Scala analysis: Indonesia_Tetratonic
Tetratonic (Angklung), Indonesia
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 243.000 cents 243.000000 2: 492.000 cents 492.000000 3: 743.000 cents 743.000000
SHOW/INTERVAL
0: 251.0000 cents 251.0000 1: 243.0000 cents 243.0000 2: 249.0000 cents 249.0000 3: 251.0000 cents 251.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 243.00000 cents 1: 1 249.00000 cents 1: 1 251.00000 cents 2: 1 492.00000 cents 2: 1 494.00000 cents 2: 1 500.00000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 243.0 492.0 743.0 243.0: 249.0 500.0 743.0 492.0: 251.0 494.0 743.0 743.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 243.0000 .. 251.0000 cents 8.00000 cents 243.00000 cents 2: 492.0000 .. 500.0000 cents 8.00000 cents 241.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 243.00000 cents, class 1 Average step (divided formal octave): 247.6667 cents Largest one step interval : 251.00000 cents Average / Smallest step : 1.019204 Largest / Average step : 1.013459 Largest / Smallest step : 1.032922 Median interval of one step : 249.00000 cents, amount: 1 Least squares average step : 246.85714 cents, oct.: 740.57143 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 743-tone equal temperament with octave 743.000 cents degrees: 243 492 743 Least number of segments generator : 372 of 372.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 496 of 496.000 cents and inv. generated superset size: 8 = 5 more = 266.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 241.00000 cents Scale diversity : 1.398254 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.978466 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2.00000 cents Number of recognisable fifths : 0 Number of recognisable fourths : 3, average 495.3333 cents Best major thirds form a closed circle Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited transpositions with margin 8.0000 cents: 1 2 Limited inverse transpositions with margin 6.0000 cents: 1 2 -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 3.3110 c. M:-4.6667 c. 50: 16 17 17 SP M ME S SD: 3.1666 c. M: 5.2400 c. 53: 17 18 18 SP M ME S SD: 2.8101 c. M: 4.6792 c. 56: 18 19 19 SP M ME S SD: 2.4931 c. M: 4.1786 c. 59: 19 20 20 SP M ME S SD: 2.2099 c. M: 3.7288 c. 62: 20 21 21 SP M ME S SD: 1.9559 c. M: 3.3226 c. 65: 21 22 22 SP M ME S SD: 1.7275 c. M: 2.9538 c. 68: 22 23 23 SP M ME S SD: 1.5218 c. M: 2.6176 c. 71: 23 24 24 SP M ME S SD: 1.3366 c. M: 2.3099 c. 74: 24 25 25 SP M ME S SD: 1.1703 c. M: 2.0270 c. 77: 25 26 26 SP M ME S SD: 1.0220 c. M: 1.7662 c. 80: 26 27 27 SP M ME S SD: 0.8911 c. M: 1.5250 c. 83: 27 28 28 SP M ME S SD: 0.7779 c. M: 1.3012 c. 86: 28 29 29 SP M ME S SD: 0.6832 c. M: 1.0930 c. 89: 29 30 30 SP M ME S SD: 0.6086 