Scala analysis: bidiatonic
14 note modmos of meantone, mos of 12&50
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96.000 cents 96.000000 2: 192.000 cents 192.000000 3: 288.000 cents 288.000000 4: 312.000 cents 312.000000 5: 408.000 cents 408.000000 6: 504.000 cents 504.000000 7: 600.000 cents 600.000000 8: 696.000 cents 696.000000 9: 792.000 cents 792.000000 10: 888.000 cents 888.000000 11: 912.000 cents 912.000000 12: 1008.000 cents 1008.000000 13: 1104.000 cents 1104.000000 14: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 96.0000 cents 96.0000 1: 96.0000 cents 96.0000 2: 96.0000 cents 96.0000 3: 96.0000 cents 96.0000 4: 24.0000 cents 24.0000 5: 96.0000 cents 96.0000 6: 96.0000 cents 96.0000 7: 96.0000 cents 96.0000 8: 96.0000 cents 96.0000 9: 96.0000 cents 96.0000 10: 96.0000 cents 96.0000 11: 24.0000 cents 24.0000 12: 96.0000 cents 96.0000 13: 96.0000 cents 96.0000 14: 96.0000 cents 96.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 24.00000 cents 1: 12 96.00000 cents 2: 4 120.00000 cents 2: 10 192.00000 cents 3: 6 216.00000 cents 3: 8 288.00000 cents 4: 8 312.00000 cents 4: 6 384.00000 cents 5: 10 408.00000 cents 5: 4 480.00000 cents 6: 12 504.00000 cents 6: 2 576.00000 cents 7: 14 600.00000 cents 8: 2 624.00000 cents 8: 12 696.00000 cents 9: 4 720.00000 cents 9: 10 792.00000 cents 10: 6 816.00000 cents 10: 8 888.00000 cents 11: 8 912.00000 cents 11: 6 984.00000 cents 12: 10 1008.00000 cents 12: 4 1080.00000 cents 13: 12 1104.00000 cents 13: 2 1176.00000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.92308 = 25/13
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.0 : 96.0 192.0 288.0 312.0 408.0 504.0 600.0 696.0 792.0 888.0 912.0 1008.0 1104.0 1200.0 96.0 : 96.0 192.0 216.0 312.0 408.0 504.0 600.0 696.0 792.0 816.0 912.0 1008.0 1104.0 1200.0 192.0 : 96.0 120.0 216.0 312.0 408.0 504.0 600.0 696.0 720.0 816.0 912.0 1008.0 1104.0 1200.0 288.0 : 24.0 120.0 216.0 312.0 408.0 504.0 600.0 624.0 720.0 816.0 912.0 1008.0 1104.0 1200.0 312.0 : 96.0 192.0 288.0 384.0 480.0 576.0 600.0 696.0 792.0 888.0 984.0 1080.0 1176.0 1200.0 408.0 : 96.0 192.0 288.0 384.0 480.0 504.0 600.0 696.0 792.0 888.0 984.0 1080.0 1104.0 1200.0 504.0 : 96.0 192.0 288.0 384.0 408.0 504.0 600.0 696.0 792.0 888.0 984.0 1008.0 1104.0 1200.0 600.0 : 96.0 192.0 288.0 312.0 408.0 504.0 600.0 696.0 792.0 888.0 912.0 1008.0 1104.0 1200.0 696.0 : 96.0 192.0 216.0 312.0 408.0 504.0 600.0 696.0 792.0 816.0 912.0 1008.0 1104.0 1200.0 792.0 : 96.0 120.0 216.0 312.0 408.0 504.0 600.0 696.0 720.0 816.0 912.0 1008.0 1104.0 1200.0 888.0 : 24.0 120.0 216.0 312.0 408.0 504.0 600.0 624.0 720.0 816.0 912.0 1008.0 1104.0 1200.0 912.0 : 96.0 192.0 288.0 384.0 480.0 576.0 600.0 696.0 792.0 888.0 984.0 1080.0 1176.0 1200.0 1008.0: 96.0 192.0 288.0 384.0 480.0 504.0 600.0 696.0 792.0 888.0 984.0 1080.0 1104.0 1200.0 1104.0: 96.0 192.0 288.0 384.0 408.0 504.0 600.0 696.0 792.0 888.0 984.0 1008.0 1104.