Scala analysis: Indonesia_Madumurti
Madumurti (Saron Demung or Gender Barung), Indonesia
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 224.000 cents 224.000000 2: 457.000 cents 457.000000 3: 715.000 cents 715.000000 4: 958.000 cents 958.000000 5: 1216.000 cents 1216.000000
SHOW/INTERVAL
0: 258.0000 cents 258.0000 1: 224.0000 cents 224.0000 2: 233.0000 cents 233.0000 3: 258.0000 cents 258.0000 4: 243.0000 cents 243.0000 5: 258.0000 cents 258.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 224.00000 cents 1: 1 233.00000 cents 1: 1 243.00000 cents 1: 2 258.00000 cents 2: 1 457.00000 cents 2: 1 482.00000 cents 2: 1 491.00000 cents 2: 2 501.00000 cents 3: 2 715.00000 cents 3: 1 725.00000 cents 3: 1 734.00000 cents 3: 1 759.00000 cents 4: 2 958.00000 cents 4: 1 973.00000 cents 4: 1 983.00000 cents 4: 1 992.00000 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 224.0 457.0 715.0 958.0 1216.0 224.0 : 233.0 491.0 734.0 992.0 1216.0 457.0 : 258.0 501.0 759.0 983.0 1216.0 715.0 : 243.0 501.0 725.0 958.0 1216.0 958.0 : 258.0 482.0 715.0 973.0 1216.0 1216.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 224.0000 .. 258.0000 cents 34.00000 cents 224.00000 cents 2: 457.0000 .. 501.0000 cents 44.00000 cents 199.00000 cents 3: 715.0000 .. 759.0000 cents 44.00000 cents 214.00000 cents 4: 958.0000 .. 992.0000 cents 34.00000 cents 199.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 224.00000 cents, class 1 Average step (divided formal octave): 243.2000 cents Largest one step interval : 258.00000 cents Average / Smallest step : 1.085714 Largest / Average step : 1.060855 Largest / Smallest step : 1.151786 Median interval of one step : 243.00000 cents, amount: 1 Most common interval of one step : 258.00000 cents, amount: 2 Least squares average step : 239.90909 cents, oct.: 1199.54545 cents Scale is strictly proper Scale is a mode of a 1216-tone equal temperament with octave 1216.000 cents degrees: 224 457 715 958 1216 Least number of segments generator : 609 of 609.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 973 of 973.000 cents and inv. generated superset size: 148 = 143 more = 2960.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDC Step pattern size order : ABDCD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 199.00000 cents Scale diversity : 1.142030 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.871711 Rothenberg efficiency : 0.480000 redundancy: 0.520000 Efficiency x scale size : 2.400000 Number of different interval sizes : 16 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 9.00000 cents Number of recognisable fifths : 2, average 715.0000 cents Number of appreciable fifths : 0 Number of recognisable fourths : 4, average 493.7500 cents Number of appreciable fourths : 3, average 497.6667 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 20.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions with margin 44.0000 cents: 1 4 Limited inverse transpositions with margin 44.0000 cents: 1 2 3 -- Rational properties --
