Scala analysis: 31ET-11-lim
11-limit 31-equal subset
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 38.710 cents 38.709680 2: 193.548 cents 193.548390 3: 270.968 cents 270.967740 4: 387.097 cents 387.096770 5: 464.516 cents 464.516130 6: 541.935 cents 541.935480 7: 696.774 cents 696.774190 8: 774.194 cents 774.193550 9: 890.323 cents 890.322580 10: 967.742 cents 967.741940 11: 1083.871 cents 1083.870970 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.1290 cents 116.1290 1: 38.7097 cents 38.7097 2: 154.8387 cents 154.8387 3: 77.4193 cents 77.4193 4: 116.1290 cents 116.1290 5: 77.4194 cents 77.4194 6: 77.4193 cents 77.4193 7: 154.8387 cents 154.8387 8: 77.4194 cents 77.4194 9: 116.1290 cents 116.1290 10: 77.4194 cents 77.4194 11: 116.1290 cents 116.1290 12: 116.1290 cents 116.1290
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 38.70968 cents 1: 5 77.41935 cents 1: 4 116.12903 cents 1: 2 154.83871 cents 2: 2 154.83871 cents 2: 6 193.54839 cents 2: 4 232.25806 cents 3: 5 270.96774 cents 3: 5 309.67742 cents 3: 2 348.38709 cents 4: 2 348.38709 cents 4: 4 387.09677 cents 4: 6 425.80645 cents 5: 2 464.51613 cents 5: 9 503.22580 cents 5: 1 541.93549 cents 6: 2 541.93548 cents 6: 4 580.64516 cents 6: 4 619.35484 cents 6: 2 658.06451 cents 7: 1 658.06451 cents 7: 9 696.77419 cents 7: 2 735.48387 cents 8: 6 774.19355 cents 8: 4 812.90323 cents 8: 2 851.61290 cents 9: 2 851.61291 cents 9: 5 890.32258 cents 9: 5 929.03226 cents 10: 4 967.74194 cents 10: 6 1006.45161 cents 10: 2 1045.16129 cents 11: 2 1045.16129 cents 11: 4 1083.87097 cents 11: 5 1122.58065 cents 11: 1 1161.29032 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 38.7 193.5 271.0 387.1 464.5 541.9 696.8 774.2 890.3 967.7 1083.9 1200.0 38.7 : 154.8 232.3 348.4 425.8 503.2 658.1 735.5 851.6 929.0 1045.2 1161.3 1200.0 193.5 : 77.4 193.5 271.0 348.4 503.2 580.6 696.8 774.2 890.3 1006.5 1045.2 1200.0 271.0 : 116.1 193.5 271.0 425.8 503.2 619.4 696.8 812.9 929.0 967.7 1122.6 1200.0 387.1 : 77.4 154.8 309.7 387.1 503.2 580.6 696.8 812.9 851.6 1006.5 1083.9 1200.0 464.5 : 77.4 232.3 309.7 425.8 503.2 619.4 735.5 774.2 929.0 1006.5 1122.6 1200.0 541.9 : 154.8 232.3 348.4 425.8 541.9 658.1 696.8 851.6 929.0 1045.2 1122.6 1200.0 696.8 : 77.4 193.5 271.0 387.1 503.2 541.9 696.8 774.2 890.3 967.7 1045.2 1200.0 774.2 : 116.1 193.5 309.7 425.8 464.5 619.4 696.8 812.9 890.3 967.7 1122.6 1200.0 890.3 : 77.4 193.5 309.7 348.4 503.2 580.6 696.8 774.2 851.6 1006.5 1083.9 1200.0 967.7 : 116.1 232.3 271.0 425.8 503.2 619.4 696.8 774.2 929.0 1006.5 1122.6 1200.0 1083.9: 116.1 154.8 309.7 387.1 503.2 580.6 658.1 812.9 890.3 1006.5 1083.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.7097 .. 154.8387 cents 116.12903 cents 38.70968 cents 2: 154.8387 .. 232.2581 cents 77.41935 cents 1/1, 0.0000 cents 3: 270.9677 .. 348.3871 cents 77.41935 cents 38.70968 cents 4: 348.3871 .. 425.8064 cents 77.41936 cents 1/1, 0.0000 cents 5: 464.5161 .. 541.9355 cents 77.41936 cents 38.70968 cents 6: 541.9355 .. 658.0645 cents 116.12903 cents -0.00001 cents 7: 658.0645 .. 735.4839 cents 77.41936 cents 1/1, 0.0000 cents 8: 774.1935 .. 