11]]
 | rowspan="2" |3
 |27
 |149.31
+|[[12/11]]
 | rowspan="2" |3
 |34
 |151.{{Overline|1}}
 |-
-|[[11/10]]
 | rowspan="2" |1
 |13
 |165.96
+|[[11/10]]
 | rowspan="2" |3
 |30
 |165.9
+|[[11/10]]
 | rowspan="2" |4
 |37
 |164.{{Overline|4}}
 |-
-|[[10/9]]
 | rowspan="2" |2
 |14
 |178.72
+|[[10/9]]
 | rowspan="2" |4
 |33
 |182.49
+|[[10/9]]
 | rowspan="2" |5
 |41
 |182.{{Overline|2}}
 |-
-|[[9/8]]
 | rowspan="2" |2
 |16
 |204.26
+|[[9/8]]
 | rowspan="2" |5
 |37
 |204.61
+|[[9/8]]
 | rowspan="2" |6
 |46
 |204.{{Overline|4}}
 |-
-|[[8/7]]
 | rowspan="2" |1
 |18
 |229.79
+|[[8/7]]
 | rowspan="2" |3
 |42
 |232.26
+|[[8/7]]
 | rowspan="2" |4
 |52
 |231.{{Overline|1}}
 |-
-|[[15/13]]
 | rowspan="2" |2
 |19
 |242.55
+|[[15/13]]
 | rowspan="2" |3
 |45
 |248.85
+|[[15/13]]
 | rowspan="2" |4
 |56
 |248.{{Overline|8}}
 |-
-|[[7/6]]
 | rowspan="2" |2
 |21
 |268.09
+|[[7/6]]
 | rowspan="2" |4
 |48
 |265.44
+|[[7/6]]
 | rowspan="2" |5
 |60
 |266.{{Overline|6}}
 |-
-|[[13/11]]
 | rowspan="2" |2
 |23
 |293.62
+|[[13/11]]
 | rowspan="2" |5
 |52
 |287.56
+|[[13/11]]
 | rowspan="2" |6
 |65
 |288.{{Overline|8}}
 |-
-|[[6/5]]
 | rowspan="2" |2
 |25
 |319.15
+|[[6/5]]
 | rowspan="2" |6
 |57
 |315.21
+|[[6/5]]
 | rowspan="2" |7
 |71
 |315.{{Overline|5}}
 |-
-|[[11/9]]
 | rowspan="2" |1
 |27
 |344.68
+|[[11/9]]
 | rowspan="2" |2
 |63
 |348.39
+|[[11/9]]
 | rowspan="2" |4
 |78
 |346.{{Overline|6}}
 |-
-|[[16/13]]
 | rowspan="2" |2
 |28
 |357.45
+|[[16/13]]
 | rowspan="2" |5
 |65
 |359.45
+|[[16/13]]
 | rowspan="2" |6
 |81
 |360.0
 |-
-|[[5/4]]
 | rowspan="2" |3
 |30
 |382.98
+|[[5/4]]
 | rowspan="2" |5
 |70
 |387.1
+|[[5/4]]
 | rowspan="2" |7
 |87
 |386.{{Overline|6}}
 |-
-|[[14/11]]
 | rowspan="2" |1
 |33
 |421.28
+|[[14/11]]
 | rowspan="2" |4
 |75
 |414.75
+|[[14/11]]
 | rowspan="2" |4
 |94
 |417.{{Overline|7}}
 |-
-|[[9/7]]
 | rowspan="2" |2
 |34
 |434.04
+|[[9/7]]
 | rowspan="2" |4
 |79
 |436.87
+|[[9/7]]
 | rowspan="2" |4
 |98
 |435.{{Overline|5}}
 |-
-|[[13/10]]
 | rowspan="2" |3
 |36
 |459.57
+|[[13/10]]
 | rowspan="2" |8
 |82
 |453.46
+|[[13/10]]
 | rowspan="2" |10
 |102
 |453.{{Overline|3}}
 |-
-|[[4/3]]
 | rowspan="2" |3
 |39
 |497.87
+|[[4/3]]
 | rowspan="2" |7
 |90
 |497.7
+|[[4/3]]
 | rowspan="2" |9
 |112
 |497.{{Overline|7}}
 |-
-|[[15/11]]
 | rowspan="2" |1
 |42
 |536.17
+|[[15/11]]
 | rowspan="2" |3