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.0000 .. 96.0000 cents 72.00000 cents 24.00000 cents 2: 120.0000 .. 192.0000 cents 72.00000 cents 24.00000 cents 3: 216.0000 .. 288.0000 cents 72.00000 cents 24.00000 cents 4: 312.0000 .. 384.0000 cents 72.00000 cents 24.00000 cents 5: 408.0000 .. 480.0000 cents 72.00000 cents 24.00000 cents 6: 504.0000 .. 576.0000 cents 72.00000 cents 24.00000 cents 7: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 24.00000 cents 8: 624.0000 .. 696.0000 cents 72.00000 cents 24.00000 cents 9: 720.0000 .. 792.0000 cents 72.00000 cents 24.00000 cents 10: 816.0000 .. 888.0000 cents 72.00000 cents 24.00000 cents 11: 912.0000 .. 984.0000 cents 72.00000 cents 24.00000 cents 12: 1008.0000 .. 1080.0000 cents 72.00000 cents 24.00000 cents 13: 1104.0000 .. 1176.0000 cents 72.00000 cents 24.00000 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 24.00000 cents, class 1 Average step (divided formal octave): 85.7143 cents Largest one step interval : 96.00000 cents Average / Smallest step : 3.571429 Largest / Average step : 1.120000 Largest / Smallest step : 4.000000 Median interval of one step : 96.00000 cents, amount: 12 Most common interval of one step : 96.00000 cents, amount: 12 Least squares average step : 85.43054 cents, oct.: 1196.02759 cents Scale is strictly proper Scale has 2 repeating blocks of 7 notes Blocks have Myhill's property chromas: 72.00000 cents and 48.00000 cents, ratio: 1.500000 generators: 1 of 96.00000 cents and 6 of 504.00000 cents ET pair of linear temperament : 38&50 Scale is distributional even Scale is a mode of a 50-tone equal temperament with octave 1200.000 cents degrees: 4 8 12 13 17 21 25 29 33 37 38 42 46 50 Least number of segments generator : 29 of 696.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 29 of 696.000 cents and inv. generated superset size: 32 = 18 more = 228.571% Number of contiguous 1-step segments: 2 Step pattern alph. order: AAABAAAAAABAAA Step pattern size order : LLLSLLLLLLSLLL Interval vector is [ 2 0 0 12 4 0 0 10 6 0 0 8 8 0 0 6 10 0 0 4 12 0 0 2 7 ] Scale is a Constant Structure, by a margin of 24.00000 cents Scale diversity : 1.144357 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.280000 Number of different interval sizes : 25 = 1.92308 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.92308 = 25/13 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 24.00000 cents Most common intervals : 600.00000 cents & inv., amount: 14 Number of recognisable fifths : 16, average 702.0000 cents Number of appreciable fifths : 12, average 696.0000 cents Scale contains two identical disjunct heptachords Formal octave complements present : 14 = 100.0000% Limited transpositions : 7 Limited inverse transpositions : 7 Inversional symmetry on degrees : 0 7 Inversional symmetry on intervals : 3-4 10-11 -- Rational properties --
