Scala analysis: lescirc13
5-limit 13-cent lesfip of tweaked 12edo with 501.0 and 699.0 cent notes
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 102.106 cents 102.105580 2: 194.736 cents 194.736040 3: 306.317 cents 306.316750 4: 395.789 cents 395.788840 5: 504.211 cents 504.211160 6: 600.000 cents 600.000000 7: 695.789 cents 695.788840 8: 804.211 cents 804.211160 9: 893.683 cents 893.683250 10: 1005.264 cents 1005.263960 11: 1097.894 cents 1097.894420 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 102.1056 cents 102.1056 1: 102.1056 cents 102.1056 2: 92.6305 cents 92.6305 3: 111.5807 cents 111.5807 4: 89.4721 cents 89.4721 5: 108.4223 cents 108.4223 6: 95.7888 cents 95.7888 7: 95.7888 cents 95.7888 8: 108.4223 cents 108.4223 9: 89.4721 cents 89.4721 10: 111.5807 cents 111.5807 11: 92.6305 cents 92.6305 12: 102.1056 cents 102.1056
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 89.47209 cents 1: 2 92.63046 cents 1: 2 95.78884 cents 1: 2 102.10558 cents 1: 2 108.42232 cents 1: 2 111.58071 cents 2: 1 191.57768 cents 2: 2 194.73604 cents 2: 2 197.89441 cents 2: 2 201.05280 cents 2: 5 204.21117 cents 3: 4 293.68326 cents 3: 2 296.84162 cents 3: 2 300.00000 cents 3: 2 306.31675 cents 3: 2 309.47512 cents 4: 3 389.47209 cents 4: 2 395.78884 cents 4: 2 402.10558 cents 4: 2 405.26396 cents 4: 3 408.42232 cents 5: 6 497.89442 cents 5: 4 501.05280 cents 5: 2 504.21116 cents 6: 1 587.36650 cents 6: 2 590.52488 cents 6: 2 593.68326 cents 6: 2 600.00000 cents 6: 2 606.31674 cents 6: 2 609.47512 cents 6: 1 612.63350 cents 7: 2 695.78884 cents 7: 4 698.94721 cents 7: 6 702.10558 cents 8: 3 791.57767 cents 8: 2 794.73604 cents 8: 2 797.89442 cents 8: 2 804.21116 cents 8: 3 810.52792 cents 9: 2 890.52488 cents 9: 2 893.68325 cents 9: 2 900.00000 cents 9: 2 903.15838 cents 9: 4 906.31674 cents 10: 5 995.78884 cents 10: 2 998.94720 cents 10: 2 1002.10559 cents 10: 2 1005.26396 cents 10: 1 1008.42232 cents 11: 2 1088.41929 cents 11: 2 1091.57768 cents 11: 2 1097.89442 cents 11: 2 1104.21116 cents 11: 2 1107.36954 cents 11: 2 1110.52791 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 102.1 194.7 306.3 395.8 504.2 600.0 695.8 804.2 893.7 1005.3 1097.9 1200.0 102.1 : 92.6 204.2 293.7 402.1 497.9 593.7 702.1 791.6 903.2 995.8 1097.9 1200.0 194.7 : 111.6 201.1 309.5 405.3 501.1 609.5 698.9 810.5 903.2 1005.3 1107.4 1200.0 306.3 : 89.5 197.9 293.7 389.5 497.9 587.4 698.9 791.6 893.7 995.8 1088.4 1200.0 395.8 : 108.4 204.2 300.0 408.4 497.9 609.5 702.1 804.2 906.3 998.9 1110.5 1200.0 504.2 : 95.8 191.6 300.0 389.5 501.1 593.7 695.8 797.9 890.5 1002.1 1091.6 1200.0 600.0 : 95.8 204.2 293.7 405.3 497.9 600.0 702.1 794.7 906.3 995.8 1104.2 1200.0 695.8 : 108.4 197.9 309.5 402.1 504.2 606.3 698.9 810.5 900.0 1008.4 1104.2 1200.0 804.2 : 89.5 201.1 293.7 395.8 497.9 590.5 702.1 791.6 900.0 995.8 1091.6 1200.0 893.7 : 111.6 204.2 306.3 408.4 501.1 612.6 702.1 810.5 906.3 1002.1 1110.5 1200.0 1005.3: 92.6 194.7 296.8 389.5 501.1 590.5 698.9 794.7 890.5 998.9 1088.4 1200.0 1097.9: 102.1 204.2 296.8 408.4 497.9 606.3 702.1 797.9 906.3 995.8 1107.