Scala analysis: keen6
Keenanismic tempering of [12/11, 5/4, 3/2, 7/4, 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: 967.606 cents 967.605630 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 232.3944 cents 232.3944 1: 152.1127 cents 152.1127 2: 232.3944 cents 232.3944 3: 316.9014 cents 316.9014 4: 266.1972 cents 266.1972 5: 232.3944 cents 232.3944
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: 2 384.50704 cents 2: 1 498.59155 cents 2: 1 549.29577 cents 2: 1 583.09859 cents 3: 1 616.90141 cents 3: 1 650.70423 cents 3: 1 701.40845 cents 3: 2 815.49295 cents 4: 1 883.09859 cents 4: 1 933.80282 cents 4: 2 967.60563 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 : 152.1 384.5 701.4 967.6 1200.0 152.1 : 232.4 549.3 815.5 1047.9 1200.0 384.5 : 316.9 583.1 815.5 967.6 1200.0 701.4 : 266.2 498.6 650.7 883.1 1200.0 967.6 : 232.4 384.5 616.9 933.8 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 .. 583.0986 cents 198.59155 cents 67.60563 cents 3: 616.9014 .. 815.4930 cents 198.59154 cents 33.80282 cents 4: 883.0986 .. 1047.8873 cents 164.78873 cents 67.60564 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 : 234.46863 cents, oct.: 1172.34315 cents Scale is strictly proper Scale is a mode of a 284-tone equal temperament with octave 2/1 degrees: 36 91 166 229 284 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: 55 = 50 more = 1100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDB Step pattern size order : ABDCB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 33.80282 cents Scale diversity : 1.596132 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.394366 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 : 33.80281 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: 58.7309 c. M:-95.4930 c. 6: 1 1 2 1 1 P M ME I SD: 51.5808 c. M:-98.5916 c. 7: 1 1 2 2 1 N D3 S SD: 34.8452 c. M:-60.9658 c. 9: 1 2 2 2 2 SP M ME S SD: 24.3897 c. M: 34.7418 c. 10: 1 2 3 2 2 P T3 SD: 20.1758 c. M: 32.1127 c. 15: 2 3 4 3 3 SP T3 SD: 11.8805 c. M:-18.5916 c. 22: 3 4 6 5 4 P SD: 8.9559 c. M:-14.2126 c. 31: 4 6 8 7 6 SP SD: 2.6696 c. M: 4.6343 c. 63: 8 12 17 14 12 SP SD: 2.7773 c. M:-3.8229 c. 72: 9 14 19 16 14 SP SD: 1.3196 c. M: 2.1127 c. 87: 11 17 23 19 17 SP SD: 1.5207 c. M: 2.0884 c. 94: 12 18 25 21 18 SP SD: 1.4706 c. M:-2.6071 c. 103: 13 20 27 23 20 SP SD: 1.1377 c. M: 2.3793 c. 118: 15 23 31 26 23 SP SD: 1.1196 c. M:-1.9336 c. 156: 20 30 41 35 30 SP SD: 1.2362 c. M:-1.7335 c. 159: 20 31 42 35 31 SP SD: 0.9180 c. M: 1.5679 c. 166: 21 32 44 37 32 SP SD: 0.7959 c. M: 1.3745 c. 181: 23 35 48 40 35 SP SD: 0.6474 c. M:-1.3540 c. 190: 24 37 50 42 37 SP SD: 0.7276 c. M: 1.2898 c. 197: 25 38 52 44 38 SP SD: 0.6716 c. M:-0.9223 c. 212: 27 41 56 47 41 SP SD: 0.4482 c. M:-0.7175 c. 253: 32 49 67 56 49 SP SD: 0.3271 c. M:-0.5678 c. 284: 36 55 75 63 55 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: 46.9289 cents 4 x 5:6:7:8 S SD: 0.5619 cents 5 x 6:8:9:10 S SD: 35.2206 cents 7:8:9:11:12:14 SD: 25.7464 cents 8:9:10:12:14:16 S SD: 10.3692 cents 12:13:15:18:21:24 SD: 2.7451 cents 20:22:25:30:35:40 SD: 2.6172 cents 32:35:40:48:56:64 SD: 0.7540 cents 44:48:55:66:77:88 SD: 0.5377 cents 76:83:95:114:133:152 SD: 0.4574 cents 120:131:150:180:210:240 SD: 0.4528 cents 196:214:245:294:343:392 SD: 0.4495 cents 206:225:257:309:360:412 SD: 0.4250 cents 218:238:272:327:381:436 SD: 0.3638 cents 238:260:297:357:416:476 SD: 0.3553 cents 250:273:312:375:437:500 SD: 0.2737 cents 262:286:327:393:458:524 SD: 0.2521 cents 282:308:352:423:493:564 SD: 0.2309 cents 294:321:367:441:514:588 SD: 0.1807 cents 326:356:407:489:570:652 SD: 0.1517 cents 338:369:422:507:591:676 SD: 0.1350 cents 370:404:462:555:647:740 SD: 0.1138 cents