Scala analysis: 12of26-IbnSina-plus
Tempering of Ibn Sina's 1/1-14/13-7/6-4/3-3/2-21/13-7/4-2/1
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 138.462 cents 138.461540 2: 184.615 cents 184.615380 3: 276.923 cents 276.923080 4: 369.231 cents 369.230770 5: 507.692 cents 507.692310 6: 553.846 cents 553.846150 7: 692.308 cents 692.307690 8: 830.769 cents 830.769230 9: 876.923 cents 876.923080 10: 969.231 cents 969.230770 11: 1061.538 cents 1061.538460 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 138.4615 cents 138.4615 1: 138.4615 cents 138.4615 2: 46.1538 cents 46.1538 3: 92.3077 cents 92.3077 4: 92.3077 cents 92.3077 5: 138.4615 cents 138.4615 6: 46.1538 cents 46.1538 7: 138.4615 cents 138.4615 8: 138.4615 cents 138.4615 9: 46.1539 cents 46.1539 10: 92.3077 cents 92.3077 11: 92.3077 cents 92.3077 12: 138.4615 cents 138.4615
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 46.15384 cents 1: 4 92.30770 cents 1: 5 138.46154 cents 2: 2 138.46154 cents 2: 6 184.61538 cents 2: 2 230.76923 cents 2: 2 276.92308 cents 3: 2 230.76923 cents 3: 3 276.92308 cents 3: 6 323.07693 cents 3: 1 369.23077 cents 4: 6 369.23077 cents 4: 4 415.38461 cents 4: 2 461.53846 cents 5: 1 415.38461 cents 5: 1 461.53846 cents 5: 9 507.69231 cents 5: 1 553.84615 cents 6: 4 553.84615 cents 6: 4 600.00000 cents 6: 4 646.15385 cents 7: 1 646.15385 cents 7: 9 692.30769 cents 7: 1 738.46154 cents 7: 1 784.61539 cents 8: 2 738.46154 cents 8: 4 784.61539 cents 8: 6 830.76923 cents 9: 1 830.76923 cents 9: 6 876.92308 cents 9: 3 923.07692 cents 9: 2 969.23077 cents 10: 2 923.07692 cents 10: 2 969.23077 cents 10: 6 1015.38462 cents 10: 2 1061.53846 cents 11: 5 1061.53846 cents 11: 4 1107.69230 cents 11: 3 1153.84616 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.54545 = 39/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 138.5 184.6 276.9 369.2 507.7 553.8 692.3 830.8 876.9 969.2 1061.5 1200.0 138.5 : 46.2 138.5 230.8 369.2 415.4 553.8 692.3 738.5 830.8 923.1 1061.5 1200.0 184.6 : 92.3 184.6 323.1 369.2 507.7 646.2 692.3 784.6 876.9 1015.4 1153.8 1200.0 276.9 : 92.3 230.8 276.9 415.4 553.8 600.0 692.3 784.6 923.1 1061.5 1107.7 1200.0 369.2 : 138.5 184.6 323.1 461.5 507.7 600.0 692.3 830.8 969.2 1015.4 1107.7 1200.0 507.7 : 46.2 184.6 323.1 369.2 461.5 553.8 692.3 830.8 876.9 969.2 1061.5 1200.0 553.8 : 138.5 276.9 323.1 415.4 507.7 646.2 784.6 830.8 923.1 1015.4 1153.8 1200.0 692.3 : 138.5 184.6 276.9 369.2 507.7 646.2 692.3 784.6 876.9 1015.4 1061.5 1200.0 830.8 : 46.2 138.5 230.8 369.2 507.7 553.8 646.2 738.5 876.9 923.1 1061.5 1200.0 876.9 : 92.3 184.6 323.1 461.5 507.7 600.0 692.3 830.8 876.9 1015.4 1153.8 1200.0 969.2 : 92.3 230.8 369.2 415.4 507.7 600.0 738.5 784.6 923.1 1061.5 1107.7 1200.0 1061.5: 138.5 276.9 323.1 415.4 507.7 646.2 692.3 830.8 969.2 1015.4 1107.