Scala analysis: ozan80_tuning-math_11729_11784
80-et version of Ozan Yarman scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135.000 cents 135.000000 2: 210.000 cents 210.000000 3: 345.000 cents 345.000000 4: 420.000 cents 420.000000 5: 495.000 cents 495.000000 6: 630.000 cents 630.000000 7: 705.000 cents 705.000000 8: 840.000 cents 840.000000 9: 915.000 cents 915.000000 10: 1050.000 cents 1050.000000 11: 1125.000 cents 1125.000000 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 75.0000 cents 75.0000 1: 135.0000 cents 135.0000 2: 75.0000 cents 75.0000 3: 135.0000 cents 135.0000 4: 75.0000 cents 75.0000 5: 75.0000 cents 75.0000 6: 135.0000 cents 135.0000 7: 75.0000 cents 75.0000 8: 135.0000 cents 135.0000 9: 75.0000 cents 75.0000 10: 135.0000 cents 135.0000 11: 75.0000 cents 75.0000 12: 75.0000 cents 75.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 75.00000 cents 1: 5 135.00000 cents 2: 2 150.00000 cents 2: 10 210.00000 cents 3: 9 285.00000 cents 3: 3 345.00000 cents 4: 4 360.00000 cents 4: 8 420.00000 cents 5: 11 495.00000 cents 5: 1 555.00000 cents 6: 6 570.00000 cents 6: 6 630.00000 cents 7: 1 645.00000 cents 7: 11 705.00000 cents 8: 8 780.00000 cents 8: 4 840.00000 cents 9: 3 855.00000 cents 9: 9 915.00000 cents 10: 10 990.00000 cents 10: 2 1050.00000 cents 11: 5 1065.00000 cents 11: 7 1125.00000 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 : 135.0 210.0 345.0 420.0 495.0 630.0 705.0 840.0 915.0 1050.0 1125.0 1200.0 135.0 : 75.0 210.0 285.0 360.0 495.0 570.0 705.0 780.0 915.0 990.0 1065.0 1200.0 210.0 : 135.0 210.0 285.0 420.0 495.0 630.0 705.0 840.0 915.0 990.0 1125.0 1200.0 345.0 : 75.0 150.0 285.0 360.0 495.0 570.0 705.0 780.0 855.0 990.0 1065.0 1200.0 420.0 : 75.0 210.0 285.0 420.0 495.0 630.0 705.0 780.0 915.0 990.0 1125.0 1200.0 495.0 : 135.0 210.0 345.0 420.0 555.0 630.0 705.0 840.0 915.0 1050.0 1125.0 1200.0 630.0 : 75.0 210.0 285.0 420.0 495.0 570.0 705.0 780.0 915.0 990.0 1065.0 1200.0 705.0 : 135.0 210.0 345.0 420.0 495.0 630.0 705.0 840.0 915.0 990.0 1125.0 1200.0 840.0 : 75.0 210.0 285.0 360.0 495.0 570.0 705.0 780.0 855.0 990.0 1065.0 1200.0 915.0 : 135.0 210.0 285.0 420.0 495.0 630.0 705.0 780.0 915.0 990.0 1125.0 1200.0 1050.0: 75.0 150.0 285.0 360.0 495.0 570.0 645.0 780.0 855.0 990.0 1065.0 1200.0 1125.0: 75.0 210.0 285.0 420.0 495.0 570.0 705.0 780.0 915.0 990.0 1125.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.0000 .. 135.0000 cents 60.00000 cents 75.00000 cents 2: 150.0000 .. 210.0000 cents 60.00000 cents 15.00000 cents 3: 285.0000 .. 345.0000 cents 60.00000 cents 75.00000 cents 4: 360.0000 .. 420.0000 cents 60.00000 cents 15.00000 cents 5: 495.0000 .. 555.0000 cents 60.00000 cents 75.00000 cents 6: 570.0000 .. 630.0000 cents 60.00000 cents 15.00000 cents 7: 645.0000 .. 705.0000 cents 60.00000 cents 15.00000 cents 8: 780.0000 .. 840.0000 cents 60.00000 cents 75.00000 cents 9: 855.0000 .. 915.0000 cents 60.00000 cents 15.00000 cents 10: 990.0000 .. 1050.0000 cents 60.00000 cents 75.00000 cents 11: 1065.0000 .. 1125.0000 cents 60.00000 cents 15.00000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 75.00000 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 135.00000 cents Average / Smallest step : 1.333333 Largest / Average step : 1.350000 Largest / Smallest step : 1.800000 Median interval of one step : 75.00000 cents, amount: 7 Most common interval of one step : 75.00000 cents, amount: 7 Least squares average step : 102.60000 cents, oct.: 1231.20000 cents Scale is strictly proper Scale has Myhill's property chromas: 60.00000 cents and 15.00000 cents, ratio: 4.000000 generators: 5 of 495.00000 cents and 7 of 705.00000 cents 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 80-tone equal temperament with octave 1200.000 cents degrees: 9 14 23 28 33 42 47 56 61 70 75 80 generators: 33 and 47 