Scala analysis: keentet
The five keenanismic triads, plus o- and u-tonal, in 284edo
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 152.113 cents 152.112680 2: 316.901 cents 316.901410 3: 384.507 cents 384.507040 4: 650.704 cents 650.704230 5: 701.408 cents 701.408450 6: 933.803 cents 933.802820 7: 967.606 cents 967.605630 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 232.3944 cents 232.3944 1: 152.1127 cents 152.1127 2: 164.7887 cents 164.7887 3: 67.6056 cents 67.6056 4: 266.1972 cents 266.1972 5: 50.7042 cents 50.7042 6: 232.3944 cents 232.3944 7: 33.8028 cents 33.8028 8: 232.3944 cents 232.3944
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33.80281 cents 1: 1 50.70422 cents 1: 1 67.60563 cents 1: 1 152.11268 cents 1: 1 164.78873 cents 1: 2 232.39437 cents 1: 1 266.19719 cents 2: 1 232.39436 cents 2: 2 266.19718 cents 2: 1 283.09859 cents 2: 2 316.90141 cents 2: 1 333.80282 cents 2: 1 384.50705 cents 3: 1 316.90140 cents 3: 2 384.50704 cents 3: 1 418.30986 cents 3: 2 498.59155 cents 3: 2 549.29578 cents 4: 2 549.29577 cents 4: 2 583.09859 cents 4: 2 616.90141 cents 4: 2 650.70423 cents 5: 2 650.70422 cents 5: 2 701.40845 cents 5: 1 781.69014 cents 5: 2 815.49296 cents 5: 1 883.09860 cents 6: 1 815.49295 cents 6: 1 866.19718 cents 6: 2 883.09859 cents 6: 1 916.90141 cents 6: 2 933.80282 cents 6: 1 967.60564 cents 7: 1 933.80281 cents 7: 2 967.60563 cents 7: 1 1035.21127 cents 7: 1 1047.88732 cents 7: 1 1132.39437 cents 7: 1 1149.29578 cents 7: 1 1166.19719 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.71429 = 40/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 152.1 316.9 384.5 650.7 701.4 933.8 967.6 1200.0 152.1 : 164.8 232.4 498.6 549.3 781.7 815.5 1047.9 1200.0 316.9 : 67.6 333.8 384.5 616.9 650.7 883.1 1035.2 1200.0 384.5 : 266.2 316.9 549.3 583.1 815.5 967.6 1132.4 1200.0 650.7 : 50.7 283.1 316.9 549.3 701.4 866.2 933.8 1200.0 701.4 : 232.4 266.2 498.6 650.7 815.5 883.1 1149.3 1200.0 933.8 : 33.8 266.2 418.3 583.1 650.7 916.9 967.6 1200.0 967.6 : 232.4 384.5 549.3 616.9 883.1 933.8 1166.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.8028 .. 266.1972 cents 232.39438 cents 33.80281 cents 2: 232.3944 .. 384.5070 cents 152.11269 cents -33.80283 cents 3: 316.9014 .. 549.2958 cents 232.39438 cents -67.60565 cents 4: 549.2958 .. 650.7042 cents 101.40846 cents -0.00001 cents 5: 650.7042 .. 883.0986 cents 232.39438 cents -0.00001 cents 6: 815.4930 .. 967.6056 cents 152.11269 cents -67.60565 cents 7: 933.8028 .. 1166.1972 cents 232.39438 cents -33.80283 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 33.80281 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 266.19719 cents Average / Smallest step : 4.437501 Largest / Average step : 1.774648 Largest / Smallest step : 7.875002 Median interval of one step : 158.45071 cents, amount: 0 Most common interval of one step : 232.39437 cents, amount: 2 Least squares average step : 147.18310 cents, oct.: 1177.46479 cents Scale is not proper Scale is a mode of a 284-tone equal temperament with octave 2/1 degrees: 36 75 91 154 166 221 229 284 Least number of segments generator : 143 of 604.225 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 193 of 815.493 cents and inv. generated superset size: 101 = 93 more = 1262.500% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFGF Step pattern size order : DECGBFAF Scale is not a Constant Structure Scale diversity : 1.514313 Lumma stability : 0.056338 