Scala analysis: keenan
Dave Keenan 31-tet mode with three 4:5:6:7 tetrads plus three inverted
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.129 cents 116.129030 2: 193.548 cents 193.548390 3: 270.968 cents 270.967740 4: 387.097 cents 387.096770 5: 503.226 cents 503.225810 6: 580.645 cents 580.645160 7: 696.774 cents 696.774190 8: 812.903 cents 812.903230 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: 116.1290 cents 116.1290 2: 77.4194 cents 77.4194 3: 77.4193 cents 77.4193 4: 116.1290 cents 116.1290 5: 116.1290 cents 116.1290 6: 77.4193 cents 77.4193 7: 116.1290 cents 116.1290 8: 116.1290 cents 116.1290 9: 77.4194 cents 77.4194 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: 5 77.41936 cents 1: 7 116.12903 cents 2: 2 154.83871 cents 2: 6 193.54839 cents 2: 4 232.25807 cents 3: 4 270.96774 cents 3: 7 309.67742 cents 3: 1 348.38709 cents 4: 8 387.09677 cents 4: 4 425.80645 cents 5: 2 464.51613 cents 5: 9 503.22581 cents 5: 1 541.93549 cents 6: 6 580.64516 cents 6: 6 619.35484 cents 7: 1 658.06451 cents 7: 9 696.77419 cents 7: 2 735.48387 cents 8: 4 774.19355 cents 8: 8 812.90323 cents 9: 1 851.61291 cents 9: 7 890.32258 cents 9: 4 929.03226 cents 10: 4 967.74194 cents 10: 6 1006.45161 cents 10: 2 1045.16129 cents 11: 7 1083.87097 cents 11: 5 1122.58064 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.54545 = 28/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 116.1 193.5 271.0 387.1 503.2 580.6 696.8 812.9 890.3 967.7 1083.9 1200.0 116.1 : 77.4 154.8 271.0 387.1 464.5 580.6 696.8 774.2 851.6 967.7 1083.9 1200.0 193.5 : 77.4 193.5 309.7 387.1 503.2 619.4 696.8 774.2 890.3 1006.5 1122.6 1200.0 271.0 : 116.1 232.3 309.7 425.8 541.9 619.4 696.8 812.9 929.0 1045.2 1122.6 1200.0 387.1 : 116.1 193.5 309.7 425.8 503.2 580.6 696.8 812.9 929.0 1006.5 1083.9 1200.0 503.2 : 77.4 193.5 309.7 387.1 464.5 580.6 696.8 812.9 890.3 967.7 1083.9 1200.0 580.6 : 116.1 232.3 309.7 387.1 503.2 619.4 735.5 812.9 890.3 1006.5 1122.6 1200.0 696.8 : 116.1 193.5 271.0 387.1 503.2 619.4 696.8 774.2 890.3 1006.5 1083.9 1200.0 812.9 : 77.4 154.8 271.0 387.1 503.2 580.6 658.1 774.2 890.3 967.7 1083.9 1200.0 890.3 : 77.4 193.5 309.7 425.8 503.2 580.6 696.8 812.9 890.3 1006.5 1122.6 1200.0 967.7 : 116.1 232.3 348.4 425.8 503.2 619.4 735.5 812.9 929.0 1045.2 1122.6 1200.0 1083.9: 116.1 232.3 309.7 387.1 503.2 619.4 696.8 812.9 929.0 1006.5 1083.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 77.4194 .. 116.1290 cents 38.70967 cents 77.41936 cents 2: 154.8387 .. 232.2581 cents 77.41936 cents 38.70968 cents 3: 270.9677 .. 348.3871 cents 77.41935 cents 38.70967 cents 4: 387.0968 .. 425.8064 cents 38.70968 cents 38.70968 cents 5: 464.5161 .. 541.9355 cents 77.41936 cents 38.70968 cents 6: 580.6452 .. 619.3548 cents 38.70968 cents 38.70967 cents 7: 658.0645 .. 735.4839 cents 77.41936 cents 38.70967 cents 8: 774.1936 .. 812.9032 cents 38.70968 cents 38.70968 cents 9: 851.6129 .. 929.0323 cents 77.41935 cents 38.70968 cents 10: 967.7419 .. 1045.1613 cents 77.41935 cents 38.70968 cents 11: 1083.8710 .. 1122.5806 cents 38.70967 cents 38.70968 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 77.41935 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 116.12903 cents Average / Smallest step : 1.291667 Largest / Average step : 1.161290 Largest / Smallest step : 1.500000 Median interval of one step : 116.12903 cents, amount: 7 Most common interval of one step : 116.12903 cents, amount: 7 Least squares average step : 98.85856 cents, oct.: 1186.30273 cents Scale is strictly proper Scale is 3-distributional even Scale is a mode of a 31-tone equal temperament with octave 2/1 degrees: 3 5 7 10 13 15 18 21 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: 16 = 4 more = 