Scala analysis: secab
{126/125, 176/175} tempering of decab, 328-et version
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 80.488 cents 80.487805 2: 186.585 cents 186.585366 3: 310.976 cents 310.975610 4: 497.561 cents 497.560976 5: 578.049 cents 578.048780 6: 702.439 cents 702.439024 7: 808.537 cents 808.536585 8: 889.024 cents 889.024390 9: 1075.610 cents 1075.609756 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 124.3902 cents 124.3902 1: 80.4878 cents 80.4878 2: 106.0976 cents 106.0976 3: 124.3902 cents 124.3902 4: 186.5854 cents 186.5854 5: 80.4878 cents 80.4878 6: 124.3902 cents 124.3902 7: 106.0976 cents 106.0976 8: 80.4878 cents 80.4878 9: 186.5854 cents 186.5854 10: 124.3902 cents 124.3902
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 80.48780 cents 1: 2 106.09756 cents 1: 3 124.39024 cents 1: 2 186.58537 cents 2: 2 186.58537 cents 2: 2 204.87805 cents 2: 2 230.48780 cents 2: 2 267.07317 cents 2: 2 310.97561 cents 3: 4 310.97561 cents 3: 1 373.17073 cents 3: 4 391.46341 cents 3: 1 417.07317 cents 4: 1 391.46341 cents 4: 1 435.36585 cents 4: 1 471.95122 cents 4: 6 497.56098 cents 4: 1 515.85366 cents 5: 5 578.04878 cents 5: 5 621.95122 cents 6: 1 684.14634 cents 6: 6 702.43902 cents 6: 1 728.04878 cents 6: 1 764.63415 cents 6: 1 808.53659 cents 7: 1 782.92683 cents 7: 4 808.53659 cents 7: 1 826.82927 cents 7: 4 889.02439 cents 8: 2 889.02439 cents 8: 2 932.92683 cents 8: 2 969.51220 cents 8: 2 995.12195 cents 8: 2 1013.41463 cents 9: 2 1013.41463 cents 9: 3 1075.60976 cents 9: 2 1093.90244 cents 9: 3 1119.51220 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.22222 = 38/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 80.5 186.6 311.0 497.6 578.0 702.4 808.5 889.0 1075.6 1200.0 80.5 : 106.1 230.5 417.1 497.6 622.0 728.0 808.5 995.1 1119.5 1200.0 186.6 : 124.4 311.0 391.5 515.9 622.0 702.4 889.0 1013.4 1093.9 1200.0 311.0 : 186.6 267.1 391.5 497.6 578.0 764.6 889.0 969.5 1075.6 1200.0 497.6 : 80.5 204.9 311.0 391.5 578.0 702.4 782.9 889.0 1013.4 1200.0 578.0 : 124.4 230.5 311.0 497.6 622.0 702.4 808.5 932.9 1119.5 1200.0 702.4 : 106.1 186.6 373.2 497.6 578.0 684.1 808.5 995.1 1075.6 1200.0 808.5 : 80.5 267.1 391.5 472.0 578.0 702.4 889.0 969.5 1093.9 1200.0 889.0 : 186.6 311.0 391.5 497.6 622.0 808.5 889.0 1013.4 1119.5 1200.0 1075.6: 124.4 204.9 311.0 435.4 622.0 702.4 826.8 932.9 1013.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.4878 .. 186.5854 cents 106.09756 cents 80.48780 cents 2: 186.5854 .. 310.9756 cents 124.39024 cents 0.00000 cents 3: 310.9756 .. 417.0732 cents 106.09756 cents 0.00000 cents 4: 391.4634 .. 515.8537 cents 124.39024 cents -25.60976 cents 5: 578.0488 .. 621.9512 cents 43.90244 cents 62.19512 cents 6: 684.1463 .. 808.5366 cents 124.39024 cents 62.19512 cents 7: 782.9268 .. 889.0244 cents 106.09756 cents -25.60976 cents 8: 889.0244 .. 1013.4146 cents 124.39024 cents 0.00000 cents 9: 1013.4146 .. 1119.5122 cents 106.09756 cents 0.00000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 80.48780 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 186.58537 cents Average / Smallest step : 1.490909 Largest / Average step : 1.554878 Largest / Smallest step : 2.318182 Median interval of one step : 115.24390 cents, amount: 0 Least squares average step : 116.71207 cents, oct.: 1167.12068 cents Scale is not proper Scale is a mode of a 328-tone equal temperament with octave 2/1 degrees: 22 51 85 136 158 192 221 243 294 328 Least number of segments generator : 165 of 603.659 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 311 of 1137.805 cents and inv. generated superset size: 32 = 22 more = 320.