Scala analysis: mavchrome1
First 25/24&135/128 scale = diff7b helmholtz trab7
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: 8/5 813.686286 minor 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: 16/15 111.7313 minor diatonic semitone 6: 75/64 274.5824 classic augmented second 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 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: 2 128/75 925.418 cents diminished seventh 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 15/8 1088.269 cents classic major seventh 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 4 5 6 7 0.0 : 111.7 386.3 498.0 702.0 813.7 1088.3 1200.0 111.7 : 274.6 386.3 590.2 702.0 976.5 1088.3 1200.0 386.3 : 111.7 315.6 427.4 702.0 813.7 925.4 1200.0 498.0 : 203.9 315.6 590.2 702.0 813.7 1088.3 1200.0 702.0 : 111.7 386.3 498.0 609.8 884.4 996.1 1200.0 813.7 : 274.6 386.3 498.0 772.6 884.4 1088.3 1200.0 1088.3: 111.7 223.5 498.0 609.8 813.7 925.4 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 : 16/15, 111.7313 cents, amount: 4 Most common interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 172.74541 cents, oct.: 1209.21787 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.413252 Lumma stability : 0.270944 Lumma impropriety factor : 0.085200 Rothenberg efficiency : 0.506122 redundancy: 0.493878 Efficiency x scale size : 3.542857 Number of different interval sizes : 18 = 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 : 2048/2025, 19.5526 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Scale is fully connected 5-limit major-minor triadic Scale is a complete diamond : 1 3 15 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 100.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- 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 : 0.267406 Specific harmonicity : 0.212201 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 : 45.5, average 6.50000 Mersenne's string divisions : 2919735 Sum of van Prooijen's expressibility: 4.70437, average 0.67205 Sum of Tenney's harmonic distance : 9.52084, average 1.36012 Vogel's harmonic complexity : 11.57143 Wille's k value : 112 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 93.76698, average 3.34882 Lattice compactness (without 2's) : 39.08641, average 1.39594 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.57143 16 1 3: -1 .. 1 0.00000 4 2 5: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is weakly epimorphic with val: <7 11 15| Scale is JI-epimorphic with val: <7 11 16| = patent Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 40.4122 c. M:-59.6973 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 23.2946 c. M:-35.2883 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 17.6182 c. M:-26.3137 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 9.6918 c. M: 13.6863 c. Double Harmonic Major, Major Gipsy, Bhairav That, Mela Mayamalavagaula, Raga Paraj, Kalingada, Gaulipantu, Lalitapancamam, Gandhakriya, Kalingda, Manjiri, Chromatic 2nd Byzantine Liturgical, Hitzazkiar: Greece, Maqam Zengule, Hijaz Kar, Suzidil 19: 2 4 2 3 2 4 2 P T3 I SD: 9.5480 c. M: 14.5845 c. 22: 2 5 2 4 2 5 2 N T3 I SD: 4.7239 c. M:-7.1359 c. Double Harmonic Major 31: 3 7 3 5 3 7 3 N T3 I SD: 3.6565 c. M: 5.1808 c. Double Harmonic Major, Major Gipsy 43: 4 10 4 7 4 10 4 N T3 I SD: 3.2756 c. M: 4.3840 c. 53: 5 12 5 9 5 12 5 N T3 I SD: 1.0911 c. M:-1.4763 c. 65: 6 15 6 11 6 15 6 N T3 I SD: 0.9258 c. M:-1.3786 c. 118: 11 27 11 20 11 27 11 N T3 I SD: 0.1703 c. M:-0.2601 c. 376: 35 86 35 64 35 86 35 N T3 I SD: 0.1210 c. M:-0.1727 c. 441: 41 101 41 75 41 101 41 N T3 I SD: 0.1091 c. M:-0.1667 c. 494: 46 113 46 84 46 113 46 N T3 I SD: 0.0564 c. M: 0.0789 c. 612: 57 140 57 104 57 140 57 N T3 I SD: 0.0277 c. M: 0.0392 c. 1171: 109 268 109 199 109 268 109 N T3 I SD: 0.0215 c. M:-0.0319 c. 1289: 120 295 120 219 120 295 120 N T3 I SD: 0.0211 c. M:-0.0323 c. 1665: 155 381 155 283 155 381 155 N T3 I SD: 0.0183 c. M: 0.0270 c. 1783: 166 408 166 303 166 408 166 N T3 I SD: 0.0067 c. M:-0.0095 c. 1901: 177 435 177 323 177 435 177 N T3 I SD: 0.0068 c. M: 0.0093 c. 2395: 223 548 223 407 223 548 223 N T3 I SD: 0.0063 c. M: 0.0089 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: 23.5575 cents 4 x 5 x 6 x x 8 S SD: 0.0000 cents 5 x 6:7 x 8:9:10 S SD: 26.1717 cents 6 x x 8:9:10:11:12 S SD: 16.1347 cents 7:8:9 x x 11:13:14 SD: 26.7527 cents 8:9:10:11:12:13:15:16 SD: 15.6853 cents 9:10:11:12 x 14:17:18 SD: 15.8553 cents 10:11 x 13:15:16:19:20 SD: 12.1163 cents 12:13:15:16:18:19:23:24 SD: 7.1385 cents 15:16:19:20:23:24:28:30 SD: 6.4415 cents 16:17:20:21:24:26:30:32 SD: 5.5507 cents 24:26:30:32:36:38:45:48 SD: 4.6271 cents 27:29:34:36:41:43:51:54 SD: 4.4854 cents 28:30:35:37:42:45:53:56 SD: 3.5837 cents 30:32:38:40:45:48:56:60 SD: 3.4561 cents 32:34:40:43:48:51:60:64 SD: 2.3619 cents 48:51:60:64:72:77:90:96 SD: 1.1622 cents 60:64:75:80:90:96:113:120 SD: 1.0968 cents 72:77:90:96:108:115:135:144 SD: 0.7736 cents 120:128:150:160:180:192:225:240 SD: 0.0000 cents