Scala analysis: edo-11
11 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 109.091 cents 109.090909 2: 218.182 cents 218.181818 3: 327.273 cents 327.272727 4: 436.364 cents 436.363636 5: 545.455 cents 545.454545 6: 654.545 cents 654.545455 7: 763.636 cents 763.636364 8: 872.727 cents 872.727273 9: 981.818 cents 981.818182 10: 1090.909 cents 1090.909091 11: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 109.0909 cents 109.0909 1: 109.0909 cents 109.0909 2: 109.0909 cents 109.0909 3: 109.0909 cents 109.0909 4: 109.0909 cents 109.0909 5: 109.0909 cents 109.0909 6: 109.0909 cents 109.0909 7: 109.0909 cents 109.0909 8: 109.0909 cents 109.0909 9: 109.0909 cents 109.0909 10: 109.0909 cents 109.0909 11: 109.0909 cents 109.0909
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 109.09091 cents 2: 11 218.18182 cents 3: 11 327.27273 cents 4: 11 436.36364 cents 5: 11 545.45454 cents 6: 11 654.54545 cents 7: 11 763.63636 cents 8: 11 872.72727 cents 9: 11 981.81818 cents 10: 11 1090.90909 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 109.1 218.2 327.3 436.4 545.5 654.5 763.6 872.7 981.8 1090.9 1200.0 109.1 : 109.1 218.2 327.3 436.4 545.5 654.5 763.6 872.7 981.8 1090.9 1200.0 218.2 : 109.1 218.2 327.3 436.4 545.5 654.5 763.6 872.7 981.8 1090.9 1200.0 327.3 : 109.1 218.2 327.3 436.4 545.5 654.5 763.6 872.7 981.8 1090.9 1200.0 436.4 : 109.1 218.2 327.3 436.4 545.5 654.5 763.6 872.7 981.8 1090.9 1200.0 545.5 : 109.1 218.2 327.3 436.4 545.5 654.5 763.6 872.7 981.8 1090.9 1200.0 654.5 : 109.1 218.2 327.3 436.4 545.5 654.5 763.6 872.7 981.8 1090.9 1200.0 763.6 : 109.1 218.2 327.3 436.4 545.5 654.5 763.6 872.7 981.8 1090.9 1200.0 872.7 : 109.1 218.2 327.3 436.4 545.5 654.5 763.6 872.7 981.8 1090.9 1200.0 981.8 : 109.1 218.2 327.3 436.4 545.5 654.5 763.6 872.7 981.8 1090.9 1200.0 1090.9: 109.1 218.2 327.3 436.4 545.5 654.5 763.6 872.7 981.8 1090.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 109.0909 .. 109.0909 cents 1/1, 0.0000 cents 109.09091 cents 2: 218.1818 .. 218.1818 cents 1/1, 0.0000 cents 109.09091 cents 3: 327.2727 .. 327.2727 cents 1/1, 0.0000 cents 109.09091 cents 4: 436.3636 .. 436.3636 cents 1/1, 0.0000 cents 109.09091 cents 5: 545.4545 .. 545.4545 cents 1/1, 0.0000 cents 109.09091 cents 6: 654.5455 .. 654.5455 cents 1/1, 0.0000 cents 109.09091 cents 7: 763.6364 .. 763.6364 cents 1/1, 0.0000 cents 109.09091 cents 8: 872.7273 .. 872.7273 cents 1/1, 0.0000 cents 109.09091 cents 9: 981.8182 .. 981.8182 cents 1/1, 0.0000 cents 109.09091 cents 10: 1090.9091 .. 1090.9091 cents 1/1, 0.0000 cents 109.09091 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 109.09091 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 109.09091 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 109.09091 cents, amount: 11 Most common interval of one step : 109.09091 cents, amount: 11 Least squares average step : 109.09091 cents, oct.: 1200.00000 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 109.09091 