Scala analysis: 26EDO-IbnSina
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: 276.923 cents 276.923080 3: 507.692 cents 507.692310 4: 692.308 cents 692.307690 5: 830.769 cents 830.769230 6: 969.231 cents 969.230770 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 230.7692 cents 230.7692 1: 138.4615 cents 138.4615 2: 138.4615 cents 138.4615 3: 230.7692 cents 230.7692 4: 184.6154 cents 184.6154 5: 138.4615 cents 138.4615 6: 138.4615 cents 138.4615 7: 230.7692 cents 230.7692
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 138.46154 cents 1: 1 184.61538 cents 1: 2 230.76923 cents 2: 2 276.92308 cents 2: 1 323.07692 cents 2: 3 369.23077 cents 2: 1 415.38461 cents 3: 1 461.53846 cents 3: 4 507.69231 cents 3: 2 553.84615 cents 4: 2 646.15385 cents 4: 4 692.30769 cents 4: 1 738.46154 cents 5: 1 784.61539 cents 5: 3 830.76923 cents 5: 1 876.92308 cents 5: 2 923.07692 cents 6: 2 969.23077 cents 6: 1 1015.38462 cents 6: 4 1061.53846 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 138.5 276.9 507.7 692.3 830.8 969.2 1200.0 138.5 : 138.5 369.2 553.8 692.3 830.8 1061.5 1200.0 276.9 : 230.8 415.4 553.8 692.3 923.1 1061.5 1200.0 507.7 : 184.6 323.1 461.5 692.3 830.8 969.2 1200.0 692.3 : 138.5 276.9 507.7 646.2 784.6 1015.4 1200.0 830.8 : 138.5 369.2 507.7 646.2 876.9 1061.5 1200.0 969.2 : 230.8 369.2 507.7 738.5 923.1 1061.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.4615 .. 230.7692 cents 92.30769 cents 138.46154 cents 2: 276.9231 .. 415.3846 cents 138.46153 cents 46.15385 cents 3: 461.5385 .. 553.8461 cents 92.30769 cents 46.15385 cents 4: 646.1539 .. 738.4615 cents 92.30769 cents 92.30770 cents 5: 784.6154 .. 923.0769 cents 138.46153 cents 46.15385 cents 6: 969.2308 .. 1061.5385 cents 92.30769 cents 46.15385 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 138.46154 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 230.76923 cents Average / Smallest step : 1.238095 Largest / Average step : 1.346154 Largest / Smallest step : 1.666667 Median interval of one step : 138.46154 cents, amount: 4 Most common interval of one step : 138.46154 cents, amount: 4 Least squares average step : 166.81319 cents, oct.: 1167.69231 cents Scale is strictly proper Scale is a mode of a 26-tone equal temperament with octave 2/1 degrees: 3 6 11 15 18 21 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: 12 = 5 more = 171.429% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABCAAB Step pattern size order : SSLMSSL Interval vector is [ 0 0 4 1 2 2 1 3 1 1 4 2 0 ] Scale is a Constant Structure, by a margin of 46.15385 cents Scale diversity : 1.452952 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.461538 Rothenberg efficiency : 0.478912 redundancy: 0.521088 Efficiency x scale size : 3.352381 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 46.15384 cents Most common triad is 0.0 138.462 507.692 cents, amount: 3 Number of recognisable fifths : 4, average 692.3077 cents Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 37.2979 c. M:-65.9341 c. Lebeng 9: 1 1 2 1 1 1 2 P M ME S SD: 22.9340 c. M: 35.8974 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 2 2 1 1 2 P D3 S SD: 22.0658 c. M: 36.9231 c. 14: 2 1 3 2 2 1 3 P T3 SD: 20.5502 c. M:-32.9670 c. 16: 2 2 3 2 2 2 3 SP M ME S SD: 13.7911 c. M:-23.0769 c. Pseudo Pelog, Pelogic-7, Antiionian 17: 2 2 3 3 2 2 3 SP D3 S SD: 12.1415 c. M:-19.0045 c. 19: 2 2 4 3 2 2 4 P SD: 13.7413 c. M: 24.2915 c. 26: 3 3 5 4 3 3 5 SP SD: 0.0000 c. M: 0.0000 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: 4.8237 cents 3 x x 4 x 5 x 6 S SD: 18.1503 cents 4 x 5 x 6 x 7:8 S SD: 27.4540 cents 5 x 6:7 x 8:9:10 S SD: 19.7263 cents 6 x 7:8:9:10:11:12 S SD: 16.3131 cents 7 x 8:9:10:11:12:14 S SD: 21.4715 cents 8:9 x 11:12:13:14:16 SD: 13.3074 cents 10:11:12:13:15:16:18:20 SD: 12.6068 cents 11:12:13:15:16:18:19:22 SD: 9.1086 cents 12:13:14:16:18:19:21:24 SD: 5.5828 cents 23:25:27:31:34:37:40:46 SD: 3.3385 cents 24:26:28:32:36:39:42:48 S SD: 2.7943 cents 35:38:41:47:52:57:61:70 SD: 2.5524 cents 36:39:42:48:54:58:63:72 SD: 2.5290 cents 45:49:53:60:67:73:79:90 SD: 2.4591 cents 47:51:55:63:70:76:82:94 SD: 1.2188 cents 73:79:86:98:109:118:128:146 SD: 1.1622 cents 85:92:100:114:127:137:149:170 SD: 1.0668 cents 96:104:113:129:143:155:168:192 SD: 1.0204 cents 97:105:114:130:145:157:170:194 SD: 0.8531 cents 109:118:128:146:163:176:191:218 SD: 0.7792 cents 120:130:141:161:179:194:210:240 SD: 0.3876 cents 167:181:196:224:249:270:292:334 SD: 0.3623 cents 179:194:210:240:267:289:313:358 SD: 0.3545 cents 252:273:296:338:376:407:441:504 SD: 0.2974 cents 276:299:324:370:412:446:483:552 SD: 0.2164 cents 323:350:379:433:482:522:565:646 SD: 0.2160 cents 346:375:406:464:516:559:606:692 SD: 0.2103 cents 385:417:452:516:574:622:674:770 SD: 0.2083 cents 409:443:480:548:610:661:716:818 SD: 0.1874 cents 466:505:547:625:695:753:816:932 SD: 0.1779 cents 484:524:568:649:722:782:847:968 SD: 0.1582 cents 490:531:575:657:731:792:858:980 SD: 0.1484 cents 576:624:676:772:859:931:1008:1152 SD: 0.1463 cents 578:626:678:775:862:934:1012:1156 SD: 0.1360 cents