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABBABABABB Step pattern size order : LSLSSLSLSLSS Interval vector is [ 0 0 0 0 7 0 0 0 5 2 0 0 0 10 0 0 0 0 9 0 0 0 3 4 0 0 0 8 0 0 0 0 11 0 0 0 1 6 0 0 ] Scale is a Constant Structure, by a margin of 15.00000 cents Ratio Whole / Half tone : 2.800000 ( 14/5 ) Scale diversity : 1.190756 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.450000 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 : 15.00000 cents Most common intervals : 495.00000 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 75.000 705.000 cents Most common triad is 0.0 495.000 705.000 cents, amount: 10 Number of recognisable fifths : 11, average 705.0000 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 7-8 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 28.3578 c. M: 50.0000 c. Twelve-tone Chromatic (1/11-comma) 14: 2 0 2 1 1 1 1 2 1 1 1 1 P D3 SD: 22.6947 c. M: 38.5714 c. 15: 2 1 1 1 1 2 1 2 0 2 1 1 N D3 SD: 22.4537 c. M:-40.0000 c. 16: 2 1 2 1 1 1 1 2 1 2 1 1 N D3 S SD: 21.2132 c. M:-30.0000 c. 17: 2 1 2 1 1 2 1 2 1 2 1 1 P M ME SD: 5.0043 c. M:-8.8235 c. 46: 5 3 5 3 3 5 3 5 3 5 3 3 SP M DE SD: 3.6988 c. M: 6.5217 c. 63: 7 4 7 4 4 7 4 7 4 7 4 4 SP M DE SD: 1.3504 c. M: 2.3810 c. 80: 9 5 9 5 5 9 5 9 5 9 5 5 SP M DE 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: 1.5225 cents 3 x x x x 4 x x x 5 x x 6 S SD: 10.2641 cents 4 x x x 5 x x 6 x 7 x x 8 S SD: 15.8927 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 13.9419 cents 6 x 7 x x 8 x 9 x 10:11 x 12 S SD: 10.7911 cents 7 x 8 x 9 x 10 x 11:12:13 x 14 S SD: 10.0399 cents 8 x 9 x 10:11 x 12:13:14 x 15:16 S SD: 11.5917 cents 9 x 10:11 x 12:13:14 x 15 x 17:18 SD: 9.6202 cents 10:11 x 12:13 x 14:15:16:17:18:19:20 S SD: 8.4518 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 8.7317 cents 12:13:14 x 15:16:17:18 x 20:22:23:24 S SD: 7.7913 cents 13:14:15:16 x 17:19:20:21:22:24:25:26 SD: 6.6176 cents 14:15:16:17:18:19:20:21:23:24:26:27:28 SD: 5.0139 cents 16:17:18 x 20:21:23:24:26:27:29:31:32 SD: 5.4360 cents 18:19:20:22:23:24:26:27:29:31:33:34:36 SD: 5.2867 cents 19 x 21:23:24:25:27:29:31:32:35:36:38 SD: 5.7553 cents 21:23:24:26:27:28:30:32:34:36:39:40:42 SD: 4.9088 cents 22:24:25:27:28:29:32:33:36:37:40:42:44 SD: 3.4830 cents 24:26:27:29:31:32:35:36:39:41:44:46:48 SD: 3.3225 cents 30:32:34:37:38:40:43:45:49:51:55:57:60 SD: 3.1011 cents 32:35:36:39:41:43:46:48:52:54:59:61:64 SD: 2.7002 cents 36:39:41:44:46:48:52:54:58:61:66:69:72 SD: 1.9387 cents 37:40:42:45:47:49:53:56:60:63:68:71:74 SD: 1.9148 cents 46:50:52:56:59:61:66:69:75:78:84:88:92 SD: 1.6804 cents 48:52:54:59:61:64:69:72:78:81:88:92:96 SD: 1.5189 cents 61:66:69:74:78:81:88:92:99:103:112:117:122 SD: 1.4695 cents 62:67:70:76:79:83:89:93:101:105:114:119:124 SD: 1.3150 cents 69:75:78:84:88:92:99:104:112:117:127:132:138 SD: 1.2379 cents 72:78:81:88:92:96:104:108:117:122:132:138:144 SD: 0.9985 cents 85:92:96:104:108:113:122:128:138:144:156:163:170 SD: 0.8423 cents 109:118:123:133:139:145:157:164:177:185:200:209:218 SD: 0.3905 cents 187:202:211:228:238:249:269:281:304:317:343:358:374 SD: 0.3422 cents 223:241:252:272:284:297:321:335:362:378:409:427:446 SD: 0.2862 cents 248:268:280:303:316:330:357:373:403:421:455:475:496 SD: 0.2537 cents 294:318:332:359:375:391:423:442:478:499:539:563:588 SD: 0.2526 cents 296:320:334:361:377:394:426:445:481:502:543:567:592 SD: 0.1990 cents 332:359:375:405:423:442:478:499:539:563:609:636:664 SD: 0.1919 cents 372:402:420:454:474:495:535:559:604:631:682:712:744 SD: 0.1738 cents 408:441:461:498:520:543:587:613:663:692:748:781:816 SD: 0.1655 cents 444:480:501:542:566:591:639:667:721:753:814:850:888 SD: 0.1418 cents 458:495:517:559:584:610:659:688:744:777:840:877:916 SD: 0.1341 cents 481:520:543:587:613:640:692:723:781:816:882:921:962 SD: 0.1118 cents 517:559:584:631:659:688:744:777:840:877:948:990:1034 SD: 0.1016 cents