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.4721 .. 111.5807 cents 22.10862 cents 89.47209 cents 2: 191.5777 .. 204.2112 cents 12.63349 cents 79.99697 cents 3: 293.6833 .. 309.4751 cents 15.79186 cents 89.47209 cents 4: 389.4721 .. 408.4223 cents 18.95023 cents 79.99697 cents 5: 497.8944 .. 504.2112 cents 6.31674 cents 89.47210 cents 6: 587.3665 .. 612.6335 cents 25.26700 cents 83.15534 cents 7: 695.7888 .. 702.1056 cents 6.31674 cents 83.15534 cents 8: 791.5777 .. 810.5279 cents 18.95025 cents 89.47209 cents 9: 890.5249 .. 906.3167 cents 15.79186 cents 79.99696 cents 10: 995.7888 .. 1008.4223 cents 12.63348 cents 89.47210 cents 11: 1088.4193 .. 1110.5279 cents 22.10862 cents 79.99697 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 89.47209 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 111.58071 cents Average / Smallest step : 1.117667 Largest / Average step : 1.115807 Largest / Smallest step : 1.247101 Median interval of one step : 98.94721 cents, amount: 0 Least squares average step : 99.98704 cents, oct.: 1199.84451 cents Scale is strictly proper Scale is a mode of a 1140-tone equal temperament with octave 1200.000 cents degrees: 97 185 291 376 479 570 661 764 849 955 1043 1140 Least number of segments generator : 571 of 601.053 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 607 of 638.947 cents and inv. generated superset size: 748 = 736 more = 6233.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFFEDCBA Step pattern size order : DBFAECCEAFBD Scale is a Constant Structure, by a margin of 79.99696 cents Scale diversity : 1.123641 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.852609 Rothenberg efficiency : 0.268509 redundancy: 0.731491 Efficiency x scale size : 3.222114 Number of different interval sizes : 55 = 5.00000 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 5.00000 = 5 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 3.15836 cents Most common intervals : 497.89442 cents & inv., amount: 6 Most common triad is 0.0 497.894 702.106 cents, amount: 5 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 12 = 100.0000% Limited transpositions with margin 12.6335 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions with margin 12.6335 cents: 1 2 3 4 5 6 7 8 9 10 11 Inversional symmetry on degrees : 0 6 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 4.2330 c. M: 6.3168 c. Twelve-tone Chromatic (1/11-comma) 67: 6 5 6 5 6 5 6 6 5 6 5 6 SP M ME SD: 3.8266 c. M: 8.9552 c. 74: 6 6 7 5 7 6 6 7 5 7 6 6 SP D3 I SD: 3.4684 c. M: 6.5997 c. 78: 7 6 7 6 7 6 6 7 6 7 6 7 SP D3 I SD: 3.8873 c. M: 5.5867 c. 79: 7 6 7 6 7 6 7 7 6 7 6 7 SP M ME SD: 3.4130 c. M: 