Scala analysis: 152_C4
Chromatic tetrachord 36/35 * 21/20 * 100/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 100/81 364.8074 grave major third 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 21/20 84.4672 minor semitone 3: 100/81 364.8074 grave major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 21/20 84.467 cents minor semitone 1: 1 100/81 364.807 cents grave major third 2: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 1 80/63 413.578 cents wide major third 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 : 48.8 133.2 498.0 48.8 : 84.5 449.3 498.0 133.2: 364.8 413.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 364.8074 cents 875/729, 316.0370 cents 36/35, 48.7704 cents 2: 133.2376 .. 449.2746 cents 875/729, 316.0370 cents 2187/2500,-231.5698 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 100/81, 364.8074 cents Average / Smallest step : 3.404013 Largest / Average step : 2.197437 Largest / Smallest step : 7.480102 Median interval of one step : 21/20, 84.4672 cents, amount: 1 Least squares average step : 129.24147 cents, oct.: 387.72440 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1256-tone equal temperament with octave 4/3 degrees: 123 336 1256 Least number of segments generator : 629 of 249.419 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 963 of 381.861 cents and inv. generated superset size: 56 = 53 more = 1866.667% 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 48.77038 cents Scale diversity : 0.644809 Lumma stability : 0.195847 Lumma impropriety factor : 0.464958 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 : 49/48, 35.6968 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 35 U: 81) Highest odd numerator or denominator: 35 Scale harmonicity : 0.027970 Average absolute harmonicity : 0.101332 Specific harmonicity : 0.132241 Fundamental : 1/525, -9.0362 octaves, 0.4983 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 5.670000E+04, 15.79106 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 65.0, average 21.66667 Mersenne's string divisions : 25844 Sum of van Prooijen's expressibility: 3.45255, average 1.15085 Sum of Tenney's harmonic distance : 7.00886, average 2.33629 Vogel's harmonic complexity : 18.00000 Wille's k value : 283 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 19.86525, average 3.31088 Lattice compactness (without 2's) : 16.57585, average 2.76264 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -1 .. 3 1.33333 6 1 5: -2 .. 0 -1.00000 3 1 7: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 11 15 20| Scale is weakly epimorphic with val: <7 11 16 18| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 11 17 18| Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 11 19 21| Scale is weakly epimorphic with val: <7 12 16 19| Scale is weakly epimorphic with val: <8 11 15 19| Scale is weakly epimorphic with val: <8 11 15 22| Scale is weakly epimorphic with val: <8 11 16 19| Scale is weakly epimorphic with val: <8 12 17 20|
FIT/MODE
3: 0 1 2 N G T3 SD: 33.9259 c. M: 48.7704 c. 4: 0 1 3 N G T3 SD: 28.6048 c. M: 48.7704 c. 5: 0 1 4 N G T3 SD: 34.2025 c. M: 48.7704 c. 7: 1 1 5 N M DE S SD: 13.9394 c. M:-22.3789 c. 8: 1 1 6 N M DE S SD: 9.2736 c. M:-13.4852 c. 10: 1 2 7 N T3 SD: 9.3582 c. M:-16.1759 c. 11: 1 2 8 N T3 SD: 2.5118 c. M: 3.4936 c. 19: 2 3 14 N T3 SD: 2.4552 c. M:-3.6554 c. 29: 3 5 21 N T3 SD: 2.8768 c. M:-4.1541 c. 30: 3 5 22 N T3 SD: 0.6456 c. M:-1.0341 c. 41: 4 7 30 N T3 SD: 0.2451 c. M:-0.3843 c. 71: 7 12 52 N T3 SD: 0.1936 c. M:-0.3326 c. 112: 11 19 82 N T3 SD: 0.1277 c. M:-0.1673 c. 348: 34 59 255 N T3 SD: 0.1028 c. M: 0.1393 c. 378: 37 64 277 N T3 SD: 0.0943 c. M: 0.1621 c. 389: 38 66 285 N T3 SD: 0.0838 c. M: 0.1182 c. 419: 41 71 307 N T3 SD: 0.0660 c. M: 0.1086 c. 460: 45 78 337 N T3 SD: 0.0467 c. M: 0.0647 c. 501: 49 85 367 N T3 SD: 0.0379 c. M: 0.0594 c. 531: 52 90 389 N T3 SD: 0.0291 c. M: 0.0504 c. 572: 56 97 419 N T3 SD: 0.0127 c. M: 0.0192 c. 684: 67 116 501 N T3 SD: 0.0107 c. M:-0.0147 c. 1185: 116 201 868 N T3 SD: 0.0101 c. M: 0.0166 c. 1256: 123 213 920 N T3 SD: 0.0024 c. M:-0.0031 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 100.5060 cents 6 x 7:8 S SD: 66.8167 cents 7 x 8:9 S SD: 58.2143 cents 8 x 9:11 SD: 44.2510 cents 9 x 10:12 S SD: 24.5831 cents 10 x 11:13 SD: 27.0660 cents 11 x 12:15 S SD: 21.3096 cents 12 x 13:16 SD: 2.6675 cents 13 x 14:17 SD: 16.9891 cents 14 x 15:19 SD: 16.8020 cents 15 x 16:20 S SD: 10.7531 cents 16 x 17:21 SD: 19.6419 cents 17 x 18:23 SD: 21.2961 cents 18 x 19:24 SD: 19.8173 cents 20:21:22:27 SD: 17.4671 cents 21:22:23:28 SD: 13.3228 cents 22:23:24:29 SD: 12.8611 cents 23:24:25:31 SD: 11.0271 cents 24:25:26:32 SD: 7.5142 cents 27:28:29:36 SD: 5.6970 cents 35:36:38:47 SD: 5.1131 cents 36:37:39:48 SD: 1.8333 cents 63:65:68:84 SD: 1.8105 cents 75:77:81:100 SD: 1.0697 cents 99:102:107:132 SD: 1.0623 cents 102:105:110:136 SD: 0.9621 cents 138:142:149:184 SD: 0.2792 cents 174:179:188:232 SD: 0.2623 cents 213:219:230:284 SD: 0.2471 cents 312:321:337:416 SD: 0.1687 cents 351:361:379:468 SD: 0.1301 cents 387:398:418:516 SD: 0.0996 cents 525:540:567:700 SD: 0.0000 cents