Scala analysis: qm2
Qm(2) 7-note quasi-miracle scale
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: 383.333 cents 383.333333 3: 500.000 cents 500.000000 4: 700.000 cents 700.000000 5: 816.667 cents 816.666667 6: 1083.333 cents 1083.333333 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.6667 cents 116.6667 1: 116.6667 cents 116.6667 2: 266.6667 cents 266.6667 3: 116.6667 cents 116.6667 4: 200.0000 cents 200.0000 5: 116.6667 cents 116.6667 6: 266.6667 cents 266.6667 7: 116.6667 cents 116.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 116.66667 cents 1: 1 200.00000 cents 1: 2 266.66667 cents 2: 1 233.33333 cents 2: 2 316.66667 cents 2: 4 383.33333 cents 3: 1 433.33333 cents 3: 4 500.00000 cents 3: 2 583.33333 cents 4: 2 616.66667 cents 4: 4 700.00000 cents 4: 1 766.66667 cents 5: 4 816.66667 cents 5: 2 883.33333 cents 5: 1 966.66667 cents 6: 2 933.33333 cents 6: 1 1000.00000 cents 6: 4 1083.33333 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 116.7 383.3 500.0 700.0 816.7 1083.3 1200.0 116.7 : 266.7 383.3 583.3 700.0 966.7 1083.3 1200.0 383.3 : 116.7 316.7 433.3 700.0 816.7 933.3 1200.0 500.0 : 200.0 316.7 583.3 700.0 816.7 1083.3 1200.0 700.0 : 116.7 383.3 500.0 616.7 883.3 1000.0 1200.0 816.7 : 266.7 383.3 500.0 766.7 883.3 1083.3 1200.0 1083.3: 116.7 233.3 500.0 616.7 816.7 933.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 116.6667 .. 266.6667 cents 150.00000 cents 116.66667 cents 2: 233.3333 .. 383.3333 cents 150.00000 cents -33.33333 cents 3: 433.3333 .. 583.3333 cents 150.00000 cents 50.00000 cents 4: 616.6667 .. 766.6667 cents 150.00000 cents 33.33333 cents 5: 816.6667 .. 966.6667 cents 150.00000 cents 50.00000 cents 6: 933.3333 .. 1083.3333 cents 150.00000 cents -33.33333 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 116.66667 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 266.66667 cents Average / Smallest step : 1.469388 Largest / Average step : 1.555556 Largest / Smallest step : 2.285714 Median interval of one step : 116.66667 cents, amount: 4 Most common interval of one step : 116.66667 cents, amount: 4 Least squares average step : 172.61905 cents, oct.: 1208.33333 cents Scale is not proper Scale has trivalence property Scale is a mode of a 72-tone equal temperament with octave 2/1 degrees: 7 23 30 42 49 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: 15 = 8 more = 214.286% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 72-tone equal temperament Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Interval vector is [ 0 0 0 0 0 0 4 0 0 0 0 1 0 1 0 2 0 0 2 0 0 0 4 0 0 1 0 0 0 4 0 0 0 0 2 0 ] Scale is a Constant Structure, by a margin of 33.33333 cents Scale diversity : 1.434435 Lumma stability : 0.305556 Lumma impropriety factor : 0.055556 Rothenberg efficiency : 0.506122 redundancy: 0.493878 Efficiency x scale size : 3.542857 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 33.33333 cents Number of recognisable fifths : 4, average 700.0000 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Formal octave complements present : 7 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 37.1917 c. M:-54.7619 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 21.8218 c. M: 33.3333 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 16.5232 c. M:-23.3333 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 12.5988 c. M:-16.6667 c. Double Harmonic Major, Major Gipsy, Bhairav That, Mela Mayamalavagaula, Raga Paraj, Kalingada, Gaulipantu, Lalitapancamam, Gandhakriya, Kalingda, Manjiri, Chromatic 2nd Byzantine Liturgical, Hitzazkiar: Greece, Maqam Zengule, Hijaz Kar, Suzidil 19: 2 4 2 3 2 4 2 P T3 I SD: 6.3255 c. M:-9.6491 c. 22: 2 5 2 4 2 5 2 N T3 I SD: 6.3770 c. M: 9.0909 c. Double Harmonic Major 31: 3 7 3 5 3 7 3 N T3 I SD: 2.6650 c. M:-3.7634 c. Double Harmonic Major, Major Gipsy 41: 4 9 4 7 4 9 4 N T3 I SD: 2.0150 c. M:-2.8455 c. 72: 7 16 7 12 7 16 7 N T3 I SD: 0.0000 c. M:-0.0000 c. Xenakis Byzantine Liturgical Soft Chromatic, Quasi-Miracle-7
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.9775 cents 3 x x 4 x 5 x 6 S SD: 22.5734 cents 4 x 5 x 6 x 7:8 S SD: 28.6407 cents 5 x 6:7 x 8:9:10 S SD: 25.0765 cents 6 x x 8:9:10:11:12 S SD: 15.1576 cents 7:8:9 x x 11:13:14 SD: 26.1483 cents 8:9:10:11:12:13:15:16 SD: 14.8814 cents 10:11:12:13:15:16:19:20 SD: 14.1452 cents 11:12:14:15:16:18:21:22 S SD: 13.4898 cents 12:13:15:16:18:19:22:24 SD: 6.5402 cents 15:16:19:20:22:24:28:30 SD: 6.5176 cents 16:17:20:21:24:26:30:32 SD: 5.7095 cents 24:26:30:32:36:38:45:48 SD: 4.4408 cents 28:30:35:37:42:45:52:56 SD: 3.1419 cents 30:32:37:40:45:48:56:60 SD: 3.0605 cents 32:34:40:43:48:51:60:64 SD: 2.8645 cents 40:43:50:53:60:64:75:80 SD: 2.4028 cents 44:47:55:59:66:71:82:88 SD: 2.2539 cents 45:48:56:60:67:72:84:90 SD: 1.9500 cents 48:51:60:64:72:77:90:96 SD: 1.9185 cents 56:60:70:75:84:90:105:112 SD: 1.4306 cents 60:64:75:80:90:96:112:120 SD: 1.0830 cents 84:90:105:112:126:135:157:168 SD: 0.9788 cents 98:105:122:131:147:157:183:196 SD: 0.8987 cents 101:108:126:135:151:162:189:202 SD: 0.7026 cents 113:121:141:151:169:181:211:226 SD: 0.6802 cents 116:124:145:155:174:186:217:232 SD: 0.6189 cents 129:138:161:172:193:207:241:258 SD: 0.5761 cents 146:156:182:195:219:234:273:292 SD: 0.4927 cents 161:172:201:215:241:258:301:322 SD: 0.4296 cents 201:215:251:268:301:322:376:402 SD: 0.3982 cents 229:245:286:306:343:367:428:458 SD: 0.3574 cents 245:262:306:327:367:393:458:490 SD: 0.3206 cents 259:277:323:346:388:415:484:518 SD: 0.2914 cents 275:294:343:367:412:441:514:550 SD: 0.2475 cents 287:307:358:383:430:460:537:574 SD: 0.2186 cents 299:320:373:399:448:479:559:598 SD: 0.1961 cents 343:367:428:458:514:550:641:686 SD: 0.1941 cents 400:428:499:534:599:641:748:800 SD: 0.1773 cents 415:444:518:554:622:665:776:830 SD: 0.1290 cents 460:492:574:614:689:737:860:920 SD: 0.1259 cents 516:552:644:689:773:827:965:1032 SD: 0.1194 cents 544:582:679:726:815:872:1017:1088 SD: 0.0976 cents