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User:Eufalesio/Important Tables

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Revision as of 15:49, 13 May 2026 by Eufalesio (talk | contribs) (Updated Ultimate temp data (thanks Godtone!))

Data I deem important!

Temperament properties of Ultimate edos (I care about)

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}
  • 94 & 270: Gariwizmic {S11/S12, S64, S65, S99) = {1716/1715, 2080/2079, 4096/4095, 35035/34992}
  • 41 & 217: Cotoneum {S21, S282*S29, S64, S65} = {441/440, 2080/2079, 4096/4095, 10976/10935}
  • 41 & 53: Cassandra {S25*S26, S15, S64, S65} = {225/224, 325/324, 352/351, 385/384}
    • 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}
    • 12e: {S8, S9, S15, S64, S65} = {22/21, 50/49, 64/63, 65/63, 81/80}

Which can implicitly be seen in this table:

311 41 53 12e 94 270 217 Ultimate r3
2080/2079
4096/4095
35035/34492
2401/2400 676/675 81/80 1716/1715 441/440 –
625/624 385/384 1001/1000 –


Table of Ultimate edos' intervals

A good and regular set of intervals I care about.

15-odd-limit ratios
Ratios 94edo 217edo 270edo
16/15 1 9 114.89 2 20 110.6 2 25 111.1
15/14 1 22 121.66 2 27 120
14/13 1 10 127.66 2 23 127.19 2 29 128.8
13/12 1 11 140.43 2 25 138.25 3 31 137.7
12/11 1 12 153.19 3 27 149.31 3 34 151.1
11/10 1 13 165.96 3 30 165.9 4 37 164.4
10/9 2 14 178.72 4 33 182.49 5 41 182.2
9/8 2 16 204.26 5 37 204.61 6 46 204.4
8/7 1 18 229.79 3 42 232.26 4 52 231.1
15/13 2 19 242.55 3 45 248.85 4 56 248.8
7/6 2 21 268.09 4 48 265.44 5 60 266.6
13/11 2 23 293.62 5 52 287.56 6 65 288.8
6/5 2 25 319.15 6 57 315.21 7 71 315.5
11/9 1 27 344.68 2 63 348.39 4 78 346.6
16/13 2 28 357.45 5 65 359.45 6 81 360.0
5/4 3 30 382.98 5 70 387.1 7 87 386.6
14/11 1 33 421.28 4 75 414.75 4 94 417.7
9/7 2 34 434.04 4 79 436.87 4 98 435.5
13/10 3 36 459.57 8 82 453.46 10 102 453.3
4/3 3 39 497.87 7 90 497.7 9 112 497.7
15/11 1 42 536.17 3 97 536.41 3 121 537.7
11/8 1 43 548.94 2 100 553.0 3 124 551.1
18/13 2 44 561.7 3 102 564.06 4 127 564.4
7/5 2 46 587.23 7 105 580.65 8 131 582.2
10/7 2 48 612.77 3 112 619.35 4 139 617.7
13/9 1 50 638.3 2 115 635.94 3 143 635.5
16/11 1 51 651.06 3 117 647.0 3 146 648.8
22/15 3 52 663.83 7 120 663.59 9 149 662.2
3/2 3 55 702.13 8 127 702.3 10 158 702.2
20/13 2 58 740.43 4 135 746.54 4 168 746.6
14/9 1 60 765.96 4 138 763.13 4 172 764.4
11/7 3 61 778.72 5 142 785.25 5 176 782.2
8/5 2 64 817.02 5 147 812.9 6 183 813.3
13/8 1 66 842.55 2 152 840.55 3 189 840.0
18/11 2 67 855.32 6 154 851.61 7 192 853.3
5/3 2 69 880.85 5 160 884.79 6 199 884.4
22/13 2 71 906.38 5 165 912.44 5 205 911.1
12/7 2 73 931.91 4 169 934.56 4 210 933.3
26/15 1 75 957.45 4 172 951.15 4 214 951.1
7/4 2 76 970.21 6 175 967.74 6 218 968.8
16/9 2 78 995.74 5 180 995.39 5 224 995.5
9/5 1 80 1021.28 4 184 1017.51 4 229 1017.7
20/11 1 81 1034.04 4 187 1034.1 4 233 1035.5
11/6 1 82 1046.81 3 190 1050.69 3 236 1048.8
24/13 1 83 1059.57 2 192 1061.75 2 239 1062.2
13/7 1 84 1072.34 2 194 1072.81 2 241 1071.1
28/15 0 85 1085.11 2 195 1078.34 2 243 1080.0
15/8 197 1089.4 245 1088.8

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.

