Scala analysis: keen2
Keenanismic tempering of [8/7, 5/4, 11/8, 12/7, 2], 284et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 232.394 cents 232.394370 2: 384.507 cents 384.507040 3: 549.296 cents 549.295770 4: 933.803 cents 933.802820 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 266.1972 cents 266.1972 1: 232.3944 cents 232.3944 2: 152.1127 cents 152.1127 3: 164.7887 cents 164.7887 4: 384.5071 cents 384.5071 5: 266.1972 cents 266.1972
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 152.11267 cents 1: 1 164.78873 cents 1: 1 232.39437 cents 1: 1 266.19718 cents 1: 1 384.50705 cents 2: 1 316.90140 cents 2: 1 384.50704 cents 2: 1 498.59155 cents 2: 1 549.29578 cents 2: 1 650.70423 cents 3: 1 549.29577 cents 3: 1 650.70422 cents 3: 1 701.40845 cents 3: 1 815.49296 cents 3: 1 883.09860 cents 4: 1 815.49295 cents 4: 1 933.80282 cents 4: 1 967.60563 cents 4: 1 1035.21127 cents 4: 1 1047.88733 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 232.4 384.5 549.3 933.8 1200.0 232.4 : 152.1 316.9 701.4 967.6 1200.0 384.5 : 164.8 549.3 815.5 1047.9 1200.0 549.3 : 384.5 650.7 883.1 1035.2 1200.0 933.8 : 266.2 498.6 650.7 815.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 152.1127 .. 384.5071 cents 232.39438 cents 152.11267 cents 2: 316.9014 .. 650.7042 cents 333.80283 cents -67.60565 cents 3: 549.2958 .. 883.0986 cents 333.80283 cents -101.40846 cents 4: 815.4929 .. 1047.8873 cents 232.39438 cents -67.60565 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 152.11267 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 384.50705 cents Average / Smallest step : 1.577778 Largest / Average step : 1.602113 Largest / Smallest step : 2.527778 Median interval of one step : 232.39437 cents, amount: 1 Least squares average step : 225.17286 cents, oct.: 1125.86428 cents Scale is not proper Scale is a mode of a 284-tone equal temperament with octave 2/1 degrees: 55 91 130 221 284 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: 59 = 54 more = 1180.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : CABED Scale is not a Constant Structure Scale diversity : 1.577122 Lumma stability : 0.253521 Lumma impropriety factor : 0.197183 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 : 5 Highest interval variety : 5 Mean interval variety : 5.00000 = 5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 12.67606 cents Number of recognisable fifths : 1, average 701.4085 cents Formal octave complements present : 1 = 20.0000% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
5: 1 1 0 2 1 N T3 SD: 54.1571 c. M:-95.4930 c. 6: 1 1 1 2 1 P M ME S SD: 40.6015 c. M:-66.1972 c. 9: 2 1 1 3 2 N SD: 18.2737 c. M:-34.2723 c. 15: 3 2 2 5 3 N SD: 14.8240 c. M:-26.1972 c. 19: 4 2 3 6 4 N SD: 14.0731 c. M:-20.2372 c. 22: 4 3 3 7 5 N SD: 7.3024 c. M: 14.2126 c. 31: 6 4 4 10 7 N SD: 4.0904 c. M: 7.3603 c. 37: 7 5 5 12 8 N SD: 4.4800 c. M:-6.7377 c. 41: 8 5 6 13 9 N SD: 3.8270 c. M:-6.8018 c. 46: 9 6 6 15 10 N SD: 4.0608 c. M:-6.7973 c. 50: 10 6 7 16 11 N SD: 3.7482 c. M:-7.6056 c. 53: 10 7 7 17 12 N SD: 4.4939 c. M: 5.9793 c. 57: 11 7 8 18 13 N SD: 4.2742 c. M: 7.4870 c. 59: 11 8 8 19 13 N SD: 4.0511 c. M: 8.6656 c. 63: 12 8 9 20 14 N SD: 2.7199 c. M: 3.8229 c. 68: 13 9 9 22 15 N SD: 2.4505 c. M:-3.7283 c. 72: 14 9 10 23 16 N SD: 0.7714 c. M: 1.1737 c. 175: 34 22 24 56 39 N SD: 0.7561 c. M: 1.2314 c. 181: 35 23 25 58 40 N SD: 0.6469 c. M:-1.0038 c. 212: 41 27 29 68 47 N SD: 0.2620 c. M:-0.3986 c. 284: 55 36 39 91 63 N 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: 76.3296 cents 3 x x 4:5:6 S SD: 23.7378 cents 4 x 5:6:7:8 S SD: 39.1589 cents 5 x 6:7:9:10 SD: 28.3584 cents 6:7 x 8:10:12 S SD: 19.7800 cents 7:8:9:10:12:14 S SD: 16.9825 cents 8:9:10:11:14:16 SD: 9.0451 cents 13:15:16:18:22:26 SD: 7.9756 cents 19:22:24:26:33:38 SD: 7.4226 cents 20:23:25:27:34:40 SD: 6.9552 cents 21:24:26:29:36:42 SD: 3.5218 cents 35:40:44:48:60:70 S SD: 2.4026 cents 48:55:60:66:82:96 SD: 1.5869 cents 56:64:70:77:96:112 SD: 0.6098 cents 153:175:191:210:262:306 SD: 0.5636 cents 161:184:201:221:276:322 SD: 0.3403 cents 217:248:271:298:372:434 SD: 0.2836 cents 257:294:321:353:441:514 SD: 0.2431 cents 313:358:391:430:537:626 SD: 0.2264 cents 354:405:442:486:607:708 SD: 0.1885 cents 362:414:452:497:621:724 SD: 0.1588 cents 410:469:512:563:703:820 SD: 0.1146 cents 418:478:522:574:717:836 SD: 0.0988 cents