Scala analysis: mavchrome3
Third 25/24&135/128 scale inverse mavchrome2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 15/8 1088.268715 classic major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 16/15 111.7313 minor diatonic semitone 2: 75/64 274.5824 classic augmented second 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 9/8 203.9100 major whole tone 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 1: 1 75/64 274.582 cents classic augmented second 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 2 6/5 315.641 cents minor third 2: 4 5/4 386.314 cents major third 3: 1 32/25 427.373 cents classic diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 2 45/32 590.224 cents diatonic tritone 4: 2 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 25/16 772.627 cents classic augmented fifth 5: 4 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 225/128 976.537 cents augmented sixth 6: 1 128/75 925.418 cents diminished seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 3 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 386.3 498.0 702.0 884.4 1088.3 1200.0 111.7 : 274.6 386.3 590.2 772.6 976.5 1088.3 1200.0 386.3 : 111.7 315.6 498.0 702.0 813.7 925.4 1200.0 498.0 : 203.9 386.3 590.2 702.0 813.7 1088.3 1200.0 702.0 : 182.4 386.3 498.0 609.8 884.4 996.1 1200.0 884.4 : 203.9 315.6 427.4 702.0 813.7 1017.6 1200.0 1088.3: 111.7 223.5 498.0 609.8 813.7 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 274.5824 cents 1125/1024, 162.8511 cents 16/15, 111.7313 cents 2: 223.4626 .. 386.3137 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents 3: 427.3726 .. 590.2237 cents 1125/1024, 162.8511 cents 128/125, 41.0589 cents 4: 609.7763 .. 772.6274 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 976.5374 cents 1125/1024, 162.8511 cents 128/125, 41.0589 cents 6: 925.4176 .. 1088.2687 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 75/64, 274.5824 cents Average / Smallest step : 1.534293 Largest / Average step : 1.601731 Largest / Smallest step : 2.457525 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Most common interval of one step : 16/15, 111.7313 cents, amount: 3 Least squares average step : 175.26943 cents, oct.: 1226.88598 cents Scale is not proper Step pattern alph. order: ABACDCA Step pattern size order : ADACBCA Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.448366 Lumma stability : 0.270944 Lumma impropriety factor : 0.085200 Rothenberg efficiency : 0.478912 redundancy: 0.521088 Efficiency x scale size : 3.352381 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common triad is 0.0 701.955 813.686 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 5 = 71.4286% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 15 Scale harmonicity : 0.039788 Average absolute harmonicity : 0.267965 Specific harmonicity : 0.222376 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 2.880000E+04, 14.81378 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 43.0, average 6.14286 Mersenne's string divisions : 1796760 Sum of van Prooijen's expressibility: 4.70437, average 0.67205 Sum of Tenney's harmonic distance : 9.09488, average 1.29927 Vogel's harmonic complexity : 12.14286 Wille's k value : 112 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 87.33702, average 3.11918 Lattice compactness (without 2's) : 40.08641, average 1.43166 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.14286 13 1 3: -1 .. 1 -0.14286 5 2 5: -1 .. 1 0.28571 4 4 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 38.3298 c. M:-59.6973 c. Lebeng 9: 1 2 1 1 2 1 1 P M ME S SD: 29.3006 c. M:-48.9746 c. Pelog Saptanada: Sunda 10: 1 2 1 2 1 2 1 P M ME I SD: 22.1943 c. M: 44.3587 c. 12: 1 3 1 2 2 2 1 N T3 SD: 10.1055 c. M:-15.6413 c. Mela Suryakanta, Bhairubahar That, Raga Supradhipam, Sowrashtram (Sourashtra), Jaganmohini, Major-Melodic Phrygian, Hungarian Gipsy inverse 19: 2 4 2 3 3 3 2 P T3 SD: 9.1332 c. M: 14.5845 c. 22: 2 5 2 4 3 4 2 N SD: 6.2254 c. M: 11.6314 c. 31: 3 7 3 5 5 5 3 N T3 SD: 4.2852 c. M:-5.9639 c. 34: 3 8 3 6 5 6 3 N SD: 3.9094 c. M:-5.8489 c. 43: 4 10 4 7 7 7 4 N T3 SD: 4.3254 c. M:-8.6645 c. 53: 5 12 5 9 8 9 5 N SD: 1.0787 c. M:-1.4763 c. 65: 6 15 6 11 10 11 6 N SD: 1.0227 c. M:-1.7951 c. 118: 11 27 11 20 18 20 11 N SD: 0.2193 c. M:-0.3870 c. 289: 27 66 27 49 44 49 27 N SD: 0.2443 c. M:-0.3794 c. 323: 30 74 30 55 49 55 30 N SD: 0.1959 c. M:-0.2762 c. 376: 35 86 35 64 57 64 35 N SD: 0.1612 c. M: 0.3162 c. 441: 41 101 41 75 67 75 41 N SD: 0.1048 c. M:-0.1667 c. 494: 46 113 46 84 75 84 46 N SD: 0.0737 c. M: 0.1482 c. 559: 52 128 52 95 85 95 52 N SD: 0.0717 c. M:-0.1034 c. 612: 57 140 57 104 93 104 57 N SD: 0.0289 c. M: 0.0450 c. 1171: 109 268 109 199 178 199 109 N SD: 0.0204 c. M:-0.0319 c. 1783: 166 408 166 303 271 303 166 N SD: 0.0071 c. M:-0.0095 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 0.0000 cents 4 x 5 x 6:7 x 8 S SD: 21.1168 cents 5 x 6:7 x 8:9:10 S SD: 29.7446 cents 6 x x 8:9:10:11:12 S SD: 7.7812 cents 7:8:9 x 11:12:13:14 SD: 26.7625 cents 8:9:10:11:12:13:15:16 SD: 16.4479 cents 9:10:11:12:14:15:17:18 SD: 14.7327 cents 10:11 x 13:15:17:19:20 SD: 13.3960 cents 11:12:14:15:17:18:21:22 SD: 13.2893 cents 12:13:15:16:18:20:23:24 SD: 6.6522 cents 15:16:19:20:23:25:28:30 SD: 6.4415 cents 16:17:20:21:24:27:30:32 SD: 5.0543 cents 24:26:30:32:36:40:45:48 SD: 3.8345 cents 30:32:38:40:45:50:56:60 SD: 3.4561 cents 32:34:40:43:48:53:60:64 SD: 2.6544 cents 44:47:55:59:66:73:83:88 SD: 2.3642 cents 48:51:60:64:72:80:90:96 SD: 0.9680 cents 72:77:90:96:108:120:135:144 SD: 0.6432 cents 120:128:150:160:180:200:225:240 SD: 0.0000 cents