270edo yazalatha 225-odd-limit
1 4.4 540/539, 441/440, 5120/5103, 385/384, 352/351
Tredeks Cents Ratio
2 8.8 225/224, 196/195, 176/175, 169/168
3 13.3 144/143, 126/125, 121/120
4 17.7 105/104, 100/99, 99/98, 91/90
5 22.2 81/80, 78/77
6 26.6 66/65, 65/64, 64/63
7 31.1 56/55, 55/54
8 35.5 50/49, 49/48, 143/140
9 40.0 45/44, 128/125, 169/165
10 44.4 40/39, 77/75
11 48.8 147/143, 36/35
12 53.3 33/32, 65/63
13 57.7 125/121, 91/88, 121/117
14 62.2 175/169, 28/27
15 66.6 27/26, 80/77, 26/25
16 71.1 126/121, 176/169, 25/24, 169/162
17 75.5 117/112
18 80.0 22/21
19 84.4 150/143, 21/20, 104/99
20 88.8 81/77
21 93.3 135/128, 96/91, 132/125, 169/160
22 97.7 55/52, 128/121, 200/189, 143/135
23 102.2 35/33, 52/49
24 106.6 117/110
25 111.1 180/169, 16/15
26 115.5 125/117, 77/72
27 120.0 15/14
28 124.4 189/176, 130/121, 242/225
29 128.8 14/13
30 133.3 27/25, 175/162, 121/112
31 137.7 225/208, 13/12
32 142.2 88/81
33 146.6 99/91, 160/147, 49/45
34 151.1 12/11
35 155.5 35/32, 128/117
36 160.0 192/175, 169/154
37 164.4 100/91, 11/10, 208/189
38 168.8 54/49, 182/165
39 173.3
40 177.7 72/65, 195/176
41 182.2 10/9
42 186.6 49/44, 39/35
43 191.1 135/121, 125/112, 143/128
44 195.5 189/169, 160/143, 28/25, 121/108
45 200.0 175/156, 55/49, 91/81
46 204.4 9/8, 169/150
47 208.8 44/39
48 213.3 147/130, 112/99, 198/175
49 217.7 162/143, 143/126
50 222.2 192/169, 25/22, 91/80, 256/225
51 226.6 154/135
52 231.1 8/7, 143/125
53 235.5 63/55, 55/48
54 240.0 225/196, 147/128, 224/195, 169/147
55 244.4 144/125, 121/105
56 248.8 15/13, 52/45
57 253.3 140/121, 81/70, 125/108
58 257.7 196/169, 65/56
59 262.2 121/104, 64/55, 220/189
60 266.6 7/6
61 271.1 90/77, 117/100
62 275.5 198/169, 75/64, 88/75, 169/144
63 280.0 168/143, 147/125
64 284.4 33/28
65 288.8 189/160, 13/11
66 293.3 200/169, 77/65, 32/27
67 297.7 108/91, 196/165, 208/175
68 302.2 144/121, 25/21, 143/120
69 306.6 105/88, 117/98
70 311.1 140/117, 176/147
71 315.5 6/5
72 320.0 125/104, 77/64, 65/54
73 324.4 135/112, 169/140
74 328.8 110/91, 98/81, 121/100
75 333.3 63/52, 40/33, 91/75
76 337.7 147/121, 175/144
77 342.2 39/32, 128/105
78 346.6 11/9
79 351.1 175/143, 60/49, 49/40
80 355.5 27/22
81 360.0 16/13, 154/125
82 364.4 216/175, 100/81, 121/98
83 368.8 225/182, 99/80, 26/21
84 373.3 150/121, 242/195
85 377.7 210/169, 56/45
86 382.2 81/65, 96/77, 156/125
87 386.6 5/4, 169/135
89 391.1 49/39, 44/35
90 395.5 180/143, 63/50, 121/96, 208/165
91 400.0 125/99, 91/72
92 404.4 81/64, 195/154