Lumma impropriety factor : 0.169014 Rothenberg efficiency : 0.378571 redundancy: 0.621429 Efficiency x scale size : 3.028571 Number of different interval sizes : 30 = 4.28571 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 5.71429 = 40/7 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 12.67605 cents Most common intervals : 549.29578 cents & inv., amount: 4 Number of recognisable fifths : 2, average 701.4084 cents Formal octave complements present : 1 = 12.5000% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
8: 1 1 0 2 0 2 0 2 N T3 SD: 57.0080 c. M: 101.4084 c. 9: 1 1 1 2 0 2 0 2 N D3 SD: 26.8161 c. M: 50.2347 c. 14: 2 2 0 4 0 3 0 3 N SD: 24.8697 c. M: 41.6499 c. 15: 2 2 1 3 1 3 0 3 N SD: 13.7668 c. M:-26.1972 c. 19: 2 3 1 4 1 4 0 4 N SD: 14.5837 c. M: 25.7969 c. 22: 3 3 1 5 1 4 1 4 N SD: 8.4113 c. M:-14.2126 c. 31: 4 4 2 7 1 6 1 6 N SD: 4.5380 c. M:-7.3603 c. 41: 5 6 2 9 2 8 1 8 N SD: 4.0789 c. M: 6.8018 c. 46: 6 6 3 10 2 9 1 9 N SD: 3.9594 c. M:-6.7973 c. 53: 7 7 3 12 2 10 2 10 N SD: 4.2114 c. M:-6.3779 c. 57: 7 8 3 13 2 11 2 11 N SD: 4.4665 c. M: 7.4870 c. 63: 8 9 3 14 3 12 2 12 N SD: 3.4646 c. M:-6.9081 c. 68: 9 9 4 15 3 13 2 13 N SD: 3.4574 c. M:-6.7108 c. 72: 9 10 4 16 3 14 2 14 N SD: 1.0885 c. M: 2.1127 c. 118: 15 16 7 26 5 23 3 23 N SD: 1.2352 c. M:-1.9336 c. 140: 18 19 8 31 6 27 4 27 N SD: 1.1196 c. M:-2.1730 c. 166: 21 23 9 37 7 32 5 32 N SD: 0.8781 c. M: 1.3745 c. 181: 23 25 10 40 8 35 5 35 N SD: 0.8541 c. M:-1.3540 c. 190: 24 26 11 42 8 37 5 37 N SD: 0.7736 c. M: 1.2898 c. 212: 27 29 12 47 9 41 6 41 N SD: 0.3697 c. M:-0.7175 c. 284: 36 39 16 63 12 55 8 55 N 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: 0.2733 cents 3 x x 4 x x 5 x 6 S SD: 41.2790 cents 4 x x 5 x 6 x 7:8 S SD: 0.5619 cents 5 x 6 x 7:8 x 9:10 S SD: 28.1120 cents 6 x 7:8 x 9:10:11:12 S SD: 26.0998 cents 7:8 x 9:10:11:12 x 14 S SD: 21.4003 cents 8:9 x 10 x 12 x 14:16 S SD: 10.3692 cents 9:10:11 x 13:14:15:16:18 SD: 13.8032 cents 10:11:12 x x 15:17 x 20 SD: 3.9897 cents 11:12:13:14:16:17:19 x 22 SD: 9.8391 cents 12:13:14:15:17:18 x 21:24 SD: 10.0682 cents 13:14 x 16:19:20:22:23:26 SD: 9.1895 cents 14:15:17 x 20:21:24 x 28 SD: 8.4016 cents 15:16:18:19:22 x x 26:30 SD: 8.5507 cents 16:17:19:20:23:24:27:28:32 SD: 7.7946 cents 17:19:20:21:25 x 29:30:34 SD: 8.8836 cents 18:20:22 x 26:27:31 x 36 SD: 7.6386 cents 19:21:23:24:28 x x 33:38 SD: 6.6710 cents 20:22:24:25:29:30:34:35:40 SD: 2.6753 cents 21:23:25:26:31 x 36:37:42 SD: 4.9414 cents 22:24:26:27:32:33:38 x 44 SD: 6.1021 cents 24:26:29:30:35:36:41:42:48 SD: 2.3529 cents 26:28:31:32:38:39:45 x 52 SD: 5.7849 cents 28:31:34:35:41:42:48:49:56 SD: 4.0442 cents 31:34:37:39:45:46:53:54:62 SD: 3.4811 cents 32:35:38:40:47:48:55:56:64 SD: 3.1222 cents 35:38:42:44:51:52:60:61:70 SD: 2.8648 cents 40:44:48:50:58:60:69:70:80 SD: 2.2723 cents 44:48:53:55:64:66:75:77:88 SD: 1.5325 cents 64:70:77:80:93:96:110:112:128 SD: 0.9115 cents 88:96:106:110:128:132:151:154:176 SD: 0.7924 cents 108:118:130:135:157:162:185:189:216 SD: 0.7528 cents 120:131:144:150:175:180:206:210:240 SD: 0.4978 cents 140:153:168:175:204:210:240:245:280 SD: 0.4114 cents 164:179:197:205:239:246:281:287:328 SD: 0.3891 cents 228:249:274:285:332:342:391:399:456 SD: 0.3273 cents 250:273:300:312:364:375:429:437:500 SD: 0.2699 cents 274:299:329:342:399:411:470:479:548 SD: 0.1877 cents 294:321:353:367:428:441:504:514:588 SD: 0.1606 cents 414:452:497:517:603:621:710:724:828 SD: 0.1082 cents