Scala analysis: Ethiopia_Mus_03_Bati_Zafan
Mus 3 Bati Zafan, Ethiopia
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 348.000 cents 348.000000 2: 531.000 cents 531.000000 3: 740.000 cents 740.000000 4: 1043.000 cents 1043.000000 5: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 157.0000 cents 157.0000 1: 348.0000 cents 348.0000 2: 183.0000 cents 183.0000 3: 209.0000 cents 209.0000 4: 303.0000 cents 303.0000 5: 157.0000 cents 157.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 157.00000 cents 1: 1 183.00000 cents 1: 1 209.00000 cents 1: 1 303.00000 cents 1: 1 348.00000 cents 2: 1 392.00000 cents 2: 1 460.00000 cents 2: 1 505.00000 cents 2: 1 512.00000 cents 2: 1 531.00000 cents 3: 1 669.00000 cents 3: 1 688.00000 cents 3: 1 695.00000 cents 3: 1 740.00000 cents 3: 1 808.00000 cents 4: 1 852.00000 cents 4: 1 897.00000 cents 4: 1 991.00000 cents 4: 1 1017.00000 cents 4: 1 1043.00000 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 : 348.0 531.0 740.0 1043.0 1200.0 348.0 : 183.0 392.0 695.0 852.0 1200.0 531.0 : 209.0 512.0 669.0 1017.0 1200.0 740.0 : 303.0 460.0 808.0 991.0 1200.0 1043.0: 157.0 505.0 688.0 897.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 157.0000 .. 348.0000 cents 191.00000 cents 157.00000 cents 2: 392.0000 .. 531.0000 cents 139.00000 cents 44.00000 cents 3: 669.0000 .. 808.0000 cents 139.00000 cents 138.00000 cents 4: 852.0000 .. 1043.0000 cents 191.00000 cents 44.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 157.00000 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 348.00000 cents Average / Smallest step : 1.528662 Largest / Average step : 1.450000 Largest / Smallest step : 2.216561 Median interval of one step : 209.00000 cents, amount: 1 Least squares average step : 250.94545 cents, oct.: 1254.72727 cents Scale is strictly proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 348 531 740 1043 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 991 of 991.000 cents and inv. generated superset size: 229 = 224 more = 4580.000% 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 44.00000 cents Scale diversity : 1.593756 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.450000 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 : 7.00000 cents Number of recognisable fifths : 2, average 691.5000 cents Number of appreciable fifths : 1, average 695.0000 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: 65.6567 c. M: 108.0000 c. 6: 2 1 1 1 1 P M ME S SD: 50.8213 c. M:-69.0000 c. 7: 2 1 1 2 1 P M ME S SD: 26.3095 c. M: 54.2857 c. Thai mode 6 10: 3 1 2 3 1 P T3 SD: 30.0466 c. M: 51.0000 c. Pelog Degung: Sunda 11: 3 2 2 3 1 SP D3 S SD: 26.4292 c. M:-47.9091 c. 13: 4 2 2 3 2 P T3 SD: 18.6423 c. M: 27.6154 c. 14: 4 2 3 3 2 SP D3 S SD: 17.3306 c. M:-31.4286 c. 16: 5 2 3 4 2 P SD: 13.5204 