Scala analysis: 579_M87
Miscellaneous tetrachord 23/21 * 14/13 * 26/23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/21 157.493440 2: 46/39 285.791685 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 26/23 212.2533 1: 23/21 157.4934 2: 14/13 128.2982 2/3-tone 3: 26/23 212.2533
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 14/13 128.298 cents 2/3-tone 1: 1 23/21 157.493 cents 1: 1 26/23 212.253 cents 2: 1 46/39 285.792 cents 2: 1 28/23 340.552 cents 2: 1 26/21 369.747 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 : 157.5 285.8 498.0 157.5: 128.3 340.6 498.0 285.8: 212.3 369.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.2982 .. 212.2533 cents 169/161, 83.9551 cents 14/13, 128.2982 cents 2: 285.7917 .. 369.7468 cents 169/161, 83.9551 cents 529/507, 73.5384 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 14/13, 128.2982 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 26/23, 212.2533 cents Average / Smallest step : 1.293977 Largest / Average step : 1.278519 Largest / Smallest step : 1.654374 Median interval of one step : 23/21, 157.4934 cents, amount: 1 Least squares average step : 158.80084 cents, oct.: 476.40253 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 955-tone equal temperament with octave 4/3 degrees: 302 548 955 Least number of segments generator : 478 of 249.283 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 747 of 389.570 cents and inv. generated superset size: 30 = 27 more = 1000.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 73.53837 cents Scale diversity : 1.352215 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.662862 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 : 299/294, 29.1952 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 23 Odd number limit : 39 (O: 23 U: 39) Highest odd numerator or denominator: 39 Scale harmonicity : 0.012627 Average absolute harmonicity : 0.082393 Specific harmonicity : 0.057007 Fundamental : 1/273, -8.0928 octaves, 0.9583 Hz. Guide tone : 92, 6.5236 octaves, 24069.552 Hz. Exponens Consonantiae : 2.511600E+04, 14.61632 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 68.0, average 22.66667 Mersenne's string divisions : 26180 Sum of van Prooijen's expressibility: 3.42991, average 1.14330 Sum of Tenney's harmonic distance : 7.01695, average 2.33898 Vogel's harmonic complexity : 29.66667 Wille's k value : 149 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 4 Triangular lattice diameter : 1 Lattice compactness : 11.88171, average 1.98029 Lattice compactness (without 2's) : 8.70674, average 1.45112 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 3 3: -1 ..-1 -1.00000 3 1 7: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 2 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 18 25 32| Scale is weakly epimorphic with val: <6 10 18 26 31| Scale is weakly epimorphic with val: <6 10 18 28 35| Scale is weakly epimorphic with val: <6 10 18 29 31| Scale is weakly epimorphic with val: <6 10 19 26 33| Scale is weakly epimorphic with val: <6 10 19 27 32| Scale is weakly epimorphic with val: <6 10 19 29 36| Scale is weakly epimorphic with val: <6 10 19 30 32| Scale is weakly epimorphic with val: <6 10 20 25 33| Scale is weakly epimorphic with val: <6 10 20 27 34| Scale is weakly epimorphic with val: <6 10 20 28 33| Scale is weakly epimorphic with val: <6 10 21 25 32| Scale is weakly epimorphic with val: <6 10 21 26 34| Scale is weakly epimorphic with val: <6 10 21 28 35| Scale is weakly epimorphic with val: <6 10 21 29 34| Scale is weakly epimorphic with val: <6 10 22 26 33| Scale is weakly epimorphic with val: <6 10 22 27 35| Scale is weakly epimorphic with val: <6 10 22 29 36| Scale is weakly epimorphic with val: <6 10 22 30 35| Scale is weakly epimorphic with val: <6 11 18 25 32| Scale is weakly epimorphic with val: <6 11 18 26 34| Scale is weakly epimorphic with val: <6 11 18 28 32| Scale is weakly epimorphic with val: <6 11 19 26 33| Scale is weakly epimorphic with val: <6 11 19 27 35| Scale is weakly epimorphic with val: <6 11 19 29 33| Scale is weakly epimorphic