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.090909 redundancy: 0.909091 Efficiency x scale size : 1.000000 Number of different interval sizes : 10 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 0 Scale contains two identical disjunct hexachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x 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 x 4 S SD: 23.7048 cents 3 x x x x 4 x x 5 x x 6 S SD: 16.2718 cents 4 x x x 5 x 6 x x 7 x 8 S SD: 17.5383 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 14.5515 cents 6 x 7 x x 8:9 x 10 x 11:12 S SD: 15.5700 cents 7 x 8 x 9 x 10:11 x 12:13:14 S SD: 9.7298 cents 8 x 9 x 10:11:12 x 13:14:15:16 S SD: 9.8451 cents 9 x 10:11 x 12:13:14:15:16:17:18 S SD: 7.6157 cents 10 x 11:12:13:14:15:16:17:18:19:20 S SD: 11.4924 cents 11:12 x 13:14:15:16:17:18:19:21:22 SD: 7.8910 cents 12:13:14 x 15:16:18:19:20:21:23:24 SD: 11.3213 cents 13:14:15:16:17:18:19:20:22:23:24:26 S SD: 7.0805 cents 14:15:16:17:18:19:20:22:23:25:26:28 SD: 5.2966 cents 18:19:20:22:23:25:26:28:30:32:34:36 SD: 5.2816 cents 20:21:23:24:26:27:29:31:33:35:38:40 SD: 5.0304 cents 21:22:24:25:27:29:31:33:35:37:39:42 SD: 5.0289 cents 22:23:25:27:28:30:32:34:36:39:41:44 SD: 4.9914 cents 24:26:27:29:31:33:35:37:40:42:45:48 SD: 3.7133 cents 28:30:32:34:36:38:41:44:46:49:53:56 SD: 3.5904 cents 29:31:33:35:37:40:42:45:48:51:54:58 SD: 2.6272 cents 35:37:40:42:45:48:51:54:58:62:66:70 SD: 2.5200 cents 38:40:43:46:49:52:55:59:63:67:71:76 SD: 2.4995 cents 43:46:49:52:55:59:63:67:71:76:81:86 SD: 1.7342 cents 52:55:59:63:67:71:76:81:86:92:98:104 SD: 1.5999 cents 59:63:67:71:76:81:86:92:98:104:111:118 SD: 1.1566 cents 67:71:76:81:86:92:98:104:111:118:126:134 SD: 1.0713 cents 76:81:86:92:98:104:111:118:126:134:143:152 SD: 0.7857 cents 81:86:92:98:104:111:118:126:134:143:152:162 SD: 0.7815 cents 105:112:119:127:135:144:153:163:174:185:197:210 SD: 0.5499 cents 140:149:159:169:180:192:204:218:232:247:263:280 SD: 0.5215 cents 157:167:178:190:202:215:229:244:260:277:295:314 SD: 0.4043 cents 202:215:229:244:260:277:295:314:334:356:379:404 SD: 0.3238 cents 216:230:245:261:278:296:315:336:358:381:406:432 SD: 0.3027 cents 261:278:296:315:336:358:381:406:432:460:490:522 SD: 0.2754 cents 292:311:331:353:376:400:426:454:483:515:548:584 SD: 0.2736 cents 307:327:348:371:395:421:448:477:508:541:577:614 SD: 0.2509 cents 321:342:364:388:413:440:468:499:531:566:603:642 SD: 0.2450 cents 335:357:380:405:431:459:489:521:555:591:629:670 SD: 0.2260 cents 337:359:382:407:434:462:492:524:558:594:633:674 SD: 0.2234 cents 351:374:398:424:452:481:512:546:581:619:659:702 SD: 0.2223 cents 366:390:415:442:471:502:534:569:606:645:687:732 SD: 0.2199 cents 370:394:420:447:476:507:540:575:613:652:695:740 SD: 0.1996 cents 418:445:474:505:538:573:610:650:692:737:785:836 SD: 0.1279 cents 505:538:573:610:650:692:737:785:836:890:948:1010 SD: 0.1271 cents 566:603:642:684:728:776:826:880:937:998:1063:1132 SD: 0.1261 cents 572:609:649:691:736:784:835:889:947:1009:1074:1144 SD: 0.1132 cents