Scala analysis: Ethiopia_AI_513_121_1939
AI 513/121 - 1939, Ethiopia
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 326.000 cents 326.000000 2: 554.000 cents 554.000000 3: 712.000 cents 712.000000 4: 984.000 cents 984.000000 5: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 216.0000 cents 216.0000 1: 326.0000 cents 326.0000 2: 228.0000 cents 228.0000 3: 158.0000 cents 158.0000 4: 272.0000 cents 272.0000 5: 216.0000 cents 216.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 158.00000 cents 1: 1 216.00000 cents 1: 1 228.00000 cents 1: 1 272.00000 cents 1: 1 326.00000 cents 2: 1 386.00000 cents 2: 1 430.00000 cents 2: 1 488.00000 cents 2: 1 542.00000 cents 2: 1 554.00000 cents 3: 1 646.00000 cents 3: 1 658.00000 cents 3: 1 712.00000 cents 3: 1 770.00000 cents 3: 1 814.00000 cents 4: 1 874.00000 cents 4: 1 928.00000 cents 4: 1 972.00000 cents 4: 1 984.00000 cents 4: 1 1042.00000 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 : 326.0 554.0 712.0 984.0 1200.0 326.0 : 228.0 386.0 658.0 874.0 1200.0 554.0 : 158.0 430.0 646.0 972.0 1200.0 712.0 : 272.0 488.0 814.0 1042.0 1200.0 984.0 : 216.0 542.0 770.0 928.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 158.0000 .. 326.0000 cents 168.00000 cents 158.00000 cents 2: 386.0000 .. 554.0000 cents 168.00000 cents 60.00000 cents 3: 646.0000 .. 814.0000 cents 168.00000 cents 92.00000 cents 4: 874.0000 .. 1042.0000 cents 168.00000 cents 60.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 158.00000 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 326.00000 cents Average / Smallest step : 1.518987 Largest / Average step : 1.358333 Largest / Smallest step : 2.063291 Median interval of one step : 228.00000 cents, amount: 1 Least squares average step : 245.56364 cents, oct.: 1227.81818 cents Scale is strictly proper Scale is a mode of a 600-tone equal temperament with octave 1200.000 cents degrees: 163 277 356 492 600 Least number of segments generator : 301 of 602.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 581 of 1162.000 cents and inv. generated superset size: 133 = 128 more = 2660.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : ECADB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 60.00000 cents Scale diversity : 1.663286 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.440000 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 : 12.00000 cents Number of recognisable fifths : 1, average 712.0000 cents 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: 51.9846 c. M: 86.0000 c. 6: 2 1 1 1 1 P M ME S SD: 55.8426 c. M:-88.0000 c. 7: 2 1 1 2 1 P M ME S SD: 30.1295 c. M:-44.5714 c. Thai mode 6 10: 3 2 1 2 2 P T3 SD: 27.9714 c. M:-46.0000 c. 11: 3 2 2 2 2 SP M ME S SD: 23.4338 c. M:-51.6364 c. 13: 4 2 2 3 2 P T3 SD: 26.6613 c. M:-43.2308 c. 14: 4 2 2 3 3 P SD: 29.1378 c. M: 41.1429 c. 15: 4 3 2 3 3 SP T3 SD: 11.9331 c. M: 24.0000 c. 17: 5 3 2 4 3 P SD: 13.3851 c. M:-26.9412 c. 18: 5 3 3 4 3 SP T3 SD: 15.4402 c. M:-21.3333 c. 22: 6 4 3 5 4 SP SD: 4.1921 c. M: 8.5455 c. 45: 12 9 6 10 8 SP SD: 5.3500 c. M:-8.0000 c. 52: 14 10 7 12 9 SP SD: 4.2200 c. M:-8.3077 c. 54: 15 10 7 12 10 SP SD: 4.3750 c. M:-7.3333 c. 56: 15 11 7 13 10 SP SD: 3.3854 c. M: 4.8571 c. 67: 18 13 9 15 12 SP SD: 2.6539 c. M:-4.4179 c. 78: 21 15 10 18 14 SP SD: 2.3453 c. M: 4.3077 c. 84: 23 16 11 19 15 SP SD: 2.2205 c. M:-3.1429 c. 89: 24 17 12 20 16 SP SD: 1.6774 c. M:-2.6067 c. 106: 29 20 14 24 19 SP SD: 1.2721 c. M:-2.3019 c. 121: 33 23 16 27 22 SP SD: 1.5788 c. M: 2.1818 c. 128: 35 24 17 29 23 SP SD: 1.0651 c. M:-2.1250 c. 150: 41 28 20 34 27 SP SD: 1.2649 c. M:-2.0000 c. 162: 44 31 21 37 29 SP SD: 0.9613 c. M:-1.5556 c. 184: 50 35 24 42 33 SP SD: 0.6354 c. M: 1.1304 c. 199: 54 38 26 45 36 SP SD: 0.6497 c. M: 1.0854 c. 221: 60 42 29 50 40 SP SD: 0.6272 c. M: 1.1946 c. 251: 68 48 33 57 45 SP SD: 0.6344 c. M: 0.9004 c. 273: 74 52 36 62 49 SP SD: 0.4327 c. M: 0.7253 c. 295: 80 56 39 67 53 SP SD: 0.4741 c. M: 0.7797 c. 305: 83 58 40 69 55 SP SD: 0.4585 c. M:-0.7541 c. 327: 89 62 43 74 59 SP SD: 0.3612 c. M:-0.6055 c. 379: 103 72 50 86 68 SP SD: 0.3657 c. M:-0.6966 c. 394: 107 75 52 89 71 SP SD: 0.3599 c. M:-0.6904 c. 401: 109 76 53 91 72 SP SD: 0.3224 c. M:-0.5387 c. 416: 113 79 55 94 75 SP SD: 0.2811 c. M:-0.5000 c. 494: 134 94 65 112 89 SP SD: 0.2730 c. M: 0.4939 c. 511: 139 97 67 116 92 SP SD: 0.2921 c. M: 0.4540 c. 578: 157 110 76 131 104 SP SD: 0.1596 c. M:-0.3253 c. 600: 163 114 79 136 108 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: 5.0225 cents 3 x 4 x 5:6 S SD: 38.0925 cents 4:5 x 6:7:8 S SD: 15.7498 cents 8:10:11:12:14:16 S SD: 12.6113 cents 10:12:14:15:18:20 S SD: 9.2733 cents 14:17:19:21:25:28 SD: 7.0324 cents 16:19:22:24:28:32 SD: 6.7819 cents 18:22:25:27:32:36 SD: 6.0728 cents 21:25:29:32:37:42 SD: 6.0488 cents 24:29:33:36:42:48 SD: 3.6931 cents 29:35:40:44:51:58 SD: 2.4249 cents 39:47:54:59:69:78 SD: 2.3057 cents 43:52:59:65:76:86 SD: 1.6045 cents 63:76:87:95:111:126 SD: 1.2188 cents 77:93:106:116:136:154 SD: 0.5787 cents 106:128:146:160:187:212 SD: 0.3161 cents 183:221:252:276:323:366 SD: 0.1934 cents 289:349:398:436:510:578 SD: 0.1820 cents 342:413:471:516:604:684 SD: 0.1764 cents 358:432:493:540:632:716 SD: 0.1642 cents 401:484:552:605:708:802 SD: 0.1612 cents 448:541:617:676:791:896 SD: 0.1302 cents 464:560:639:700:819:928 SD: 0.1106 cents