Scala analysis: xen18-schulter-pelog-like
A Pelog-like pentatonic in 17-WT
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: 278.340 cents 278.340000 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: 214.4400 cents 214.4400 3: 428.8800 cents 428.8800 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 : 63.9 278.3 707.2 771.1 1200.0 63.9 : 214.4 643.3 707.2 1136.1 1200.0 278.3 : 428.9 492.8 921.7 985.6 1200.0 707.2 : 63.9 492.8 556.7 771.1 1200.0 771.1 : 428.9 492.8 707.2 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 : 215.03127 cents, oct.: 1075.15636 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: 45 196 498 543 845 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: ABCAC Step pattern size order : SMLSL Scale is sum-free (all different intervals) 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 0.0 428.880 492.780 cents Number of recognisable fifths : 3, average 707.2200 cents Formal octave complements present : 1 = 20.0000% -- Rational properties --
FIT/MODE
5: 0 1 2 0 2 N T3 SD: 40.8160 c. M: 63.9000 c. 8: 0 2 3 0 3 N T3 SD: 36.9555 c. M: 63.9000 c. 9: 0 2 3 1 3 N SD: 36.6008 c. M: 63.9000 c. 12: 1 2 4 1 4 N T3 SD: 23.0588 c. M:-36.1000 c. Phrygian Pentatonic, Balinese Pelog, Madenda Modern, Raga Bhupalam, Bhupala Todi, Bibhas 13: 1 2 5 0 5 N SD: 23.8814 c. M: 32.6585 c. 14: 1 2 5 1 5 N T3 SD: 16.6600 c. M:-21.8143 c. 17: 1 3 6 1 6 N T3 SD: 4.2721 c. M:-6.6882 c. 39: 2 7 14 2 14 N T3 SD: 1.5084 c. M: 2.3615 c. 56: 3 10 20 3 20 N T3 SD: 0.2464 c. M:-0.3857 c. 151: 8 27 54 8 54 N T3 SD: 0.2069 c. M: 0.3238 c. 207: 11 37 74 11 74 N T3 SD: 0.0842 c. M: 0.1319 c. 263: 14 47 94 14 94 N T3 SD: 0.0138 c. M: 0.0217 c. 582: 31 104 208 31 208 N T3 SD: 0.0112 c. M:-0.0175 c. 845: 45 151 302 45 302 N T3 SD: 0.0034 c. M:-0.0053 c. 1108: 59 198 396 59 396 N T3 SD: 0.0007 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 x x 5:6 SD: 56.6194 cents 4 x 5:6 x 8 S SD: 36.0340 cents 5 x 6 x 8:10 S SD: 18.8658 cents 6 x 7:9 x 12 SD: 4.2066 cents 7 x 8 x 11:14 SD: 16.1725 cents 8 x 9:12 x 16 S SD: 24.8720 cents 9 x 11 x 14:18 SD: 23.1153 cents 11:12:13 x 17:22 SD: 22.2866 cents 12:13:14:18:19:24 SD: 15.9154 cents 13:14:15 x 20:26 SD: 18.9163 cents 14:15:16:21:22:28 SD: 14.7874 cents 15:16:18 x 23:30 SD: 17.0428 cents 16:17:19:24:25:32 SD: 9.1283 cents 18:19:21:27:28:36 SD: 6.5727 cents 22:23:26:33:34:44 SD: 4.9879 cents 23:24:27:35:36:46 SD: 4.4835 cents 28:29:33:42:44:56 SD: 2.8583 cents 46:48:54:69:72:92 SD: 2.4028 cents 50:52:59:75:78:100 SD: 2.1226 cents 52:54:61:78:81:104 SD: 1.3910 cents 57:59:67:86:89:114 SD: 1.3156 cents 75:78:88:113:117:150 SD: 1.0197 cents 103:107:121:155:161:206 SD: 0.6114 cents 109:113:128:164:170:218 SD: 0.4513 cents 184:191:216:277:287:368 SD: 0.4181 cents 212:220:249:319:331:424 SD: 0.0763 cents 533:553:626:802:832:1066 SD: 0.0557 cents