133.333% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 31-tone equal temperament Step pattern alph. order: ABBAABAABBAA Step pattern size order : LSSLLSLLSSLL Interval vector is [ 0 5 7 2 6 4 4 7 1 8 4 2 9 1 6 ] Scale is a Constant Structure, by a margin of 38.70967 cents Scale diversity : 1.333099 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.451613 Rothenberg efficiency : 0.455910 redundancy: 0.544090 Efficiency x scale size : 5.470924 Number of different interval sizes : 28 = 2.54545 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.54545 = 28/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 38.70967 cents Most common intervals : 503.22581 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 Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- 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: 16.5011 c. M:-32.2581 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 1 2 2 1 2 2 1 1 2 2 P D3 SD: 10.4217 c. M: 20.3735 c. 31: 3 2 2 3 3 2 3 3 2 2 3 3 SP D3 SD: 0.0000 c. M: 0.0000 c. Fokker 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: 2.6333 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: 13.3944 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.0019 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 12.2448 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 5.2716 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 10.1203 cents 10 x 11:12 x 13:14:15:16:17 x 19:20 SD: 9.1573 cents 11:12 x 13:14:15 x 16 x 18:19:21:22 SD: 10.5721 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 4.6381 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 7.3073 cents 14:15:16 x 18:19:20:21:22:23:24:26:28 S SD: 8.6178 cents 15:16:17:18:19:20:21:22:24:25:26:28:30 S SD: 5.5874 cents 16:17:18:19:20:21:22:24:26:27:28:30:32 S SD: 5.2057 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.9898 cents 18:19:20:21:23:24:25:27:29:30:31:34:36 SD: 4.8842 cents 23:25:26:27:29:31:32:34:37:38:40:43:46 SD: 4.3310 cents 24:26:27:28:30:32:34:36:38:40:42:45:48 S SD: 3.2690 cents 28:30:31:33:35:37:39:42:45:47:49:52:56 SD: 2.9583 cents 32:34:36:37:40:43:45:48:51:54:56:60:64 SD: 2.7679 cents 35:37:39:41:44:47:49:52:56:59:61:65:70 SD: 2.7430 cents 40:43:45:47:50:53:56:60:64:67:70:75:80 SD: 1.9960 cents 45:48:50:53:56:60:63:67:72:75:79:84:90 SD: 1.9492 cents 48:51:54:56:60:64:67:72:77:80:84:90:96 SD: 1.6628 cents 53:57:59:62:66:71:74:79:85:89:93:99:106 SD: 1.6105 cents 59:63:66:69:74:79:83:88:94:99:103:110:118 SD: 1.3902 cents 60:64:67:70:75:80:84:90:96:100:105:112:120 SD: 1.0156 cents 77:82:86:90:96:103:108:115:123:129:135:144:154 SD: 1.0152 cents 83:89:93:97:104:111:116:124:133:139:145:155:166 SD: 0.7362 cents 100:107:112:117:125:134:140:150:160:167:175:187:200 SD: 0.6440 cents 128:137:143:150:160:171:179:191:205:214:224:239:256 SD: 0.6045 cents 143:153:160:167:179:191:200:214:229:239:250:267:286 SD: 0.4652 cents 160:171:179:187:200:214:224:239:256:268:280:299:320 SD: 0.3886 cents 219:234:245:256:274:293:306:328:350:366:383:410:438 SD: 0.3635 cents 220:235:246:257:275:294:308:329:352:368:385:411:440 SD: 0.3576 cents 228:244:255:267:285:305:319:341:365:381:399:426:456 SD: 0.3533 cents 244:261:273:285:305:326:341:365:390:408:427:456:488 SD: 0.3124 cents 260:278:291:304:325:348:364:389:416:435:455:486:520 SD: 0.2910 cents 271:290:303:317:339:362:379:405:433:453:474:507:542 SD: 0.2776 cents 272:291:304:318:340:364:380:407:435:455:476:509:544 SD: 0.2650 cents 287:307:321:336:359:384:401:429:459:480:502:537:574 SD: 0.2475 cents 314:336:351:367:393:420:439:470:502:525:549:587:628 SD: 0.2447 cents 331:354:370:387:414:443:463:495:529:554:579:619:662 SD: 0.2045 cents 347:371:388:406:434:464:485:519:555:580:607:649:694 SD: 0.1484 cents 507:542:567:593:634:678:709:758:811:848:887:948:1014 SD: 0.0972 cents