c. M: 0.8989 c. 92: 30 31 31 SP M ME S SD: 0.5556 c. M: 0.7174 c. 95: 31 32 32 SP M ME S SD: 0.5251 c. M:-0.7263 c. 98: 32 33 33 SP M ME S SD: 0.5165 c. M:-0.8061 c. 101: 33 34 34 SP M ME S SD: 0.5269 c. M:-0.8812 c. 104: 34 35 35 SP M ME S SD: 0.5524 c. M:-0.9519 c. 107: 35 36 36 SP M ME S SD: 0.5885 c. M:-1.0187 c. 174: 57 58 59 SP T3 SD: 0.5873 c. M: 0.9368 c. 177: 58 59 60 SP T3 SD: 0.5678 c. M: 0.8644 c. 180: 59 60 61 SP T3 SD: 0.5542 c. M: 0.7944 c. 183: 60 61 62 SP T3 SD: 0.5465 c. M: 0.7268 c. 186: 61 62 63 SP T3 SD: 0.5443 c. M:-0.6720 c. 187: 61 63 63 SP M DE S SD: 0.5375 c. M:-0.6845 c. 193: 63 65 65 SP M DE S SD: 0.5182 c. M:-0.7668 c. 211: 69 71 71 SP M DE S SD: 0.5694 c. M:-0.9858 c. 233: 76 78 79 SP T3 SD: 0.6490 c. M: 0.9185 c. 236: 77 79 80 SP T3 SD: 0.6012 c. M: 0.8644 c. 239: 78 80 81 SP T3 SD: 0.5549 c. M: 0.8117 c. 242: 79 81 82 SP T3 SD: 0.5102 c. M: 0.7603 c. 245: 80 82 83 SP T3 SD: 0.4672 c. M: 0.7102 c. 248: 81 83 84 SP T3 SD: 0.4258 c. M: 0.6613 c. 251: 82 84 85 SP T3 SD: 0.3863 c. M: 0.6135 c. 254: 83 85 86 SP T3 SD: 0.3488 c. M: 0.5669 c. 257: 84 86 87 SP T3 SD: 0.3135 c. M: 0.5214 c. 260: 85 87 88 SP T3 SD: 0.2809 c. M: 0.4769 c. 263: 86 88 89 SP T3 SD: 0.2514 c. M: 0.4335 c. 266: 87 89 90 SP T3 SD: 0.2258 c. M: 0.3910 c. 269: 88 90 91 SP T3 SD: 0.2050 c. M: 0.3494 c. 272: 89 91 92 SP T3 SD: 0.1901 c. M: 0.3088 c. 275: 90 92 93 SP T3 SD: 0.1818 c. M: 0.2691 c. 278: 91 93 94 SP T3 SD: 0.1808 c. M: 0.2302 c. 349: 114 117 118 SP T3 SD: 0.2135 c. M: 0.3009 c. 352: 115 118 119 SP T3 SD: 0.1834 c. M: 0.2585 c. 355: 116 119 120 SP T3 SD: 0.1539 c. M: 0.2169 c. 358: 117 120 121 SP T3 SD: 0.1249 c. M: 0.1760 c. 361: 118 121 122 SP T3 SD: 0.0963 c. M: 0.1357 c. 364: 119 122 123 SP T3 SD: 0.0682 c. M: 0.0962 c. 367: 120 123 124 SP T3 SD: 0.0406 c. M: 0.0572 c. 370: 121 124 125 SP T3 SD: 0.0134 c. M: 0.0189 c. 373: 122 125 126 SP T3 SD: 0.0133 c. M:-0.0188 c. 743: 243 249 251 SP T3 SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 457.0000 cents 2 x x 3 S SD: 41.0450 cents 3 x 4:5 S SD: 70.7440 cents 4 x 5:6 S SD: 56.6884 cents 5:6:7:8 H SD: 45.2963 cents 6:7:8:9 H SD: 15.9550 cents 13:15:17:20 SD: 9.3718 cents 15:17:20:23 SD: 9.0548 cents 19:22:25:29 SD: 7.6118 cents 21:24:28:32 S SD: 6.3797 cents 28:32:37:43 SD: 5.0536 cents 33:38:44:51 SD: 4.0993 cents 34:39:45:52 SD: 3.8070 cents 39:45:52:60 SD: 2.7240 cents 52:60:69:80 SD: 1.9867 cents 67:77:89:103 SD: 0.8877 cents 73:84:97:112 SD: 0.6555 cents 140:161:186:215 SD: 0.3648 cents 192:221:255:295 SD: 0.3487 cents 252:290:335:387 SD: 0.3166 cents 265:305:352:407 SD: 0.2159 cents 332:382:441:510 SD: 0.1778 cents 405:466:538:622 SD: 0.1488 cents 444:511:590:682 SD: 0.1237 cents 511:588:679:785 SD: 0.0885 cents 584:672:776:897 SD: 0.0370 cents