Scala analysis: Ethiopia_AI_544_14_1939
AI 544/14 - 1939, Ethiopia
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 339.000 cents 339.000000 2: 507.000 cents 507.000000 3: 682.000 cents 682.000000 4: 1043.000 cents 1043.000000 5: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 157.0000 cents 157.0000 1: 339.0000 cents 339.0000 2: 168.0000 cents 168.0000 3: 175.0000 cents 175.0000 4: 361.0000 cents 361.0000 5: 157.0000 cents 157.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 157.00000 cents 1: 1 168.00000 cents 1: 1 175.00000 cents 1: 1 339.00000 cents 1: 1 361.00000 cents 2: 1 343.00000 cents 2: 1 496.00000 cents 2: 1 507.00000 cents 2: 1 518.00000 cents 2: 1 536.00000 cents 3: 1 664.00000 cents 3: 1 682.00000 cents 3: 1 693.00000 cents 3: 1 704.00000 cents 3: 1 857.00000 cents 4: 1 839.00000 cents 4: 1 861.00000 cents 4: 1 1025.00000 cents 4: 1 1032.00000 cents 4: 1 1043.00000 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 : 339.0 507.0 682.0 1043.0 1200.0 339.0 : 168.0 343.0 704.0 861.0 1200.0 507.0 : 175.0 536.0 693.0 1032.0 1200.0 682.0 : 361.0 518.0 857.0 1025.0 1200.0 1043.0: 157.0 496.0 664.0 839.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 157.0000 .. 361.0000 cents 204.00000 cents 157.00000 cents 2: 343.0000 .. 536.0000 cents 193.00000 cents -18.00000 cents 3: 664.0000 .. 857.0000 cents 193.00000 cents 128.00000 cents 4: 839.0000 .. 1043.0000 cents 204.00000 cents -18.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 157.00000 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 361.00000 cents Average / Smallest step : 1.528662 Largest / Average step : 1.504167 Largest / Smallest step : 2.299363 Median interval of one step : 175.00000 cents, amount: 1 Least squares average step : 246.74545 cents, oct.: 1233.72727 cents Scale is not proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 339 507 682 1043 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 631 of 631.000 cents and inv. generated superset size: 73 = 68 more = 1460.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : DBCEA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 4.00000 cents Scale diversity : 1.372729 Lumma stability : 0.368333 Lumma impropriety factor : 0.030000 Rothenberg efficiency : 0.400000 redundancy: 0.600000 Efficiency x scale size : 2.000000 Number of different interval sizes : 20 = 5.00000 / 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 : 4.00000 cents Number of recognisable fifths : 2, average 698.5000 cents Best fifths form a closed circle Formal octave complements present : 1 = 20.0000% Limited inverse transpositions with margin 204.0000 cents: 4 -- Rational properties --