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 46.1538 .. 138.4615 cents 92.30770 cents 46.15384 cents 2: 138.4615 .. 276.9231 cents 138.46154 cents 1/1, 0.0000 cents 3: 230.7692 .. 369.2308 cents 138.46154 cents -46.15385 cents 4: 369.2308 .. 461.5385 cents 92.30769 cents 1/1, 0.0000 cents 5: 415.3846 .. 553.8461 cents 138.46154 cents -46.15385 cents 6: 553.8461 .. 646.1538 cents 92.30770 cents 1/1, 0.0000 cents 7: 646.1539 .. 784.6154 cents 138.46154 cents 1/1, 0.0000 cents 8: 738.4615 .. 830.7692 cents 92.30769 cents -46.15385 cents 9: 830.7692 .. 969.2308 cents 138.46154 cents 1/1, 0.0000 cents 10: 923.0769 .. 1061.5385 cents 138.46154 cents -46.15385 cents 11: 1061.5385 .. 1153.8462 cents 92.30770 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 46.15384 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 138.46154 cents Average / Smallest step : 2.166667 Largest / Average step : 1.384615 Largest / Smallest step : 3.000000 Median interval of one step : 92.30770 cents, amount: 4 Most common interval of one step : 138.46154 cents, amount: 5 Least squares average step : 98.20118 cents, oct.: 1178.41420 cents Scale is not proper Scale is a mode of a 26-tone equal temperament with octave 2/1 degrees: 3 4 6 8 11 12 15 18 19 21 23 26 Least number of segments generator : 15 of 692.308 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 15 of 692.308 cents and inv. generated superset size: 17 = 5 more = 141.667% Number of contiguous 1-step segments: 3 Step pattern alph. order: ABCCABAABCCA Step pattern size order : LSMMLSLLSMML Interval vector is [ 3 4 7 6 4 5 6 7 5 3 9 5 2 ] Scale is not a Constant Structure Scale diversity : 1.311155 Lumma stability : 0.076923 Lumma impropriety factor : 0.153846 Rothenberg efficiency : 0.444222 redundancy: 0.555778 Efficiency x scale size : 5.330664 Number of different interval sizes : 25 = 2.27273 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.54545 = 39/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 46.15384 cents Most common intervals : 507.69231 cents & inv., amount: 9 Most common triad is 0.0 507.692 692.308 cents, amount: 6 Number of recognisable fifths : 9, average 692.3077 cents Scale contains two identical disjunct hexachords Formal octave complements present : 7 = 58.3333% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 2 0 1 1 1 1 1 2 0 1 1 1 N T3 SD: 35.9432 c. M:-69.2308 c. 14: 1 1 1 1 2 0 2 1 1 1 1 2 P D3 SD: 30.8085 c. M: 59.3407 c. 15: 1 1 1 1 2 1 1 2 1 1 1 2 P D3 SD: 32.7323 c. M: 58.4615 c. 16: 2 0 2 1 2 0 2 2 1 1 1 2 N D3 SD: 18.3953 c. M: 34.6154 c. 17: 2 1 1 1 2 1 2 2 0 2 1 2 N D3 SD: 15.9466 c. M: 29.8643 c. 19: 2 1 1 2 2 1 2 2 1 1 2 2 P D3 SD: 12.4259 c. M: 24.2915 c. 26: 3 1 2 2 3 1 3 3 1 2 2 3 N SD: 0.0000 c. M:-0.0000 c.
