Scala analysis: keen3
Keenanismic tempering of [6/5, 11/8, 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: 316.901 cents 316.901410 2: 549.296 cents 549.295770 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: 316.9014 cents 316.9014 2: 232.3944 cents 232.3944 3: 152.1127 cents 152.1127 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: 1 384.50704 cents 2: 1 418.30986 cents 2: 1 498.59155 cents 2: 2 549.29577 cents 3: 2 650.70422 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: 2 967.60563 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 : 316.9 549.3 701.4 967.6 1200.0 316.9 : 232.4 384.5 650.7 883.1 1200.0 549.3 : 152.1 418.3 650.7 967.6 1200.0 701.4 : 266.2 498.6 815.5 1047.9 1200.0 967.6 : 232.4 549.3 781.7 933.8 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 .. 549.2958 cents 164.78873 cents 67.60563 cents 3: 650.7042 .. 815.4930 cents 164.78874 cents 101.40845 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 : 243.45711 cents, oct.: 1217.28553 cents Scale is strictly proper Scale is a mode of a 284-tone equal temperament with octave 2/1 degrees: 75 130 166 229 284 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: 56 = 51 more = 1120.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDB Step pattern size order : DBACB 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 : 33.80281 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: 47.1577 c. M: 76.9014 c. 7: 2 1 1 2 1 P M ME S SD: 34.2419 c. M:-60.9658 c. Thai mode 6 9: 2 2 1 2 2 SP M ME I SD: 32.1245 c. M: 50.2347 c. 10: 3 2 1 2 2 P T3 SD: 31.0866 c. M:-50.7042 c. 11: 3 2 1 3 2 P T3 SD: 22.4520 c. M: 46.8630 c. 13: 3 3 2 2 3 SP D3 S SD: 31.5427 c. M: 44.5287 c. 15: 4 3 2 3 3 SP T3 SD: 10.2730 c. M:-18.5916 c. 22: 6 4 3 5 4 SP SD: 8.7560 c. M:-14.2126 c. 26: 7 5 3 6 5 SP SD: 5.3723 c. M: 9.1008 c. 31: 8 6 4 7 6 SP SD: 5.0568 c. M: 7.3603 c. 41: 11 8 5 9 8 SP SD: 3.8961 c. M:-6.8018 c. 46: 12 9 6 10 9 SP SD: 2.5055 c. M: 3.8579 c. 72: 19 14 9 16 14 SP SD: 0.8266 c. M: 1.4084 c. 166: 44 32 21 37 32 SP SD: 0.7163 c. M:-1.1709 c. 197: 52 38 25 44 38 SP SD: 0.7530 c. M: 1.0724 c. 212: 56 41 27 47 41 SP SD: 0.2807 c. M:-0.4783 c. 284: 75 55 36 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: 32.5861 cents 4:5 x 6:7:8 S SD: 17.3563 cents 8:10:11:12:14:16 S SD: 13.8909 cents 10:12:14:15:17:20 SD: 11.8367 cents 14:17:19:21:24:28 SD: 8.9070 cents 16:19:22:24:28:32 SD: 3.9079 cents 24:29:33:36:42:48 SD: 2.1983 cents 40:48:55:60:70:80 SD: 0.5464 cents 134:161:184:201:234:268 SD: 0.5414 cents 144:173:198:216:252:288 SD: 0.5071 cents 150:180:206:225:262:300 SD: 0.4988 cents 164:197:225:246:287:328 SD: 0.4627 cents 174:209:239:261:304:348 SD: 0.3545 cents 204:245:280:306:357:408 SD: 0.3435 cents 214:257:294:321:374:428 SD: 0.2686 cents 254:305:349:381:444:508 SD: 0.2414 cents 338:406:464:507:591:676 SD: 0.2151 cents 354:425:486:531:619:708 SD: 0.1947 cents 378:454:519:567:661:756 SD: 0.1556 cents 418:502:574:627:731:836 SD: 0.1219 cents 458:550:629:687:801:916 SD: 0.1131 cents 573:688:787:859:1002:1146 SD: 0.1081 cents 597:717:820:895:1044:1194 SD: 0.0988 cents