7.5949 c. 82: 7 6 8 6 7 7 7 7 6 8 6 7 SP D3 I SD: 3.3156 c. M:-6.6502 c. 86: 7 7 8 6 8 7 7 8 6 8 7 7 SP D3 I SD: 2.8845 c. M: 5.0912 c. 98: 8 8 9 7 9 8 8 9 7 9 8 8 SP D3 I SD: 2.5481 c. M: 4.1464 c. 106: 9 8 10 8 10 8 8 10 8 10 8 9 SP D3 I SD: 2.3509 c. M:-5.2228 c. 110: 9 9 10 8 10 9 9 10 8 10 9 9 SP D3 I SD: 2.3765 c. M: 3.9238 c. 118: 10 9 11 9 11 9 9 11 9 11 9 10 SP D3 I SD: 1.9509 c. M:-4.2634 c. 122: 10 10 11 9 11 10 10 11 9 11 10 10 SP D3 I SD: 2.3109 c. M: 3.7449 c. 128: 11 10 12 9 12 10 10 12 9 12 10 11 SP I SD: 1.9698 c. M: 3.0583 c. 130: 11 10 12 10 12 10 10 12 10 12 10 11 SP D3 I SD: 1.7036 c. M:-3.4811 c. 140: 12 11 13 10 13 11 11 13 10 13 11 12 SP I SD: 1.6309 c. M: 2.4068 c. 142: 12 11 13 11 13 11 11 13 11 13 11 12 SP D3 I SD: 1.5788 c. M:-2.8311 c. 152: 13 12 14 11 14 12 12 14 11 14 12 13 SP I SD: 1.4089 c. M: 2.6324 c. 164: 14 13 15 12 15 13 13 15 12 15 13 14 SP I SD: 1.2898 c. M: 2.8249 c. 176: 15 14 16 13 16 14 14 16 13 16 14 15 SP I SD: 1.2550 c. M: 2.9912 c. 184: 16 14 17 14 16 15 15 16 14 17 14 16 SP I SD: 1.5389 c. M: 2.2422 c. 185: 16 14 17 14 17 14 15 17 14 17 14 16 SP SD: 1.4847 c. M: 3.2432 c. 188: 16 14 18 14 17 15 15 17 14 17 15 16 SP SD: 1.3037 c. M: 3.2467 c. 192: 16 15 18 14 18 15 15 18 14 18 15 16 SP I SD: 1.5124 c. M: 2.1056 c. 197: 17 15 18 15 18 15 16 18 15 18 15 17 SP SD: 1.3983 c. M: 3.0457 c. 200: 17 15 19 15 18 16 16 18 15 19 15 17 SP I SD: 1.1319 c. M: 2.7360 c. 212: 18 16 20 16 19 17 17 19 16 20 16 18 SP I SD: 1.0062 c. M: 2.2832 c. 222: 19 17 21 16 20 18 18 20 16 21 17 19 SP I SD: 1.1021 c. M: 1.7914 c. 224: 19 17 21 17 20 18 18 20 17 21 17 19 SP I SD: 0.9462 c. M: 1.8789 c. 234: 20 18 22 17 21 19 19 21 17 22 18 20 SP I SD: 0.9725 c. M:-1.6471 c. 236: 20 18 22 18 21 19 19 21 18 22 18 20 SP I SD: 0.9428 c. M: 1.5157 c. 246: 21 19 23 18 22 20 20 22 18 23 19 21 SP I SD: 0.8987 c. M:-1.7721 c. 248: 21 19 23 19 22 20 20 22 19 23 19 21 SP I SD: 0.9815 c. M: 1.4780 c. 258: 22 20 24 19 23 21 21 23 19 24 20 22 SP I SD: 0.8764 c. M:-1.8856 c. 290: 25 22 27 22 26 23 23 26 22 27 22 25 SP I SD: 0.8533 c. M: 1.4525 c. 298: 25 23 28 22 27 24 24 27 22 28 23 25 SP I SD: 1.0248 c. M: 1.4474 c. 302: 26 23 28 23 27 24 24 27 23 28 23 26 SP I SD: 0.8369 c. M: 1.5622 c. 316: 27 24 30 23 29 25 25 29 23 30 24 27 SP I SD: 0.8566 c. M: 1.2782 c. 321: 27 25 30 24 29 25 26 29 24 30 25 27 SP SD: 0.7878 c. M: 1.8692 c. 328: 28 25 31 24 30 26 26 30 24 31 25 28 SP I SD: 0.6703 c. M: 1.0003 c. 340: 29 26 32 25 31 27 27 31 25 32 26 29 SP I SD: 0.4973 c. M: 0.7421 c. 352: 30 27 33 26 32 28 28 32 26 33 27 30 SP I SD: 0.3360 c. M: 0.5014 c. 364: 31 28 34 27 33 29 29 33 27 34 28 31 SP I SD: 0.1854 c. M: 0.2767 c. 376: 32 29 35 28 34 30 30 34 28 35 29 32 SP I SD: 0.0444 c. M: 0.0662 c. 764: 65 59 71 57 69 61 61 69 57 71 59 65 SP I SD: 0.0228 c. M: 0.0340 c. 1140: 97 88 106 85 103 91 91 103 85 106 88 97 SP I SD: 0.0006 