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDACBADC Step pattern size order : ABCDACBADC Scale is not a Constant Structure Scale diversity : 1.410987 Lumma stability : 0.237805 Lumma impropriety factor : 0.042683 Rothenberg efficiency : 0.388929 redundancy: 0.611071 Efficiency x scale size : 3.889286 Number of different interval sizes : 32 = 3.55556 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.22222 = 38/9 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 18.29268 cents Most common triad is 0.0 310.976 702.439 cents, amount: 5 Number of recognisable fifths : 6, average 702.4390 cents Formal octave complements present : 5 = 50.0000% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 37.3673 c. M:-70.9756 c. 11: 1 1 1 2 0 1 1 1 2 1 N D3 SD: 32.0121 c. M: 47.8936 c. 12: 1 1 1 2 1 1 1 1 2 1 P B ME S SD: 14.0111 c. M:-24.3902 c. 19: 1 2 2 3 1 2 2 1 3 2 N D3 SD: 8.5248 c. M: 17.3299 c. 27: 2 2 3 4 2 3 2 2 4 3 P SD: 6.7196 c. M: 8.9431 c. 31: 2 3 3 5 2 3 3 2 5 3 N SD: 4.6852 c. M:-8.2612 c. 46: 3 4 5 7 3 5 4 3 7 5 N SD: 3.0046 c. M: 6.0445 c. 58: 4 5 6 9 4 6 5 4 9 6 N SD: 1.1170 c. M:-2.2708 c. 135: 9 12 14 21 9 14 12 9 21 14 N SD: 0.2400 c. M: 0.4878 c. 193: 13 17 20 30 13 20 17 13 30 20 N SD: 0.1678 c. M:-0.3412 c. 328: 22 29 34 51 22 34 29 22 51 34 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 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 4 S SD: 0.2420 cents 3 x x x 4 x x x 5 x 6 S SD: 1.5636 cents 4 x x 5 x x 6 x 7 x 8 S SD: 27.4367 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 11.7197 cents 6 x x 7:8 x 9 x 10:11:12 S SD: 8.5900 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 14.3468 cents 8 x 9:10 x 11:12:13 x 15:16 SD: 12.6768 cents 9 x 10:11:12:13 x 14:15:17:18 SD: 10.7142 cents 10 x 11:12:13:14:15:16:17:19:20 SD: 7.5006 cents 11 x 12:13:15 x 17 x 18:20:22 SD: 13.4890 cents 12 x 13:14:16:17:18:19:20:22:24 S SD: 8.4273 cents 13:14 x 16:17:18:20:21:22:24:26 S SD: 10.5270 cents 14:15:16:17:19:20:21:22:23:26:28 SD: 9.0726 cents 15:16:17:18:20:21:23:24:25:28:30 SD: 5.8380 cents 18:19:20:22:24:25:27:29:30:34:36 SD: 5.0661 cents 20:21:22:24:27:28:30:32:33:37:40 SD: 4.0403 cents 25:26:28:30:33:35:38:40:42:47:50 SD: 3.8609 cents 27:28:30:32:36:38:41:43:45:50:54 SD: 3.6507 cents 30:31:33:36:40:42:45:48:50:56:60 SD: 3.3814 cents 35:37:39:42:47:49:53:56:58:65:70 SD: 3.1008 cents 36:38:40:43:48:50:54:57:60:67:72 SD: 2.1878 cents 42:44:47:50:56:59:63:67:70:78:84 SD: 1.7149 cents 60:63:67:72:80:84:90:96:100:112:120 SD: 1.2271 cents 78:82:87:93:104:109:117:124:130:145:156 SD: 1.2230 cents 80:84:89:96:107:112:120:128:134:149:160 SD: 1.1829 cents 81:85:90:97:108:113:122:129:135:151:162 SD: 1.0558 cents 86:90:96:103:115:120:129:137:144:160:172 SD: 0.8357 cents 106:111:118:127:141:148:159:169:177:197:212 SD: 0.5323 cents 166:174:185:199:221:232:249:265:277:309:332 SD: 0.5074 cents 168:176:187:201:224:235:252:268:281:313:336 SD: 0.3973 cents 192:201:214:230:256:268:288:306:321:357:384 SD: 0.3621 cents 210:220:234:251:280:293:315:335:351:391:420 SD: 0.2894 cents 255:267:284:305:340:356:383:407:426:475:510 SD: 0.2865 cents 274:287:305:328:365:383:411:437:458:510:548 SD: 0.2473 cents 316:331:352:378:421:441:474:504:528:588:632 SD: 0.1819 cents 376:394:419:450:501:525:564:600:628:700:752 SD: 0.1751 cents 396:415:441:474:528:553:594:632:662:737:792 SD: 0.1417 cents 484:507:539:579:645:676:726:772:809:901:968 SD: 0.1151 cents