Scala analysis: Ethiopia_Mus_03_Yammatbal
Mus 3 Yammatbal, Ethiopia
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 330.000 cents 330.000000 2: 521.000 cents 521.000000 3: 718.000 cents 718.000000 4: 1038.000 cents 1038.000000 5: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 162.0000 cents 162.0000 1: 330.0000 cents 330.0000 2: 191.0000 cents 191.0000 3: 197.0000 cents 197.0000 4: 320.0000 cents 320.0000 5: 162.0000 cents 162.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 162.00000 cents 1: 1 191.00000 cents 1: 1 197.00000 cents 1: 1 320.00000 cents 1: 1 330.00000 cents 2: 1 388.00000 cents 2: 1 482.00000 cents 2: 1 492.00000 cents 2: 1 517.00000 cents 2: 1 521.00000 cents 3: 1 679.00000 cents 3: 1 683.00000 cents 3: 1 708.00000 cents 3: 1 718.00000 cents 3: 1 812.00000 cents 4: 1 870.00000 cents 4: 1 880.00000 cents 4: 1 1003.00000 cents 4: 1 1009.00000 cents 4: 1 1038.00000 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 : 330.0 521.0 718.0 1038.0 1200.0 330.0 : 191.0 388.0 708.0 870.0 1200.0 521.0 : 197.0 517.0 679.0 1009.0 1200.0 718.0 : 320.0 482.0 812.0 1003.0 1200.0 1038.0: 162.0 492.0 683.0 880.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 162.0000 .. 330.0000 cents 168.00000 cents 162.00000 cents 2: 388.0000 .. 521.0000 cents 133.00000 cents 58.00000 cents 3: 679.0000 .. 812.0000 cents 133.00000 cents 158.00000 cents 4: 870.0000 .. 1038.0000 cents 168.00000 cents 58.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 162.00000 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 330.00000 cents Average / Smallest step : 1.481481 Largest / Average step : 1.375000 Largest / Smallest step : 2.037037 Median interval of one step : 197.00000 cents, amount: 1 Least squares average step : 248.69091 cents, oct.: 1243.45455 cents Scale is strictly proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 330 521 718 1038 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 731 of 731.000 cents and inv. generated superset size: 194 = 189 more = 3880.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : EBCDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 58.00000 cents Scale diversity : 1.468269 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.498333 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 713.0000 cents Number of appreciable fifths : 1, average 708.0000 cents Best fifths form a closed circle Formal octave complements present : 1 = 20.0000% Limited inverse transpositions with margin 158.0000 cents: 4 -- Rational properties --
