Scala analysis: Ethiopia_Bati
Bati (Baganna or Krar or Masinko), Ethiopia
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 325.000 cents 325.000000 2: 535.000 cents 535.000000 3: 710.000 cents 710.000000 4: 1050.000 cents 1050.000000 5: 1190.000 cents 1190.000000
SHOW/INTERVAL
0: 140.0000 cents 140.0000 1: 325.0000 cents 325.0000 2: 210.0000 cents 210.0000 3: 175.0000 cents 175.0000 4: 340.0000 cents 340.0000 5: 140.0000 cents 140.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 140.00000 cents 1: 1 175.00000 cents 1: 1 210.00000 cents 1: 1 325.00000 cents 1: 1 340.00000 cents 2: 1 385.00000 cents 2: 1 465.00000 cents 2: 1 480.00000 cents 2: 1 515.00000 cents 2: 1 535.00000 cents 3: 1 655.00000 cents 3: 1 675.00000 cents 3: 1 710.00000 cents 3: 1 725.00000 cents 3: 1 805.00000 cents 4: 1 850.00000 cents 4: 1 865.00000 cents 4: 1 980.00000 cents 4: 1 1015.00000 cents 4: 1 1050.00000 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 : 325.0 535.0 710.0 1050.0 1190.0 325.0 : 210.0 385.0 725.0 865.0 1190.0 535.0 : 175.0 515.0 655.0 980.0 1190.0 710.0 : 340.0 480.0 805.0 1015.0 1190.0 1050.0: 140.0 465.0 675.0 850.0 1190.0 1190.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 140.0000 .. 340.0000 cents 200.00000 cents 140.00000 cents 2: 385.0000 .. 535.0000 cents 150.00000 cents 45.00000 cents 3: 655.0000 .. 805.0000 cents 150.00000 cents 120.00000 cents 4: 850.0000 .. 1050.0000 cents 200.00000 cents 45.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 140.00000 cents, class 1 Average step (divided formal octave): 238.0000 cents Largest one step interval : 340.00000 cents Average / Smallest step : 1.700000 Largest / Average step : 1.428571 Largest / Smallest step : 2.428571 Median interval of one step : 210.00000 cents, amount: 1 Least squares average step : 248.63636 cents, oct.: 1243.18182 cents Scale is strictly proper Scale is a mode of a 238-tone equal temperament with octave 1190.000 cents degrees: 65 107 142 210 238 Least number of segments generator : 121 of 605.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 233 of 1165.000 cents and inv. generated superset size: 77 = 72 more = 1540.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : DCBEA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 45.00000 cents Scale diversity : 1.626840 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.411765 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 : 15.00000 cents Number of recognisable fifths : 1, average 710.0000 cents Number of recognisable fourths : 1, average 480.0000 cents Number of appreciable fourths : 0 Best fifths form a closed circle Formal octave complements present : 1 = 20.0000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 200.0000 cents: 4 -- Rational properties --
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 64.2962 c. M: 98.0000 c. 7: 2 1 1 2 1 P M ME S SD: 23.0217 c. M: 30.0000 c. Thai mode 6 15: 4 3 2 4 2 SP T3 SD: 12.9357 c. M:-20.3333 c. 18: 5 3 3 5 2 SP T3 S SD: 9.2229 c. M:-17.2222 c. 25: 7 4 4 7 3 SP T3 S SD: 6.6489 c. M: 11.4000 c. 33: 9 6 5 9 4 SP SD: 5.9805 c. M:-11.2121 c. 34: 9 6 5 10 4 SP SD: 7.7460 c. M: 10.0000 c. 37: 10 7 5 11 4 SP SD: 7.5419 c. M:-11.7568 c. 40: 11 7 6 11 5 SP SD: 4.4244 c. M: 8.7500 c. 44: 12 8 6 13 5 SP SD: 4.5693 c. M: 6.8182 c. 52: 14 9 8 15 6 SP SD: 4.5557 c. M: 8.6538 c. 58: 16 10 9 16 7 SP SD: 4.2875 c. M:-8.1034 c. 60: 16 11 9 17 7 SP SD: 3.9087 c. M: 7.6667 c. 62: 17 11 9 18 7 SP SD: 2.8076 c. M:-5.6452 c. 67: 18 12 10 19 8 SP SD: 2.7322 c. M: 5.2985 c. 69: 19 12 10 20 8 SP SD: 1.9919 c. M: 2.8986 c. 84: 23 15 12 24 10 SP SD: 1.8634 c. M:-3.3333 c. 102: 28 18 15 29 12 SP SD: 1.2910 c. M:-1.6667 c. 129: 35 23 19 37 15 SP SD: 1.2077 c. M: 2.1318 c. 136: 37 24 20 39 16 SP SD: 0.9682 c. M: 1.2500 c. 169: 46 30 25 48 20 SP SD: 0.8133 c. M:-1.1834 c. 213: 58 38 31 61 25 SP SD: 0.7804 c. M:-1.3380 c. 220: 60 39 32 63 26 SP SD: 0.7546 c. M: 1.4091 c. 231: 63 41 34 66 27 SP SD: 0.6976 c. M:-0.9091 c. 238: 65 42 35 68 28 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x 2 S SD: 10.0000 cents 2 x x 3 x 4 S SD: 6.4172 cents 3 x 4 x x 6 S SD: 19.1420 cents 4:5 x 6:7:8 S SD: 25.6336 cents 5:6:7:8:9:10 H SD: 23.8712 cents 6:7:8:9:11:12 SD: 14.0140 cents 10:12:14:15:18:20 S SD: 11.9327 cents 11:13:15:17:20:22 SD: 11.8560 cents 13:16:18:20:24:26 SD: 11.8408 cents 14:17:19:21:26:28 SD: 5.6548 cents 19:23:26:29:35:38 SD: 5.4495 cents 20:24:27:30:37:40 SD: 5.3549 cents 24:29:33:36:44:48 SD: 4.1870 cents 30:36:41:45:55:60 SD: 3.3840 cents 44:53:60:66:81:87 SD: 2.9290 cents 47:57:64:71:86:93 SD: 2.7317 cents 49:59:67:74:90:97 SD: 2.3393 cents 53:64:72:80:97:105 SD: 1.8477 cents 63:76:86:95:116:125 SD: 1.7521 cents 67:81:91:101:123:133 SD: 1.3987 cents 77:93:105:116:141:153 SD: 0.8091 cents 83:100:113:125:152:165 SD: 0.7591 cents 97:117:132:146:178:193 SD: 0.6117 cents 160:193:218:241:293:318 SD: 0.5874 cents 169:204:230:255:310:336 SD: 0.5568 cents 174:210:237:262:319:346 SD: 0.3319 cents 199:240:271:300:365:396 SD: 0.3262 cents 276:333:376:416:506:549 SD: 0.1889 cents 373:450:508:562:684:742 SD: 0.1660 cents 489:590:666:737:897:972 SD: 0.1559 cents 513:619:699:773:941:1020 SD: 0.1457 cents 519:626:707:782:952:1032 SD: 0.1295 cents 596:719:812:898:1093:1185 SD: 0.1175 cents