851.6129 cents 77.41935 cents 38.70968 cents 9: 851.6129 .. 929.0323 cents 77.41935 cents 0.00001 cents 10: 967.7419 .. 1045.1613 cents 77.41935 cents 38.70968 cents 11: 1045.1613 .. 1161.2903 cents 116.12903 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 38.70968 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 154.83871 cents Average / Smallest step : 2.583333 Largest / Average step : 1.548387 Largest / Smallest step : 4.000000 Median interval of one step : 96.77419 cents, amount: 0 Most common interval of one step : 77.41935 cents, amount: 5 Least squares average step : 97.60794 cents, oct.: 1171.29529 cents Scale is proper Scale is a mode of a 31-tone equal temperament with octave 2/1 degrees: 1 5 7 10 12 14 18 20 23 25 28 31 Least number of segments generator : 18 of 696.774 cents and inv. number of contiguous generator circle segments: 2 Shortest superset generator : 18 of 696.774 cents and inv. generated superset size: 20 = 8 more = 166.667% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABCDCCBCDCDD Step pattern size order : ADBCBBDBCBCC Interval vector is [ 1 5 4 4 6 4 5 5 4 4 6 2 9 3 4 ] Scale is not a Constant Structure Scale diversity : 1.381938 Rothenberg stability : 0.833333 = 5/6 Lumma stability : 0.193548 Rothenberg efficiency : 0.417977 redundancy: 0.582023 Efficiency x scale size : 5.015729 Number of different interval sizes : 30 = 2.72727 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 38.70967 cents Most common intervals : 503.22580 cents & inv., amount: 9 Most common triad is 0.0 503.226 696.774 cents, amount: 6 Number of recognisable fifths : 9, average 696.7742 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 0 2 1 1 1 0 2 1 1 1 1 1 N T3 SD: 25.2287 c. M: 41.9355 c. 18: 1 2 1 2 1 1 2 2 1 2 1 2 P D3 SD: 19.4838 c. M:-32.2581 c. 19: 0 3 1 2 1 1 3 1 2 1 2 2 N SD: 19.5593 c. M: 38.7097 c. 20: 1 2 2 2 1 1 3 1 2 1 2 2 N D3 SD: 17.1939 c. M:-32.9032 c. 22: 1 3 1 2 2 1 3 1 2 2 2 2 P D3 S SD: 14.1949 c. M:-26.3930 c. 23: 1 3 1 2 2 1 3 2 2 2 2 2 N SD: 14.5593 c. M:-23.5624 c. 24: 1 3 1 3 1 2 3 2 2 1 3 2 P T3 SD: 14.1302 c. M:-25.8065 c. 26: 1 3 2 2 2 2 3 2 2 2 2 3 SP D3 SD: 10.9912 c. M: 22.3325 c. 27: 1 3 2 3 1 2 4 1 3 2 2 3 N SD: 12.5670 c. M: 20.0717 c. 28: 1 4 1 3 2 2 3 2 3 2 2 3 P SD: 11.6217 c. M:-20.7373 c. 30: 1 4 2 3 2 2 3 2 3 2 3 3 P SD: 11.2611 c. M:-18.0645 c. 31: 1 4 2 3 2 2 4 2 3 2 3 3 P SD: 0.0000 c. M: 0.0000 c. Secor 12-tone
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: 2.5904 cents 3 x x x x 4 x x x 5 x x 6 S SD: 11.3517 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 1.3377 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 17.5355 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.1551 cents 7 x 8 x x 9:10 x 11 x 12:13:14 S SD: 13.8543 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 6.5227 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 9.7263 cents 10 x 11:12 x 13:14:15:16:17 x 19:20 SD: 9.7490 cents 11 x 12:13:14 x 15:16:17:18:19:21:22 SD: 9.4942 cents 12 x 13:14:15:16 x 18:19:20:21:22:24 S SD: 7.6647 cents 13 x x 