c. M: 0.0010 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 3.0831 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.7263 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.5379 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 5.0384 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.0881 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.9651 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 8.9881 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.8131 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.9687 cents 11 x 12:13:14:15 x 16 x 18:20:21:22 S SD: 10.5630 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.6545 cents 13:14:15 x 16:17:18:19:21:22:23:25:26 SD: 9.8297 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.1376 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.4780 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.7024 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.0098 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.2492 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.1357 cents 46:49:51:55:58:62:65:69:73:77:82:87:92 SD: 2.0808 cents 47:50:53:56:59:63:66:70:75:79:84:89:94 SD: 1.8992 cents 50:53:56:60:63:67:71:75:80:84:89:94:100 SD: 1.6402 cents 51:54:57:61:64:68:72:76:81:85:91:96:102 SD: 1.2449 cents 67:71:75:80:84:90:95:100:107:112:120:126:134 SD: 1.1296 cents 77:82:86:92:97:103:109:115:123:129:138:145:154 SD: 1.0342 cents 83:88:93:99:104:111:117:124:132:139:148:156:166 SD: 0.8959 cents 98:104:110:117:123:131:139:146:156:164:175:185:196 SD: 0.8625 cents 109:116:122:130:137:146:154:163:173:183:195:206:218 SD: 0.7957 cents 113:120:126:135:142:151:160:169:180:189:202:213:226 SD: 0.6976 cents 118:125:132:141:148:158:167:176:188:198:211:222:236 SD: 0.6675 cents 133:141:149:159:167:178:188:199:212:223:238:251:266 SD: 0.5049 cents 145:154:162:173:182:194:205:217:231:243:259:273:290 SD: 0.4897 cents 160:170:179:191:201:214:226:239:255:268:286:302:320 SD: 0.4299 cents 166:176:186:198:209:222:235:248:264:278:297:313:332 SD: 0.4251 cents 186:197:208:222:234:249:263:278:296:312:332:351:372 SD: 0.3934 cents 198:210:222:236:249:265:280:296:315:332:354:373:396 SD: 0.3917 cents 201:213:225:240:253:269:284:300:320:337:359:379:402 SD: 0.3884 cents 210:223:235:251:264:281:297:314:334:352:375:396:420 SD: 0.3041 cents 234:248:262:279:294:313:331:350:372:392:418:441:468 SD: 0.3024 cents 269:285:301:321:338:360:380:402:428:451:481:507:538 SD: 0.2718 cents 295:313:330:352:371:395:417:441:469:494:527:556:590 SD: 0.2460 cents 311:330:348:371:391:416:440:465:495:521:556:586:622 SD: 0.1773 cents 394:418:441:470:495:527:557:589:627:660:704:743:788 SD: 0.1479 cents 428:454:479:511:538:573:605:640:681:717:765:807:856 SD: 0.1359 cents 497:527:556:593:625:665:703:743:791:833:888:937:994 SD: 0.1358 cents 580:615:649:692:729:776:820:867:923:972:1037:1094:1160 SD: 0.1246 cents