Scala analysis: bihexany-octoid
Octoid tempering of bihexany, 600-equal
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 102.000 cents 102.000000 2: 268.000 cents 268.000000 3: 386.000 cents 386.000000 4: 418.000 cents 418.000000 5: 536.000 cents 536.000000 6: 702.000 cents 702.000000 7: 804.000 cents 804.000000 8: 884.000 cents 884.000000 9: 970.000 cents 970.000000 10: 1034.000 cents 1034.000000 11: 1120.000 cents 1120.000000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 80.0000 cents 80.0000 1: 102.0000 cents 102.0000 2: 166.0000 cents 166.0000 3: 118.0000 cents 118.0000 4: 32.0000 cents 32.0000 5: 118.0000 cents 118.0000 6: 166.0000 cents 166.0000 7: 102.0000 cents 102.0000 8: 80.0000 cents 80.0000 9: 86.0000 cents 86.0000 10: 64.0000 cents 64.0000 11: 86.0000 cents 86.0000 12: 80.0000 cents 80.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 32.00000 cents 1: 1 64.00000 cents 1: 2 80.00000 cents 1: 2 86.00000 cents 1: 2 102.00000 cents 1: 2 118.00000 cents 1: 2 166.00000 cents 2: 4 150.00000 cents 2: 2 166.00000 cents 2: 2 182.00000 cents 2: 2 268.00000 cents 2: 2 284.00000 cents 3: 2 230.00000 cents 3: 1 236.00000 cents 3: 3 268.00000 cents 3: 2 316.00000 cents 3: 2 348.00000 cents 3: 2 386.00000 cents 4: 2 316.00000 cents 4: 2 332.00000 cents 4: 2 418.00000 cents 4: 4 434.00000 cents 4: 2 466.00000 cents 5: 1 396.00000 cents 5: 2 418.00000 cents 5: 4 498.00000 cents 5: 2 536.00000 cents 5: 2 552.00000 cents 5: 1 600.00000 cents 6: 2 498.00000 cents 6: 4 584.00000 cents 6: 4 616.00000 cents 6: 2 702.00000 cents 7: 1 600.00000 cents 7: 2 648.00000 cents 7: 2 664.00000 cents 7: 4 702.00000 cents 7: 2 782.00000 cents 7: 1 804.00000 cents 8: 2 734.00000 cents 8: 4 766.00000 cents 8: 2 782.00000 cents 8: 2 868.00000 cents 8: 2 884.00000 cents 9: 2 814.00000 cents 9: 2 852.00000 cents 9: 2 884.00000 cents 9: 3 932.00000 cents 9: 1 964.00000 cents 9: 2 970.00000 cents 10: 2 916.00000 cents 10: 2 932.00000 cents 10: 2 1018.00000 cents 10: 2 1034.00000 cents 10: 4 1050.00000 cents 11: 2 1034.00000 cents 11: 2 1082.00000 cents 11: 2 1098.00000 cents 11: 2 1114.00000 cents 11: 2 1120.00000 cents 11: 1 1136.00000 cents 11: 1 1168.00000 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.63636 = 62/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 102.0 268.0 386.0 418.0 536.0 702.0 804.0 884.0 970.0 1034.0 1120.0 1200.0 102.0 : 166.0 284.0 316.0 434.0 600.0 702.0 782.0 868.0 932.0 1018.0 1098.0 1200.0 268.0 : 118.0 150.0 268.0 434.0 536.0 616.0 702.0 766.0 852.0 932.0 1034.0 1200.0 386.0 : 32.0 150.0 316.0 418.0 498.0 584.0 648.0 734.0 814.0 916.0 1082.0 1200.0 418.0 : 118.0 284.0 386.0 466.0 552.0 616.0 702.0 782.0 884.0 1050.0 1168.0 1200.0 536.0 : 166.0 268.0 348.0 434.0 498.0 584.0 664.0 766.0 932.0 1050.0 1082.0 1200.0 702.0 : 102.0 182.0 268.0 332.0 418.0 498.0 600.0 766.0 884.0 916.0 1034.0 1200.0 804.0 : 80.0 166.0 230.0 316.0 396.0 498.0 664.0 782.0 814.0 932.0 1098.0 1200.0 884.0 : 86.0 150.0 236.0 316.0 418.0 584.0 702.0 734.0 852.0 1018.0 1120.0 1200.0 970.0 : 64.0 150.0 230.0 332.0 498.0 616.0 648.0 766.0 932.0 1034.0 1114.0 1200.0 1034.0: 86.0 166.0 268.0 434.0 552.0 584.0 702.0 868.0 970.0 1050.0 1136.0 1200.0 1120.0: 80.0 182.0 348.0 466.0 498.0 616.0 782.0 884.0 964.0 1050.0 1114.