93 408.8 33/26, 80/63, 286/225
94 413.3 14/11
95 417.7 125/98, 143/112
96 422.2 216/169, 225/176, 32/25, 169/132, 242/189
97 426.6 50/39, 77/60, 104/81
98 431.1 9/7
99 435.5 165/128, 156/121
100 440.0 84/65, 128/99
101 444.4 162/125, 35/27
102 448.8 135/104, 100/77, 13/10
103 453.3 220/169, 125/96, 176/135
104 457.7 64/49, 98/75
105 462.2 72/55, 55/42
106 466.6 21/16, 256/195, 130/99
107 471.1 154/117
108 475.5 120/91, 33/25, 169/128
109 480.0 189/143, 160/121, 250/189, 143/108
110 484.4 224/169, 175/132, 65/49
111 488.8 117/88, 121/91
112 493.3 *225/169*, 4/3
113 497.7 147/110, 234/175
114 502.2 162/121, 75/56, 169/126
115 506.6 192/143, 168/125, 121/90
116 511.1 35/26, 66/49, 182/135
117 515.5 27/20, 104/77, 169/125
118 520.0 88/65, 65/48, 256/189
119 524.4 224/165, 110/81
120 528.8 200/147, 49/36, 143/105
121 533.3 15/11
122 537.7 175/128, 160/117, 308/225
123 542.2 196/143, 48/35
124 546.6 125/91, 11/8, 260/189
125 551.1 135/98, 91/66
126 555.5 112/81, 242/175
127 560.0 18/13, 104/75
128 564.4 168/121, 25/18
129 568.8 39/28
130 573.3 169/121, 88/63
131 577.7 200/143, 7/5
132 582.2 108/77
133 586.6 45/32, 128/91, 176/125, 169/120
134 591.1 55/39
135 595.5 147/104, 140/99, 99/70, 208/147
136 600.0 78/55
137 604.4 240/169, 125/88, 91/64, 64/45
138 608.8 77/54
139 613.3 10/7, 143/100
140 617.7 63/44, 242/169
141 622.2 56/39
142 626.6 36/25, 121/84
143 631.1 75/52, 13/9
144 635.5 175/121, 81/56
145 640.0 132/91, 196/135
146 644.4 189/130, 16/11, 182/125
147 648.8 35/24, 143/98
148 653.3 225/154, 117/80, 256/175
149 657.7 22/15
150 662.2 210/143, 72/49, 147/100
151 666.6 81/55, 165/112
152 671.1 189/128, 96/65, 65/44
153 675.5 250/169, 77/52, 40/27
154 680.0 135/91, 49/33, 52/35
155 684.4 180/121, 125/84, 143/96
156 688.8 252/169, 112/75, 121/81
157 693.3 175/117, 220/147
158 697.7 3/2, *338/225*
159 702.2 182/121, 176/117
160 706.6 98/65, 264/175, 169/112
161 711.1 216/143, 189/125, 121/80, 286/189
162 715.5 256/169, 50/33, 91/60
163 720.0 117/77
164 724.4 99/65, 195/128, 32/21
165 728.8 84/55, 55/36
166 733.3 75/49, 49/32
167 737.7 135/88, 192/125, 169/110
168 742.2 20/13, 77/50, 208/135
169 746.6 54/35, 125/81
170 751.1 99/64, 65/42
171 755.5 121/78, 256/165
172 760.0 14/9
173 764.4 81/52, 120/77, 39/25
174 768.8 189/121, 264/169, 25/16, 352/225, 169/108
175 773.3 224/143, 196/125
176 777.7 11/7
177 782.2 225/143, 63/40, 52/33
178 786.6 308/195, 128/81
179 791.1 144/91, 198/125
180 795.5 165/104, 192/121, 100/63, 143/90
