Scala analysis: Ethiopia_AI_540_83_1939
AI 540/83 - 1939, Ethiopia
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 309.000 cents 309.000000 2: 531.000 cents 531.000000 3: 692.000 cents 692.000000 4: 1014.000 cents 1014.000000 5: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 186.0000 cents 186.0000 1: 309.0000 cents 309.0000 2: 222.0000 cents 222.0000 3: 161.0000 cents 161.0000 4: 322.0000 cents 322.0000 5: 186.0000 cents 186.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 161.00000 cents 1: 1 186.00000 cents 1: 1 222.00000 cents 1: 1 309.00000 cents 1: 1 322.00000 cents 2: 1 383.00000 cents 2: 1 483.00000 cents 2: 1 495.00000 cents 2: 1 508.00000 cents 2: 1 531.00000 cents 3: 1 669.00000 cents 3: 1 692.00000 cents 3: 1 705.00000 cents 3: 1 717.00000 cents 3: 1 817.00000 cents 4: 1 878.00000 cents 4: 1 891.00000 cents 4: 1 978.00000 cents 4: 1 1014.00000 cents 4: 1 1039.00000 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 : 309.0 531.0 692.0 1014.0 1200.0 309.0 : 222.0 383.0 705.0 891.0 1200.0 531.0 : 161.0 483.0 669.0 978.0 1200.0 692.0 : 322.0 508.0 817.0 1039.0 1200.0 1014.0: 186.0 495.0 717.0 878.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 161.0000 .. 322.0000 cents 161.00000 cents 161.00000 cents 2: 383.0000 .. 531.0000 cents 148.00000 cents 61.00000 cents 3: 669.0000 .. 817.0000 cents 148.00000 cents 138.00000 cents 4: 878.0000 .. 1039.0000 cents 161.00000 cents 61.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 161.00000 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 322.00000 cents Average / Smallest step : 1.490683 Largest / Average step : 1.341667 Largest / Smallest step : 2.000000 Median interval of one step : 222.00000 cents, amount: 1 Least squares average step : 245.50909 cents, oct.: 1227.54545 cents Scale is strictly proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 309 531 692 1014 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 767 of 767.000 cents and inv. generated superset size: 94 = 89 more = 1880.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : DCAEB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 61.00000 cents Scale diversity : 1.547438 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.485000 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 : 3, average 704.6667 cents Number of appreciable fifths : 2, average 698.5000 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: 47.0362 c. M: 69.0000 c. 7: 2 1 1 2 1 P M ME S SD: 18.3167 c. M:-33.8571 c. Thai mode 6 12: 3 2 2 3 2 SP M ME S SD: 16.1369 c. M: 31.0000 c. Minor Pentatonic, Blues Pentatonic, Raga Dhani (Suddha Dhanyasi), Abheri, Udhayaravi Chandrika, Qing Shang, Gu Xian, Jia Zhong, Yu: China, P'yongjo-kyemyonjo: Korea, Minyo: Japan, Lai Yai, Lai Noi: Laos, Nam, Northern Sa mac: Vietnam, Peruvian Pentatonic 2, Batti Minor: Ethiopia 15: 