Scala analysis: xen18-schulter-harrison-17-wt
17-WT realization of a JI scale of Lou Harrison
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 63.900 cents 63.900000 2: 492.780 cents 492.780000 3: 707.220 cents 707.220000 4: 771.120 cents 771.120000 5: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 428.8800 cents 428.8800 1: 63.9000 cents 63.9000 2: 428.8800 cents 428.8800 3: 214.4400 cents 214.4400 4: 63.9000 cents 63.9000 5: 428.8800 cents 428.8800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 63.90000 cents 1: 1 214.44000 cents 1: 2 428.88000 cents 2: 1 278.34000 cents 2: 3 492.78000 cents 2: 1 643.32000 cents 3: 1 556.68000 cents 3: 3 707.22000 cents 3: 1 921.66000 cents 4: 2 771.12000 cents 4: 1 985.56000 cents 4: 2 1136.10000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 63.9 492.8 707.2 771.1 1200.0 63.9 : 428.9 643.3 707.2 1136.1 1200.0 492.8 : 214.4 278.3 707.2 771.1 1200.0 707.2 : 63.9 492.8 556.7 985.6 1200.0 771.1 : 428.9 492.8 921.7 1136.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.9000 .. 428.8800 cents 364.98000 cents 63.90000 cents 2: 278.3400 .. 643.3200 cents 364.98000 cents -150.54000 cents 3: 556.6800 .. 921.6600 cents 364.98000 cents -86.64000 cents 4: 771.1200 .. 1136.1000 cents 364.98000 cents -150.54000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 63.90000 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 428.88000 cents Average / Smallest step : 3.755869 Largest / Average step : 1.787000 Largest / Smallest step : 6.711737 Median interval of one step : 214.44000 cents, amount: 1 Least squares average step : 222.82909 cents, oct.: 1114.14545 cents Scale is not proper Scale has trivalence property Scale is a mode of a 845-tone equal temperament with octave 1200.000 cents degrees: 45 347 498 543 845 Least number of segments generator : 423 of 600.710 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 498 of 707.219 cents and inv. generated superset size: 7 = 2 more = 140.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCAB Step pattern size order : SLMSL Scale is a Constant Structure, by a margin of 63.90000 cents Scale diversity : 1.490313 Lumma stability : 0.106500 Lumma impropriety factor : 0.323100 Rothenberg efficiency : 0.580000 redundancy: 0.420000 Efficiency x scale size : 2.900000 Number of different interval sizes : 12 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 63.90000 cents Most common intervals : 492.78000 cents & inv., amount: 3 Scale is a chain of 2 triads 0.0 63.900 492.780 cents Number of recognisable fifths : 3, average 707.2200 cents Formal octave complements present : 3 = 60.0000% -- Rational properties --
FIT/MODE
5: 0 2 1 0 2 N T3 SD: 37.4783 c. M: 63.9000 c. 10: 1 3 2 0 4 N SD: 34.8916 c. M:-56.1000 c. 12: 1 4 2 1 4 N T3 SD: 21.1732 c. M:-36.1000 c. Hon-kumoi-joshi, Sakura, Akebono II: Japan, Olympos Enharmonic, Raga Gunakri (Gunakali), Latantapriya, Salanganata, Saveri, Ambassel: Ethiopia 13: 1 4 3 0 5 N SD: 27.6609 c. M: 32.6585 c. 14: 1 5 2 1 5 N T3 SD: 16.7389 c. M:-21.8143 c. 15: 1 5 3 1 5 N T3 SD: 16.8518 c. M:-28.8800 c. 17: 1 6 3 1 6 N T3 SD: 3.9228 c. M:-6.6882 c. 39: 2 14 7 2 14 N T3 SD: 1.3851 c. M: 2.3615 c. 56: 3 20 10 3 20 N T3 SD: 0.2262 c. M:-0.3857 c. 151: 8 54 27 8 54 N T3 SD: 0.1899 c. M: 0.3238 c. 207: 11 74 37 11 74 N T3 SD: 0.0774 c. M: 0.1319 c. 263: 14 94 47 14 94 N T3 SD: 0.0127 c. M: 0.0217 c. 582: 31 208 104 31 208 N T3 SD: 0.0103 c. M:-0.0175 c. 845: 45 302 151 45 302 N T3 SD: 0.0031 c. M:-0.0053 c. 1108: 59 396 198 59 396 N T3 SD: 0.0006 c. M: 0.0011 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 2.6325 cents 3 x 4 x 5:6 S SD: 37.7870 cents 4 x 5:6 x 8 S SD: 35.5321 cents 5 x 7 x 8:10 SD: 33.1055 cents 6:7:8:9 x 12 S SD: 50.7769 cents 7:8:9 x 11:14 SD: 44.3274 cents 8:9:11:12 x 16 SD: 37.9615 cents 9:10:12 x 14:18 SD: 29.6957 cents 10:11:13:15:16:20 SD: 23.2800 cents 11:12:15 x 17:22 SD: 24.7235 cents 12:13:16:18:19:24 SD: 15.7844 cents 13:14:17 x 20:26 SD: 18.6962 cents 14:15:19:21:22:28 SD: 13.4631 cents 15:16:20 x 23:30 SD: 14.3258 cents 16:17:21:24:25:32 SD: 9.3798 cents 18:19:24:27:28:36 SD: 6.2488 cents 21:22:28:32:33:42 SD: 6.0590 cents 22:23:29:33:34:44 SD: 5.3467 cents 24:25:32:36:37:48 SD: 4.7897 cents 25:26:33:38:39:50 SD: 4.3677 cents 27:28:36:41:42:54 SD: 3.5909 cents 28:29:37:42:44:56 SD: 3.3001 cents 30:31:40:45:47:60 SD: 2.3979 cents 48:50:64:72:75:96 SD: 2.0355 cents 52:54:69:78:81:104 SD: 1.4685 cents 55:57:73:83:86:110 SD: 1.3532 cents 73:76:97:110:114:146 SD: 1.2893 cents 79:82:105:119:123:158 SD: 1.0211 cents 103:107:137:155:161:206 SD: 0.6394 cents 107:111:142:161:167:214 SD: 0.5804 cents 109:113:145:164:170:218 SD: 0.5188 cents 137:142:182:206:214:274 SD: 0.5157 cents 155:161:206:233:242:310 SD: 0.4879 cents 182:189:242:274:284:364 SD: 0.4028 cents 210:218:279:316:328:420 SD: 0.3043 cents 212:220:282:319:331:424 SD: 0.2455 cents 264:274:351:397:412:528 SD: 0.2442 cents 319:331:424:480:498:638 SD: 0.0464 cents