Table of 270edo intervals: Difference between revisions

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Checked up to the 63-odd-limit
Basically finished
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| 104
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Line 1,009: Line 1,009:
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| 65/49
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| 111
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Line 1,018: Line 1,018:
| 512/385
| 512/385
| 117/88
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| 85/64
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| 112
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Line 1,036: Line 1,036:
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| 91/68
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| 114
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Line 1,045: Line 1,045:
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| 115
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Line 1,081: Line 1,081:
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| 65/48
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| "
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| 119
| 119
Line 1,144: Line 1,144:
| "
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| 91/66
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| 69/50
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| 126
| 126
Line 1,153: Line 1,153:
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Line 1,315: Line 1,315:
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| 145
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Line 1,324: Line 1,324:
| "
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| 100/69
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| 146
| 146
Line 1,387: Line 1,387:
| "
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| 65/44
| 65/44
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| "
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| 153
| 153
Line 1,423: Line 1,423:
| "
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| "
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| 85/57
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| 157
| 157
Line 1,432: Line 1,432:
| 220/147
| 220/147
| 175/117
| 175/117
|  
| 136/91
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|-
| 158
| 158
Line 1,450: Line 1,450:
| 385/256
| 385/256
| 176/117
| 176/117
|  
| 128/85
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| 160
| 160
Line 1,459: Line 1,459:
| 264/175
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| 98/65
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| 95/63
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| 161
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Line 1,522: Line 1,522:
| 135/88
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| 168
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Line 1,675: Line 1,675:
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| 185
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Line 1,693: Line 1,693:
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| 187
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Line 1,801: Line 1,801:
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| 199
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Line 1,819: Line 1,819:
| 147/88
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| 117/70
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| 201
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Line 1,828: Line 1,828:
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Line 1,891: Line 1,891:
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Line 1,900: Line 1,900:
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Line 2,215: Line 2,215:
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Line 2,296: Line 2,296:
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Line 2,332: Line 2,332:
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Revision as of 07:28, 4 July 2024

This table of 270edo intervals assumes the 23-limit patent val of 270edo ⟨270 428 647 758 934 999 1104 1147 1221]. Prime harmonics are in bold.

# Cents Marks 5-limit 7-limit 11-limit 13-limit Higher Limits
0 0.0 P1 1/1 " " " "
1 4.4 32805/32768 3136/3125 385/384 325/324
2 8.8 15625/15552 225/224 176/175 169/168
3 13.3 78732/78125 126/125 121/120 "
4 17.7 2048/2025 " 99/98 91/90 "
5 22.2 81/80 " " 78/77 76/75
6 26.6 20000/19683 64/63 " " "
7 31.1 3125/3072 " 55/54 " 52/51
8 35.5 1594323/1562500 49/48 " " 46/45
9 40.0 128/125 " 45/44 " "
10 44.4 6561/6400 525/512 77/75 40/39 39/38
11 48.8 250/243 36/35 " " 35/34
12 53.3 16875/16384 4096/3969 33/32 " 34/33
13 57.7 262144/253125 405/392 125/121 91/88 88/85
14 62.2 648/625 28/27 " " "
15 66.6 20480/19683 8192/7875 80/77 26/25 "
16 71.1 25/24 " " " "
17 75.5 273375/262144 256/245 " 117/112 23/22
18 80.0 16384/15625 1875/1792 22/21 " "
19 84.4 6561/6250 21/20 " " "
20 88.8 m2 256/243 " 81/77 " 20/19
21 93.3 135/128 " 132/125 96/91 19/18
22 97.7 62500/59049 200/189 128/121 55/52 18/17
23 102.2 78125/73728 3584/3375 35/33 " "
24 106.6 524288/492075 625/588 " 117/110 17/16
25 111.1 16/15 " " " "
26 115.5 2187/2048 " 77/72 " "
27 120.0 3125/2916 15/14 " " "
28 124.4 140625/131072 672/625 189/176 130/121 102/95
29 128.8 32768/30375 2205/2048 264/245 14/13 "
30 133.3 27/25 " " " "
31 137.7 64000/59049 1024/945 250/231 13/12 "
32 142.2 625/576 243/224 88/81 " 38/35
33 146.6 2125764/1953125 49/45 " " 25/23
34 151.1 2048/1875 " 12/11 " "
35 155.5 2187/2000 35/32 " " 23/21
36 160.0 800/729 192/175 " 169/154 56/51
37 164.4 1125/1024 " 11/10 " "
38 168.8 390625/354294 54/49 " " "
39 173.3 3456/3125 448/405 243/220 " 21/19
40 177.7 65536/59049 567/512 256/231 72/65 "
41 182.2 10/9 " " " "
42 186.6 18225/16384 4096/3675 49/44 39/35 "
43 191.1 78125/69984 125/112 " " 19/17
44 195.5 17496/15625 28/25 " " "
45 200.0 4096/3645 " 55/49 " "
46 204.4 M2 9/8 " " " "
47 208.8 200000/177147 640/567 " 44/39 "
48 213.3 15625/13824 2025/1792 112/99 " 26/23
49 217.7 177147/156250 245/216 " 143/126 17/15
50 222.2 256/225 " 25/22 " "
51 226.6 729/640 " 154/135 " 57/50
52 231.1 2500/2187 8/7 " " "
53 235.5 9375/8192 3584/3125 55/48 " 39/34
54 240.0 524288/455625 147/128 " " 23/20
55 244.4 144/125 " 121/105 " 38/33
56 248.8 59049/51200 4725/4096 231/200 15/13 "
57 253.3 125/108 81/70 " " 22/19
58 257.7 151875/131072 512/441 297/256 65/56 "
59 262.2 32768/28125 3125/2688 64/55 " 57/49
60 266.6 729/625 7/6 " " "
61 271.1 2560/2187 1024/875 90/77 " 76/65
62 275.5 75/64 " " " "
63 280.0 625000/531441 147/125 " " 20/17
64 284.4 18432/15625 7168/6075 33/28 " "
65 288.8 59049/50000 189/160 " 13/11 "
66 293.3 m3 32/27 " " " "
67 297.7 1215/1024 " 196/165 108/91 19/16
68 302.2 15625/13122 25/21 " " "
69 306.6 78125/65536 448/375 105/88 68/57 "
70 311.1 65536/54675 1225/1024 176/147 140/117 91/76
71 315.5 6/5 " " " "
72 320.0 19683/16384 2048/1701 77/64 65/54 "
73 324.4 3125/2592 135/112 " " 76/63
74 328.8 472392/390625 98/81 " " 23/19
75 333.3 4096/3375 " 40/33 " "
76 337.7 243/200 175/144 147/121 " 17/14
77 342.2 8000/6561 128/105 " 39/32 28/23
78 346.6 625/512 " 11/9 " "
79 351.1 1953125/1594323 49/40 " " "
80 355.5 768/625 " 27/22 " "
81 360.0 19683/16000 315/256 154/125 16/13 "
82 364.4 100/81 " " " 21/17