15:16:17:18:19:20:22:23:24:26 SD: 7.3997 cents 14 x 16 x x 18:19:21:22:23:24:26:28 SD: 7.7400 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 6.2471 cents 19:20:21:22:24:25:26:28:30:32:33:36:38 S SD: 6.0958 cents 22:23:25:26:28:29:30:33:34:37:38:41:44 SD: 5.7435 cents 23:24:26:27:29:30:31:34:36:38:40:43:46 SD: 4.8717 cents 24:25:27:28:30:31:33:36:38:40:42:45:48 SD: 3.9381 cents 25:26:28:29:31:33:34:37:39:42:44:47:50 SD: 3.9362 cents 28:29:31:33:35:37:38:42:44:47:49:52:56 SD: 3.4898 cents 32:33:36:37:40:42:44:48:50:54:56:60:64 SD: 2.7936 cents 35:36:39:41:44:46:48:52:55:59:61:65:70 SD: 2.4994 cents 36:37:40:42:45:47:49:54:56:60:63:67:72 SD: 1.8908 cents 43:44:48:50:54:56:59:64:67:72:75:80:86 SD: 1.7942 cents 48:49:54:56:60:63:66:72:75:80:84:90:96 SD: 1.5512 cents 52:53:58:61:65:68:71:78:81:87:91:97:104 SD: 1.1390 cents 76:78:85:89:95:99:104:114:119:127:133:142:152 SD: 0.9508 cents 84:86:94:98:105:110:115:126:131:140:147:157:168 SD: 0.9142 cents 85:87:95:99:106:111:116:127:133:142:149:159:170 SD: 0.9072 cents 92:94:103:108:115:120:126:138:144:154:161:172:184 SD: 0.8751 cents 95:97:106:111:119:124:130:142:149:159:166:178:190 SD: 0.7649 cents 101:103:113:118:126:132:138:151:158:169:177:189:202 SD: 0.6571 cents 131:134:146:153:164:171:179:196:205:219:229:245:262 SD: 0.6360 cents 135:138:151:158:169:177:185:202:211:226:236:252:270 SD: 0.6138 cents 136:139:152:159:170:178:186:203:213:227:238:254:272 SD: 0.5314 cents 168:172:188:196:210:220:230:251:263:281:294:314:336 SD: 0.5282 cents 171:175:191:200:214:224:234:256:267:286:299:320:342 SD: 0.4506 cents 172:176:192:201:215:225:235:257:269:288:301:322:344 SD: 0.4303 cents 176:180:197:206:220:230:241:263:275:294:308:329:352 SD: 0.3942 cents 218:223:244:255:273:285:298:326:341:365:381:408:436 SD: 0.3358 cents 220:225:246:257:275:288:301:329:344:368:385:411:440 SD: 0.2985 cents 264:270:295:309:330:345:361:395:413:442:462:494:528 SD: 0.2980 cents 270:276:302:316:338:353:369:404:422:452:472:505:540 SD: 0.2960 cents 271:277:303:317:339:354:371:405:424:453:474:507:542 SD: 0.2823 cents 272:278:304:318:340:356:372:407:425:455:476:509:544 SD: 0.2678 cents 296:303:331:346:370:387:405:443:463:495:518:554:592 SD: 0.2600 cents 302:309:338:353:378:395:413:452:472:505:528:565:604 SD: 0.2597 cents 312:319:349:365:390:408:427:467:488:522:546:584:624 SD: 0.2494 cents 315:322:352:368:394:412:431:471:493:527:551:589:630 SD: 0.2415 cents 347:355:388:406:434:454:475:519:543:580:607:649:694 SD: 0.2204 cents 348:356:389:407:435:455:476:520:544:582:609:651:696 SD: 0.2025 cents 354:362:396:414:443:463:484:529:554:592:619:662:708 SD: 0.1909 cents 390:399:436:456:488:510:533:583:610:652:682:729:780 SD: 0.1902 cents 403:412:451:471:504:527:551:603:630:674:705:754:806 SD: 0.1868 cents 406:415:454:475:508:531:555:607:635:679:710:759:812 SD: 0.1536 cents 490:501:548:573:613:641:670:733:766:819:857:916:980 SD: 0.1507 cents 523:535:585:612:654:684:715:782:818:875:915:978:1046 SD: 0.1451 cents 531:543:594:621:664:694:726:794:830:888:929:993:1062 SD: 0.1428 cents 585:598:654:684:732:765:800:875:915:978:1023:1094:1170 SD: 0.1281 cents