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 18.2494 c. M:-29.4000 c. 17: 3 3 4 3 4 SP M ME S SD: 18.1847 c. M: 28.1176 c. Seventeen-tone Major Pentatonic 18: 3 4 4 3 4 SP M ME S SD: 18.1504 c. M:-28.1111 c. 19: 3 4 4 4 4 SP M ME S SD: 15.6844 c. M: 32.0000 c. Godzilla-5 21: 4 4 4 5 4 SP M ME S SD: 15.4832 c. M:-26.3810 c. 22: 4 4 5 4 5 SP M ME S SD: 10.7502 c. M: 18.3636 c. 24: 4 5 5 5 5 SP M ME S SD: 10.0995 c. M: 21.3333 c. Godzilla-5 27: 5 5 6 5 6 SP M ME S SD: 6.7233 c. M: 12.2222 c. 32: 6 6 7 6 7 SP M ME S SD: 5.0990 c. M: 8.0000 c. 37: 7 7 8 7 8 SP M ME S SD: 5.1950 c. M:-8.0270 c. 42: 8 8 9 8 9 SP M ME S SD: 6.0197 c. M:-8.8095 c. 43: 8 8 9 9 9 SP D3 S SD: 4.5186 c. M: 8.0233 c. 48: 9 9 10 10 10 SP D3 S SD: 3.7653 c. M: 5.6667 c. 53: 10 10 11 11 11 SP D3 S SD: 3.9681 c. M:-5.6226 c. 56: 10 11 12 11 12 SP T3 SD: 3.3794 c. M: 6.8571 c. 61: 11 12 13 12 13 SP T3 SD: 2.5612 c. M: 4.7213 c. 66: 12 13 14 13 14 SP T3 SD: 2.6092 c. M:-3.6061 c. 75: 14 14 16 15 16 SP T3 S SD: 2.1298 c. M: 3.0267 c. 80: 15 15 17 16 17 SP T3 S SD: 1.8719 c. M:-4.0000 c. 85: 16 16 18 17 18 SP T3 S SD: 2.2318 c. M:-4.8941 c. 99: 18 19 21 20 21 SP SD: 2.0801 c. M: 2.9091 c. 104: 19 20 22 21 22 SP SD: 1.2752 c. M: 1.8462 c. 109: 20 21 23 22 23 SP SD: 0.8904 c. M:-1.4128 c. 136: 25 26 29 27 29 SP SD: 0.7724 c. M: 1.2941 c. 141: 26 27 30 28 30 SP SD: 0.4946 c. M:-0.8014 c. 245: 45 47 52 49 52 SP SD: 0.3640 c. M: 0.6531 c. 250: 46 48 53 50 53 SP SD: 0.1764 c. M: 0.2560 c. 391: 72 75 83 78 83 SP SD: 0.1656 c. M:-0.2941 c. 575: 106 110 122 115 122 SP SD: 0.1497 c. M: 0.2070 c. 580: 107 111 123 116 123 SP SD: 0.1631 c. M:-0.3310 c. 636: 117 122 135 127 135 SP SD: 0.1488 c. M: 0.3019 c. 641: 118 123 136 128 136 SP SD: 0.1343 c. M:-0.1856 c. 716: 132 137 152 143 152 SP SD: 0.1232 c. M:-0.1788 c. 825: 152 158 175 165 175 SP SD: 0.0785 c. M: 0.1394 c. 966: 178 185 205 193 205 SP SD: 0.0456 c. M:-0.0663 c. 1216: 224 233 258 243 258 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x 2 S SD: 16.0000 cents 2 x x 3 x 4 S SD: 10.3220 cents 3 x 4 x 5:6 S SD: 28.6041 cents 4 x 5:6:7:8 S SD: 18.6077 cents 7:8:9:11:12:14 SD: 15.4422 cents 8:9:10:12:14:16 S SD: 15.4189 cents 10:11:13:15:17:20 SD: 14.7831 cents 12:14:16:18:21:24 S SD: 12.7530 cents 13:15:17:20:23:26 SD: 10.4066 cents 14:16:18:21:24:28 S SD: 7.9411 cents 16:18:21:24:28:32 S SD: 6.7436 cents 20:23:26:30:35:40 SD: 5.9117 cents 23:26:30:35:40:46 SD: 4.6636 cents 30:34:39:45:52:61 SD: 4.1160 cents 35:40:46:53:61:71 SD: 4.0515 cents 36:41:47:54:63:73 SD: 3.8570 cents 37:42:48:56:64:75 SD: 2.8810 cents 43:49:56:65:75:87 SD: 1.3641 cents 80:91:104:121:139:161 SD: 1.2668 cents 92:105:120:139:160:186 SD: 1.2630 cents 96:109:125:145:167:194 SD: 0.9429 cents 100:114:130:151:174:202 SD: 0.9062 cents 115:131:150:174:200:232 SD: 0.8020 cents 123:140:160:186:214:248 SD: 0.5777 cents 166:189:216:251:289:335 SD: 0.4946 cents 211:240:275:319:367:426 SD: 0.4123 cents 225:256:293:340:391:454 SD: 0.3201 cents 268:305:349:405:466:541 SD: 0.0813 cents