with val: <6 11 20 25 33| Scale is weakly epimorphic with val: <6 11 20 27 34| Scale is weakly epimorphic with val: <6 11 20 28 36| Scale is weakly epimorphic with val: <6 11 20 30 34| Scale is weakly epimorphic with val: <6 11 21 25 35| Scale is weakly epimorphic with val: <6 11 21 26 34| Scale is weakly epimorphic with val: <6 11 21 28 35| Scale is weakly epimorphic with val: <6 11 22 26 36| Scale is weakly epimorphic with val: <6 11 22 27 35| Scale is weakly epimorphic with val: <6 11 22 29 36| Scale is weakly epimorphic with val: <7 10 18 26 31| Scale is weakly epimorphic with val: <7 10 18 27 33| Scale is weakly epimorphic with val: <7 10 18 29 31| Scale is weakly epimorphic with val: <7 10 18 30 36| Scale is weakly epimorphic with val: <7 10 19 25 31| Scale is weakly epimorphic with val: <7 10 19 27 32| Scale is weakly epimorphic with val: <7 10 19 28 34| Scale is weakly epimorphic with val: <7 10 19 30 32| Scale is weakly epimorphic with val: <7 10 20 25 33| Scale is weakly epimorphic with val: <7 10 20 26 32| Scale is weakly epimorphic with val: <7 10 20 28 33| Scale is weakly epimorphic with val: <7 10 20 29 35| Scale is weakly epimorphic with val: <7 10 21 26 34| Scale is weakly epimorphic with val: <7 10 21 27 33| Scale is weakly epimorphic with val: <7 10 21 29 34| Scale is weakly epimorphic with val: <7 10 21 30 36| Scale is weakly epimorphic with val: <7 10 22 25 31| Scale is weakly epimorphic with val: <7 10 22 27 35| Scale is weakly epimorphic with val: <7 10 22 28 34| Scale is weakly epimorphic with val: <7 10 22 30 35| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 26 34| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 18 27 36| Scale is weakly epimorphic with val: <7 11 18 29 31| Scale is weakly epimorphic with val: <7 11 18 29 34| Scale is weakly epimorphic with val: <7 11 18 30 30| Scale is weakly epimorphic with val: <7 11 18 30 33| Scale is weakly epimorphic with val: <7 11 18 30 36| Scale is JI-epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 25 34| Scale is weakly epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 11 19 27 35| Scale is weakly epimorphic with val: <7 11 19 28 31| Scale is weakly epimorphic with val: <7 11 19 28 34| Scale is weakly epimorphic with val: <7 11 19 30 32| Scale is weakly epimorphic with val: <7 11 19 30 35| Scale is weakly epimorphic with val: <7 11 20 25 30| Scale is weakly epimorphic with val: <7 11 20 25 33| Scale is weakly epimorphic with val: <7 11 20 25 36| Scale is JI-epimorphic with val: <7 11 20 26 32| Scale is weakly epimorphic with val: <7 11 20 26 35| Scale is weakly epimorphic with val: <7 11 20 28 30| Scale is weakly epimorphic with val: <7 11 20 28 33| Scale is weakly epimorphic with val: <7 11 20 28 36| Scale is weakly epimorphic with val: <7 11 20 29 32| Scale is weakly epimorphic with val: <7 11 20 29 35| Scale is weakly epimorphic with val: <7 11 21 26 31| Scale is weakly epimorphic with val: <7 11 21 26 34| Scale is weakly epimorphic with val: <7 11 21 27 30| Scale is JI-epimorphic with val: <7 11 21 27 33| Scale is weakly epimorphic with val: <7 11 21 27 36| Scale is weakly epimorphic with val: <7 11 21 29 31| Scale is weakly epimorphic with val: <7 11 21 29 34| Scale is weakly epimorphic with val: <7 11 21 30 30| Scale is weakly epimorphic with val: <7 11 21 30 33| Scale is weakly epimorphic with val: <7 11 21 30 36| Scale is weakly epimorphic with val: <7 11 22 25 31| Scale is weakly epimorphic with val: <7 11 22 25 34| Scale is weakly epimorphic with val: <7 11 22 27 32| Scale is weakly epimorphic with val: <7 11 22 27 35| Scale is weakly epimorphic with val: <7 11 22 28 31| Scale is JI-epimorphic with val: <7 11 22 28 34| Scale is weakly epimorphic with val: <7 11 22 30 32| Scale is weakly epimorphic with val: <7 11 22 30 35| Scale is weakly epimorphic with val: <7 12 18 26 34| Scale is weakly epimorphic with val: <7 12 18 27 33| Scale is weakly epimorphic with val: <7 12 18 30 33| Scale is weakly epimorphic with val: <7 12 19 25 34| Scale is weakly epimorphic with val: <7 12 19 27 35| Scale