Scala analysis: edo-10
10 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 120.000 cents 120.000000 2: 240.000 cents 240.000000 3: 360.000 cents 360.000000 4: 480.000 cents 480.000000 5: 600.000 cents 600.000000 6: 720.000 cents 720.000000 7: 840.000 cents 840.000000 8: 960.000 cents 960.000000 9: 1080.000 cents 1080.000000 10: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 120.0000 cents 120.0000 1: 120.0000 cents 120.0000 2: 120.0000 cents 120.0000 3: 120.0000 cents 120.0000 4: 120.0000 cents 120.0000 5: 120.0000 cents 120.0000 6: 120.0000 cents 120.0000 7: 120.0000 cents 120.0000 8: 120.0000 cents 120.0000 9: 120.0000 cents 120.0000 10: 120.0000 cents 120.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 120.00000 cents 2: 10 240.00000 cents 3: 10 360.00000 cents 4: 10 480.00000 cents 5: 10 600.00000 cents 6: 10 720.00000 cents 7: 10 840.00000 cents 8: 10 960.00000 cents 9: 10 1080.00000 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 0.0 : 120.0 240.0 360.0 480.0 600.0 720.0 840.0 960.0 1080.0 1200.0 120.0 : 120.0 240.0 360.0 480.0 600.0 720.0 840.0 960.0 1080.0 1200.0 240.0 : 120.0 240.0 360.0 480.0 600.0 720.0 840.0 960.0 1080.0 1200.0 360.0 : 120.0 240.0 360.0 480.0 600.0 720.0 840.0 960.0 1080.0 1200.0 480.0 : 120.0 240.0 360.0 480.0 600.0 720.0 840.0 960.0 1080.0 1200.0 600.0 : 120.0 240.0 360.0 480.0 600.0 720.0 840.0 960.0 1080.0 1200.0 720.0 : 120.0 240.0 360.0 480.0 600.0 720.0 840.0 960.0 1080.0 1200.0 840.0 : 120.0 240.0 360.0 480.0 600.0 720.0 840.0 960.0 1080.0 1200.0 960.0 : 120.0 240.0 360.0 480.0 600.0 720.0 840.0 960.0 1080.0 1200.0 1080.0: 120.0 240.0 360.0 480.0 600.0 720.0 840.0 960.0 1080.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 120.0000 .. 120.0000 cents 1/1, 0.0000 cents 120.00000 cents 2: 240.0000 .. 240.0000 cents 1/1, 0.0000 cents 120.00000 cents 3: 360.0000 .. 360.0000 cents 1/1, 0.0000 cents 120.00000 cents 4: 480.0000 .. 480.0000 cents 1/1, 0.0000 cents 120.00000 cents 5: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 120.00000 cents 6: 720.0000 .. 720.0000 cents 1/1, 0.0000 cents 120.00000 cents 7: 840.0000 .. 840.0000 cents 1/1, 0.0000 cents 120.00000 cents 8: 960.0000 .. 960.0000 cents 1/1, 0.0000 cents 120.00000 cents 9: 1080.0000 .. 1080.0000 cents 1/1, 0.0000 cents 120.00000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 120.00000 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 120.00000 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 120.00000 cents, amount: 10 Most common interval of one step : 120.00000 cents, amount: 10 Least squares average step : 120.00000 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 120.00000 cents Ratio Whole / Half tone : infinite Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.100000 redundancy: 0.900000 Efficiency x scale size : 1.000000 Number of different interval sizes : 9 = 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 pentachords 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
10: 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 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 9.0225 cents 3 x x x 4 x x 5 x x 6 S SD: 15.9629 cents 4 x x 5 x x 6 x 7 x 8 S SD: 8.2762 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 15.8534 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 10.9031 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 11.5168 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 8.6936 cents 9 x 10:11:12:13:14:15:16:17:18 S SD: 11.5859 cents 10:11 x 12:13:14:15:16:17:19:20 SD: 10.3433 cents 12:13:14:15:16:17:18:20:21:22:24 S SD: 7.3511 cents 13:14:15:16:17:18:20:21:23:24:26 SD: 5.9893 cents 16:17:18:20:21:23:24:26:28:30:32 SD: 5.9815 cents 19:20:22:23:25:27:29:31:33:35:38 SD: 5.3228 cents 21:23:24:26:28:30:32:34:37:39:42 SD: 5.3111 cents 22:24:25:27:29:31:33:36:38:41:44 SD: 4.5167 cents 25:27:29:31:33:35:38:41:44:47:50 SD: 4.1616 cents 26:28:30:32:34:37:39:42:45:49:52 SD: 3.6174 cents 27:29:31:33:36:38:41:44:47:50:54 SD: 2.7995 cents 31:33:36:38:41:44:47:50:54:58:62 SD: 2.7971 cents 38:41:44:47:50:54:58:62:66:71:76 SD: 2.6578 cents 39:42:45:48:51:55:59:63:68:73:78 SD: 2.3137 cents 43:46:49:53:57:61:65:70:75:80:86 SD: 1.9241 cents 53:57:61:65:70:75:80:86:92:99:106 SD: 1.3461 cents 66:71:76:81:87:93:100:107:115:123:132 SD: 1.2290 cents 74:79:85:91:98:105:112:120:129:138:148 SD: 1.2031 cents 81:87:93:100:107:115:123:132:141:151:162 SD: 1.1413 cents 82:88:94:101:108:116:124:133:143:153:164 SD: 0.7763 cents 109:117:125:134:144:154:165:177:190:203:218 SD: 0.7058 cents 113:121:130:139:149:160:171:184:197:211:226 SD: 0.6930 cents 126:135:145:155:166:178:191:205:219:235:252 SD: 0.6297 cents 128:137:147:158:169:181:194:208:223:239:256 SD: 0.5477 cents 155:166:178:191:205:219:235:252:270:289:310 SD: 0.5297 cents 169:181:194:208:223:239:256:275:294:315:338 SD: 0.4330 cents 181:194:208:223:239:256:274:294:315:338:362 SD: 0.3249 cents 194:208:223:239:256:274:294:315:338:362:388 SD: 0.3220 cents 256:274:294:315:338:362:388:416:446:478:512 SD: 0.3212 cents 263:282:302:324:347:372:399:427:458:491:526 SD: 0.2563 cents 304:326:349:374:401:430:461:494:529:567:608 SD: 0.2561 cents 316:339:363:389:417:447:479:513:550:590:632 SD: 0.2347 cents 351:376:403:432:463:496:532:570:611:655:702 SD: 0.2098 cents 363:389:417:447:479:513:550:590:632:677:726 SD: 0.1962 cents 376:403:432:463:496:532:570:611:655:702:752 SD: 0.1770 cents 403:432:463:496:532:570:611:655:702:752:806 SD: 0.1657 cents 432:463:496:532:570:611:655:702:752:806:864 SD: 0.1325 cents 485:520:557:597:640:686:735:788:844:905:970 SD: 0.1288 cents 545:584:626:671:719:771:826:885:949:1017:1090 SD: 0.1047 cents