Scala analysis: Ethiopia_AI_512_20_1939
AI 512/20 - 1939, Ethiopia
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 353.000 cents 353.000000 2: 548.000 cents 548.000000 3: 719.000 cents 719.000000 4: 1010.000 cents 1010.000000 5: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 190.0000 cents 190.0000 1: 353.0000 cents 353.0000 2: 195.0000 cents 195.0000 3: 171.0000 cents 171.0000 4: 291.0000 cents 291.0000 5: 190.0000 cents 190.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 171.00000 cents 1: 1 190.00000 cents 1: 1 195.00000 cents 1: 1 291.00000 cents 1: 1 353.00000 cents 2: 1 366.00000 cents 2: 1 462.00000 cents 2: 1 481.00000 cents 2: 1 543.00000 cents 2: 1 548.00000 cents 3: 1 652.00000 cents 3: 1 657.00000 cents 3: 1 719.00000 cents 3: 1 738.00000 cents 3: 1 834.00000 cents 4: 1 847.00000 cents 4: 1 909.00000 cents 4: 1 1005.00000 cents 4: 1 1010.00000 cents 4: 1 1029.00000 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 : 353.0 548.0 719.0 1010.0 1200.0 353.0 : 195.0 366.0 657.0 847.0 1200.0 548.0 : 171.0 462.0 652.0 1005.0 1200.0 719.0 : 291.0 481.0 834.0 1029.0 1200.0 1010.0: 190.0 543.0 738.0 909.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 171.0000 .. 353.0000 cents 182.00000 cents 171.00000 cents 2: 366.0000 .. 548.0000 cents 182.00000 cents 13.00000 cents 3: 652.0000 .. 834.0000 cents 182.00000 cents 104.00000 cents 4: 847.0000 .. 1029.0000 cents 182.00000 cents 13.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 171.00000 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 353.00000 cents Average / Smallest step : 1.403509 Largest / Average step : 1.470833 Largest / Smallest step : 2.064327 Median interval of one step : 195.00000 cents, amount: 1 Least squares average step : 248.10909 cents, oct.: 1240.54545 cents Scale is strictly proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 353 548 719 1010 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 751 of 751.000 cents and inv. generated superset size: 208 = 203 more = 4160.000% 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 13.00000 cents Scale diversity : 1.526499 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.393333 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 : 5.00000 cents Number of recognisable fifths : 1, average 719.0000 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: 63.0777 c. M: 113.0000 c. 6: 2 1 1 1 1 P M ME S SD: 48.1124 c. M:-81.0000 c. 7: 2 1 1 2 1 P M ME S SD: 23.2050 c. M: 33.7143 c. Thai mode 6 13: 4 2 2 3 2 P T3 SD: 11.8774 c. M:-19.4615 c. 20: 6 3 3 5 3 P T3 SD: 6.5422 c. M:-10.0000 c. 33: 10 5 5 8 5 P T3 SD: 7.1413 c. M:-10.6364 c. 37: 11 6 5 9 6 P SD: 3.9130 c. M: 5.4865 c. 50: 15 8 7 12 8 P SD: 3.7417 c. M:-7.0000 c. 55: 16 9 8 13 9 SP SD: 3.5569 c. M: 6.3636 c. 57: 17 9 8 14 9 P SD: 2.6436 c. M:-4.8947 c. 68: 20 11 10 16 11 SP SD: 2.7698 c. M:-4.5294 c. 75: 22 12 11 18 12 SP SD: 2.0976 c. M: 4.0000 c. 88: 26 14 13 21 14 SP SD: 2.1719 c. M:-3.7273 c. 103: 30 17 15 25 16 SP SD: 2.6953 c. M:-3.5922 c. 105: 31 17 15 25 17 SP SD: 2.0662 c. M: 4.2857 c. 108: 32 17 16 26 17 SP SD: 2.4815 c. M: 3.5556 c. 109: 32 18 15 27 17 SP SD: 2.2899 c. M: 3.4037 c. 112: 33 18 16 27 18 SP SD: 1.5662 c. M: 2.8571 c. 125: 37 20 18 30 20 SP SD: 1.4478 c. M:-2.2000 c. 132: 39 21 19 32 21 SP SD: 1.4397 c. M: 2.5455 c. 140: 41 23 20 34 22 SP SD: 1.0804 c. M: 1.5714 c. 177: 52 29 25 43 28 SP SD: 0.5819 c. M:-1.1525 c. 197: 58 32 28 48 31 SP SD: 0.5568 c. M:-1.1675 c. 234: 69 38 33 57 37 SP SD: 0.6932 c. M: 1.0513 c. 245: 72 40 35 59 39 SP SD: 0.7054 c. M: 1.0204 c. 252: 74 41 36 61 40 SP SD: 0.3892 c. M: 0.6190 c. 309: 91 50 44 75 49 SP SD: 0.3826 c. M: 0.5534 c. 429: 126 70 61 104 68 SP SD: 0.2921 c. M: 0.5524 c. 442: 130 72 63 107 70 SP SD: 0.2784 c. M:-0.4570 c. 449: 132 73 64 109 71 SP SD: 0.1580 c. M:-0.2450 c. 701: 206 114 100 170 111 SP SD: 0.1875 c. M: 0.3609 c. 714: 210 116 102 173 113 SP SD: 0.1601 c. M:-0.3277 c. 738: 217 120 105 179 117 SP SD: 0.1870 c. M: 0.3008 c. 751: 221 122 107 182 119 SP SD: 0.0945 c. M: 0.1465 c. 948: 279 154 135 230 150 SP SD: 0.1035 c. M:-0.1646 c. 1023: 301 166 146 248 162 SP SD: 0.1007 c. M: 0.1994 c. 1200: 353 195 171 291 190 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: 8.5225 cents 3 x 4 x 5:6 S SD: 45.0694 cents 4:5 x 6:7:8 S SD: 13.9096 cents 8:10:11:12:14:16 S SD: 11.1475 cents 10:12:14:15:18:20 S SD: 10.8351 cents 13:16:18:20:23:26 SD: 7.7232 cents 14:17:19:21:25:28 SD: 6.2819 cents 18:22:25:27:32:36 SD: 6.1466 cents 19:23:26:29:34:38 SD: 5.2787 cents 27:33:37:41:48:54 SD: 3.1543 cents 35:43:48:53:63:70 SD: 1.6843 cents 62:76:85:94:111:124 SD: 0.5856 cents 97:119:133:147:174:194 SD: 0.5057 cents 150:184:206:227:269:300 SD: 0.5024 cents 159:195:218:241:285:318 SD: 0.3958 cents 177:217:243:268:317:354 SD: 0.3109 cents 212:260:291:321:380:424 SD: 0.1959 cents 274:336:376:415:491:548 SD: 0.0735 cents