Scala analysis: qm3b
Qm(3) 10-note quasi-miracle scale, mode B
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.667 cents 116.666667 2: 233.333 cents 233.333333 3: 383.333 cents 383.333333 4: 500.000 cents 500.000000 5: 616.667 cents 616.666667 6: 700.000 cents 700.000000 7: 816.667 cents 816.666667 8: 933.333 cents 933.333333 9: 1083.333 cents 1083.333333 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.6667 cents 116.6667 1: 116.6667 cents 116.6667 2: 116.6667 cents 116.6667 3: 150.0000 cents 150.0000 4: 116.6667 cents 116.6667 5: 116.6667 cents 116.6667 6: 83.3333 cents 83.3333 7: 116.6667 cents 116.6667 8: 116.6667 cents 116.6667 9: 150.0000 cents 150.0000 10: 116.6667 cents 116.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 83.33333 cents 1: 7 116.66667 cents 1: 2 150.00000 cents 2: 2 200.00000 cents 2: 4 233.33333 cents 2: 4 266.66667 cents 3: 3 316.66667 cents 3: 1 350.00000 cents 3: 6 383.33333 cents 4: 2 433.33333 cents 4: 2 466.66667 cents 4: 6 500.00000 cents 5: 1 550.00000 cents 5: 4 583.33333 cents 5: 4 616.66667 cents 5: 1 650.00000 cents 6: 6 700.00000 cents 6: 2 733.33333 cents 6: 2 766.66667 cents 7: 6 816.66667 cents 7: 1 850.00000 cents 7: 3 883.33333 cents 8: 4 933.33333 cents 8: 4 966.66667 cents 8: 2 1000.00000 cents 9: 2 1050.00000 cents 9: 7 1083.33333 cents 9: 1 1116.66667 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.11111 = 28/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 116.7 233.3 383.3 500.0 616.7 700.0 816.7 933.3 1083.3 1200.0 116.7 : 116.7 266.7 383.3 500.0 583.3 700.0 816.7 966.7 1083.3 1200.0 233.3 : 150.0 266.7 383.3 466.7 583.3 700.0 850.0 966.7 1083.3 1200.0 383.3 : 116.7 233.3 316.7 433.3 550.0 700.0 816.7 933.3 1050.0 1200.0 500.0 : 116.7 200.0 316.7 433.3 583.3 700.0 816.7 933.3 1083.3 1200.0 616.7 : 83.3 200.0 316.7 466.7 583.3 700.0 816.7 966.7 1083.3 1200.0 700.0 : 116.7 233.3 383.3 500.0 616.7 733.3 883.3 1000.0 1116.7 1200.0 816.7 : 116.7 266.7 383.3 500.0 616.7 766.7 883.3 1000.0 1083.3 1200.0 933.3 : 150.0 266.7 383.3 500.0 650.0 766.7 883.3 966.7 1083.3 1200.0 1083.3: 116.7 233.3 350.0 500.0 616.7 733.3 816.7 933.3 1050.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.3333 .. 150.0000 cents 66.66667 cents 83.33333 cents 2: 200.0000 .. 266.6667 cents 66.66667 cents 50.00000 cents 3: 316.6667 .. 383.3333 cents 66.66667 cents 50.00000 cents 4: 433.3333 .. 500.0000 cents 66.66667 cents 50.00000 cents 5: 550.0000 .. 650.0000 cents 100.00000 cents 50.00000 cents 6: 700.0000 .. 766.6667 cents 66.66667 cents 50.00000 cents 7: 816.6667 .. 883.3333 cents 66.66667 cents 50.00000 cents 8: 933.3333 .. 1000.0000 cents 66.66667 cents 50.00000 cents 9: 1050.0000 .. 1116.6667 cents 66.66667 cents 50.00000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 83.33333 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 150.00000 cents Average / Smallest step : 1.440000 Largest / Average step : 1.250000 Largest / Smallest step : 1.800000 Median interval of one step : 116.66667 cents, amount: 7 Most common interval of one step : 116.66667 cents, amount: 7 Least squares average step : 119.35065 cents, oct.: 1193.50649 cents Scale is strictly proper Scale is a mode of a 72-tone equal temperament with octave 2/1 degrees: 7 14 23 30 37 42 49 56 65 72 Least number of segments generator : 37 of 616.