181 800.0 35/22, 78/49
183 804.4 270/169, 8/5
184 808.8 125/78, 77/48, 130/81
185 813.3 45/28, 169/105
186 817.7 195/121, 121/75
187 822.2 21/13, 160/99, 364/225
188 826.6 196/121, 81/50, 175/108
189 831.1 125/77, 13/8
190 835.5 44/27
191 840.0 80/49, 49/30, 286/175
192 844.4 18/11
193 848.8 105/64, 64/39
194 853.3 288/175, 242/147
195 857.7 150/91, 33/20, 104/63
196 862.2 200/121, 81/49, 91/55
197 866.6 280/169, 224/135
198 871.1 108/65, 128/77, 208/125
199 875.5 5/3
200 880.0 147/88, 117/70
201 884.4 196/117, 176/105
202 888.8 240/143, 42/25, 121/72
203 893.3 175/104, 165/98, 91/54
204 897.7 27/16, 130/77, 169/100
205 902.2 22/13, 320/189
206 906.6 56/33
207 911.1 250/147, 143/84
208 915.5 288/169, 75/44, 128/75, 169/99
209 920.0 200/117, 77/45
210 924.4 12/7
211 928.8 189/110, 55/32, 208/121
212 933.3 112/65, 169/98
213 937.7 216/125, 140/81, 121/70
214 942.2 45/26, 26/15
215 946.6 210/121, 125/72
216 951.1 294/169, 195/112, 256/147, 392/225
217 955.5 96/55, 110/63
218 960.0 250/143, 7/4
219 964.4 135/77
220 968.8 225/128, 160/91, 44/25, 169/96
221 973.3 252/143, 143/81
222 977.7 175/99, 99/56, 260/147
223 982.2 39/22
224 986.6 300/169, 16/9
225 991.1 162/91, 98/55, 312/175
226 995.5 216/121, 25/14, 143/80, 338/189
227 1000.0 256/143, 224/125, 242/135
228 1004.4 70/39, 88/49
229 1008.8 9/5
230 1013.3 352/195, 65/36
231 1026.6
232 1022.2 165/91, 49/27
233 1026.6 189/104, 20/11, 91/50
234 1031.1 308/169, 175/96
235 1035.5 117/64, 64/35
236 1040.0 11/6
237 1044.4 90/49, 147/80, 182/99
238 1048.8 81/44
239 1053.3 24/13, 416/225
240 1057.7 224/121, 324/175, 50/27
241 1062.2 13/7
242 1066.6 225/121, 121/65, 352/189
243 1071.1 28/15
244 1075.5 144/77, 234/125
245 1080.0 15/8, 169/90
246 1084.4 220/117
247 1088.8 49/26, 66/35
248 1093.3 270/143, 189/100, 121/64, 104/55
249 1097.7 320/169, 125/66, 91/48, 256/135
250 1102.2 154/81
251 1106.6 99/52, 40/21, 143/75
252 1111.1 21/11
253 1115.5 224/117
254 1120.0 324/169, 48/25, 169/88, 121/63
255 1124.4 25/13, 77/40, 52/27
256 1128.8 27/14, 338/175
257 1133.3 234/121, 176/91, 242/125
258 1137.7 126/65, 64/33
259 1142.2 35/18, 286/147
260 1146.6 150/77, 39/20
261 1151.1 330/169, 125/64, 88/45
262 1155.5 280/143, 96/49, 49/25
263 1160.0 108/55, 55/28
264 1164.4 63/32, 128/65, 65/33
265 1168.8 77/39, 160/81
266 1173.3 180/91, 196/99, 99/50, 208/105
267 1177.7 240/121, 125/63, 143/72
268 1182.2 336/169, 175/88, 195/98, 448/225
269 1186.6
270 1191.1 2/1

