Scala analysis: 12-31
12 out of 31-tET, meantone Eb-G#
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 77.419 cents 77.419350 2: 193.548 cents 193.548390 3: 309.677 cents 309.677420 4: 387.097 cents 387.096770 5: 503.226 cents 503.225810 6: 580.645 cents 580.645160 7: 696.774 cents 696.774190 8: 774.194 cents 774.193550 9: 890.323 cents 890.322580 10: 1006.452 cents 1006.451610 11: 1083.871 cents 1083.870970 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.1290 cents 116.1290 1: 77.4193 cents 77.4193 2: 116.1290 cents 116.1290 3: 116.1290 cents 116.1290 4: 77.4194 cents 77.4194 5: 116.1290 cents 116.1290 6: 77.4193 cents 77.4193 7: 116.1290 cents 116.1290 8: 77.4194 cents 77.4194 9: 116.1290 cents 116.1290 10: 116.1290 cents 116.1290 11: 77.4194 cents 77.4194 12: 116.1290 cents 116.1290
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 77.41935 cents 1: 7 116.12904 cents 2: 10 193.54839 cents 2: 2 232.25807 cents 3: 3 270.96774 cents 3: 9 309.67742 cents 4: 8 387.09677 cents 4: 4 425.80646 cents 5: 1 464.51613 cents 5: 11 503.22581 cents 6: 6 580.64516 cents 6: 6 619.35484 cents 7: 11 696.77419 cents 7: 1 735.48387 cents 8: 4 774.19355 cents 8: 8 812.90323 cents 9: 9 890.32258 cents 9: 3 929.03226 cents 10: 2 967.74193 cents 10: 10 1006.45161 cents 11: 7 1083.87097 cents 11: 5 1122.58065 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 : 77.4 193.5 309.7 387.1 503.2 580.6 696.8 774.2 890.3 1006.5 1083.9 1200.0 77.4 : 116.1 232.3 309.7 425.8 503.2 619.4 696.8 812.9 929.0 1006.5 1122.6 1200.0 193.5 : 116.1 193.5 309.7 387.1 503.2 580.6 696.8 812.9 890.3 1006.5 1083.9 1200.0 309.7 : 77.4 193.5 271.0 387.1 464.5 580.6 696.8 774.2 890.3 967.7 1083.9 1200.0 387.1 : 116.1 193.5 309.7 387.1 503.2 619.4 696.8 812.9 890.3 1006.5 1122.6 1200.0 503.2 : 77.4 193.5 271.0 387.1 503.2 580.6 696.8 774.2 890.3 1006.5 1083.9 1200.0 580.6 : 116.1 193.5 309.7 425.8 503.2 619.4 696.8 812.9 929.0 1006.5 1122.6 1200.0 696.8 : 77.4 193.5 309.7 387.1 503.2 580.6 696.8 812.9 890.3 1006.5 1083.9 1200.0 774.2 : 116.1 232.3 309.7 425.8 503.2 619.4 735.5 812.9 929.0 1006.5 1122.6 1200.0 890.3 : 116.1 193.5 309.7 387.1 503.2 619.4 696.8 812.9 890.3 1006.5 1083.9 1200.0 1006.5: 77.4 193.5 271.0 387.1 503.2 580.6 696.8 774.2 890.3 967.7 1083.9 1200.0 1083.9: 116.1 193.5 309.7 425.8 503.2 619.4 696.8 812.9 890.3 1006.5 1122.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 77.4193 .. 116.1290 cents 38.70969 cents 77.41935 cents 2: 193.5484 .. 232.2581 cents 38.70968 cents 77.41935 cents 3: 270.9677 .. 309.6774 cents 38.70968 cents 38.70967 cents 4: 387.0968 .. 425.8065 cents 38.70969 cents 77.41935 cents 5: 464.5161 .. 503.2258 cents 38.70968 cents 38.70967 cents 6: 580.6452 .. 619.3548 cents 38.70968 cents 77.41935 cents 7: 696.7742 .. 735.4839 cents 38.70968 cents 77.41935 cents 8: 774.1935 .. 812.9032 cents 38.70968 cents 38.70968 cents 9: 890.3226 .. 929.0323 cents 38.70968 cents 77.41935 cents 10: 967.7419 .. 1006.4516 cents 38.70968 cents 38.70967 cents 11: 1083.8710 .. 1122.5807 cents 38.70968 cents 77.41936 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 77.41935 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 116.12904 cents Average / Smallest step : 1.291667 Largest / Average step : 1.161290 Largest / Smallest step : 1.500000 Median interval of one step : 116.12904 cents, amount: 7 Most common interval of one step : 116.12904 cents, amount: 7 Least squares average step : 99.09677 cents, oct.: 1189.16129 cents Scale is strictly proper Scale has Myhill's property chromas: 38.70969 cents and 38.70966 cents, ratio: 1.000001 generators: 5 of 503.22581 cents and 7 of 696.77419 cents Scale is maximally even in 31-tone equal temperament ET pair of linear temperament : 12&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 31-tone equal temperament with octave 2/1 degrees: 2 5 8 10 13 15 18 20 23 26 28 31 generators: 13 and 18 Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 31-tone equal temperament Step pattern alph. order: ABBABABABBAB Step pattern size order : SLLSLSLSLLSL Interval vector is [ 0 5 7 0 10 2 3 9 0 8 4 1 11 0 6 ] Scale is a Constant Structure, by a margin of 38.70967 cents Ratio Whole / Half tone : 1.666666 Scale diversity : 1.214463 