Scala analysis: Ethiopia_AI_541_84_1939
AI 541/84 -1939, Ethiopia
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 375.000 cents 375.000000 2: 554.000 cents 554.000000 3: 759.000 cents 759.000000 4: 1091.000 cents 1091.000000 5: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 109.0000 cents 109.0000 1: 375.0000 cents 375.0000 2: 179.0000 cents 179.0000 3: 205.0000 cents 205.0000 4: 332.0000 cents 332.0000 5: 109.0000 cents 109.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 109.00000 cents 1: 1 179.00000 cents 1: 1 205.00000 cents 1: 1 332.00000 cents 1: 1 375.00000 cents 2: 1 384.00000 cents 2: 1 441.00000 cents 2: 1 484.00000 cents 2: 1 537.00000 cents 2: 1 554.00000 cents 3: 1 646.00000 cents 3: 1 663.00000 cents 3: 1 716.00000 cents 3: 1 759.00000 cents 3: 1 816.00000 cents 4: 1 825.00000 cents 4: 1 868.00000 cents 4: 1 995.00000 cents 4: 1 1021.00000 cents 4: 1 1091.00000 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 : 375.0 554.0 759.0 1091.0 1200.0 375.0 : 179.0 384.0 716.0 825.0 1200.0 554.0 : 205.0 537.0 646.0 1021.0 1200.0 759.0 : 332.0 441.0 816.0 995.0 1200.0 1091.0: 109.0 484.0 663.0 868.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 109.0000 .. 375.0000 cents 266.00000 cents 109.00000 cents 2: 384.0000 .. 554.0000 cents 170.00000 cents 9.00000 cents 3: 646.0000 .. 816.0000 cents 170.00000 cents 92.00000 cents 4: 825.0000 .. 1091.0000 cents 266.00000 cents 9.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 109.00000 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 375.00000 cents Average / Smallest step : 2.201835 Largest / Average step : 1.562500 Largest / Smallest step : 3.440367 Median interval of one step : 205.00000 cents, amount: 1 Least squares average step : 256.80000 cents, oct.: 1284.00000 cents Scale is strictly proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 375 554 759 1091 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 827 of 827.000 cents and inv. generated superset size: 285 = 280 more = 5700.000% 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 9.00000 cents Scale diversity : 1.683332 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.273333 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 : 9.00000 cents Number of recognisable fifths : 1, average 716.0000 cents Number of appreciable fifths : 0 Best fifths form a closed circle Formal octave complements present : 1 = 20.0000% -- Rational properties --
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 92.0685 c. M: 135.0000 c. 6: 2 1 1 1 1 P M ME S SD: 50.4044 c. M: 91.0000 c. 7: 2 1 1 2 1 P M ME S SD: 48.7412 c. M: 73.2857 c. Thai mode 6 9: 3 1 2 2 1 P D3 S SD: 25.7885 c. M:-41.0000 c. 11: 3 2 2 3 1 SP D3 S SD: 21.7827 c. M: 47.7273 c. 13: 4 2 2 4 1 P T3 S SD: 12.1142 c. M: 20.5385 c. 19: 6 3 3 5 2 P SD: 10.2431 c. M: 17.3158 c. 22: 7 3 4 6 2 P SD: 5.3107 c. M: 8.5455 c. 35: 11 5 6 10 3 P SD: 4.3364 c. M:-6.1429 c. 52: 16 8 9 14 5 SP SD: 4.0128 c. M: 6.3846 c. 54: 17 8 9 15 5 P SD: 2.3003 c. M: 3.4444 c. 76: 24 11 13 21 7 P SD: 2.0497 c. M:-3.9474 c. 87: 27 13 15 24 8 SP SD: 1.6626 c. M: 2.5862 c. 128: 40 19 22 35 12 SP SD: 1.6221 c. M: 3.5000 c. 134: 42 20 23 37 12 SP SD: 1.4091 c. M:-2.1940 c. 141: 44 21 24 39 13 SP SD: 1.0985 c. M: 1.6383 c. 188: 59 28 32 52 17 SP SD: 0.9855 c. M:-1.5957 c. 199: 62 30 34 55 18 SP SD: 0.7382 c. M: 1.1307 c. 221: 69 33 38 61 20 SP SD: 0.5824 c. M:-1.1810 c. 240: 75 36 41 66 22 SP SD: 0.7746 c. M:-1.0000 c. 253: 79 38 43 70 23 SP SD: 0.4455 c. M:-0.9407 c. 275: 86 41 47 76 25 SP SD: 0.1950 c. M:-0.2727 c. 563: 176 84 96 156 51 SP SD: 0.1893 c. M:-0.2966 c. 637: 199 95 109 176 58 SP SD: 0.1673 c. M: 0.2622 c. 650: 203 97 111 180 59 SP SD: 0.1650 c. M: 0.2308 c. 784: 245 117 134 217 71 SP SD: 0.1715 c. M:-0.3265 c. 838: 262 125 143 232 76 SP SD: 0.1374 c. M:-0.1790 c. 912: 285 136 156 252 83 SP SD: 0.1352 c. M:-0.2105 c. 925: 289 138 158 256 84 SP SD: 0.0580 c. M: 0.0811 c. 1200: 375 179 205 332 109 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: 28.5225 cents 3 x 4:5 x 6 S SD: 45.7600 cents 4:5 x 6 x 8 S SD: 19.3854 cents 7:9:10:11:13:14 SD: 18.5096 cents 8:10:11:12:15:16 S SD: 11.6564 cents 11:14:15:17:21:22 SD: 10.8379 cents 13:16:18:20:24:26 SD: 7.4251 cents 16:20:22:25:30:32 SD: 3.6241 cents 24:30:33:37:45:48 SD: 3.0661 cents 29:36:40:45:54:58 SD: 3.0139 cents 40:50:55:62:75:80 SD: 2.3894 cents 42:52:58:65:79:84 SD: 1.6351 cents 58:72:80:90:109:116 SD: 0.6983 cents 82:102:113:127:154:164 SD: 0.6968 cents 124:154:171:192:233:248 SD: 0.6638 cents 133:165:183:206:250:266 SD: 0.6404 cents 140:174:193:217:263:280 SD: 0.4735 cents 149:185:205:231:280:298 SD: 0.4033 cents 178:221:245:276:334:356 SD: 0.3564 cents 207:257:285:321:389:414 SD: 0.2825 cents 231:287:318:358:434:462 SD: 0.2745 cents 236:293:325:366:443:472 SD: 0.2249 cents 289:359:398:448:543:578 SD: 0.1994 cents 302:375:416:468:567:604 SD: 0.1838 cents 318:395:438:493:597:636 SD: 0.1480 cents 451:560:621:699:847:902 SD: 0.1066 cents 467:580:643:724:877:934 SD: 0.0739 cents 525:652:723:814:986:1050 SD: 0.0581 cents