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 32.0000 .. 166.0000 cents 134.00000 cents 32.00000 cents 2: 150.0000 .. 284.0000 cents 134.00000 cents -16.00000 cents 3: 230.0000 .. 386.0000 cents 156.00000 cents -54.00000 cents 4: 316.0000 .. 466.0000 cents 150.00000 cents -70.00000 cents 5: 396.0000 .. 600.0000 cents 204.00000 cents -70.00000 cents 6: 498.0000 .. 702.0000 cents 204.00000 cents -102.00000 cents 7: 600.0000 .. 804.0000 cents 204.00000 cents -102.00000 cents 8: 734.0000 .. 884.0000 cents 150.00000 cents -70.00000 cents 9: 814.0000 .. 970.0000 cents 156.00000 cents -70.00000 cents 10: 916.0000 .. 1050.0000 cents 134.00000 cents -54.00000 cents 11: 1034.0000 .. 1168.0000 cents 134.00000 cents -16.00000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 32.00000 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 166.00000 cents Average / Smallest step : 3.125000 Largest / Average step : 1.660000 Largest / Smallest step : 5.187500 Median interval of one step : 94.00000 cents, amount: 0 Least squares average step : 105.92308 cents, oct.: 1271.07692 cents Scale is not proper Scale is a mode of a 600-tone equal temperament with octave 2/1 degrees: 51 134 193 209 268 351 402 442 485 517 560 600 Least number of segments generator : 301 of 602.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 329 of 658.000 cents and inv. generated superset size: 301 = 289 more = 2508.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCBAEFGFE Step pattern size order : EGFAFGECDBDC Scale is not a Constant Structure Scale diversity : 1.510940 Lumma stability : 0.053333 Lumma impropriety factor : 0.520000 Rothenberg efficiency : 0.291721 redundancy: 0.708279 Efficiency x scale size : 3.500649 Number of different interval sizes : 51 = 4.63636 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 5.63636 = 62/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 6.00000 cents Most common intervals : 498.00000 cents & inv., amount: 6 Most common triad is 0.0 702.000 1168.000 cents, amount: 1 Number of recognisable fifths : 6, average 702.0000 cents Formal octave complements present : 1 = 8.3333% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 2 1 0 1 2 1 1 1 0 1 1 N T3 SD: 21.5561 c. M: 36.0000 c. 14: 1 2 1 1 1 2 1 1 1 1 1 1 N D3 SD: 21.7447 c. M: 43.1429 c. 15: 1 2 2 0 2 2 1 1 1 1 1 1 N SD: 15.4272 c. M: 28.0000 c. 21: 2 3 2 0 2 3 2 1 2 1 2 1 N SD: 15.8449 c. M: 26.8571 c. 22: 2 3 2 1 2 3 2 1 2 1 2 1 N SD: 11.8617 c. M:-25.4545 c. 24: 2 3 3 0 3 3 2 2 1 2 1 2 N SD: 14.0712 c. M: 20.0000 c. 26: 2 4 2 1 2 4 2 2 2 1 2 2 N SD: 13.7881 c. M: 28.3077 c. 27: 2 4 3 0 3 4 2 2 2 1 2 2 N SD: 9.5826 c. M: 18.0000 c. 31: 3 4 3 1 3 4 3 2 2 2 2 2 N SD: 7.0041 c. M:-14.1290 c. 40: 3 6 4 1 4 5 4 2 3 2 3 3 N SD: 8.9256 c. M: 14.0000 c. 41: 3 6 4 1 4 6 3 3 3 2 3 3 N SD: 8.1663 c. M: 14.1951 c. 42: 4 5 5 1 4 6 3 3 3 2 3 3 N SD: 8.4540 c. M:-14.0000 c. 43: 4 6 4 1 4 6 4 3 3 2 3 3 N SD: 6.1953 c. M:-11.0698 c. 46: 4 6 5 1 5 6 4 3 3 3 3 3 N SD: 5.6032 c. M:-11.8261 c. 48: 4 7 4 2 4 7 4 3 4 2 4 3 N SD: 6.9282 c. M: 11.0000 c. 49: 4 7 5 1 5 7 4 3 4 2 4 3 N SD: 5.1413 c. M:-9.5918 c. 57: 5 8 5 2 5 8 5 4 4 3 4 4 N SD: 4.9217 c. M: 9.6842 c. 58: 5 8 6 1 6 8 5 4 4 3 4 4 N SD: 