Scala analysis: keen4
Keenanismic tempering of [12/11, 5/4, 3/2, 12/7, 2], 284et tuning
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: 384.507 cents 384.507040 3: 701.408 cents 701.408450 4: 933.803 cents 933.802820 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 266.1972 cents 266.1972 1: 152.1127 cents 152.1127 2: 232.3944 cents 232.3944 3: 316.9014 cents 316.9014 4: 232.3944 cents 232.3944 5: 266.1972 cents 266.1972
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 152.11268 cents 1: 2 232.39436 cents 1: 1 266.19718 cents 1: 1 316.90141 cents 2: 1 384.50704 cents 2: 1 418.30986 cents 2: 1 498.59155 cents 2: 2 549.29577 cents 3: 2 650.70423 cents 3: 1 701.40845 cents 3: 1 781.69014 cents 3: 1 815.49296 cents 4: 1 883.09859 cents 4: 1 933.80282 cents 4: 2 967.60564 cents 4: 1 1047.88732 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 152.1 384.5 701.4 933.8 1200.0 152.1 : 232.4 549.3 781.7 1047.9 1200.0 384.5 : 316.9 549.3 815.5 967.6 1200.0 701.4 : 232.4 498.6 650.7 883.1 1200.0 933.8 : 266.2 418.3 650.7 967.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 152.1127 .. 316.9014 cents 164.78873 cents 152.11268 cents 2: 384.5070 .. 549.2958 cents 164.78873 cents 67.60563 cents 3: 650.7042 .. 815.4930 cents 164.78873 cents 101.40846 cents 4: 883.0986 .. 1047.8873 cents 164.78873 cents 67.60563 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 152.11268 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 316.90141 cents Average / Smallest step : 1.577778 Largest / Average step : 1.320423 Largest / Smallest step : 2.083333 Median interval of one step : 232.39436 cents, amount: 2 Most common interval of one step : 232.39436 cents, amount: 2 Least squares average step : 232.01024 cents, oct.: 1160.05122 cents Scale is strictly proper Scale is a mode of a 284-tone equal temperament with octave 2/1 degrees: 36 91 166 221 284 Least number of segments generator : 143 of 604.225 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 229 of 967.606 cents and inv. generated superset size: 56 = 51 more = 1120.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBD Step pattern size order : ABDBC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 67.60563 cents Scale diversity : 1.619071 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.450704 Rothenberg efficiency : 0.480000 redundancy: 0.520000 Efficiency x scale size : 2.400000 Number of different interval sizes : 16 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 33.80282 cents Number of recognisable fifths : 1, average 701.4084 cents Best fifths form a closed circle Formal octave complements present : 1 = 20.0000% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 59.7913 c. M:-95.4930 c. 6: 1 1 2 1 1 P M ME I SD: 57.6812 c. M:-98.5916 c. 7: 1 1 2 1 2 P M ME S SD: 40.5731 c. M: 76.6600 c. Thai mode 1 8: 1 2 2 1 2 P M ME S SD: 39.4907 c. M:-65.4930 c. 9: 1 2 2 2 2 SP M ME S SD: 18.9732 c. M: 34.7418 c. 10: 1 2 3 2 2 P T3 SD: 23.0814 c. M: 32.1127 c. 14: 2 2 4 3 3 P SD: 22.0731 c. M: 41.6499 c. 15: 2 3 4 3 3 SP T3 SD: 16.3351 c. M:-26.1972 c. 19: 2 4 5 4 4 SP T3 SD: 13.6009 c. M: 25.7969 c. 21: 3 4 5 4 5 SP T3 SD: 15.7503 c. M: 19.5171 c. 22: 3 4 6 4 5 SP SD: 6.9525 c. M:-11.5237 c. 31: 4 6 8 6 7 SP SD: 3.4168 c. M: 4.7706 c. 41: 5 8 11 8 9 SP SD: 3.4137 c. M: 5.7712 c. 63: 8 12 17 12 14 SP SD: 2.1988 c. M: 3.5547 c. 72: 9 14 19 14 16 SP SD: 1.2685 c. M: 2.1127 c. 94: 12 18 25 18 21 SP SD: 1.2313 c. M: 1.8879 c. 118: 15 23 31 23 26 SP SD: 1.2009 c. M:-1.9336 c. 135: 17 26 36 26 30 SP SD: 1.1922 c. M: 2.2848 c. 149: 19 29 39 29 33 SP SD: 1.0801 c. M:-2.0701 c. 166: 21 32 44 32 37 SP SD: 0.8537 c. M: 1.3745 c. 181: 23 35 48 35 40 SP SD: 0.7721 c. M:-1.3540 c. 190: 24 37 50 37 42 SP SD: 0.6092 c. M:-0.9340 c. 212: 27 41 56 41 47 SP SD: 0.4308 c. M:-0.7175 c. 253: 32 49 67 49 56 SP SD: 0.4187 c. M:-0.5845 c. 284: 36 55 75 55 63 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 0.2733 cents 3 x 4 x 5:6 S SD: 41.2790 cents 4 x 5:6:7:8 S SD: 8.7685 cents 5 x 6:8:9:10 S SD: 39.0274 cents 6:7:8:9:10:12 S SD: 33.7670 cents 7:8:9:11:12:14 SD: 24.8062 cents 8:9:10:12:14:16 S SD: 12.5110 cents 12:13:15:18:21:24 SD: 7.5193 cents 20:22:25:30:34:40 SD: 3.9981 cents 24:26:30:36:41:48 SD: 3.0445 cents 32:35:40:48:55:64 SD: 1.0466 cents 56:61:70:84:96:112 SD: 0.9044 cents 88:96:110:132:151:176 SD: 0.5166 cents 120:131:150:180:206:240 SD: 0.5149 cents 140:153:175:210:240:280 SD: 0.5145 cents 164:179:205:246:281:328 SD: 0.5033 cents 186:203:232:279:319:372 SD: 0.4237 cents 196:214:245:294:336:392 SD: 0.4008 cents 218:238:272:327:374:436 SD: 0.3242 cents 250:273:312:375:429:500 SD: 0.3106 cents 270:295:337:405:463:540 SD: 0.3047 cents 274:299:342:411:470:548 SD: 0.2732 cents 294:321:367:441:504:588 SD: 0.2055 cents 326:356:407:489:559:652 SD: 0.1470 cents 382:417:477:573:655:764 SD: 0.1420 cents 414:452:517:621:710:828 SD: 0.1138 cents