is weakly epimorphic with val: <7 12 19 28 34| Scale is weakly epimorphic with val: <7 12 20 25 33| Scale is weakly epimorphic with val: <7 12 20 26 35| Scale is weakly epimorphic with val: <7 12 20 28 36| Scale is weakly epimorphic with val: <7 12 20 29 35| Scale is weakly epimorphic with val: <7 12 21 26 34| Scale is weakly epimorphic with val: <7 12 21 27 36| Scale is weakly epimorphic with val: <7 12 21 30 36| Scale is weakly epimorphic with val: <7 12 22 27 35| Scale is weakly epimorphic with val: <8 11 18 25 32| Scale is weakly epimorphic with val: <8 11 18 27 33| Scale is weakly epimorphic with val: <8 11 18 28 32| Scale is weakly epimorphic with val: <8 11 18 30 36| Scale is weakly epimorphic with val: <8 11 19 25 31| Scale is weakly epimorphic with val: <8 11 19 26 33| Scale is weakly epimorphic with val: <8 11 19 28 34| Scale is weakly epimorphic with val: <8 11 19 29 33| Scale is weakly epimorphic with val: <8 11 20 26 32| Scale is weakly epimorphic with val: <8 11 20 27 34| Scale is weakly epimorphic with val: <8 11 20 29 35| Scale is weakly epimorphic with val: <8 11 20 30 34| Scale is weakly epimorphic with val: <8 11 21 25 35| Scale is weakly epimorphic with val: <8 11 21 27 33| Scale is weakly epimorphic with val: <8 11 21 28 35| Scale is weakly epimorphic with val: <8 11 21 30 36| Scale is weakly epimorphic with val: <8 11 22 25 31| Scale is weakly epimorphic with val: <8 11 22 26 36| Scale is weakly epimorphic with val: <8 11 22 28 34| Scale is weakly epimorphic with val: <8 11 22 29 36| Scale is weakly epimorphic with val: <8 12 18 25 32| Scale is weakly epimorphic with val: <8 12 18 27 33| Scale is weakly epimorphic with val: <8 12 18 28 35| Scale is weakly epimorphic with val: <8 12 18 30 33| Scale is weakly epimorphic with val: <8 12 19 25 34| Scale is weakly epimorphic with val: <8 12 19 26 33| Scale is weakly epimorphic with val: <8 12 19 28 34| Scale is weakly epimorphic with val: <8 12 19 29 36| Scale is weakly epimorphic with val: <8 12 20 26 35| Scale is weakly epimorphic with val: <8 12 20 27 34| Scale is weakly epimorphic with val: <8 12 20 29 35| Scale is weakly epimorphic with val: <8 12 21 25 32| Scale is weakly epimorphic with val: <8 12 21 27 36| Scale is weakly epimorphic with val: <8 12 21 28 35| Scale is weakly epimorphic with val: <8 12 21 30 36| Scale is weakly epimorphic with val: <8 12 22 26 33| Scale is weakly epimorphic with val: <8 12 22 29 36|
FIT/MODE
3: 1 1 1 SP B ME I SD: 27.1453 c. M:-46.2383 c. 4: 1 1 2 P M ME S SD: 28.5178 c. M: 36.7692 c. 5: 2 1 2 SP M ME I SD: 25.2379 c. M:-41.7246 c. 6: 2 1 3 P T3 SD: 21.7914 c. M: 36.7692 c. 7: 2 2 3 SP M ME S SD: 8.7998 c. M: 15.1949 c. 9: 3 2 4 SP T3 SD: 7.1979 c. M: 9.1000 c. 12: 4 3 5 SP T3 SD: 5.6283 c. M:-8.5216 c. Raga Malasri, Peruvian tritonic 1 16: 5 4 7 SP T3 SD: 3.4285 c. M: 5.6414 c. 19: 6 5 8 SP T3 SD: 1.4776 c. M:-2.5502 c. 35: 11 9 15 SP T3 SD: 0.8866 c. M: 1.1945 c. 47: 15 12 20 SP T3 SD: 0.8612 c. M:-1.4571 c. 54: 17 14 23 SP T3 SD: 0.4112 c. M: 0.7015 c. 82: 26 21 35 SP T3 SD: 0.3088 c. M:-0.4233 c. 101: 32 26 43 SP T3 SD: 0.2143 c. M:-0.3030 c. 136: 43 35 58 SP T3 SD: 0.0866 c. M: 0.1482 c. 237: 75 61 101 SP T3 SD: 0.0669 c. M:-0.1157 c. 291: 92 75 124 SP T3 SD: 0.0263 c. M: 0.0359 c. 427: 135 110 182 SP T3 SD: 0.0246 c. M: 0.0319 c. 528: 167 136 225 SP T3 SD: 0.0213 c. M:-0.0322 c. 664: 210 171 283 SP T3 SD: 0.0151 c. M:-0.0208 c. 819: 259 211 349 SP T3 SD: 0.0133 c. M:-0.0217 c. 955: 302 246 407 SP T3 SD: 0.0025 c. M:-0.0035 c. 2201: 696 567 938 SP T3 SD: 0.0013 c. M: 0.0017 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 5 x S SD: 100.5220 cents 5 x 6:7 S SD: 44.7932 cents 6 x 7:8 S SD: 9.4604 cents 7 x 8:9 S SD: 41.6748 cents 8:9 x 11 SD: 35.3288 cents 9:10:11:12 H SD: 22.1537 cents 10:11:12:13 H SD: 17.8530 cents 11:12:13:15 SD: 13.2176 cents 12:13:14:16 S SD: 8.9193 cents 21:23:25:28 SD: 5.3516 cents 33:36:39:44 SD: 2.5537 cents 51:56:60:68 SD: 2.0872 cents 72:79:85:96 SD: 1.1679 cents 84:92:99:112 SD: 0.4482 cents 189:207:223:252 SD: 0.1991 cents 273:299:322:364 SD: 0.0000 cents