Scala analysis: canton-esque
17\29 (3/2) generator, accurate 2.3.7/5.11/5.13/5 canton-like scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 124.138 cents 124.137960 2: 206.897 cents 206.896560 3: 289.655 cents 289.655160 4: 413.793 cents 413.793120 5: 496.552 cents 496.551720 6: 620.690 cents 620.689680 7: 703.448 cents 703.448280 8: 786.207 cents 786.206880 9: 910.345 cents 910.344840 10: 993.103 cents 993.103440 11: 1117.241 cents 1117.241400 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 82.7586 cents 82.7586 1: 124.1380 cents 124.1380 2: 82.7586 cents 82.7586 3: 82.7586 cents 82.7586 4: 124.1380 cents 124.1380 5: 82.7586 cents 82.7586 6: 124.1380 cents 124.1380 7: 82.7586 cents 82.7586 8: 82.7586 cents 82.7586 9: 124.1380 cents 124.1380 10: 82.7586 cents 82.7586 11: 124.1380 cents 124.1380 12: 82.7586 cents 82.7586
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 82.75860 cents 1: 5 124.13796 cents 2: 2 165.51720 cents 2: 10 206.89656 cents 3: 9 289.65516 cents 3: 3 331.03452 cents 4: 4 372.41376 cents 4: 8 413.79312 cents 5: 11 496.55172 cents 5: 1 537.93108 cents 6: 6 579.31032 cents 6: 6 620.68968 cents 7: 1 662.06892 cents 7: 11 703.44828 cents 8: 8 786.20688 cents 8: 4 827.58624 cents 9: 3 868.96548 cents 9: 9 910.34484 cents 10: 10 993.10344 cents 10: 2 1034.48280 cents 11: 5 1075.86204 cents 11: 7 1117.24140 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 124.1 206.9 289.7 413.8 496.6 620.7 703.4 786.2 910.3 993.1 1117.2 1200.0 124.1 : 82.8 165.5 289.7 372.4 496.6 579.3 662.1 786.2 869.0 993.1 1075.9 1200.0 206.9 : 82.8 206.9 289.7 413.8 496.6 579.3 703.4 786.2 910.3 993.1 1117.2 1200.0 289.7 : 124.1 206.9 331.0 413.8 496.6 620.7 703.4 827.6 910.3 1034.5 1117.2 1200.0 413.8 : 82.8 206.9 289.7 372.4 496.6 579.3 703.4 786.2 910.3 993.1 1075.9 1200.0 496.6 : 124.1 206.9 289.7 413.8 496.6 620.7 703.4 827.6 910.3 993.1 1117.2 1200.0 620.7 : 82.8 165.5 289.7 372.4 496.6 579.3 703.4 786.2 869.0 993.1 1075.9 1200.0 703.4 : 82.8 206.9 289.7 413.8 496.6 620.7 703.4 786.2 910.3 993.1 1117.2 1200.0 786.2 : 124.1 206.9 331.0 413.8 537.9 620.7 703.4 827.6 910.3 1034.5 1117.2 1200.0 910.3 : 82.8 206.9 289.7 413.8 496.6 579.3 703.4 786.2 910.3 993.1 1075.9 1200.0 993.1 : 124.1 206.9 331.0 413.8 496.6 620.7 703.4 827.6 910.3 993.1 1117.2 1200.0 1117.2: 82.8 206.9 289.7 372.4 496.6 579.3 703.4 786.2 869.0 993.1 1075.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 82.7586 .. 124.1380 cents 41.37936 cents 82.75860 cents 2: 165.5172 .. 206.8966 cents 41.37936 cents 41.37924 cents 3: 289.6552 .. 331.0345 cents 41.37936 cents 82.75860 cents 4: 372.4138 .. 413.7931 cents 41.37936 cents 41.37924 cents 5: 496.5517 .. 537.9311 cents 41.37936 cents 82.75860 cents 6: 579.3103 .. 620.6897 cents 41.37936 cents 41.37924 cents 7: 662.0689 .. 703.4483 cents 41.37936 cents 41.37924 cents 8: 786.2069 .. 827.5862 cents 41.37936 cents 82.75860 cents 9: 868.9655 .. 910.3448 cents 41.37936 cents 41.37924 cents 10: 993.1034 .. 1034.4828 cents 41.37936 cents 82.75860 cents 11: 1075.8620 .. 1117.2414 cents 41.37936 cents 41.37924 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 82.75860 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 124.13796 cents Average / Smallest step : 1.208334 Largest / Average step : 1.241380 Largest / Smallest step : 1.500001 Median interval of one step : 82.75860 cents, amount: 7 Most common interval of one step : 82.75860 cents, amount: 7 Least squares average step : 100.45623 cents, oct.: 1205.47481 cents Scale is strictly proper Scale has Myhill's property chromas: 41.37936 cents and 41.37924 cents, ratio: 1.000003 generators: 5 of 496.55172 cents and 7 of 703.44828 cents Scale is maximally even in 29-tone equal temperament ET pair of linear temperament : 12&17 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 29-tone equal temperament with octave 2/1 degrees: 3 5 7 10 12 15 17 19 22 24 27 29 generators: 12 and 17 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABBABAB Step pattern size order : LSSLSLSSLSLS Interval