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.645161 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 : 38.70967 cents Most common intervals : 503.22581 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 116.129 696.774 cents Most common triad is 0.0 503.226 696.774 cents, amount: 10 Number of recognisable fifths : 11, average 696.7742 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- 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: 13.7492 c. M:-25.8065 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 8.6837 c. M: 16.2988 c. Meantone Chromatic (1/3-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 0.0000 c. M:-0.0000 c. Meantone Chromatic (53/220-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: 2.5904 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.6333 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.4972 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 8.3016 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2982 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.0587 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.7585 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.0366 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.0719 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.2777 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 8.3850 cents 13:14:15 x 16:17:18:19:20:22:23:24:26 S SD: 9.8562 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.0768 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 5.7410 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.1044 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 4.1348 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.2808 cents 25:26:28:30:31:33:35:37:39:42:45:47:50 SD: 3.1993 cents 32:33:36:38:40:43:45:48:50:54:57:60:64 SD: 3.0488 cents 35:37:39:42:44:47:49:52:55:59:63:65:70 SD: 2.9139 cents 36:38:40:43:45:48:50:54:56:60:64:67:72 SD: 2.4830 cents 40:42:45:48:50:53:56:60:63:67:72:75:80 SD: 2.3287 cents 41:43:46:49:51:55:57:61:64:69:73:77:82 SD: 2.0371 cents 45:47:50:54:56:60:63:67:70:75:80:84:90 SD: 1.9825 cents 48:50:54:57:60:64:67:72:75:80:86:90:96 SD: 1.7341 cents 51:53:57:61:64:68:71:76:80:85:91:95:102 SD: 1.6833 cents 60:63:67:72:75:80:84:90:94:100:107:112:120 SD: 1.2631 cents 67:70:75:80:84:90:94:100:105:112:120:125:134 SD: 1.0914 cents 83:87:93:99:104:111:116:124:130:139:148:155:166 SD: 0.8727 cents 85:89:95:102:106:114:119:127:133:142:152:159:170 SD: 0.8347 cents 92:96:103:110:115:123:129:138:144:154:165:172:184 SD: 0.8118 cents 101:106:113:121:126:135:141:151:158:169:181:189:202 SD: 0.7971 cents 103:108:115:123:129:138:144:154:161:172:184:193:206 SD: 0.7210 cents 113:118:126:135:141:151:158:169:177:189:202:211:226 SD: 0.6809 cents 127:133:142:152:159:170:178:190:199:212:227:238:254 SD: 0.6691 cents 128:134:143:153:160:171:179:191:200:214:229:239:256 SD: 0.5070 cents 153:160:171:183:191:205:214:229:239:256:274:286:306 SD: 0.4866 cents 168:176:188:201:210:225:235:251:263:281:300:314:336 SD: 0.4795 cents 175:183:196:209:219:234:245:262:274:293:313:327:350 SD: 0.4635 cents 178:186:199:213:223:238:249:266:278:298:318:333:356 SD: 0.4356 cents 193:202:216:231:241:258:270:289:302:323:345:361:386 SD: 0.3875 cents 195:204:218:233:244:261:273:292:305:326:349:365:390 SD: 0.3583 cents 220:230:246:263:275:294:308:329:344:368:393:411:440 SD: 0.3140 cents 236:247:264:282:295:316:330:353:369:395:422:441:472 SD: 0.3111 cents 246:257:275:294:308:329:344:368:385:411:440:460:492 SD: 0.3064 cents 261:273:292:312:326:349:365:390:408:437:467:488:522 SD: 0.3028 cents 264:276:295:316:330:353:369:395:413:442:472:494:528 SD: 0.2850 cents 287:300:321:343:359:384:401:429:449:480:513:537:574 SD: 0.2330 cents 311:325:348:372:389:416:435:465:486:520:556:582:622 SD: 0.2152 cents 347:363:388:415:434:464:485:519:543:580:621:649:694 SD: 0.1836 cents 415:434:464:496:519:555:580:621:649:694:742:776:830 SD: 0.1613 cents 439:459:491:525:549:587:614:657:687:734:785:821:878 SD: 0.1514 cents 454:475:508:543:568:607:635:679:710:759:812:849:908 SD: 0.1459 cents 500:523:559:598:625:669:699:748:782:836:894:935:1000 SD: 0.1421 cents 507:530:567:606:634:678:709:758:793:848:907:948:1014 SD: 0.1151 cents 567:593:634:678:709:758:793:848:887:948:1014:1060:1134 SD: 0.1021 cents