 |97
 |536.41
+|[[15/11]]
 | rowspan="2" |3
 |121
 |537.{{Overline|7}}
 |-
-|[[11/8]]
 | rowspan="2" |1
 |43
 |548.94
+|[[11/8]]
 | rowspan="2" |2
 |100
 |553.0
+|[[11/8]]
 | rowspan="2" |3
 |124
 |551.{{Overline|1}}
 |-
-|[[18/13]]
 | rowspan="2" |2
 |44
 |561.7
+|[[18/13]]
 | rowspan="2" |3
 |102
 |564.06
+|[[18/13]]
 | rowspan="2" |4
 |127
 |564.{{Overline|4}}
 |-
-|[[7/5]]
 | rowspan="2" |2
 |46
 |587.23
+|[[7/5]]
 | rowspan="2" |7
 |105
 |580.65
+|[[7/5]]
 | rowspan="2" |8
 |131
 |582.{{Overline|2}}
 |-
-|[[10/7]]
 | rowspan="2" |2
 |48
 |612.77
+|[[10/7]]
 | rowspan="2" |3
 |112
 |619.35
+|[[10/7]]
 | rowspan="2" |4
 |139
 |617.{{Overline|7}}
 |-
-|[[13/9]]
 | rowspan="2" |1
 |50
 |638.3
+|[[13/9]]
 | rowspan="2" |2
 |115
 |635.94
+|[[13/9]]
 | rowspan="2" |3
 |143
 |635.{{Overline|5}}
 |-
-|[[16/11]]
 | rowspan="2" |1
 |51
 |651.06
+|[[16/11]]
 | rowspan="2" |3
 |117
 |647.0
+|[[16/11]]
 | rowspan="2" |3
 |146
 |648.{{Overline|8}}
 |-
-|[[22/15]]
 | rowspan="2" |3
 |52
 |663.83
+|[[22/15]]
 | rowspan="2" |7
 |120
 |663.59
+|[[22/15]]
 | rowspan="2" |9
 |149
 |662.{{Overline|2}}
 |-
-|[[3/2]]
 | rowspan="2" |3
 |55
 |702.13
+|[[3/2]]
 | rowspan="2" |8
 |127
 |702.3
+|[[3/2]]
 | rowspan="2" |10
 |158
 |702.{{Overline|2}}
 |-
-|[[20/13]]
 | rowspan="2" |2
 |58
 |740.43
+|[[20/13]]
 | rowspan="2" |4
 |135
 |746.54
+|[[20/13]]
 | rowspan="2" |4
 |168
 |746.{{Overline|6}}
 |-
-|[[14/9]]
 | rowspan="2" |1
 |60
 |765.96
+|[[14/9]]
 | rowspan="2" |4
 |138
 |763.13
+|[[14/9]]
 | rowspan="2" |4
 |172
 |764.{{Overline|4}}
 |-
-|[[11/7]]
 | rowspan="2" |3
 |61
 |778.72
+|[[11/7]]
 | rowspan="2" |5
 |142
 |785.25
+|[[11/7]]
 | rowspan="2" |5
 |176
 |782.{{Overline|2}}
 |-
-|[[8/5]]
 | rowspan="2" |2
 |64
 |817.02
+|[[8/5]]
 | rowspan="2" |5
 |147
 |812.9
+|[[8/5]]
 | rowspan="2" |6
 |183
 |813.{{Overline|3}}
 |-
-|[[13/8]]
 | rowspan="2" |1
 |66
 |842.55
+|[[13/8]]
 | rowspan="2" |2
 |152
 |840.55
+|[[13/8]]
 | rowspan="2" |3
 |189
 |840.0
 |-
-|[[18/11]]
 | rowspan="2" |2
 |67
 |855.32
+|[[18/11]]
 | rowspan="2" |6
 |154
 |851.61
+|[[18/11]]
 | rowspan="2" |7
 |192
 |853.{{Overline|3}}
 |-
-|[[5/3]]
 | rowspan="2" |2
 |69
 |880.85
+|[[5/3]]
 | rowspan="2" |5
 |160
 |884.79
+|[[5/3]]
 | rowspan="2" |6
 |199
 |884.{{Overline|4}}
 |-
-|[[22/13]]
 | rowspan="2" |2
 |71
 |906.38
+|[[22/13]]
