Scala analysis: moantone12
Moantone[12] in 86edo
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 97.674 cents 97.674420 2: 195.349 cents 195.348840 3: 293.023 cents 293.023260 4: 390.698 cents 390.697670 5: 488.372 cents 488.372090 6: 586.047 cents 586.046510 7: 711.628 cents 711.627910 8: 809.302 cents 809.302330 9: 906.977 cents 906.976740 10: 1004.651 cents 1004.651160 11: 1102.326 cents 1102.325580 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 97.6744 cents 97.6744 1: 97.6744 cents 97.6744 2: 97.6744 cents 97.6744 3: 97.6744 cents 97.6744 4: 97.6744 cents 97.6744 5: 97.6744 cents 97.6744 6: 97.6744 cents 97.6744 7: 125.5814 cents 125.5814 8: 97.6744 cents 97.6744 9: 97.6744 cents 97.6744 10: 97.6744 cents 97.6744 11: 97.6744 cents 97.6744 12: 97.6744 cents 97.6744
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 97.67442 cents 1: 1 125.58140 cents 2: 10 195.34884 cents 2: 2 223.25582 cents 3: 9 293.02326 cents 3: 3 320.93024 cents 4: 8 390.69767 cents 4: 4 418.60465 cents 5: 7 488.37209 cents 5: 5 516.27907 cents 6: 6 586.04651 cents 6: 6 613.95349 cents 7: 5 683.72093 cents 7: 7 711.62791 cents 8: 4 781.39535 cents 8: 8 809.30233 cents 9: 3 879.06976 cents 9: 9 906.97674 cents 10: 2 976.74418 cents 10: 10 1004.65116 cents 11: 1 1074.41860 cents 11: 11 1102.32558 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 97.7 195.3 293.0 390.7 488.4 586.0 711.6 809.3 907.0 1004.7 1102.3 1200.0 97.7 : 97.7 195.3 293.0 390.7 488.4 614.0 711.6 809.3 907.0 1004.7 1102.3 1200.0 195.3 : 97.7 195.3 293.0 390.7 516.3 614.0 711.6 809.3 907.0 1004.7 1102.3 1200.0 293.0 : 97.7 195.3 293.0 418.6 516.3 614.0 711.6 809.3 907.0 1004.7 1102.3 1200.0 390.7 : 97.7 195.3 320.9 418.6 516.3 614.0 711.6 809.3 907.0 1004.7 1102.3 1200.0 488.4 : 97.7 223.3 320.9 418.6 516.3 614.0 711.6 809.3 907.0 1004.7 1102.3 1200.0 586.0 : 125.6 223.3 320.9 418.6 516.3 614.0 711.6 809.3 907.0 1004.7 1102.3 1200.0 711.6 : 97.7 195.3 293.0 390.7 488.4 586.0 683.7 781.4 879.1 976.7 1074.4 1200.0 809.3 : 97.7 195.3 293.0 390.7 488.4 586.0 683.7 781.4 879.1 976.7 1102.3 1200.0 907.0 : 97.7 195.3 293.0 390.7 488.4 586.0 683.7 781.4 879.1 1004.7 1102.3 1200.0 1004.7: 97.7 195.3 293.0 390.7 488.4 586.0 683.7 781.4 907.0 1004.7 1102.3 1200.0 1102.3: 97.7 195.3 293.0 390.7 488.4 586.0 683.7 809.3 907.0 1004.7 1102.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.6744 .. 125.5814 cents 27.90698 cents 97.67442 cents 2: 195.3488 .. 223.2558 cents 27.90698 cents 69.76744 cents 3: 293.0233 .. 320.9302 cents 27.90698 cents 69.76744 cents 4: 390.6977 .. 418.6047 cents 27.90698 cents 69.76743 cents 5: 488.3721 .. 516.2791 cents 27.90698 cents 69.76744 cents 6: 586.0465 .. 613.9535 cents 27.90698 cents 69.76744 cents 7: 683.7209 .. 711.6279 cents 27.90698 cents 69.76744 cents 8: 781.3954 .. 809.3023 cents 27.90698 cents 69.76744 cents 9: 879.0698 .. 906.9767 cents 27.90698 cents 69.76743 cents 10: 976.7442 .. 1004.6512 cents 27.90698 cents 69.76744 cents 11: 1074.4186 .. 1102.3256 cents 27.90698 cents 69.76744 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 97.67441 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 125.58140 cents Average / Smallest step : 1.023810 Largest / Average step : 1.255814 Largest / Smallest step : 1.285714 Median interval of one step : 97.67442 cents, amount: 11 Most common interval of one step : 97.67442 cents, amount: 11 Least squares average step : 100.12165 cents, oct.: 1201.45975 cents Scale is strictly proper Scale has Myhill's property chromas: 27.90698 cents and 69.76744 cents, ratio: 2.500000 generators: 1 of 97.67442 cents and 11 of 1102.32558 cents ET pair of linear temperament : 12&37 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 86-tone equal temperament with octave 2/1 degrees: 7 14 21 28 35 42 51 58 65 72 79 86 generators: 7 and 79 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAAAABAAAAA Step pattern size order : SSSSSSLSSSSS Interval vector is [ 0 0 0 0 0 0 11 0 1 0 0 0 0 10 0 2 0 0 0 0 9 0 3 0 0 0 0 8 0 4 0 0 0 0 7 0 5 0 0 0 0 6 0 ] Scale is a Constant Structure, by a margin of 69.76743 cents Scale diversity : 1.182110 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.744186 