Scala analysis: edo-12
12 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 100.000 cents 100.000000 2: 200.000 cents 200.000000 3: 300.000 cents 300.000000 4: 400.000 cents 400.000000 5: 500.000 cents 500.000000 6: 600.000 cents 600.000000 7: 700.000 cents 700.000000 8: 800.000 cents 800.000000 9: 900.000 cents 900.000000 10: 1000.000 cents 1000.000000 11: 1100.000 cents 1100.000000 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 100.0000 cents 100.0000 1: 100.0000 cents 100.0000 2: 100.0000 cents 100.0000 3: 100.0000 cents 100.0000 4: 100.0000 cents 100.0000 5: 100.0000 cents 100.0000 6: 100.0000 cents 100.0000 7: 100.0000 cents 100.0000 8: 100.0000 cents 100.0000 9: 100.0000 cents 100.0000 10: 100.0000 cents 100.0000 11: 100.0000 cents 100.0000 12: 100.0000 cents 100.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 100.00000 cents 2: 12 200.00000 cents 3: 12 300.00000 cents 4: 12 400.00000 cents 5: 12 500.00000 cents 6: 12 600.00000 cents 7: 12 700.00000 cents 8: 12 800.00000 cents 9: 12 900.00000 cents 10: 12 1000.00000 cents 11: 12 1100.00000 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 12 0.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 100.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 200.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 300.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 400.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 500.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 600.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 700.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 800.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 900.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 1000.0: 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 1100.0: 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 100.0000 .. 100.0000 cents 1/1, 0.0000 cents 100.00000 cents 2: 200.0000 .. 200.0000 cents 1/1, 0.0000 cents 100.00000 cents 3: 300.0000 .. 300.0000 cents 1/1, 0.0000 cents 100.00000 cents 4: 400.0000 .. 400.0000 cents 1/1, 0.0000 cents 100.00000 cents 5: 500.0000 .. 500.0000 cents 1/1, 0.0000 cents 100.00000 cents 6: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 100.00000 cents 7: 700.0000 .. 700.0000 cents 1/1, 0.0000 cents 100.00000 cents 8: 800.0000 .. 800.0000 cents 1/1, 0.0000 cents 100.00000 cents 9: 900.0000 .. 900.0000 cents 1/1, 0.0000 cents 100.00000 cents 10: 1000.0000 .. 1000.0000 cents 1/1, 0.0000 cents 100.00000 cents 11: 1100.0000 .. 1100.0000 cents 1/1, 0.0000 cents 100.00000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 100.00000 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 100.00000 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 100.00000 cents, amount: 12 Most common interval of one step : 100.00000 cents, amount: 12 Least squares average step : 100.00000 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 100.00000 cents Ratio Whole / Half tone : 2.000000 ( 2 ) Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.083333 redundancy: 0.916667 Efficiency x scale size : 1.000000 Number of different interval sizes : 11 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 12, average 700.0000 cents Scale contains two identical disjunct hexachords Scale is a well-temperament and equal. It has 1 size of fifth Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0000 c. M:-0.0000 c. Twelve-tone Chromatic (1/11-comma)
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: 0.9775 cents 3 x x x x 4 x x x 5 x x 6 S SD: 5.2543 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.5256 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.4728 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.2558 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.8077 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.1244 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.1602 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.9608 cents 11 x 12:13:14:15:16 x 17:19:20:21:22 SD: 11.1723 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.2445 cents 13:14:15 x 16:17:18:19:21:22:23:25:26 SD: 9.7027 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.0897 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.9587 cents 19:20:21:23:24:25:27:28:30:32:34:36:38 SD: 4.9343 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 4.0786 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 4.0275 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.5786 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.3911 cents 31:33:35:37:39:41:44:46:49:52:55:59:62 SD: 2.7905 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1818 cents 46:49:52:55:58:61:65:69:73:77:82:87:92 SD: 1.9374 cents 48:51:54:57:60:64:68:72:76:81:86:91:96 SD: 1.7684 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.7024 cents 51:54:57:61:64:68:72:76:81:86:91:96:102 SD: 1.5755 cents 54:57:61:64:68:72:76:81:86:91:96:102:108 SD: 1.5264 cents 63:67:71:75:79:84:89:94:100:106:112:119:126 SD: 1.2877 cents 65:69:73:77:82:87:92:97:103:109:116:123:130 SD: 1.1602 cents 80:85:90:95:101:107:113:120:127:135:143:151:160 SD: 0.9991 cents 84:89:94:100:106:112:119:126:133:141:150:159:168 SD: 0.9219 cents 89:94:100:106:112:119:126:133:141:150:159:168:178 SD: 0.9200 cents 96:102:108:114:121:128:136:144:152:161:171:181:192 SD: 0.8792 cents 99:105:111:118:125:132:140:148:157:166:176:187:198 SD: 0.8396 cents 101:107:113:120:127:135:143:151:160:170:180:191:202 SD: 0.8067 cents 104:110:117:124:131:139:147:156:165:175:185:196:208 SD: 0.7068 cents 116:123:130:138:146:155:164:174:184:195:207:219:232 SD: 0.4529 cents 169:179:190:201:213:226:239:253:268:284:301:319:338 SD: 0.4238 cents 170:180:191:202:214:227:240:255:270:286:303:321:340 SD: 0.3988 cents 189:200:212:225:238:252:267:283:300:318:337:357:378 SD: 0.3873 cents 215:228:241:256:271:287:304:322:341:362:383:406:430 SD: 0.3798 cents 220:233:247:262:277:294:311:330:349:370:392:415:440 SD: 0.3641 cents 238:252:267:283:300:318:337:357:378:400:424:449:476 SD: 0.3470 cents 239:253:268:284:301:319:338:358:379:402:426:451:478 SD: 0.2842 cents 269:285:302:320:339:359:380:403:427:452:479:508:538 SD: 0.2428 cents 301:319:338:358:379:402:426:451:478:506:536:568:602 SD: 0.2225 cents 349:370:392:415:440:466:494:523:554:587:622:659:698 SD: 0.2225 cents 353:374:396:420:445:471:499:529:560:594:629:666:706 SD: 0.2195 cents 385:408:432:458:485:514:544:577:611:647:686:727:770 SD: 0.1986 cents 400:424:449:476:504:534:566:599:635:673:713:755:800 SD: 0.1866 cents 403:427:452:479:508:538:570:604:640:678:718:761:806 SD: 0.1863 cents 418:443:469:497:527:558:591:626:664:703:745:789:836 SD: 0.1831 cents 434:460:487:516:547:579:614:650:689:730:773:819:868 SD: 0.1682 cents 439:465:493:522:553:586:621:658:697:738:782:829:878 SD: 0.1393 cents 490:519:550:583:617:654:693:734:778:824:873:925:980 SD: 0.1285 cents 538:570:604:640:678:718:761:806:854:905:959:1016:1076 SD: 0.1168 cents 570:604:640:678:718:761:806:854:905:959:1016:1076:1140 SD: 0.1124 cents