Scala analysis: octo
octone in 612 equal
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 119.608 cents 119.607840 2: 350.980 cents 350.980390 3: 386.275 cents 386.274510 4: 617.647 cents 617.647060 5: 701.961 cents 701.960780 6: 933.333 cents 933.333330 7: 968.627 cents 968.627450 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 231.3725 cents 231.3725 1: 119.6078 cents 119.6078 2: 231.3726 cents 231.3726 3: 35.2941 cents 35.2941 4: 231.3725 cents 231.3725 5: 84.3137 cents 84.3137 6: 231.3725 cents 231.3725 7: 35.2941 cents 35.2941 8: 231.3725 cents 231.3725
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 35.29412 cents 1: 1 84.31372 cents 1: 1 119.60784 cents 1: 4 231.37255 cents 2: 4 266.66667 cents 2: 2 315.68627 cents 2: 2 350.98039 cents 3: 2 350.98039 cents 3: 2 386.27451 cents 3: 2 498.03922 cents 3: 1 547.05882 cents 3: 1 582.35294 cents 4: 4 582.35294 cents 4: 4 617.64706 cents 5: 1 617.64706 cents 5: 1 652.94118 cents 5: 2 701.96078 cents 5: 2 813.72549 cents 5: 2 849.01961 cents 6: 2 849.01961 cents 6: 2 884.31373 cents 6: 4 933.33333 cents 7: 4 968.62745 cents 7: 1 1080.39216 cents 7: 1 1115.68628 cents 7: 2 1164.70588 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.71429 = 26/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 119.6 351.0 386.3 617.6 702.0 933.3 968.6 1200.0 119.6 : 231.4 266.7 498.0 582.4 813.7 849.0 1080.4 1200.0 351.0 : 35.3 266.7 351.0 582.4 617.6 849.0 968.6 1200.0 386.3 : 231.4 315.7 547.1 582.4 813.7 933.3 1164.7 1200.0 617.6 : 84.3 315.7 351.0 582.4 702.0 933.3 968.6 1200.0 702.0 : 231.4 266.7 498.0 617.6 849.0 884.3 1115.7 1200.0 933.3 : 35.3 266.7 386.3 617.6 652.9 884.3 968.6 1200.0 968.6 : 231.4 351.0 582.4 617.6 849.0 933.3 1164.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.2941 .. 231.3726 cents 196.07843 cents 35.29412 cents 2: 266.6667 .. 350.9804 cents 84.31372 cents 35.29412 cents 3: 350.9804 .. 582.3529 cents 231.37255 cents 1/1, 0.0000 cents 4: 582.3529 .. 617.6471 cents 35.29412 cents 1/1, 0.0000 cents 5: 617.6471 .. 849.0196 cents 231.37255 cents 1/1, 0.0000 cents 6: 849.0196 .. 933.3333 cents 84.31372 cents 1/1, 0.0000 cents 7: 968.6274 .. 1164.7059 cents 196.07843 cents 35.29412 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 35.29412 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 231.37255 cents Average / Smallest step : 4.250000 Largest / Average step : 1.542484 Largest / Smallest step : 6.555555 Median interval of one step : 175.49019 cents, amount: 0 Most common interval of one step : 231.37255 cents, amount: 4 Least squares average step : 146.77047 cents, oct.: 1174.16378 cents Scale is proper Scale is a mode of a 612-tone equal temperament with octave 1200.000 cents degrees: 61 179 197 315 358 476 494 612 Least number of segments generator : 307 of 601.961 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 533 of 1045.098 cents and inv. generated superset size: 110 = 102 more = 1375.