Scala analysis: keen5
Keenanismic tempering of [6/5, 11/8, 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: 316.901 cents 316.901410 2: 549.296 cents 549.295770 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: 316.9014 cents 316.9014 2: 232.3944 cents 232.3944 3: 152.1127 cents 152.1127 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: 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: 2 815.49296 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 : 316.9 549.3 701.4 933.8 1200.0 316.9 : 232.4 384.5 616.9 883.1 1200.0 549.3 : 152.1 384.5 650.7 967.6 1200.0 701.4 : 232.4 498.6 815.5 1047.9 1200.0 933.8 : 266.2 583.1 815.5 967.6 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 .. 583.0986 cents 198.59155 cents 67.60563 cents 3: 616.9014 .. 815.4930 cents 198.59155 cents 33.80282 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 : 240.99872 cents, oct.: 1204.99360 cents Scale is strictly proper Scale is a mode of a 284-tone equal temperament with octave 2/1 degrees: 75 130 166 221 284 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: 55 = 50 more = 1100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBD Step pattern size order : DBABC 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 : 33.80282 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: 48.4720 c. M: 76.9014 c. 7: 2 1 1 1 2 N D3 I SD: 40.0561 c. M: 76.6600 c. 8: 2 2 1 1 2 P D3 S SD: 35.6661 c. M:-50.7042 c. 9: 2 2 1 2 2 SP M ME I SD: 28.2331 c. M: 50.2347 c. 10: 3 2 1 2 2 P T3 SD: 33.0465 c. M:-50.7042 c. 11: 3 2 1 3 2 P T3 SD: 30.4103 c. M:-48.0154 c. 12: 3 2 2 2 3 P D3 I SD: 27.7861 c. M: 49.2958 c. Minor added sixth Pentatonic, Kyemyonjo: Korea 13: 3 3 2 2 3 SP D3 S SD: 24.9277 c. M: 39.9783 c. 14: 4 2 2 3 3 P SD: 21.1078 c. M: 35.0101 c. 15: 4 3 2 3 3 SP T3 SD: 15.2060 c. M:-26.1972 c. 19: 5 4 2 4 4 SP T3 SD: 10.9137 c. M:-19.1253 c. 22: 6 4 3 4 5 P SD: 6.6930 c. M:-10.3713 c. 31: 8 6 4 6 7 SP SD: 5.4881 c. M: 7.3603 c. 41: 11 8 5 8 9 SP SD: 4.0142 c. M:-6.8018 c. 46: 12 9 6 9 10 SP SD: 3.2884 c. M:-5.3276 c. 68: 18 13 9 13 15 SP SD: 2.3580 c. M:-4.4739 c. 72: 19 14 9 14 16 SP SD: 0.7423 c. M: 1.4084 c. 166: 44 32 21 32 37 SP SD: 0.7801 c. M: 1.2727 c. 190: 50 37 24 37 42 SP SD: 0.6734 c. M: 1.1119 c. 212: 56 41 27 41 47 SP SD: 0.2521 c. M:-0.4783 c. 284: 75 55 36 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: 23.7378 cents 4:5 x 6:7:8 S SD: 19.4374 cents 6:7:8:9:10:12 S SD: 17.4066 cents 8:10:11:12:14:16 S SD: 15.5552 cents 10:12:14:15:17:20 SD: 7.3077 cents 14:17:19:21:24:28 SD: 5.6398 cents 24:29:33:36:41:48 SD: 2.5624 cents 40:48:55:60:69:80 SD: 2.0808 cents 46:55:63:69:79:92 SD: 1.8615 cents 54:65:74:81:93:108 SD: 1.8449 cents 56:67:77:84:96:112 SD: 1.3574 cents 64:77:88:96:110:128 SD: 1.0874 cents 70:84:96:105:120:140 SD: 0.5829 cents 134:161:184:201:230:268 SD: 0.3681 cents 190:228:261:285:326:380 SD: 0.3306 cents 204:245:280:306:350:408 SD: 0.2834 cents 214:257:294:321:367:428 SD: 0.1562 cents 284:341:390:426:487:568 SD: 0.1303 cents 498:598:684:747:854:996 SD: 0.1155 cents 597:717:820:895:1024:1194 SD: 0.1147 cents