4 3 2 4 2 SP T3 SD: 22.0091 c. M:-29.0000 c. 16: 4 3 2 4 3 SP T3 SD: 19.6316 c. M: 39.0000 c. 19: 5 3 3 5 3 SP M DE S SD: 12.0668 c. M: 25.7368 c. Nineteen-tone Minor Pentatonic 21: 5 4 3 6 3 SP SD: 14.6522 c. M: 23.2857 c. 23: 6 4 3 6 4 SP T3 SD: 12.6962 c. M: 22.6957 c. 24: 6 5 3 6 4 SP SD: 11.8491 c. M:-19.0000 c. 25: 6 5 3 7 4 SP SD: 13.3116 c. M: 21.0000 c. 26: 7 5 3 7 4 SP SD: 12.0176 c. M:-22.8462 c. 27: 7 5 4 7 4 SP T3 SD: 9.4100 c. M:-19.1111 c. 31: 8 6 4 8 5 SP SD: 6.3216 c. M:-10.9355 c. 38: 10 7 5 10 6 SP SD: 4.4673 c. M:-6.7895 c. 47: 12 9 6 13 7 SP SD: 4.3241 c. M:-7.2766 c. 50: 13 9 7 13 8 SP SD: 3.7417 c. M: 6.0000 c. 54: 14 10 7 15 8 SP SD: 4.1758 c. M:-8.2222 c. 59: 15 11 8 16 9 SP SD: 2.4097 c. M: 3.9153 c. 90: 23 17 12 24 14 SP SD: 1.6193 c. M:-2.3333 c. 97: 25 18 13 26 15 SP SD: 0.5997 c. M:-0.9588 c. 276: 71 51 37 74 43 SP SD: 0.6018 c. M: 0.9565 c. 303: 78 56 41 81 47 SP SD: 0.5029 c. M:-1.0693 c. 310: 80 57 42 83 48 SP SD: 0.5952 c. M:-0.9032 c. 323: 83 60 43 87 50 SP SD: 0.5475 c. M: 0.9783 c. 350: 90 65 47 94 54 SP SD: 0.5345 c. M:-0.8571 c. 361: 93 67 48 97 56 SP SD: 0.4733 c. M:-0.8560 c. 362: 93 67 49 97 56 SP SD: 0.5806 c. M:-0.8177 c. 366: 94 68 49 98 57 SP SD: 0.5458 c. M: 0.8852 c. 368: 95 68 49 99 57 SP SD: 0.5264 c. M:-0.7826 c. 373: 96 69 50 100 58 SP SD: 0.3171 c. M: 0.5952 c. 380: 98 70 51 102 59 SP SD: 0.3810 c. M:-0.4737 c. 439: 113 81 59 118 68 SP SD: 0.3762 c. M: 0.7039 c. 470: 121 87 63 126 73 SP SD: 0.1800 c. M: 0.3830 c. 567: 146 105 76 152 88 SP SD: 0.1486 c. M: 0.2434 c. 633: 163 117 85 170 98 SP SD: 0.1331 c. M:-0.2180 c. 730: 188 135 98 196 113 SP SD: 0.1159 c. M:-0.2466 c. 1006: 259 186 135 270 156 SP SD: 0.1156 c. M: 0.1849 c. 1103: 284 204 148 296 171 SP SD: 0.0527 c. M: 0.0843 c. 1200: 309 222 161 322 186 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: 4.9775 cents 3 x 4 x 5:6 S SD: 44.5881 cents 4:5 x 6:7:8 S SD: 22.5239 cents 5:6:7 x 9:10 SD: 13.0157 cents 6:7:8:9:11:12 SD: 12.9777 cents 7:8 x 10:13:14 SD: 30.5557 cents 8:10:11:12:14:16 S SD: 18.4716 cents 9:11:12:13:16:18 SD: 15.4262 cents 10:12:14:15:18:20 S SD: 10.6012 cents 11:13:15:16:20:22 SD: 10.4773 cents 14:17:19:21:25:28 SD: 6.1464 cents 16:19:22:24:29:32 SD: 5.9549 cents 20:24:27:30:36:40 S SD: 3.3895 cents 25:30:34:37:45:50 SD: 3.0676 cents 31:37:42:46:56:62 SD: 2.8807 cents 36:43:49:54:65:72 SD: 2.7446 cents 41:49:56:61:74:82 SD: 2.5535 cents 45:54:61:67:81:90 SD: 1.8371 cents 61:73:83:91:110:122 SD: 1.4703 cents 67:80:91:100:120:134 SD: 1.1316 cents 87:104:118:130:156:174 SD: 1.1233 cents 92:110:125:137:165:184 SD: 0.7592 cents 98:117:133:146:176:196 SD: 0.7438 cents 108:129:147:161:194:216 SD: 0.6338 cents 122:146:166:182:219:244 SD: 0.6269 cents 128:153:174:191:230:256 SD: 0.2436 cents 220:263:299:328:395:440 SD: 0.1968 cents 348:416:473:519:625:696 SD: 0.0824 cents