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 56.3365 c. M: 90.0000 c. 7: 2 1 1 2 1 P M ME S SD: 16.3808 c. M: 32.2857 c. Thai mode 6 16: 4 3 3 4 2 SP D3 S SD: 20.4157 c. M:-32.0000 c. 17: 5 2 3 5 2 P T3 SD: 19.1281 c. M: 26.8824 c. 18: 5 3 3 5 2 SP T3 S SD: 15.6212 c. M:-28.6667 c. 19: 5 3 3 5 3 SP M DE S SD: 18.6846 c. M: 27.4737 c. Nineteen-tone Minor Pentatonic 20: 6 3 3 5 3 P T3 SD: 17.8269 c. M:-30.0000 c. 21: 6 3 4 5 3 SP SD: 13.5437 c. M:-24.8571 c. 22: 6 4 3 6 3 SP T3 SD: 11.7261 c. M:-24.4545 c. 23: 6 4 4 6 3 SP T3 S SD: 9.7232 c. M: 16.9565 c. 25: 7 4 4 7 3 SP T3 S SD: 9.0885 c. M:-18.0000 c. 28: 8 4 5 7 4 SP SD: 9.0669 c. M:-12.8571 c. 30: 8 5 5 8 4 SP T3 S SD: 4.6690 c. M: 10.0000 c. 37: 10 6 6 10 5 SP T3 S SD: 3.3675 c. M: 5.6757 c. 65: 18 10 11 17 9 SP SD: 2.9394 c. M: 4.1538 c. 80: 22 13 13 21 11 SP SD: 2.4083 c. M:-4.0000 c. 83: 23 13 14 22 11 SP SD: 2.8065 c. M:-4.8916 c. 87: 24 14 14 23 12 SP SD: 2.1846 c. M: 3.5172 c. 90: 25 14 15 24 12 SP SD: 2.0055 c. M:-3.3333 c. 95: 26 15 16 25 13 SP SD: 2.0505 c. M: 3.1053 c. 97: 27 15 16 26 13 SP SD: 1.9883 c. M:-4.0206 c. 102: 28 16 17 27 14 SP SD: 1.9511 c. M: 3.3529 c. 110: 30 18 18 29 15 SP SD: 2.0526 c. M: 2.7273 c. 117: 32 19 19 31 16 SP SD: 1.5465 c. M: 2.1026 c. 120: 33 19 20 32 16 SP SD: 1.3416 c. M:-2.0000 c. 127: 35 20 21 34 17 SP SD: 0.9078 c. M:-1.3701 c. 164: 45 26 27 44 22 SP SD: 0.9651 c. M: 1.4878 c. 200: 55 32 33 53 27 SP SD: 1.0000 c. M:-2.0000 c. 207: 57 33 34 55 28 SP SD: 0.5556 c. M:-0.8406 c. 214: 59 34 35 57 29 SP SD: 0.5277 c. M:-0.8411 c. 244: 67 39 40 65 33 SP SD: 0.2922 c. M: 0.4918 c. 371: 102 59 61 99 50 SP SD: 0.1708 c. M:-0.2749 c. 578: 159 92 95 154 78 SP SD: 0.1680 c. M:-0.3391 c. 585: 161 93 96 156 79 SP SD: 0.1197 c. M:-0.2564 c. 615: 169 98 101 164 83 SP SD: 0.1139 c. M: 0.2439 c. 829: 228 132 136 221 112 SP SD: 0.0764 c. M: 0.1230 c. 956: 263 152 157 255 129 SP SD: 0.0746 c. M:-0.1255 c. 1200: 330 191 197 320 162 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: 8.0225 cents 3 x 4 x 5:6 S SD: 51.7822 cents 4:5 x 6:7:8 S SD: 22.6574 cents 6:7:8:9:11:12 SD: 13.9982 cents 9:11:12:14:16:18 SD: 13.8384 cents 10:12:14:15:18:20 S SD: 13.6582 cents 11:13:15:17:20:22 SD: 11.3090 cents 14:17:19:21:26:28 SD: 7.7199 cents 18:22:24:27:33:36 SD: 6.9757 cents 19:23:26:29:35:38 SD: 6.5368 cents 20:24:27:30:36:40 S SD: 5.9398 cents 23:28:31:35:42:46 SD: 3.0213 cents 29:35:39:44:53:58 SD: 2.3181 cents 43:52:58:65:78:86 SD: 1.6283 cents 57:69:77:86:104:114 SD: 1.3484 cents 62:75:84:94:113:124 SD: 1.0995 cents 80:97:108:121:146:160 SD: 1.0922 cents 91:110:123:138:166:182 SD: 0.8702 cents 105:127:142:159:191:210 SD: 0.5623 cents 128:155:173:194:233:256 SD: 0.5167 cents 134:162:181:203:244:268 SD: 0.3916 cents 185:224:250:280:337:370 SD: 0.2672 cents 257:311:347:389:468:514 SD: 0.2626 cents 276:334:373:418:503:552 SD: 0.2620 cents 290:351:392:439:528:580 SD: 0.2238 cents 296:358:400:448:539:592 SD: 0.2073 cents 319:386:431:483:581:638 SD: 0.0351 cents