vector is [ 0 7 5 2 10 0 9 3 4 8 0 11 1 6 ] Scale is a Constant Structure, by a margin of 41.37924 cents Ratio Whole / Half tone : 2.500001 Scale diversity : 1.215748 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.620689 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 41.37924 cents Most common intervals : 496.55172 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 82.759 703.448 cents Most common triad is 0.0 496.552 703.448 cents, amount: 10 Number of recognisable fifths : 11, average 703.4483 cents Scale contains two identical conjunct hexachords Best fifths form a closed circle Formal octave complements present : 9 = 75.0000% Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 10-11 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 12.9789 c. M: 24.1380 c. Twelve-tone Chromatic (1/11-comma) 17: 2 1 1 2 1 2 1 1 2 1 2 1 P M ME SD: 9.1615 c. M:-17.0385 c. 29: 3 2 2 3 2 3 2 2 3 2 3 2 SP M ME 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: 0.7466 cents 3 x x x x 4 x x x 5 x x 6 S SD: 8.6763 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.1745 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.8115 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 11.0101 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 8.6423 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 11.2813 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.3081 cents 10:11 x 12:13 x 14:15:16:17:18:19:20 S SD: 8.3062 cents 11:12 x 13:14:15:16 x 17:19:20:21:22 SD: 8.5075 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.1702 cents 13:14:15 x x 17:19 x 20:22:23:25:26 SD: 8.5479 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.0720 cents 16:17:18:19:20:21:23:24:25:27:28:31:32 SD: 4.9188 cents 22:24:25:26:28:29:31:33:35:37:39:42:44 SD: 4.0941 cents 23:25:26:27:29:31:33:35:36:39:41:44:46 SD: 3.6644 cents 26:28:29:31:33:35:37:39:41:44:46:50:52 SD: 2.9327 cents 30:32:34:35:38:40:43:45:47:51:53:57:60 SD: 2.6981 cents 38:41:43:45:48:51:54:57:60:64:67:72:76 SD: 2.4290 cents 39:42:44:46:50:52:56:59:61:66:69:74:78 SD: 2.2842 cents 40:43:45:47:51:53:57:60:63:68:71:76:80 SD: 1.7036 cents 54:58:61:64:69:72:77:81:85:91:96:103:108 SD: 1.3219 cents 66:71:74:78:84:88:94:99:104:112:117:126:132 SD: 1.2076 cents 70:75:79:83:89:93:100:105:110:118:124:133:140 SD: 1.1628 cents 78:84:88:92:99:104:112:117:123:132:138:149:156 SD: 0.9074 cents 93:100:105:110:118:124:133:140:146:157:165:177:186 SD: 0.8154 cents 94:101:106:111:119:125:135:141:148:159:167:179:188 SD: 0.7962 cents 108:116:122:128:137:144:155:162:170:183:192:206:216 SD: 0.7716 cents 111:119:125:131:141:148:159:167:175:188:197:212:222 SD: 0.6308 cents 120:129:135:142:152:160:172:180:189:203:213:229:240 SD: 0.5739 cents 148:159:167:175:188:197:212:222:233:250:263:282:296 SD: 0.4235 cents 160:172:180:189:203:213:229:240:252:271:284:305:320 SD: 0.3930 cents 174:187:196:206:221:232:249:261:274:294:309:332:348 SD: 0.3761 cents 204:219:230:241:259:272:292:306:321:345:362:389:408 SD: 0.2745 cents 214:230:241:253:272:285:306:321:337:362:380:408:428 SD: 0.2626 cents 259:278:292:306:329:345:371:389:408:438:460:494:518 SD: 0.2610 cents 285:306:321:337:362:380:408:428:449:482:506:543:570 SD: 0.2362 cents 292:314:329:345:371:389:418:438:460:494:518:557:584 SD: 0.2358 cents 308:331:347:364:391:410:441:462:485:521:547:587:616 SD: 0.2341 cents 325:349:366:384:413:433:465:488:512:550:577:620:650 SD: 0.2087 cents 385:414:434:455:489:513:551:578:606:651:683:734:770 SD: 0.1923 cents 418:449:471:494:531:557:598:628:658:707:742:797:836 SD: 0.1618 cents 457:491:515:540:580:609:654:686:720:773:811:871:914 SD: 0.1556 cents 471:506:531:557:598:627:674:707:742:797:836:898:942 SD: 0.1547 cents 473:508:533:559:601:630:677:710:745:800:839:902:946 SD: 0.1373 cents 527:566:594:623:669:702:754:791:830:892:935:1005:1054 SD: 0.1294 cents 577:620:650:682:733:769:826:866:909:976:1024:1100:1154 SD: 0.1280 cents 578:621:651:683:734:770:827:868:910:978:1026:1102:1156 SD: 0.1276 cents 593:637:668:701:753:790:849:890:934:1003:1052:1131:1186 SD: 0.1264 cents