 | rowspan="2" |5
 |165
 |912.44
+|[[22/13]]
 | rowspan="2" |5
 |205
 |911.{{Overline|1}}
 |-
-|[[12/7]]
 | rowspan="2" |2
 |73
 |931.91
+|[[12/7]]
 | rowspan="2" |4
 |169
 |934.56
+|[[12/7]]
 | rowspan="2" |4
 |210
 |933.{{Overline|3}}
 |-
-|[[26/15]]
 | rowspan="2" |1
 |75
 |957.45
+|[[26/15]]
 | rowspan="2" |4
 |172
 |951.15
+|[[26/15]]
 | rowspan="2" |4
 |214
 |951.{{Overline|1}}
 |-
-|[[7/4]]
 | rowspan="2" |2
 |76
 |970.21
+|[[7/4]]
 | rowspan="2" |6
 |175
 |967.74
+|[[7/4]]
 | rowspan="2" |6
 |218
 |968.{{Overline|8}}
 |-
-|[[16/9]]
 | rowspan="2" |2
 |78
 |995.74
+|[[16/9]]
 | rowspan="2" |5
 |180
 |995.39
+|[[16/9]]
 | rowspan="2" |5
 |224
 |995.{{Overline|5}}
 |-
-|[[9/5]]
 | rowspan="2" |1
 |80
 |1021.28
+|[[9/5]]
 | rowspan="2" |4
 |184
 |1017.51
+|[[9/5]]
 | rowspan="2" |4
 |229
 |1017.{{Overline|7}}
 |-
-|[[20/11]]
 | rowspan="2" |1
 |81
 |1034.04
+|[[20/11]]
 | rowspan="2" |4
 |187
 |1034.1
+|[[20/11]]
 | rowspan="2" |4
 |233
 |1035.{{Overline|5}}
 |-
-|[[11/6]]
 | rowspan="2" |1
 |82
 |1046.81
+|[[11/6]]
 | rowspan="2" |3
 |190
 |1050.69
+|[[11/6]]
 | rowspan="2" |3
 |236
 |1048.{{Overline|8}}
 |-
-|[[24/13]]
 | rowspan="2" |1
 |83
 |1059.57
+|[[24/13]]
 | rowspan="2" |2
 |192
 |1061.75
+|[[24/13]]
 | rowspan="2" |2
 |239
 |1062.{{Overline|2}}
 |-
-|[[13/7]]
 | rowspan="2" |1
 |84
 |1072.34
+|[[13/7]]
 | rowspan="2" |2
 |194
 |1072.81
+|[[13/7]]
 | rowspan="2" |2
 |241
 |1071.{{Overline|1}}
 |-
-|[[28/15]]
 | rowspan="2" |0
 | rowspan="2" |85
 | rowspan="2" |1085.11
+|[[28/15]]
 | rowspan="2" |2
 |195
 |1078.34
+|[[28/15]]
 | rowspan="2" |2
 |243
 |1080.0
 |-
+|
 |[[15/8]]
-|
 |
 |197
 |1089.4
+|[[15/8]]
 |
 |245
@@ Line 569: / Line 630: @@
 == 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=""
 |+270edo yazalatha 225-odd-limit
-|1
-|4.{{overline|4}}
-|[[540/539]], [[441/440]], [[5120/5103]], [[385/384]], [[352/351]]
 |-
 !Tredeks
 !Cents
-!Ratio
+!Ratios
+|-
+|1
+|4.{{overline|4}}
+|–
 |-
 |2
@@ Line 730: / Line 792: @@
 |39
 |173.{{overline|3}}
-|
+|–
 |-
 |40
@@ Line 1,490: / Line 1,552: @@
 |231
 |1026.{{overline|6}}
-|
+|–
 |-
 |232
@@ Line 1,642: / Line 1,704: @@
 |269
 |1186.{{overline|6}}
-|
+|–
 |-
 |270
@@ Line 1,653: / Line 1,715: @@
 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'''
 !31

User:Eufalesio/Important Tables: Difference between revisions