83 368.8 10125/8192 8192/6615 99/80 26/21 "
84 373.3 390625/314928 243/196 150/121 " 57/46
85 377.7 3888/3125 56/45 " " "
86 382.2 8192/6561 5103/4096 96/77 81/65 "
87 386.6 5/4 " " " "
88 391.1 164025/131072 784/625 441/352 351/280 64/51
89 395.5 78125/62208 1125/896 44/35 " "
90 400.0 19683/15625 63/50 " " 34/27
91 404.4 512/405 " 125/99 91/72 24/19
92 408.8 M3 81/64 " " " 19/15
93 412.2 25000/19683 80/63 " 33/26 "
94 417.7 15625/12288 7168/5625 14/11 " "
95 422.2 1048576/820125 125/98 " " 23/18
96 426.6 32/25 " " " "
97 431.1 6561/5120 2625/2048 77/60 50/39 "
98 435.5 625/486 9/7 " " "
99 440.0 84375/65536 1568/1215 165/128 156/121 49/38
100 444.4 65536/50625 1323/1024 128/99 84/65 22/17
101 448.8 162/125 35/27 " " "
102 453.3 25600/19683 2048/1575 100/77 13/10 "
103 457.7 125/96 " " " 99/76
104 462.2 1366875/1048576 64/49 " " 30/23
105 466.6 4096/3125 " 55/42 " 17/13
106 471.1 6561/5000 21/16 " " "
107 475.5 320/243 " " 154/117 25/19
108 480.0 675/512 " 33/25 " "
109 484.4 78125/59049 250/189 160/121 143/108 45/34
110 488.8 20736/15625 896/675 175/132 65/49 "
111 493.3 131072/98415 1701/1280 512/385 117/88 85/64
112 497.7 P4 4/3 " " " "
113 502.2 10935/8192 8192/6125 147/110 " 91/68
114 506.6 15625/11664 75/56 " " "
115 511.1 104976/78125 168/125 121/90 " 51/38
116 515.5 8192/6075 " 66/49 35/26 "
117 520.0 27/20 " " " 23/17
118 524.4 80000/59049 256/189 " 65/48 "
119 528.8 3125/2304 1215/896 110/81 " 19/14
120 533.3 531441/390625 49/36 " " 34/25
121 537.7 512/375 " 15/11 " "
122 542.2 2187/1600 175/128 " 160/117 26/19
123 546.6 1000/729 48/35 " " "
124 551.1 5625/4096 " 11/8 " "
125 555.5 1048576/759375 135/98 " 91/66 69/50
126 560.0 864/625 112/81 " " 105/76
127 564.4 81920/59049 2835/2048 320/231 18/13 "
128 568.8 25/18 " " " "
129 573.3 91125/65536 1024/735 245/176 39/28 32/23
130 577.7 65536/46875 625/448 88/63 " "
131 582.2 4374/3125 7/5 " " "
132 586.6 d5 1024/729 " 108/77 " 80/57
133 591.1 45/32 " " " 38/27
134 595.5 250000/177147 343/243 " 55/39 24/17
135 600.0 78125/55296 10125/7168 99/70 " "
136 604.4 177147/125000 486/343 343/242 78/55 17/12
137 608.8 64/45 " " " 27/19
138 613.3 A4 729/512 " 77/54 " 57/40
139 617.7 3125/2187 10/7 " " "
140 622.2 46875/32768 896/625 63/44 " "
141 626.6 131072/91125 735/512 352/245 56/39 23/16
142 631.1 36/25 " " " "
143 635.5 59049/40960 4096/2835 231/160 13/9 "
144 640.0 625/432 81/56 " " "
145 644.4 759375/524288 196/135 " 132/91 100/69
146 648.8 8192/5625 " 16/11 " "
147 653.3 729/500 35/24 " " "
148 657.7 3200/2187 256/175 225/154 117/80 19/13
149 662.2 375/256 " 22/15 " "
150 666.6 781250/531441 72/49 " " 25/17
151 671.1 4608/3125 1792/1215 81/55 " 28/19
152 675.5 59049/40000 189/128 " 65/44 "
153 680.0 40/27 " " " 34/23
154 684.4 6075/4096 " 49/33 " "
155 688.8 78125/52488 125/84 " " 76/51
156 693.3 23328/15625 112/75 " " 85/57
157 697.7 16384/10935 6125/4096 220/147 175/117 136/91
158 702.2 P5 3/2 " " " "
159 706.6 98415/65536 2560/1701 385/256 176/117 128/85
160 711.1 15625/10368 675/448 264/175 98/65 95/63
161 715.5 118098/78125 189/125 121/80 " 68/45
162 720.0 1024/675 " 50/33 " "
163 724.4 243/160 " " 117/77 38/25
164 728.8 10000/6561 32/21 " " "
165 733.3 3125/2048 " 55/36 " 26/17
166 737.7 2097152/1366875 49/32 " " 23/15
167 742.2 192/125 " 135/88 " "
168 746.6 19683/12800 1575/1024 77/50 20/13 "
169 751.1 125/81 54/35 " " "
170 755.5 50625/32768 2048/1323 99/64 65/42 17/11
171 760.0 131072/84375 1215/784 256/165 121/78 76/49
172 764.4 972/625 14/9 " " "
173 768.8 10240/6561 4096/2625 120/77 39/25 "
174 773.3 25/16 " " " "
175 777.7 820125/524288 196/125 " " 36/23
176 782.2 24576/15625 5625/3584 11/7 " "
177 786.6 19683/12500 63/40 " 52/33 "
