Scala analysis: secac
{126/125, 176/175} tempering of decac, 328-et version
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 124.390 cents 124.390244 2: 230.488 cents 230.487805 3: 310.976 cents 310.975610 4: 497.561 cents 497.560976 5: 621.951 cents 621.951219 6: 702.439 cents 702.439024 7: 808.537 cents 808.536585 8: 932.927 cents 932.926829 9: 1119.512 cents 1119.512195 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 80.4878 cents 80.4878 1: 124.3902 cents 124.3902 2: 106.0976 cents 106.0976 3: 80.4878 cents 80.4878 4: 186.5854 cents 186.5854 5: 124.3902 cents 124.3902 6: 80.4878 cents 80.4878 7: 106.0976 cents 106.0976 8: 124.3902 cents 124.3902 9: 186.5854 cents 186.5854 10: 80.4878 cents 80.4878
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 : 124.4 230.5 311.0 497.6 622.0 702.4 808.5 932.9 1119.5 1200.0 124.4 : 106.1 186.6 373.2 497.6 578.0 684.1 808.5 995.1 1075.6 1200.0 230.5 : 80.5 267.1 391.5 472.0 578.0 702.4 889.0 969.5 1093.9 1200.0 311.0 : 186.6 311.0 391.5 497.6 622.0 808.5 889.0 1013.4 1119.5 1200.0 497.6 : 124.4 204.9 311.0 435.4 622.0 702.4 826.8 932.9 1013.4 1200.0 622.0 : 80.5 186.6 311.0 497.6 578.0 702.4 808.5 889.0 1075.6 1200.0 702.4 : 106.1 230.5 417.1 497.6 622.0 728.0 808.5 995.1 1119.5 1200.0 808.5 : 124.4 311.0 391.5 515.9 622.0 702.4 889.0 1013.4 1093.9 1200.0 932.9 : 186.6 267.1 391.5 497.6 578.0 764.6 889.0 969.5 1075.6 1200.0 1119.5: 80.5 204.9 311.0 391.5 578.0 702.4 782.9 889.0 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 : 119.56288 cents, oct.: 1195.62876 cents Scale is not proper Scale is a mode of a 328-tone equal temperament with octave 2/1 degrees: 34 63 85 136 170 192 221 255 306 328 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 : CBADCABCDA 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 : 3 = 30.0000% -- 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: 26.2600 c. M:-49.0244 c. 11: 1 1 1 2 1 0 1 2 1 1 N D3 SD: 33.9494 c. M:-48.8914 c. 12: 1 1 1 2 1 1 1 1 2 1 P B ME S SD: 19.1739 c. M: 32.9268 c. 15: 2 1 1 2 2 1 1 2 2 1 P D3 SD: 17.8566 c. M:-35.6098 c. 17: 2 1 1 3 2 1 1 2 3 1 N SD: 17.3581 c. M: 32.0660 c. 18: 2 1 2 2 2 2 1 2 3 1 N T3 SD: 20.4063 c. M: 30.8943 c. 19: 2 2 1 3 2 1 2 2 3 1 N D3 SD: 11.8072 c. M:-22.1438 c. 27: 3 2 2 4 3 2 2 3 4 2 P SD: 6.6514 c. M:-8.9431 c. 31: 3 3 2 5 3 2 3 3 5 2 N SD: 4.3317 c. M: 8.2612 c. 46: 5 4 3 7 5 3 4 5 7 3 N SD: 3.5654 c. M:-6.2036 c. 58: 6 5 4 9 6 4 5 6 9 4 N SD: 1.5472 c. M: 2.9016 c. 104: 11 9 7 16 11 7 9 11 16 7 N SD: 1.2523 c. M:-2.5328 c. 135: 14 12 9 21 14 9 12 14 21 9 N SD: 0.3324 c. M:-0.6233 c. 193: 20 17 13 30 20 13 17 20 30 13 N SD: 0.2325 c. M: 0.4360 c. 328: 34 29 22 51 34 22 29 34 51 22 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: 16.1902 cents 4 x x 5 x x 6 x 7 x 8 S SD: 20.8639 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 18.7325 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 15.4596 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 11.8562 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 14.0093 cents 9 x 10:11:12:13 x 14:15:17:18 SD: 11.4955 cents 10:11 x 12:13:14:15:16:17:19:20 SD: 8.1692 cents 11:12 x 13:15:16:17:18:19:21:22 SD: 10.0412 cents 12:13:14 x 16:17:18:19:21:23:24 SD: 6.4674 cents 14:15:16:17:19:20:21:22:24:27:28 SD: 5.1305 cents 21:23:24:25:28:30:32:34:36:40:42 SD: 5.0893 cents 22:24:25:26:29:32:33:35:38:42:44 SD: 5.0324 cents 24:26:27:29:32:34:36:38:41:46:48 SD: 4.2342 cents 26:28:30:31:35:37:39:41:45:50:52 SD: 4.0118 cents 27:29:31:32:36:39:41:43:46:52:54 SD: 3.6799 cents 28:30:32:34:37:40:42:45:48:53:56 SD: 3.5911 cents 30:32:34:36:40:43:45:48:51:57:60 SD: 2.5968 cents 40:43:46:48:53:57:60:64:69:76:80 SD: 2.3571 cents 42:45:48:50:56:60:63:67:72:80:84 SD: 1.2023 cents 76:82:87:91:101:109:114:121:130:145:152 SD: 1.1109 cents 90:97:103:108:120:129:135:144:154:172:180 SD: 1.0005 cents 92:99:105:110:123:132:138:147:158:176:184 SD: 0.8931 cents 106:114:121:127:141:152:159:169:182:202:212 SD: 0.6712 cents 132:142:151:158:176:189:198:211:226:252:264 SD: 0.5161 cents 148:159:169:177:197:212:222:236:254:283:296 SD: 0.4577 cents 162:174:185:194:216:232:243:258:278:309:324 SD: 0.4163 cents 188:202:215:225:251:269:282:300:322:359:376 SD: 0.4061 cents 210:226:240:251:280:301:315:335:360:401:420 SD: 0.3893 cents 238:256:272:285:317:341:357:380:408:454:476 SD: 0.3413 cents 240:258:274:287:320:344:360:383:411:458:480 SD: 0.3069 cents 252:271:288:302:336:361:378:402:432:481:504 SD: 0.2997 cents 280:301:320:335:373:401:420:447:480:535:560 SD: 0.2543 cents 294:316:336:352:392:421:441:469:504:561:588 SD: 0.1651 cents 442:475:505:529:589:633:663:705:758:844:884 SD: 0.1232 cents 472:507:539:565:629:676:708:753:809:901:944 SD: 0.1193 cents