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 65 of 1083.333 cents and inv. generated superset size: 16 = 6 more = 160.000% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 72-tone equal temperament Step pattern alph. order: AABAACAABA Step pattern size order : MMLMMSMMLM Interval vector is [ 0 0 0 0 1 0 7 0 2 0 0 2 0 4 0 4 0 0 3 0 1 0 6 0 0 2 0 2 0 6 0 0 1 0 4 0 ] Scale is a Constant Structure, by a margin of 50.00000 cents Scale diversity : 1.418000 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.472222 Rothenberg efficiency : 0.447857 redundancy: 0.552143 Efficiency x scale size : 4.478571 Number of different interval sizes : 28 = 3.11111 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.11111 = 28/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 33.33333 cents Most common intervals : 116.66667 cents & inv., amount: 7 Number of recognisable fifths : 6, average 700.0000 cents Scale contains two identical disjunct pentachords Formal octave complements present : 7 = 70.0000% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 5-6 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 17.1594 c. M:-26.6667 c. 19: 2 2 2 2 2 1 2 2 2 2 SP M ME SD: 10.3531 c. M:-19.2982 c. 21: 2 2 3 2 2 1 2 2 3 2 P SD: 12.2567 c. M: 19.0476 c. 22: 2 2 3 2 2 2 2 2 3 2 SP D3 SD: 9.1035 c. M: 16.6667 c. 27: 3 2 4 2 3 2 2 3 3 3 P SD: 12.2977 c. M:-16.6667 c. 28: 3 2 4 3 2 2 3 3 3 3 P SD: 11.9760 c. M: 19.0476 c. 29: 3 3 3 3 3 2 3 3 3 3 SP M ME SD: 9.7549 c. M:-18.3908 c. 31: 3 3 4 3 3 2 3 3 4 3 SP SD: 2.7676 c. M: 4.3011 c. 41: 4 4 5 4 4 3 4 4 5 4 SP SD: 2.0926 c. M:-3.2520 c. 72: 7 7 9 7 7 5 7 7 9 7 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 0.9775 cents 3 x x x 4 x x x 5 x 6 S SD: 16.3379 cents 4 x x 5 x x 6 x 7 x 8 S SD: 8.9178 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 20.0788 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 11.4077 cents 7 x 8:9 x 10 x 11:12:13:14 S SD: 9.0201 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 9.1561 cents 9 x 10:11:12:13 x 14:15:17:18 SD: 12.2963 cents 10:11 x 12:13:14:15:16:17:19:20 SD: 11.7519 cents 11:12:13:14:15:16 x 18:19:21:22 SD: 11.4373 cents 12:13:14:15:16:17:18:19:21:22:24 SD: 6.8317 cents 13:14:15:16:17:19 x 21:22:24:26 SD: 7.8378 cents 14:15:16:17:19:20:21:22:24:26:28 SD: 6.6115 cents 15:16:17:19:20:21:22:24:26:28:30 SD: 6.2316 cents 16:17:18:20:21:23:24:26:27:30:32 SD: 5.7899 cents 20:21:23:25:27:29:30:32:34:37:40 SD: 5.2662 cents 21:22:24:26:28:30:31:34:36:39:42 SD: 5.1027 cents 24:26:27:30:32:34:36:38:41:45:48 SD: 4.5361 cents 26:28:30:32:35:37:39:42:45:49:52 SD: 4.2501 cents 27:29:31:34:36:39:40:43:46:50:54 SD: 4.0390 cents 28:30:32:35:37:40:42:45:48:52:56 SD: 2.2115 cents 40:43:46:50:53:57:60:64:69:75:80 SD: 2.1947 cents 42:45:48:52:56:60:63:67:72:79:84 SD: 1.9499 cents 48:51:55:60:64:69:72:77:82:90:96 SD: 1.8956 cents 54:58:62:67:72:77:81:87:93:101:108 SD: 1.8359 cents 56:60:64:70:75:80:84:90:96:105:112 SD: 1.0280 cents 84:90:96:105:112:120:126:135:144:157:168 SD: 0.7233 cents 98:105:112:122:131:140:147:157:168:183:196 SD: 0.6705 cents 126:135:144:157:168:180:189:202:216:236:252 SD: 0.6077 cents 146:156:167:182:195:208:219:234:250:273:292 SD: 0.5705 cents 158:169:181:197:211:226:237:253:271:295:316 SD: 0.5298 cents 161:172:184:201:215:230:241:258:276:301:322 SD: 0.3797 cents 201:215:230:251:268:287:301:322:345:376:402 SD: 0.3401 cents 215:230:246:268:287:307:322:345:369:402:430 SD: 0.3388 cents 229:245:262:286:306:327:343:367:393:428:458 SD: 0.3029 cents 257:275:294:321:343:367:385:412:441:481:514 SD: 0.2981 cents 269:288:308:336:359:384:403:431:461:503:538 SD: 0.2736 cents 299:320:342:373:399:427:448:479:513:559:598 SD: 0.1999 cents 388:415:444:484:518:554:581:622:665:725:776 SD: 0.1742 cents 416:445:476:519:555:594:623:667:713:778:832 SD: 0.1618 cents 484:518:554:604:646:691:725:776:830:905:968 SD: 0.1359 cents 528:565:604:659:705:754:791:846:905:987:1056 SD: 0.1296 cents 561:600:642:700:749:801:841:899:962:1049:1122 SD: 0.1159 cents