c. M:-27.0000 c. 18: 5 3 3 5 2 SP T3 S SD: 12.8461 c. M:-23.6667 c. 20: 6 3 3 5 3 P T3 SD: 15.1921 c. M: 23.0000 c. 21: 6 3 4 5 3 SP SD: 10.2192 c. M: 16.7143 c. 23: 7 3 4 6 3 P SD: 9.7358 c. M:-17.2174 c. 24: 7 4 4 6 3 SP SD: 10.1390 c. M:-19.0000 c. 28: 8 4 5 7 4 SP SD: 11.3544 c. M: 16.7143 c. 29: 8 5 5 7 4 SP SD: 9.2921 c. M: 16.9655 c. 31: 9 5 5 8 4 SP SD: 5.3815 c. M:-10.9355 c. 32: 9 5 6 8 4 SP SD: 7.6844 c. M: 10.5000 c. 34: 10 5 6 9 4 SP SD: 7.4660 c. M:-15.8235 c. 38: 11 6 6 10 5 SP SD: 6.6721 c. M: 13.6842 c. 39: 11 6 7 10 5 SP SD: 5.7632 c. M: 9.5385 c. 45: 13 7 8 11 6 SP SD: 3.4833 c. M:-6.6667 c. 52: 15 8 9 13 7 SP SD: 2.2990 c. M: 4.5385 c. 75: 22 11 13 19 10 SP SD: 3.1623 c. M:-4.0000 c. 76: 22 12 13 19 10 SP SD: 2.8200 c. M:-5.8421 c. 83: 24 13 14 21 11 SP SD: 2.3545 c. M:-3.9398 c. 86: 25 13 15 22 11 SP SD: 1.6636 c. M:-3.5116 c. 113: 33 17 20 28 15 SP SD: 2.1227 c. M:-3.3628 c. 115: 33 18 20 29 15 SP SD: 1.7721 c. M: 3.6522 c. 117: 34 18 20 30 15 SP SD: 1.9117 c. M:-3.1538 c. 120: 35 18 21 30 16 SP SD: 1.6733 c. M: 3.0000 c. 122: 35 19 21 31 16 SP SD: 1.9699 c. M: 3.7377 c. 128: 37 20 22 32 17 SP SD: 1.9333 c. M:-3.3750 c. 131: 38 20 23 33 17 SP SD: 1.0641 c. M:-1.9847 c. 138: 40 21 24 35 18 SP SD: 0.5166 c. M: 0.8696 c. 269: 78 41 47 68 35 SP SD: 0.4570 c. M:-0.8662 c. 321: 93 49 56 81 42 SP SD: 0.1863 c. M: 0.3364 c. 459: 133 70 80 116 60 SP SD: 0.1988 c. M: 0.2876 c. 689: 200 105 120 174 90 SP SD: 0.2261 c. M:-0.3309 c. 696: 202 106 121 176 91 SP SD: 0.2034 c. M: 0.3448 c. 741: 215 113 129 187 97 SP SD: 0.1231 c. M:-0.1781 c. 879: 255 134 153 222 115 SP SD: 0.0680 c. M:-0.1229 c. 1062: 308 162 185 268 139 SP SD: 0.0671 c. M:-0.1130 c. 1200: 348 183 209 303 157 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: 19.0225 cents 3 x 4:5 x 6 S SD: 49.3575 cents 4:5 x 6:7:8 S SD: 22.9363 cents 5:6:7:8:9:10 H SD: 19.7743 cents 6:7:8:9:11:12 SD: 19.1373 cents 8:10:11:12:15:16 S SD: 14.6662 cents 9:11:12:14:16:18 SD: 12.5024 cents 11:13:15:17:20:22 SD: 12.2340 cents 13:16:18:20:24:26 SD: 7.8823 cents 17:21:23:26:31:34 SD: 4.0243 cents 22:27:30:34:40:44 SD: 3.6239 cents 28:34:38:43:51:56 SD: 2.6658 cents 36:44:49:55:66:72 SD: 1.8737 cents 45:55:61:69:82:90 SD: 1.2082 cents 58:71:79:89:106:116 SD: 0.9535 cents 81:99:110:124:148:162 SD: 0.6258 cents 103:126:140:158:188:206 SD: 0.3581 cents 139:170:189:213:254:278 SD: 0.3381 cents 167:204:227:256:305:334 SD: 0.3338 cents 184:225:250:282:336:368 SD: 0.2083 cents 270:330:367:414:493:540 SD: 0.1914 cents 351:429:477:538:641:702 SD: 0.1897 cents 373:456:507:572:681:746 SD: 0.1888 cents 409:500:556:627:747:818 SD: 0.1481 cents 454:555:617:696:829:908 SD: 0.1438 cents 512:626:696:785:935:1024 SD: 0.1377 cents 521:637:708:799:952:1042 SD: 0.1364 cents 566:692:769:868:1034:1132 SD: 0.1051 cents