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 27.90698 cents Most common intervals : 97.67442 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 488.372 1102.326 cents Number of recognisable fifths : 7, average 711.6279 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 6-7 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 8.1118 c. M:-13.9535 c. Twelve-tone Chromatic (1/11-comma) 25: 2 2 2 2 2 2 3 2 2 2 2 2 SP M ME SD: 5.8405 c. M: 10.0465 c. 37: 3 3 3 3 3 3 4 3 3 3 3 3 SP M ME SD: 1.3154 c. M: 2.2627 c. Passion-12 49: 4 4 4 4 4 4 5 4 4 4 4 4 SP M ME SD: 0.9933 c. M:-1.7086 c. Passion-12 86: 7 7 7 7 7 7 9 7 7 7 7 7 SP M DE SD: 0.0000 c. M: 0.0000 c. Passion-12
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: 4.8365 cents 3 x x x x 4 x x x 5 x x 6 S SD: 8.1999 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.3416 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 5.3324 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.6922 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.5906 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.7542 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 9.4603 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 5.5739 cents 11 x 12:13:14:15 x 17:18:19:20:21:22 SD: 10.7162 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.6866 cents 13:14 x 15:16:17:18:20:21:22:23:25:26 SD: 8.0509 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 4.9945 cents 16:17:18:19:20:21:22:24:26:27:29:30:32 SD: 4.9791 cents 17:18:19:20:21:23:24:26:27:29:30:32:34 SD: 4.9783 cents 18:19:20:21:23:24:25:27:29:30:32:34:36 SD: 4.8184 cents 20:21:22:24:25:27:28:30:32:34:36:38:40 SD: 4.6442 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 4.2859 cents 25:26:28:30:31:33:35:38:40:42:45:47:50 SD: 4.0269 cents 27:29:30:32:34:36:38:41:43:46:48:51:54 SD: 3.2301 cents 28:30:31:33:35:37:39:42:45:47:50:53:56 SD: 3.1981 cents 32:34:36:38:40:42:45:48:51:54:57:60:64 S SD: 2.3828 cents 39:41:44:46:49:52:55:59:62:66:70:74:78 SD: 2.2764 cents 43:45:48:51:54:57:60:65:69:73:77:81:86 SD: 2.2517 cents 47:50:53:56:59:62:66:71:75:79:84:89:94 SD: 1.9088 cents 49:52:55:58:61:65:69:74:78:83:88:93:98 SD: 1.6844 cents 52:55:58:62:65:69:73:78:83:88:93:98:104 SD: 1.5204 cents 55:58:62:65:69:73:77:83:88:93:98:104:110 SD: 1.3418 cents 65:69:73:77:81:86:91:98:104:110:116:123:130 SD: 1.2533 cents 67:71:75:79:84:89:94:101:107:113:120:127:134 SD: 0.9401 cents 92:97:103:109:115:122:129:139:147:155:164:174:184 SD: 0.8336 cents 99:105:111:117:124:131:139:149:158:167:177:187:198 SD: 0.7254 cents 102:108:114:121:128:135:143:154:163:172:182:193:204 SD: 0.6148 cents 119:126:133:141:149:158:167:180:190:201:213:225:238 SD: 0.6046 cents 126:133:141:149:158:167:177:190:201:213:225:238:252 SD: 0.5186 cents 141:149:158:167:177:187:198:213:225:238:252:267:282 SD: 0.5015 cents 151:160:169:179:189:200:212:228:241:255:270:285:302 SD: 0.4605 cents 169:179:189:200:212:224:237:255:270:285:302:319:338 SD: 0.4351 cents 173:183:194:205:217:229:243:261:276:292:309:327:346 SD: 0.4299 cents 174:184:195:206:218:231:244:262:278:294:311:329:348 SD: 0.4205 cents 191:202:214:226:239:253:268:288:305:323:341:361:382 SD: 0.4156 cents 193:204:216:229:242:256:271:291:308:326:345:365:386 SD: 0.3626 cents 206:218:231:244:258:273:289:311:329:348:368:389:412 SD: 0.3548 cents 218:231:244:258:273:289:306:329:348:368:389:412:436 SD: 0.3448 cents 228:241:255:270:286:302:320:344:364:385:407:431:456 SD: 0.3187 cents 260:275:291:308:326:345:365:392:415:439:465:491:520 SD: 0.2819 cents 276:292:309:327:346:366:387:416:440:466:493:522:552 SD: 0.2341 cents 309:327:346:366:387:410:433:466:493:522:552:584:618 SD: 0.2323 cents 325:344:364:385:407:431:456:490:519:549:581:614:650 SD: 0.2229 cents 362:383:405:429:454:480:508:546:578:611:647:684:724 SD: 0.2095 cents 384:406:430:455:481:509:539:579:613:648:686:726:768 SD: 0.2050 cents 395:418:442:468:495:524:554:596:630:667:706:747:790 SD: 0.1769 cents 411:435:460:487:515:545:577:620:656:694:734:777:822 SD: 0.1492 cents 482:510:540:571:604:639:676:727:769:814:861:911:964 SD: 0.1380 cents 537:568:601:636:673:712:753:810:857:907:959:1015:1074 SD: 0.1117 cents