FIT/MODE
14: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 20.5714 c. M:-30.8571 c. 17: 1 2 1 0 2 1 1 2 1 2 0 1 2 1 N D3 SD: 20.3852 c. M: 35.2941 c. 19: 1 2 1 1 1 2 1 2 1 2 0 2 1 2 P D3 SD: 22.4721 c. M: 35.3684 c. 20: 2 1 2 0 2 1 2 2 1 2 0 2 1 2 N B D3 I SD: 15.7117 c. M:-24.0000 c. 24: 2 2 2 0 2 2 2 2 2 2 0 2 2 2 P B DE I SD: 8.0000 c. M:-12.0000 c. 26: 2 2 2 1 2 2 2 2 2 2 1 2 2 2 SP B ME I SD: 7.3846 c. M:-11.0769 c. 38: 3 3 3 1 3 3 3 3 3 3 1 3 3 3 SP B DE I SD: 2.5263 c. M:-3.7895 c. 50: 4 4 4 1 4 4 4 4 4 4 1 4 4 4 SP B DE I SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x 3 x x x x x 4 S SD: 2.9775 cents 3 x x x x x 4 x x x 5 x x x 6 S SD: 2.3267 cents 4 x x x x 5 x x 6 x x x 7 x 8 S SD: 11.2926 cents 5 x x x 6 x x 7 x 8 x x 9 x 10 S SD: 5.9379 cents 6 x x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 7.8908 cents 7 x 8 x x 9 x 10 x 11 x 12 x 13:14 S SD: 9.2074 cents 8 x 9 x x 10:11 x 12 x 13 x 14:15:16 S SD: 10.4000 cents 9 x 10 x 11 x 12:13 x 14:15 x 16:17:18 S SD: 6.6847 cents 10 x 11 x 12:13 x 14:15:16 x 17:18:19:20 S SD: 6.2269 cents 11 x 12:13 x 14:15 x 16:17:18:19:20:21:22 S SD: 9.0864 cents 12:13 x 14 x 15:16:17:18:19:20 x 21:23:24 SD: 6.3427 cents 13:14 x 15:16 x 17:18:19:21 x 22:23:25:26 SD: 9.9632 cents 14:15:16 x 17:18:19:20:21:22:23:24:25:26:28 S SD: 6.3262 cents 15:16:17 x 18:19:20:21:22:24:25 x 27:28:30 SD: 4.8762 cents 16:17:18:19 x 20:21:23:24:25 x 27:29:30:32 SD: 5.1688 cents 17:18:19:20 x 22:23:24:25:27:28:29:30:32:34 SD: 4.9971 cents 18:19:20:21:22:23:24:25:27:28:30 x 32:34:36 SD: 4.8728 cents 19:20:21:22:23:24:25:27:28:30 x 32:34:36:38 SD: 4.5822 cents 20:21:22 x 24:25:27:28:30:32:33:34:36:38:40 SD: 4.2339 cents 21:22:23 x 25:27:28:30:31:33:35:36:38:40:42 SD: 4.9342 cents 22:23:25:26 x 28:29:31:33:35 x 37:39:42:44 SD: 4.4540 cents 24:25:27:28:29:30:32:34:36:38:40:41:43:45:48 SD: 3.5915 cents 25:26:28 x 30:32:33:35:37:40:42 x 45:47:50 SD: 4.6658 cents 26:27:29 x 31:33:35:37:39:41:43:44:47:49:52 SD: 3.3802 cents 27:29:30:32 x 34:36:38:40:43:45:46:48:51:54 SD: 3.2479 cents 28:30:31:33:34:35:37:40:42:44:47 x 50:53:56 SD: 4.1070 cents 29:31:32:34:35:37:39:41:43:46:48:49:52:55:58 SD: 3.1813 cents 31:33:35 x 37:39:41:44:46:49:52:53:55:59:62 SD: 3.3444 cents 32:34:36:38 x 41:43:45:48:51:53:54:57:61:64 SD: 3.1271 cents 33:35:37:39:40:42:44:47:49:52:55:56:59:62:66 SD: 2.3996 cents 34:36:38:40:41:43:45:48:51:54:57:58:61:64:68 SD: 2.2291 cents 36:38:40 x 43:46:48:51:54:57:60:61:64:68:72 SD: 1.9495 cents 37:39:41:44 x 47:50:52:55:58:62:63:66:70:74 SD: 