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 61.4215 c. M: 99.0000 c. 7: 2 1 1 2 1 P M ME S SD: 7.6150 c. M: 14.4286 c. Thai mode 6 33: 9 5 5 10 4 P SD: 8.4210 c. M: 11.7273 c. 36: 10 5 5 11 5 N T3 SD: 9.0517 c. M: 15.3333 c. 38: 11 5 6 11 5 P T3 SD: 6.8713 c. M:-12.7368 c. 40: 11 6 6 12 5 P SD: 6.3718 c. M: 9.0000 c. 42: 12 6 6 13 5 N SD: 7.5070 c. M:-14.1429 c. 43: 12 6 6 13 6 N T3 SD: 7.7131 c. M: 12.2326 c. 45: 13 6 7 13 6 P T3 SD: 6.2663 c. M:-11.3333 c. 46: 13 6 7 14 6 N SD: 5.3479 c. M: 11.3478 c. 47: 13 7 7 14 6 P SD: 5.1407 c. M:-7.3617 c. 49: 14 7 7 15 6 N SD: 6.0495 c. M:-10.0612 c. 52: 15 7 8 15 7 P T3 SD: 5.9750 c. M:-10.3077 c. 53: 15 7 8 16 7 N SD: 4.2231 c. M: 8.8868 c. 54: 15 8 8 16 7 P SD: 4.4397 c. M:-6.8889 c. 56: 16 8 8 17 7 N SD: 5.1138 c. M:-7.2857 c. 60: 17 8 9 18 8 N SD: 3.5496 c. M: 7.0000 c. 61: 17 9 9 18 8 P SD: 4.0905 c. M:-6.5246 c. 63: 18 9 9 19 8 N SD: 4.5407 c. M:-7.2857 c. 64: 18 9 9 20 8 N SD: 4.4903 c. M: 7.0000 c. 67: 19 9 10 20 9 N SD: 3.2117 c. M: 5.5075 c. 74: 21 10 11 22 10 N SD: 3.1091 c. M: 5.1622 c. 78: 22 11 11 24 10 N SD: 2.7015 c. M: 5.0769 c. 85: 24 12 12 26 11 N SD: 2.1640 c. M: 4.3529 c. 92: 26 13 13 28 12 N SD: 1.8494 c. M: 3.7391 c. 99: 28 14 14 30 13 N SD: 1.7422 c. M: 3.2121 c. 100: 28 14 15 30 13 N SD: 2.1448 c. M: 3.0000 c. 102: 29 14 15 31 13 N SD: 2.1253 c. M:-4.0588 c. 106: 30 15 15 32 14 N SD: 1.7957 c. M: 2.7547 c. 107: 30 15 16 32 14 N SD: 1.8103 c. M: 2.5514 c. 109: 31 15 16 33 14 N SD: 1.6806 c. M:-2.8716 c. 114: 32 16 17 34 15 N SD: 1.6346 c. M:-2.2105 c. 116: 33 16 17 35 15 N SD: 1.3847 c. M:-2.3793 c. 123: 35 17 18 37 16 N SD: 1.2524 c. M:-2.4634 c. 178: 50 25 26 54 23 N SD: 1.4555 c. M:-1.9438 c. 183: 52 25 27 55 24 N SD: 1.2971 c. M: 2.0820 c. 185: 52 26 27 56 24 N SD: 1.1496 c. M: 1.7027 c. 192: 54 27 28 58 25 N SD: 0.8874 c. M: 1.5000 c. 199: 56 28 29 60 26 N SD: 0.6836 c. M: 1.3116 c. 206: 58 29 30 62 27 N SD: 0.5676 c. M: 1.1359 c. 213: 60 30 31 64 28 N SD: 0.5656 c. M: 0.9718 c. 315: 89 44 46 95 41 N SD: 0.3944 c. M:-0.8095 c. 322: 91 45 47 97 42 N SD: 0.2341 c. M:-0.4783 c. 329: 93 46 48 99 43 N SD: 0.1221 c. M:-0.2097 c. 857: 242 120 125 258 112 N SD: 0.1197 c. M:-0.1739 c. 864: 244 121 126 260 113 N SD: 0.0657 c. M: 0.1111 c. 871: 246 122 127 262 114 N SD: 0.0461 c. M: 0.0792 c. 1193: 337 167 174 359 156 N SD: 0.0447 c. M:-0.0847 c. 1200: 339 168 175 361 157 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: 9.9775 cents 3 x 4 x x 6 S SD: 4.4775 cents 4:5 x 6:7:8 S SD: 22.5535 cents 5:6:7 x 9:10 SD: 20.7561 cents 6:7:8:9:11:12 SD: 15.1281 cents 7 x 9:10:13:14 SD: 25.1961 cents 8:10:11:12:15:16 S SD: 16.3097 cents 9:11:12:13:16:18 SD: 13.2831 cents 10:12:13:15:18:20 SD: 13.2296 cents 12:15:16:18:22:24 SD: 10.5023 cents 14:17:19:21:26:28 SD: 8.2476 cents 15:18:20:22:27:30 SD: 8.0754 cents 17:21:23:25:31:34 SD: 6.9274 cents 18:22:24:27:33:36 SD: 4.8562 cents 23:28:31:34:42:46 SD: 2.2470 cents 41:50:55:61:75:82 SD: 1.5944 cents 56:68:75:83:102:112 SD: 1.1757 cents 70:85:94:104:128:140 SD: 1.1750 cents 74:90:99:110:135:148 SD: 1.1454 cents 79:96:106:117:144:158 SD: 0.9785 cents 97:118:130:144:177:194 SD: 0.5391 cents 120:146:161:178:219:240 SD: 0.5029 cents 162:197:217:240:296:324 SD: 0.3862 cents 203:247:272:301:371:406 SD: 0.2425 cents 259:315:347:384:473:518 SD: 0.1492 cents 323:393:433:479:590:646 SD: 0.1482 cents 379:461:508:562:692:758 SD: 0.1468 cents 462:562:619:685:844:924 SD: 0.1283 cents 485:590:650:719:886:970 SD: 0.1034 cents 582:708:780:863:1063:1164 SD: 0.0628 cents