Scala analysis: eb24-moha-bayyati-septimal_Eb
Lower Mohajira tetrachord with 21/16; upper Bayyati ~12:13:14:16
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 132.248 cents 132.248350 2: 341.462 cents 341.462170 3: 473.711 cents 473.710520 4: 704.607 cents 704.606900 5: 836.855 cents 836.855260 6: 969.104 cents 969.103610 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 230.8964 cents 230.8964 1: 132.2483 cents 132.2483 2: 209.2138 cents 209.2138 3: 132.2483 cents 132.2483 4: 230.8964 cents 230.8964 5: 132.2484 cents 132.2484 6: 132.2483 cents 132.2483 7: 230.8964 cents 230.8964
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 132.24835 cents 1: 1 209.21382 cents 1: 2 230.89638 cents 2: 1 264.49671 cents 2: 2 341.46217 cents 2: 4 363.14473 cents 3: 1 473.71052 cents 3: 4 495.39309 cents 3: 2 572.35855 cents 4: 2 627.64144 cents 4: 4 704.60690 cents 4: 1 726.28948 cents 5: 4 836.85526 cents 5: 2 858.53783 cents 5: 1 935.50329 cents 6: 2 969.10361 cents 6: 1 990.78618 cents 6: 4 1067.75165 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 : 132.2 341.5 473.7 704.6 836.9 969.1 1200.0 132.2 : 209.2 341.5 572.4 704.6 836.9 1067.8 1200.0 341.5 : 132.2 363.1 495.4 627.6 858.5 990.8 1200.0 473.7 : 230.9 363.1 495.4 726.3 858.5 1067.8 1200.0 704.6 : 132.2 264.5 495.4 627.6 836.9 969.1 1200.0 836.9 : 132.2 363.1 495.4 704.6 836.9 1067.8 1200.0 969.1 : 230.9 363.1 572.4 704.6 935.5 1067.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 132.2483 .. 230.8964 cents 98.64803 cents 132.24835 cents 2: 264.4967 .. 363.1447 cents 98.64802 cents 33.60033 cents 3: 473.7105 .. 572.3585 cents 98.64803 cents 110.56579 cents 4: 627.6414 .. 726.2895 cents 98.64804 cents 55.28289 cents 5: 836.8553 .. 935.5033 cents 98.64803 cents 110.56578 cents 6: 969.1036 .. 1067.7517 cents 98.64804 cents 33.60032 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 132.24835 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 230.89638 cents Average / Smallest step : 1.296262 Largest / Average step : 1.346896 Largest / Smallest step : 1.745930 Median interval of one step : 132.24835 cents, amount: 4 Most common interval of one step : 132.24835 cents, amount: 4 Least squares average step : 167.52593 cents, oct.: 1172.68149 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1107-tone equal temperament with octave 2/1 degrees: 122 315 437 650 772 894 1107 Least number of segments generator : 554 of 600.542 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 650 of 704.607 cents and inv. generated superset size: 17 = 10 more = 242.857% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACAAC Step pattern size order : SMSLSSL Scale is a Constant Structure, by a margin of 33.60032 cents Scale diversity : 1.354966 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.506760 