Scala analysis: secad
{126/125, 176/175} tempering of decad, 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: 310.976 cents 310.975610 3: 391.463 cents 391.463415 4: 497.561 cents 497.560976 5: 621.951 cents 621.951219 6: 702.439 cents 702.439024 7: 889.024 cents 889.024390 8: 1013.415 cents 1013.414634 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: 186.5854 cents 186.5854 3: 80.4878 cents 80.4878 4: 106.0976 cents 106.0976 5: 124.3902 cents 124.3902 6: 80.4878 cents 80.4878 7: 186.5854 cents 186.5854 8: 124.3902 cents 124.3902 9: 106.0976 cents 106.0976 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 : 124.4 311.0 391.5 497.6 622.0 702.4 889.0 1013.4 1119.5 1200.0 124.4 : 186.6 267.1 373.2 497.6 578.0 764.6 889.0 995.1 1075.6 1200.0 311.0 : 80.5 186.6 311.0 391.5 578.0 702.4 808.5 889.0 1013.4 1200.0 391.5 : 106.1 230.5 311.0 497.6 622.0 728.0 808.5 932.9 1119.5 1200.0 497.6 : 124.4 204.9 391.5 515.9 622.0 702.4 826.8 1013.4 1093.9 1200.0 622.0 : 80.5 267.1 391.5 497.6 578.0 702.4 889.0 969.5 1075.6 1200.0 702.4 : 186.6 311.0 417.1 497.6 622.0 808.5 889.0 995.1 1119.5 1200.0 889.0 : 124.4 230.5 311.0 435.4 622.0 702.4 808.5 932.9 1013.4 1200.0 1013.4: 106.1 186.6 311.0 497.6 578.0 684.1 808.5 889.0 1075.6 1200.0 1119.5: 80.5 204.9 391.5 472.0 578.0 702.4 782.9 969.5 1093.9 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 1/1, 0.0000 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 : 123.74406 cents, oct.: 1237.44061 cents Scale is not proper Scale is a mode of a 328-tone equal temperament with octave 2/1 degrees: 34 85 107 136 170 192 243 277 306 328 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 : CDABCADCBA 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 0.0 497.561 889.024 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. 12: 1 2 1 1 1 1 2 1 1 1 P B ME S SD: 14.0111 c. M: 24.3902 c. 19: 2 3 1 2 2 1 3 2 2 1 N D3 SD: 8.5248 c. M:-17.3299 c. 27: 3 4 2 2 3 2 4 3 2 2 P SD: 6.7196 c. M:-8.9431 c. 31: 3 5 2 3 3 2 5 3 3 2 N SD: 4.6852 c. M: 8.2612 c. 46: 5 7 3 4 5 3 7 5 4 3 N SD: 3.0046 c. M:-6.0445 c. 58: 6 9 4 5 6 4 9 6 5 4 N SD: 1.1170 c. M: 2.2708 c. 135: 14 21 9 12 14 9 21 14 12 9 N SD: 0.2400 c. M:-0.4878 c. 193: 20 30 13 17 20 13 30 20 17 13 N SD: 0.1678 c. M: 0.3412 c. 328: 34 51 22 29 34 22 51 34 29 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 5 x x 6 S SD: 1.5636 cents 4 x x 5 x x 6 x 7 x 8 S SD: 11.2219 cents 5 x 6 x x 7 x 8:9 x 10 S SD: 17.0535 cents 6 x 7 x 8 x 9:10:11 x 12 S SD: 9.5157 cents 7 x 8:9 x 10:11:12 x 13:14 S SD: 19.6555 cents 8:9 x 10:11 x 12:13:14:15:16 S SD: 15.0811 cents 9:10:11 x 12:13:14:15:16:17:18 S SD: 10.8152 cents 10:11:12 x 13:14:15:17:18:19:20 SD: 8.6565 cents 12:13:14:15:16:17:18:20:22:23:24 S SD: 6.2393 cents 13:14 x 16:17:19:20:22:23:25:26 SD: 8.9814 cents 14:15:17:18:19:20:21:23:25:27:28 SD: 6.9450 cents 15:16:18:19:20:21:23:25:27:29:30 SD: 6.3083 cents 16:17:19:20:21:23:24:27:29:31:32 SD: 5.0390 cents 24:26:29:30:32:34:36:40:43:46:48 SD: 3.0778 cents 30:32:36:38:40:43:45:50:54:57:60 SD: 2.4672 cents 39:42:47:49:52:56:59:65:70:74:78 SD: 2.3077 cents 40:43:48:50:53:57:60:67:72:76:80 SD: 1.8343 cents 51:55:61:64:68:73:77:85:92:97:102 SD: 1.7006 cents 54:58:65:68:72:77:81:90:97:103:108 SD: 1.5576 cents 55:59:66:69:73:79:83:92:99:105:110 SD: 1.5171 cents 66:71:79:83:88:95:99:110:119:126:132 SD: 1.3379 cents 67:72:80:84:89:96:101:112:120:128:134 SD: 1.1804 cents 78:84:93:98:104:112:117:130:140:149:156 SD: 1.0675 cents 90:97:108:113:120:129:135:150:162:172:180 SD: 1.0032 cents 92:99:110:115:123:132:138:154:165:176:184 SD: 0.9852 cents 98:105:117:123:131:140:147:164:176:187:196 SD: 0.9814 cents 102:110:122:128:136:146:153:170:183:195:204 SD: 0.8658 cents 106:114:127:133:141:152:159:177:190:202:212 SD: 0.6864 cents 118:127:141:148:157:169:177:197:212:225:236 SD: 0.5895 cents 122:131:146:153:163:175:183:204:219:233:244 SD: 0.5162 cents 146:157:175:183:195:209:219:244:262:279:292 SD: 0.5110 cents 162:174:194:203:216:232:243:271:291:309:324 SD: 0.2970 cents 240:258:287:301:320:344:360:401:431:458:480 SD: 0.2391 cents 264:284:316:331:352:378:396:441:474:504:528 SD: 0.2358 cents 280:301:335:351:373:401:420:468:503:535:560 SD: 0.2232 cents 366:393:438:459:488:524:549:612:657:699:732 SD: 0.2067 cents 375:403:449:470:500:537:563:627:673:716:750 SD: 0.2041 cents 387:416:463:485:516:554:581:647:695:739:774 SD: 0.1996 cents 402:432:481:504:536:576:603:672:722:767:804 SD: 0.1630 cents 417:448:499:523:556:597:626:697:749:796:834 SD: 0.1579 cents 442:475:529:554:589:633:663:739:794:844:884 SD: 0.1427 cents 484:520:579:607:645:693:726:809:869:924:968 SD: 0.1301 cents