Table of prime-generated MOS scales

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.

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.

Generation \ Prime 31 17 29 7 19 13 5 3 11 23
eva 1L 1s 1L 1s
1st filial scale 1L 2s 1L 2s 2L 1s
2nd filial scale 1L 3s 1L 3s 3L 1s 2L 3s 2L 3s
3rd filial scale 1L 4s 1L 4s 4L 1s 3L 4s 3L 4s 5L 2s 2L 5s
4th filial scale 1L 5s 5L 1s 4L 5s 7L 3s 3L 7s 5L 7s 2L 7s
5th filial scale 1L 6s 1L 6s 5L 6s 4L 9s 10L 7s 3L 10s 12L 5s 2L 9s
6th filial scale 1L 7s 7L 1s 5L 11s 4L 13s 10L 17s 3L 13s 12L 17s 11L 2s 2L 11s
7th filial scale 1L 8s 7L 8s 5L 16s 4L 17s 10L 27s 3L 16s 12L 29s 13L 11s 2L 13s
8th filial scale 1L 9s 7L 15s 5L 21s 4L 21s 10L 37s 3L 19s 41L 12s 24L 13s 2L 15s
9th filial scale 1L 10s 1L 10s 7L 22s 26L 5s 4L 25s 10L 47s 3L 22s 53L 41s 37L 24s 2L 17s
10th filial scale 1L 11s 11L 1s 7L 29s 26L 31s 4L 29s 10L 57s 3L 25s 53L 94s 37L 61s 2L 19s
11st filial scale 1L 12s 11L 12s 7L 36s 26L 57s 4L 33s 10L 67s 28L 3s 53L 147s 37L 98s 21L 2s
12nd filial scale 1L 13s 23L 34s 7L 43s 26L 57s 4L 37s 10L 77s 28L 31s 53L 200s 37L 135s 21L 23s
13rd filial scale 1L 14s 23L 57s 7L 50s 26L 83s 4L 41s 10L 87s 59L 28s 53L 253s 37L 172s 21L 44s
14th filial scale 1L 15s 80L 23s 7L 57s 26L 83s 4L 45s 10L 97s 59L 87s 306L 53s 37L 209s 21L 65s
15th filial scale 1L 16s 80L 103s 7L 64s 109L 26s 4L 49s 10L 107s 146L 59s 306L 359s 37L 246s 21L 86s
16th filial scale 1L 17s 80L 183s 7L 71s 109L 135s 4L 53s 10L 117s 146L 205s 37L 283s 21L 107s
17th filial scale 1L 18s 263L 80s 7L 78s 109L 244s 4L 57s 10L 127s 146L 351s 37L 320s 21L 128s
18th filial scale 1L 19s 7L 85s 109L 353s 4L 61s 10L 137s 146L 497s 37L 357s 21L 149s
19th filial scale 1L 20s 7L 92s 109L 462s 4L 65s 10L 147s 37L 394s 21L 170s
20th filial scale 21L 1s 7L 99s 4L 69s 10L 157s 37L 431s
21st filial scale 22L 21s 7L 106s 4L 73s 10L 167s 37L 468s
22nd filial scale 22L 43s 7L 113s 4L 77s 10L 177s 37L 505s
23rd filial scale 22L 65s 7L 120s 4L 81s 10L 187s 37L 542s
24th filial scale 22L 87s 7L 127s 4L 85s 10L 197s 37L 579s
25th filial scale 22L 109s 7L 134s 4L 89s 10L 207s 37L 616s
26th filial scale 7L 141s 4L 93s 10L 217s 37L 653s
27th filial scale 7L 148s 4L 97s 37L 690s
28th filial scale 7L 155s 4L 101s 37L 727s
29th filial scale 7L 162s 4L 105s 37L 764s
30th filial scale 169L 7s 4L 109s 37L 801s
31st filial scale 169L 176s 4L 113s 37L 838s
32nd filial scale 169L 345s 117L 4s 37L 875s
33rd filial scale 169L 514s 37L 912s
34th filial scale 852L 169s 37L 949s
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