Scala analysis: edo-13
13 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 92.308 cents 92.307692 2: 184.615 cents 184.615385 3: 276.923 cents 276.923077 4: 369.231 cents 369.230769 5: 461.538 cents 461.538462 6: 553.846 cents 553.846154 7: 646.154 cents 646.153846 8: 738.462 cents 738.461538 9: 830.769 cents 830.769231 10: 923.077 cents 923.076923 11: 1015.385 cents 1015.384615 12: 1107.692 cents 1107.692308 13: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 92.3077 cents 92.3077 1: 92.3077 cents 92.3077 2: 92.3077 cents 92.3077 3: 92.3077 cents 92.3077 4: 92.3077 cents 92.3077 5: 92.3077 cents 92.3077 6: 92.3077 cents 92.3077 7: 92.3077 cents 92.3077 8: 92.3077 cents 92.3077 9: 92.3077 cents 92.3077 10: 92.3077 cents 92.3077 11: 92.3077 cents 92.3077 12: 92.3077 cents 92.3077 13: 92.3077 cents 92.3077
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 13 92.30769 cents 2: 13 184.61539 cents 3: 13 276.92308 cents 4: 13 369.23077 cents 5: 13 461.53846 cents 6: 13 553.84615 cents 7: 13 646.15385 cents 8: 13 738.46154 cents 9: 13 830.76923 cents 10: 13 923.07692 cents 11: 13 1015.38462 cents 12: 13 1107.69231 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 0.0 : 92.3 184.6 276.9 369.2 461.5 553.8 646.2 738.5 830.8 923.1 1015.4 1107.7 1200.0 92.3 : 92.3 184.6 276.9 369.2 461.5 553.8 646.2 738.5 830.8 923.1 1015.4 1107.7 1200.0 184.6 : 92.3 184.6 276.9 369.2 461.5 553.8 646.2 738.5 830.8 923.1 1015.4 1107.7 1200.0 276.9 : 92.3 184.6 276.9 369.2 461.5 553.8 646.2 738.5 830.8 923.1 1015.4 1107.7 1200.0 369.2 : 92.3 184.6 276.9 369.2 461.5 553.8 646.2 738.5 830.8 923.1 1015.4 1107.7 1200.0 461.5 : 92.3 184.6 276.9 369.2 461.5 553.8 646.2 738.5 830.8 923.1 1015.4 1107.7 1200.0 553.8 : 92.3 184.6 276.9 369.2 461.5 553.8 646.2 738.5 830.8 923.1 1015.4 1107.7 1200.0 646.2 : 92.3 184.6 276.9 369.2 461.5 553.8 646.2 738.5 830.8 923.1 1015.4 1107.7 1200.0 738.5 : 92.3 184.6 276.9 369.2 461.5 553.8 646.2 738.5 830.8 923.1 1015.4 1107.7 1200.0 830.8 : 92.3 184.6 276.9 369.2 461.5 553.8 646.2 738.5 830.8 923.1 1015.4 1107.7 1200.0 923.1 : 92.3 184.6 276.9 369.2 461.5 553.8 646.2 738.5 830.8 923.1 1015.4 1107.7 1200.0 1015.4: 92.3 184.6 276.9 369.2 461.5 553.8 646.2 738.5 830.8 923.1 1015.4 1107.7 1200.0 1107.7: 92.3 184.6 276.9 369.2 461.5 553.8 646.2 738.5 830.8 923.1 1015.4 1107.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.3077 .. 92.3077 cents 1/1, 0.0000 cents 92.30769 cents 2: 184.6154 .. 184.6154 cents 1/1, 0.0000 cents 92.30769 cents 3: 276.9231 .. 276.9231 cents 1/1, 0.0000 cents 92.30769 cents 4: 369.2308 .. 369.2308 cents 1/1, 0.0000 cents 92.30769 cents 5: 461.5385 .. 461.5385 cents 1/1, 0.0000 cents 92.30769 cents 6: 553.8462 .. 553.8462 cents 1/1, 0.0000 cents 92.30769 cents 7: 646.1538 .. 646.1538 cents 1/1, 0.0000 cents 92.30769 cents 8: 738.4615 .. 738.4615 cents 1/1, 0.0000 cents 92.30769 cents 9: 830.7692 .. 830.7692 cents 1/1, 0.0000 cents 92.30769 cents 10: 923.0769 .. 923.0769 cents 1/1, 0.0000 cents 92.30769 cents 11: 1015.3846 .. 1015.3846 cents 1/1, 0.0000 cents 92.30769 cents 12: 1107.6923 .. 1107.6923 cents 1/1, 0.0000 cents 92.30769 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 92.30769 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 92.30769 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 92.30769 cents, amount: 13 Most common interval of one step : 92.30769 cents, amount: 13 Least squares average step : 92.30769 cents, oct.: 1200.00000 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 92.30769 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.076923 redundancy: 0.923077 Efficiency x scale size : 1.000000 Number of different interval sizes : 12 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 0 Scale contains two identical disjunct hexachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