3.3047 c. M:-7.1034 c. 72: 6 10 7 2 7 10 6 5 5 4 5 5 N SD: 2.3254 c. M: 4.0000 c. 94: 8 13 9 3 9 13 8 6 7 5 7 6 N SD: 1.8608 c. M:-3.4043 c. 103: 9 14 10 3 10 14 9 7 7 6 7 7 N SD: 1.8988 c. M: 3.0097 c. 121: 10 17 12 3 12 17 10 8 9 6 9 8 N SD: 1.5458 c. M: 2.8264 c. 130: 11 18 13 3 13 18 11 9 9 7 9 9 N SD: 1.4770 c. M: 3.0769 c. 152: 13 21 15 4 15 21 13 10 11 8 11 10 N SD: 0.7343 c. M:-1.2632 c. 224: 19 31 22 6 22 31 19 15 16 12 16 15 N SD: 0.2491 c. M: 0.4286 c. 376: 32 52 37 10 37 52 32 25 27 20 27 25 N SD: 0.1484 c. M:-0.2553 c. 600: 51 83 59 16 59 83 51 40 43 32 43 40 N 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 3 x x x x x 4 S SD: 0.0225 cents 3 x x x x 4 x x 5 x x x 6 S SD: 12.6522 cents 4 x x 5 x x 6 x x 7 x x 8 S SD: 0.3040 cents 5 x 6 x x 7 x 8 x x 9 x 10 S SD: 13.8506 cents 6 x 7 x x 8:9 x 10 x 11 x 12 S SD: 6.8272 cents 7 x 8 x 9:10 x 11 x 12:13 x 14 S SD: 15.3409 cents 8 x 9:10 x 11:12:13 x 14 x 15:16 S SD: 10.2201 cents 9:10 x 11 x 12 x 14:15:16 x 17:18 S SD: 13.6716 cents 10:11:12 x 13:14:15:16:17 x 18:19:20 S SD: 10.6557 cents 11:12:13 x 14:15 x x 18:19:20:21:22 S SD: 7.3459 cents 12:13:14:15 x 16:18:19:20:21:22:23:24 S SD: 5.0846 cents 14:15:16 x 18:19:21:22:23 x 25:27:28 SD: 6.5371 cents 15:16:18 x 19:20:23:24:25:26:27:29:30 SD: 7.3055 cents 16:17:19:20 x 22:24:25:27:28:29:31:32 SD: 5.1623 cents 18:19:21 x 23:25:27:29:30:32:33:34:36 SD: 4.9194 cents 19:20:22 x 24:26:29:30:32:33:35:36:38 SD: 4.9592 cents 20:21:23:25 x 27:30:32:33:35:36:38:40 SD: 4.0536 cents 23:24:27:29 x 31:35:37:38:40:42:44:46 SD: 4.9148 cents 24:25:28:30:31:33:36:38:40:42:44:46:48 SD: 3.9044 cents 27:29:32:34 x 37:41:43:45:47:49:52:54 SD: 4.2592 cents 28:30:33:35:36:38:42:45:47:49:51:53:56 SD: 3.3711 cents 30:32:35:37:38:41:45:48:50:53:55:57:60 SD: 3.0740 cents 31:33:36:39 x 42:47:49:52:54:56:59:62 SD: 3.1280 cents 32:34:37:40:41:44:48:51:53:56:58:61:64 SD: 2.3460 cents 36:38:42:45:46:49:54:57:60:63:65:69:72 SD: 1.5651 cents 48:51:56:60:61:65:72:76:80:84:87:92:96 SD: 1.3827 cents 64:68:75:80:81:87:96:102:107:112:116:122:128 SD: 1.3125 cents 66:70:77:82:84:90:99:105:110:116:120:126:132 SD: 1.0134 cents 80:85:93:100:102:109:120:127:133:140:145:153:160 SD: 0.9422 cents 84:89:98:105:107:114:126:134:140:147:153:160:168 SD: 0.9055 cents 88:93:103:110:112:120:132:140:147:154:160:168:176 SD: 0.7567 cents 96:102:112:120:122:131:144:153:160:168:174:183:192 SD: 0.6636 cents 120:127:140:150:153:164:180:191:200:210:218:229:240 SD: 0.5864 cents 132:140:154:165:168:180:198:210:220:231:240:252:264 SD: 0.1929 cents 377:400:440:471:480:514:566:600:628:660:685:720:754 SD: 0.1740 cents 443:470:517:554:564:604:665:705:738:776:805:846:886 SD: 0.1736 cents 465:493:543:581:592:634:698:740:775:814:845:888:930 SD: 0.1580 cents 476:505:556:595:606:649:714:757:793:834:865:909:952 SD: 0.1503 cents 477:506:557:596:607:650:716:759:795:835:867:911:954 SD: 0.1485 cents 509:540:594:636:648:694:764:810:848:891:925:972:1018 SD: 0.1462 cents 524:556:612:655:667:714:786:834:873:918:952:1001:1048 SD: 0.1349 cents 560:594:654:700:713:763:840:891:933:981:1018:1069:1120 SD: 0.1218 cents 590:626:689:737:751:804:885:939:983:1033:1072:1127:1180 SD: 0.1206 cents 596:632:696:745:759:812:894:948:993:1044:1083:1138:1192 SD: 0.1139 cents