178 791.1 m6 128/81 " " " 30/19
179 795.5 405/256 " 198/125 144/91 19/12
180 800.0 31250/19683 100/63 " " 27/17
181 804.4 78125/49152 1792/1125 35/22 " "
182 808.8 262144/164025 625/392 " 351/220 51/32
183 813.3 8/5 " " " "
184 817.7 6561/4096 " 77/48 " "
185 822.2 3125/1944 45/28 " " "
186 826.6 421875/262144 392/243 121/75 " 92/57
187 831.1 16384/10125 6615/4096 160/99 21/13 "
188 835.5 81/50 " " " 34/21
189 840.0 32000/19683 512/315 125/77 13/8 "
190 844.4 625/384 " 44/27 " "
191 848.8 3188646/1953125 49/30 " " "
192 853.3 1024/625 " 18/11 " "
193 857.7 6561/4000 105/64 " 64/39 23/14
194 862.2 400/243 288/175 242/147 " 28/17
195 866.6 3375/2048 " 33/20 " "
196 871.1 390625/236196 81/49 " " 38/23
197 875.5 5184/3125 224/135 " " 63/38
198 880.0 32768/19683 1701/1024 128/77 108/65 "
199 884.4 5/3 " " " "
200 888.8 54675/32768 2048/1225 147/88 117/70 "
201 893.3 78125/46656 375/224 176/105 57/34 "
202 897.7 26244/15625 42/25 " " "
203 902.2 2048/1215 " 165/98 91/54 32/19
204 906.6 M6 27/16 " " " "
205 911.1 100000/59049 320/189 " 22/13 "
206 915.5 15625/9216 6075/3584 56/33 " 39/23
207 920.0 531441/312500 245/144 " 143/84 17/10
208 924.4 128/75 " 75/44 " "
209 928.8 2187/1280 875/512 77/45 " 65/38
210 933.3 1250/729 12/7 " " "
211 937.7 28125/16384 5376/3125 55/32 " "
212 942.2 262144/151875 441/256 " 112/65 69/40
213 946.6 216/125 140/81 121/70 " 19/11
214 951.1 102400/59049 8192/4725 343/198 26/15 "
215 955.5 125/72 " " " 33/19
216 960.0 455625/262144 256/147 " 195/112 40/23
217 964.4 16384/9375 3125/1792 96/55 " 68/39
218 968.8 2187/1250 7/4 " " "
219 973.3 1280/729 " 135/77 " 100/57
220 977.7 225/128 " 44/25 " "
221 982.2 312500/177147 432/245 " 143/81 30/17
222 986.6 27648/15625 3584/2025 99/56 " 23/13
223 991.1 177147/100000 567/320 " 39/22 "
224 995.5 m7 16/9 " " " "
225 1000.0 3645/2048 " 98/55 " 57/32
226 1004.4 15625/8748 25/14 " " "
227 1008.8 139968/78125 224/125 " " 34/19
228 1013.3 32768/18225 3675/2048 88/49 70/39 "
229 1017.7 9/5 " " " "
230 1022.2 59049/32768 1024/567 231/128 65/36 "
231 1026.6 3125/1728 405/224 " " 38/21
232 1031.1 708588/390625 49/27 " " "
233 1035.5 2048/1125 " 20/11 " "
234 1040.0 729/400 175/96 " " 51/28
235 1044.4 4000/2187 64/35 " " 42/23
236 1048.8 1875/1024 " 11/6 " "
237 1053.3 1953125/1062882 90/49 " " 46/25
238 1057.7 1152/625 448/243 81/44 " 35/19
239 1062.2 59049/32000 945/512 231/125 24/13 "
240 1066.6 50/27 " " " "
241 1071.1 30375/16384 4096/2205 245/132 13/7 "
242 1075.5 262144/140625 625/336 225/121 121/65 95/51
243 1080.0 5832/3125 28/15 " " "
244 1084.4 4096/2187 " 144/77 " "
245 1088.8 15/8 " " " "
246 1093.3 492075/262144 1176/625 847/450 220/117 32/17
247 1097.7 78125/41472 3375/1792 66/35 49/26 "
248 1102.2 59049/31250 189/100 121/64 104/55 17/9
249 1106.6 256/135 " 125/66 91/48 36/19
250 1111.1 M7 243/128 " 154/81 " 19/10
251 1115.5 12500/6561 40/21 " " "
252 1120.0 15625/8192 3584/1875 21/11 " "
253 1124.4 524288/273375 245/128 " 224/117 23/12
254 1128.8 48/25 " " " "
255 1133.3 19683/10240 7875/4096 77/40 25/13 "
256 1137.7 625/324 27/14 " " "
257 1142.2 253125/131072 784/405 242/125 176/91 85/44
258 1147.7 32768/16875 3969/2048 64/33 " 33/17
259 1151.1 243/125 35/18 " " "
260 1155.5 12800/6561 1024/525 150/77 39/20 "
261 1160.0 125/64 " 88/45 " "
262 1164.4 3125000/1594323 49/25 " " 45/23
263 1168.8 6144/3125 " 55/28 " 51/26
264 1173.3 19683/10000 63/32 " " "
265 1177.7 160/81 " " 77/39 75/38
266 1182.2 2025/1024 " 99/50 " 91/46
267 1186.6 78125/39366 125/63 " "
268 1191.1 31104/15625 448/225 175/88 "
269 1195.5 65536/32805 3125/1568 768/385 648/325
270 1200.0 P8 2/1 " " " "
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