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 : 21.68256 cents Number of recognisable fifths : 4, average 704.6069 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% Limited inverse transpositions : 3 Inversional symmetry on degrees : 5 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.7072 c. M:-59.4678 c. Lebeng 10: 1 2 1 2 1 1 2 P M ME S SD: 11.1030 c. M:-18.5378 c. 17: 2 3 2 3 2 2 3 SP M ME S SD: 12.5339 c. M:-20.4071 c. 25: 3 4 3 5 2 3 5 P SD: 11.7246 c. M: 20.8553 c. 26: 3 4 3 5 3 3 5 SP T3 S SD: 10.0932 c. M: 18.3852 c. 27: 3 5 3 5 3 3 5 SP M DE S SD: 9.2992 c. M:-15.1784 c. 33: 4 5 4 6 4 4 6 SP T3 S SD: 10.1857 c. M: 14.1894 c. 35: 4 6 4 7 3 4 7 P SD: 9.1122 c. M:-15.3931 c. 36: 4 6 4 7 4 4 7 SP T3 S SD: 4.7274 c. M: 8.1288 c. 43: 5 7 5 8 5 5 8 SP T3 S SD: 5.3909 c. M:-7.6406 c. 46: 5 8 5 9 5 5 9 SP T3 S SD: 2.5460 c. M: 4.1453 c. 63: 7 11 7 12 7 7 12 SP T3 S SD: 1.5232 c. M:-2.4800 c. 99: 11 17 11 19 11 11 19 SP T3 S SD: 1.1650 c. M: 2.0682 c. 109: 12 19 12 21 12 12 21 SP T3 S SD: 0.1941 c. M: 0.3160 c. 281: 31 49 31 54 31 31 54 SP T3 S SD: 0.1909 c. M:-0.3108 c. 390: 43 68 43 75 43 43 75 SP T3 S SD: 0.0833 c. M:-0.1356 c. 499: 55 87 55 96 55 55 96 SP T3 S SD: 0.0227 c. M:-0.0370 c. 608: 67 106 67 117 67 67 117 SP T3 S SD: 0.0162 c. M: 0.0263 c. 1107: 122 193 122 213 122 122 213 SP T3 S SD: 0.0014 c. M:-0.0022 c.
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: 1.3259 cents 3 x x 4 x 5 x 6 S SD: 17.7912 cents 4 x 5 x 6 x 7:8 S SD: 11.2327 cents 5 x 6:7 x 8:9:10 S SD: 24.8136 cents 6 x 7:8:9:10:11:12 S SD: 20.3177 cents 7:8 x 9 x 11:12:14 SD: 24.9221 cents 8:9:10:11:12:13:14:16 S SD: 16.4072 cents 9:10:11:12:14:15:16:18 S SD: 14.1169 cents 10:11:12:13:15:16:18:20 SD: 10.1168 cents 12:13:15:16:18:19:21:24 SD: 9.4290 cents 13:14:16:17:20:21:23:26 SD: 7.1614 cents 22:24:27:29:33:36:39:44 SD: 5.0939 cents 23:25:28:30:35:37:40:46 SD: 4.8306 cents 24:26:29:32:36:39:42:48 SD: 4.1510 cents 26:28:32:34:39:42:46:52 SD: 4.1016 cents 28:30:34:37:42:45:49:56 SD: 3.2452 cents 36:39:44:47:54:58:63:72 SD: 2.6893 cents 40:43:49:53:60:65:70:80 SD: 2.6706 cents 47:51:57:62:71:76:82:94 SD: 2.5558 cents 48:52:58:63:72:78:84:96 SD: 2.3067 cents 50:54:61:66:75:81:88:100 SD: 1.7990 cents 51:55:62:67:77:83:89:102 SD: 1.7810 cents 60:65:73:79:90:97:105:120 SD: 1.3152 cents 64:69:78:84:96:104:112:128 SD: 0.8366 cents 101:109:123:133:152:164:177:202 SD: 0.7482 cents 111:120:135:146:167:180:194:222 SD: 0.7481 cents 124:134:151:163:186:201:217:248 SD: 0.4916 cents 137:148:167:180:206:222:240:274 SD: 0.4818 cents 175:189:213:230:263:284:306:350 SD: 0.4068 cents 201:217:245:264:302:326:352:402 SD: 0.3391 cents 225:243:274:296:338:365:394:450 SD: 0.2672 cents 289:312:352:380:434:469:506:578 SD: 0.2383 cents 340:367:414:447:511:551:595:680 SD: 0.2018 cents 404:436:492:531:607:655:707:808 SD: 0.1108 cents