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: 4.8237 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.0601 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 4.9057 cents 5 x x 6 x x 7 x 8 x x 9:10 S SD: 13.4812 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 3.6920 cents 7 x x 8:9 x 10 x 11 x 12:13:14 S SD: 17.0337 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 4.9584 cents 9 x 10 x 11:12 x 13 x 15:16:17:18 SD: 9.6930 cents 10 x 11:12 x 13:14:15:16:17 x 18:20 S SD: 10.8989 cents 11:12 x 13:14 x 15:16:18 x 19:20:22 S SD: 8.9787 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 6.0567 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 6.8939 cents 14:15 x 16:17:19 x 21 x 23:25:26:28 SD: 8.3799 cents 15:16:17:18:19:20:21:22:24:25:26:28:30 S SD: 7.2701 cents 16:17:18:19:20:21:22:24:26:27:28:30:32 S SD: 6.0783 cents 17:18:19:20:21:23 x 25:27:28:30:31:34 SD: 5.9105 cents 18 x 20:21:22:24:25:27:29:30:32:33:36 SD: 4.0046 cents 19 x 21:22:24:25:26:28:31:32:33:35:38 SD: 6.2015 cents 20 x 22:23:25:27:28:30:32:33:35:37:40 SD: 5.2678 cents 21:23 x 25:26:28:29:31:34:35:37:39:42 SD: 3.7766 cents 22:24 x 26:27 x 30:33:36:37:39:41:44 SD: 5.1450 cents 23:25:26:27:28:31:32:34:37:38:40:42:46 SD: 4.4670 cents 24:26:27:28:30:32:33:36:39:40:42:44:48 S SD: 2.9541 cents 25:27:28:29:31 x 34:37:40:41:44:46:50 SD: 4.1201 cents 26:28:29:31:32:35:36:39:42:43:46:48:52 SD: 3.3222 cents 29:31:32:34:36:39:40:43:47:48:51:54:58 SD: 2.9256 cents 30 x 33:35:37:40:41:45:48:50:53:55:60 SD: 3.6721 cents 31:34 x 36:38:42:43:46:50:51:54:57:62 SD: 4.0578 cents 32:35:36:38:40:43:44:48:52:53:56:59:64 SD: 3.3260 cents 33:36:37:39:41:44:45:49:53:55:58:61:66 SD: 2.8691 cents 34:37:38:40:42:46:47:51:55:56:60:63:68 SD: 2.5694 cents 35:38:39:41:43:47:48:52:57:58:61:65:70 SD: 2.1258 cents 45:49:50:53:56:60:62:67:73:75:79:83:90 SD: 1.7642 cents 47:51:52:55:58:63:65:70:76:78:82:87:94 SD: 1.3634 cents 59:64:66:69:73:79:81:88:95:98:103:109:118 SD: 1.2501 cents 71:77:79:83:88:95:98:106:115:118:124:131:142 SD: 0.9304 cents 88:95:98:103:109:118:121:131:142:146:154:162:176 SD: 0.8739 cents 96:104:107:113:119:129:132:143:155:159:168:177:192 SD: 0.7976 cents 97:105:108:114:120:130:134:145:157:161:170:179:194 SD: 0.6973 cents 109:118:121:128:135:146:150:163:176:181:191:201:218 SD: 0.6020 cents 132:143:147:155:163:177:182:197:213:219:231:244:264 SD: 0.5049 cents 143:155:159:168:177:192:197:213:231:237:250:264:286 SD: 0.4477 cents 144:156:160:169:178:193:198:215:233:239:252:266:288 SD: 0.4248 cents 167:181:186:196:207:224:230:249:270:277:292:308:334 SD: 0.3791 cents 214:232:238:251:265:287:295:319:346:355:375:395:428 SD: 0.3117 cents 252:273:280:296:312:338:347:376:407:418:441:465:504 SD: 0.2779 cents 265:287:295:311:328:355:365:395:428:440:464:489:530 SD: 0.2354 cents 311:337:346:365:385:417:428:464:503:516:544:574:622 SD: 0.2054 cents 358:388:398:420:443:480:493:534:578:594:627:661:716 SD: 0.2000 cents 382:414:425:448:473:512:526:570:617:634:669:705:764 SD: 0.1798 cents 408:442:454:479:505:547:562:609:659:677:714:753:816 SD: 0.1574 cents 409:443:455:480:506:548:563:610:661:679:716:755:818 SD: 0.1495 cents 496:537:552:582:614:665:683:740:801:823:868:916:992 SD: 0.1425 cents 525:569:584:616:650:704:723:783:848:871:919:969:1050 SD: 0.1249 cents 552:598:614:648:683:740:760:823:892:916:966:1019:1104 SD: 0.1169 cents