13: 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x 3 x x x x 4 S SD: 18.2533 cents 3 x x x x 4 x x x x 5 x x 6 S SD: 17.7383 cents 4 x x x 5 x x x 6 x 7 x x 8 S SD: 15.2429 cents 5 x x 6 x x 7 x x 8 x 9 x 10 S SD: 10.2324 cents 6 x x 7 x 8 x x 9 x 10:11 x 12 S SD: 12.2703 cents 7 x x 8 x 9 x 10:11 x 12 x 13:14 S SD: 11.9092 cents 8 x 9 x 10 x 11 x 12:13:14 x 15:16 S SD: 8.4490 cents 9 x 10 x 11:12 x 13:14 x 15:16:17:18 S SD: 7.4703 cents 10 x 11:12 x 13:14 x 15:16:17:18:19:20 S SD: 6.6487 cents 11 x 12:13 x 14:15:16:17:18:19:20:21:22 S SD: 6.6184 cents 12 x 13:14:15:16 x 17:18:19:20:22:23:24 S SD: 9.6556 cents 13:14 x 15:16:17:18:19:20:21:22:23:25:26 SD: 5.2857 cents 14:15 x 16:17:18:19:20:21:23:24:25:27:28 SD: 8.0498 cents 15:16:17:18:19:20:21:22:23:24:26:27:28:30 S SD: 7.2295 cents 16:17:18:19:20:21:22:23:25:26:27:29:30:32 SD: 4.7400 cents 17:18:19:20:21:22:23:25:26:27:29:31:32:34 SD: 4.5090 cents 21:22:23:25:26:27:29:31:32:34:36:38:40:42 SD: 4.4840 cents 24:25:27:28:30:31:33:35:37:39:41:43:46:48 SD: 3.6419 cents 26:27:29:31:32:34:36:38:40:42:44:47:49:52 SD: 3.6313 cents 29:31:32:34:36:38:40:42:44:47:49:52:55:58 SD: 2.8686 cents 34:36:38:40:42:44:47:49:52:55:58:61:64:68 SD: 2.1500 cents 45:47:50:53:56:59:62:65:69:73:77:81:85:90 SD: 2.0558 cents 47:50:52:55:58:61:65:68:72:76:80:84:89:94 SD: 2.0054 cents 50:53:56:59:62:65:69:73:77:81:85:90:95:100 SD: 1.8804 cents 51:54:57:60:63:67:70:74:78:82:87:92:97:102 SD: 1.6130 cents 53:56:59:62:66:69:73:77:81:86:90:95:100:106 SD: 1.5055 cents 55:58:61:65:68:72:76:80:84:89:94:99:104:110 SD: 1.4059 cents 68:72:76:80:84:89:94:99:104:110:116:122:129:136 SD: 1.2082 cents 71:75:79:83:88:93:98:103:109:115:121:128:135:142 SD: 1.0530 cents 75:79:83:88:93:98:103:109:115:121:128:135:142:150 SD: 0.9456 cents 88:93:98:103:109:115:121:128:135:142:150:158:167:176 SD: 0.6420 cents 109:115:121:128:135:142:150:158:167:176:186:196:207:218 SD: 0.5822 cents 143:151:159:168:177:187:197:208:219:231:244:257:271:286 SD: 0.4193 cents 177:187:197:208:219:231:244:257:271:286:302:318:336:354 SD: 0.4133 cents 186:196:207:218:230:243:256:270:285:301:317:334:353:372 SD: 0.3936 cents 197:208:219:231:244:257:271:286:302:318:336:354:374:394 SD: 0.3779 cents 203:214:226:238:251:265:280:295:311:328:346:365:385:406 SD: 0.3207 cents 223:235:248:262:276:291:307:324:342:360:380:401:423:446 SD: 0.3016 cents 252:266:280:296:312:329:347:366:386:407:429:453:478:504 SD: 0.2968 cents 258:272:287:303:319:337:355:375:395:417:440:464:489:516 SD: 0.2852 cents 276:291:307:324:342:360:380:401:423:446:470:496:523:552 SD: 0.2662 cents 278:293:309:326:344:363:383:404:426:449:474:500:527:556 SD: 0.2418 cents 294:310:327:345:364:384:405:427:450:475:501:529:557:588 SD: 0.2300 cents 310:327:345:364:384:405:427:450:475:501:528:557:588:620 SD: 0.2281 cents 311:328:346:365:385:406:428:452:476:503:530:559:590:622 SD: 0.2243 cents 312:329:347:366:386:407:430:453:478:504:532:561:592:624 SD: 0.2210 cents 327:345:364:384:405:427:450:475:501:528:557:588:620:654 SD: 0.2209 cents 363:383:404:426:449:474:500:527:556:587:619:653:688:726 SD: 0.2102 cents 380:401:423:446:470:496:523:552:582:614:648:683:721:760 SD: 0.1969 cents 382:403:425:448:473:499:526:555:585:617:651:687:724:764 SD: 0.1727 cents 416:439:463:488:515:543:573:604:637:672:709:748:789:832 SD: 0.1460 cents 491:518:546:576:608:641:676:713:752:793:837:883:931:982 SD: 0.1398 cents 513:541:571:602:635:670:706:745:786:829:874:922:973:1026 SD: 0.1384 cents 530:559:590:622:656:692:730:770:812:856:903:953:1005:1060 SD: 0.1294 cents 586:618:652:688:725:765:807:851:898:947:999:1053:1111:1172 SD: 0.1239 cents 588:620:654:690:728:768:810:854:901:950:1002:1057:1115:1176 SD: 0.1144 cents