2.7370 cents 38:40:42:45:46:48:51:54:57:60:63:64:68:72:76 S SD: 2.4591 cents 39:41:44:46:47:49:52:55:58:62:65:66:70:74:78 SD: 2.2280 cents 42:44:47 x 50:53:56:59:63:66:70:71:75:79:84 SD: 2.2013 cents 43:45:48:51 x 54:58:61:64:68:72:73:77:81:86 SD: 2.3393 cents 45:48:50:53:54:57:60:64:67:71:75:76:81:85:90 SD: 1.8874 cents 47:50:53 x 56:59:63:66:70:74:78:80:84:89:94 SD: 2.5599 cents 48:51:54:57 x 61:64:68:72:76:80:81:86:91:96 SD: 1.7508 cents 50:53:56:59:60:63:67:71:75:79:84:85:90:95:100 SD: 1.6017 cents 53:56:59:63 x 67:71:75:79:84:89:90:95:100:106 SD: 1.4784 cents 60:63:67:71:72:76:80:85:90:95:100:102:107:114:120 SD: 1.4368 cents 65:69:73:77:78:82:87:92:97:103:109:110:116:123:130 SD: 1.2840 cents 67:71:75:79:80:85:90:95:100:106:112:113:120:127:134 SD: 1.0638 cents 71:75:79:84:85:90:95:100:106:112:119:120:127:134:142 SD: 1.0134 cents 85:90:95:100:102:108:114:120:127:134:142:144:152:161:170 SD: 0.9035 cents 91:96:102:107:109:115:122:129:136:144:152:154:163:172:182 SD: 0.8754 cents 95:100:106:112:114:120:127:134:142:150:159:161:170:180:190 SD: 0.8360 cents 101:107:113:119:121:128:135:143:151:160:169:171:181:191:202 SD: 0.6567 cents 121:128:135:143:145:153:162:171:181:191:202:205:217:229:242 SD: 0.4105 cents 172:182:192:203:206:218:230:243:257:272:287:291:308:325:344 SD: 0.3939 cents 188:199:210:222:225:238:252:266:281:297:314:318:337:356:376 SD: 0.3938 cents 210:222:235:248:251:266:281:297:314:332:351:356:376:397:420 SD: 0.3779 cents 212:224:237:250:254:268:284:300:317:335:354:359:379:401:424 SD: 0.3599 cents 222:235:248:262:266:281:297:314:332:351:371:376:397:420:444 SD: 0.2749 cents 248:262:277:293:297:314:332:351:371:392:414:420:444:469:496 SD: 0.2073 cents 369:390:412:436:442:467:494:522:552:583:616:625:661:698:738 SD: 0.2016 cents 376:397:420:444:450:476:503:532:562:594:628:637:673:711:752 SD: 0.1938 cents 391:413:437:462:468:495:523:553:584:618:653:662:700:740:782 SD: 0.1789 cents 420:444:469:496:503:532:562:594:628:664:701:711:752:795:840 SD: 0.1770 cents 425:449:475:502:509:538:569:601:635:672:710:720:761:804:850 SD: 0.1713 cents 436:461:487:515:522:552:583:617:652:689:728:738:780:825:872 SD: 0.1693 cents 437:462:488:516:523:553:585:618:653:690:730:740:782:827:874 SD: 0.1690 cents 452:478:505:534:541:572:605:639:676:714:755:765:809:855:904 SD: 0.1617 cents 470:497:525:555:563:595:629:665:703:743:785:796:841:889:940 SD: 0.1532 cents 471:498:526:556:564:596:630:666:704:744:787:798:843:891:942 SD: 0.1371 cents 512:541:572:605:613:648:685:724:765:809:855:867:917:969:1024 SD: 0.1294 cents 548:579:612:647:656:694:733:775:819:866:915:928:981:1037:1096 SD: 0.1281 cents 562:594:628:664:673:711:752:795:840:888:939:952:1006:1063:1124 SD: 0.1171 cents 598:632:668:706:716:757:800:846:894:945:999:1013:1070:1131:1196 SD: 0.1147 cents