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBDBCB Step pattern size order : CDADBDAD Scale is not a Constant Structure Scale diversity : 1.386521 Rothenberg stability : 0.678571 = 19/28 Lumma stability : 0.117647 Rothenberg efficiency : 0.466071 redundancy: 0.533929 Efficiency x scale size : 3.728571 Number of different interval sizes : 22 = 3.14286 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 3.71429 = 26/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 35.29412 cents Most common intervals : 582.35294 cents & inv., amount: 5 Number of recognisable fifths : 2, average 701.9608 cents Formal octave complements present : 1 = 12.5000% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 4-5 -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 0 2 N T3 SD: 44.7544 c. M: 68.6274 c. 9: 1 2 0 2 0 2 0 2 N SD: 30.9717 c. M:-49.0196 c. 10: 1 2 0 2 1 2 0 2 P B D3 SD: 16.5614 c. M:-26.6667 c. 17: 2 3 1 3 1 3 1 3 P SD: 18.7560 c. M:-37.2549 c. 19: 2 4 0 4 1 4 0 4 N SD: 14.8999 c. M:-27.9670 c. 21: 2 4 1 4 1 4 1 4 P SD: 11.3834 c. M: 19.0476 c. 27: 3 5 1 5 2 5 1 5 P SD: 8.5593 c. M:-13.7255 c. 31: 3 6 1 6 2 6 1 6 P SD: 2.9284 c. M: 5.1866 c. 41: 4 8 1 8 3 8 1 8 P SD: 2.9057 c. M: 5.7867 c. 68: 7 13 2 13 5 13 2 13 P SD: 2.4015 c. M:-3.9216 c. 72: 7 14 2 14 5 14 2 14 P SD: 1.8341 c. M: 2.9412 c. 99: 10 19 3 19 7 19 3 19 P SD: 1.0004 c. M:-1.6043 c. 130: 13 25 4 25 9 25 4 25 P SD: 0.7472 c. M:-1.4178 c. 140: 14 27 4 27 10 27 4 27 P SD: 0.5741 c. M:-0.9524 c. 171: 17 33 5 33 12 33 5 33 P SD: 0.1931 c. M: 0.3096 c. 441: 44 85 13 85 31 85 13 85 P SD: 0.0749 c. M:-0.1201 c. 612: 61 118 18 118 43 118 18 118 P SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 0.0029 cents 3 x x 4 x x 5 x 6 S SD: 40.6764 cents 4 x x 5 x 6 x 7:8 S SD: 0.0506 cents 5 x 6 x 7:8 x 9:10 S SD: 26.3544 cents 6 x 7:8 x 9:10:11:12 S SD: 28.1286 cents 7:8 x 9:10:11:12 x 14 S SD: 24.3326 cents 8:9 x 10:11:12 x 14:16 S SD: 17.8780 cents 9:10:11 x 13:14:15:16:18 SD: 15.2744 cents 10:11:12:13:14:15:17:18:20 SD: 13.5633 cents 11:12:13:14:16:17:19 x 22 SD: 13.9628 cents 12:13 x 15:17:18 x 21:24 SD: 3.9938 cents 13:14:16 x 19:20:22:23:26 SD: 9.5720 cents 14:15:17:18:20:21:24:25:28 SD: 7.7462 cents 15:16:18:19:21:23 x 26:30 SD: 9.8854 cents 16:17 x 20:23:24:27:28:32 SD: 4.6995 cents 17:18:21 x 24:26:29:30:34 SD: 7.1351 cents 19:20:23:24:27:29 x 33:38 SD: 7.6213 cents 20:21 x 25:29:30:34:35:40 SD: 6.5574 cents 21:23 x 26:30:32:36:37:42 SD: 7.2759 cents 22:24:27:28:31:33:38 x 44 SD: 7.4081 cents 23:25:28:29:33:35:39:40:46 SD: 5.7270 cents 24:26:29:30:34:36:41:42:48 SD: 4.2548 cents 25:27 x 31:36:38:43:44:50 SD: 4.9932 cents 26:28:32:33:37:39:45 x 52 SD: 4.8713 cents 27:29:33:34:39:41:46:47:54 SD: 4.3388 cents 28:30:34:35:40:42:48:49:56 SD: 1.8569 cents 29:31 x 36:41:44:50:51:58 SD: 4.6316 cents 30:32:37:38:43:45:51:52:60 SD: 4.4213 cents 31:33:38:39:44:47:53:54:62 SD: 3.5633 cents 32:34:39:40:46:48:55:56:64 SD: 2.5567 cents 40:43:49:50:57:60:69:70:80 SD: 1.5991 cents 44:47:54:55:63:66:75:77:88 SD: 1.5699 cents 56:60:69:70:80:84:96:98:112 SD: 1.3037 cents 68:73:83:85:97:102:117:119:136 SD: 1.1876 cents 72:77:88:90:103:108:123:126:144 SD: 1.0306 cents 80:86:98:100:114:120:137:140:160 SD: 0.9329 cents 84:90:103:105:120:126:144:147:168 SD: 0.2590 cents 196:210:240:245:280:294:336:343:392 S SD: 0.0646 cents 280:300:343:350:400:420:480:490:560 SD: 0.0641 cents 476:510:583:595:680:714:816:833:952 SD: 0.0466 cents