Scala analysis: mavdie1
First 128/125&135/128 scale = Dwarf(<19 14 21|) = efg3355
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: 6/5 315.641287 minor third 3: 5/4 386.313714 major third 4: 4/3 498.044999 perfect fourth 5: 3/2 701.955001 perfect fifth 6: 8/5 813.686286 minor sixth 7: 5/3 884.358713 major sixth, BP sixth 8: 15/8 1088.268715 classic major seventh 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 16/15 111.7313 minor diatonic semitone 2: 9/8 203.9100 major whole tone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 16/15 111.7313 minor diatonic semitone 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 25/24 70.6724 classic chromatic semitone, minor chroma 8: 9/8 203.9100 major whole tone 9: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 4 16/15 111.731 cents minor diatonic semitone 1: 3 9/8 203.910 cents major whole tone 2: 2 10/9 182.404 cents minor whole tone 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 2 75/64 274.582 cents classic augmented second 2: 4 6/5 315.641 cents minor third 3: 6 5/4 386.314 cents major third 3: 3 32/25 427.373 cents classic diminished fourth 4: 6 4/3 498.045 cents perfect fourth 4: 2 45/32 590.224 cents diatonic tritone 4: 1 36/25 631.283 cents classic diminished fifth 5: 1 25/18 568.717 cents classic augmented fourth 5: 2 64/45 609.776 cents 2nd tritone 5: 6 3/2 701.955 cents perfect fifth 6: 3 25/16 772.627 cents classic augmented fifth 6: 6 8/5 813.686 cents minor sixth 7: 4 5/3 884.359 cents major sixth, BP sixth 7: 2 128/75 925.418 cents diminished seventh 7: 1 225/128 976.537 cents augmented sixth 7: 2 9/5 1017.596 cents just minor seventh, BP seventh 8: 3 16/9 996.090 cents Pythagorean minor seventh 8: 4 15/8 1088.269 cents classic major seventh 8: 2 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 111.7 315.6 386.3 498.0 702.0 813.7 884.4 1088.3 1200.0 111.7 : 203.9 274.6 386.3 590.2 702.0 772.6 976.5 1088.3 1200.0 315.6 : 70.7 182.4 386.3 498.0 568.7 772.6 884.4 996.1 1200.0 386.3 : 111.7 315.6 427.4 498.0 702.0 813.7 925.4 1129.3 1200.0 498.0 : 203.9 315.6 386.3 590.2 702.0 813.7 1017.6 1088.3 1200.0 702.0 : 111.7 182.4 386.3 498.0 609.8 813.7 884.4 996.1 1200.0 813.7 : 70.7 274.6 386.3 498.0 702.0 772.6 884.4 1088.3 1200.0 884.4 : 203.9 315.6 427.4 631.3 702.0 813.7 1017.6 1129.3 1200.0 1088.3: 111.7 223.5 427.4 498.0 609.8 813.7 925.4 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 203.9100 cents 27/25, 133.2376 cents 25/24, 70.6724 cents 2: 182.4037 .. 315.6413 cents 27/25, 133.2376 cents 80/81,-21.5063 cents 3: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 4: 498.0450 .. 631.2826 cents 27/25, 133.2376 cents 25/24, 70.6724 cents 5: 568.7174 .. 701.9550 cents 27/25, 133.2376 cents 625/648,-62.5651 cents 6: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 7: 884.3587 .. 1017.5963 cents 27/25, 133.2376 cents 25/24, 70.6724 cents 8: 996.0900 .. 1129.3276 cents 27/25, 133.2376 cents 80/81,-21.5063 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.886639 Largest / Average step : 1.529325 Largest / Smallest step : 2.885284 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 : 133.27259 cents, oct.: 1199.45332 cents Scale is not proper Step pattern alph. order: ABCABACBA Step pattern size order : MLSMLMSLM Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.387531 Lumma stability : 0.353362 Lumma impropriety factor : 0.087981 Rothenberg efficiency : 0.485009 redundancy: 0.514991 Efficiency x scale size : 4.365079 Number of different interval sizes : 24 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.00000 = 3 Median interval variety : 2.5 Lowest interval variety : 2 Smallest interval difference : 2048/2025, 19.5526 cents Number of recognisable fifths : 6, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale is a complete genus musicum : 2^m 3^2 5^2 Scale is a complete diamond : 1 3 5 15 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 9 = 100.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 6 and 7 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 4-5 -- 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 : 0.231275 Specific harmonicity : 0.200883 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 : 55.0, average 6.11111 Mersenne's string divisions : 256936680 Sum of van Prooijen's expressibility: 6.10231, average 0.67803 Sum of Tenney's harmonic distance : 12.17406, average 1.35267 Vogel's harmonic complexity : 11.55556 Wille's k value : 112 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 140.54145, average 3.12314 Lattice compactness (without 2's) : 68.51596, average 1.52258 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.55556 17 1 3: -1 .. 1 0.00000 6 2 5: -1 .. 1 0.00000 6 6 Average exponent except 2's : 0 / 9 = 0.00000 Average absolute exponent except 2's: 12 / 9 = 1.33333 Scale is weakly epimorphic with val: <9 13 21| Scale is JI-epimorphic with val: <9 14 21| = patent Scale is weakly epimorphic with val: <9 15 19| Scale is weakly epimorphic with val: <9 15 20| Scale is weakly epimorphic with val: <9 15 22| Scale is weakly epimorphic with val: <9 15 23|
FIT/MODE
9: 1 1 1 1 1 1 1 1 1 SP B ME I SD: 30.9039 c. M: 48.9746 c. Pelog Nawanada: Sunda 10: 1 2 0 1 2 1 0 2 1 N D3 I SD: 26.0517 c. M:-44.3587 c. 12: 1 2 1 1 2 1 1 2 1 P B ME I SD: 11.2882 c. M: 15.6413 c. Genus chromaticum, Tcherepnin Nonatonic mode 1, Augmented-9 19: 2 3 1 2 3 2 1 3 2 N D3 I SD: 8.4208 c. M: 14.5845 c. 22: 2 4 1 2 4 2 1 4 2 N I SD: 6.8863 c. M:-11.6314 c. 31: 3 5 2 3 5 3 2 5 3 N I SD: 4.2782 c. M: 5.9639 c. Genus chromaticum 34: 3 6 2 3 6 3 2 6 3 N I SD: 3.5699 c. M:-5.8489 c. Genus chromaticum 53: 5 9 3 5 9 5 3 9 5 N I SD: 1.1510 c. M:-1.4763 c. 118: 11 20 7 11 20 11 7 20 11 N I SD: 0.2363 c. M:-0.3870 c. 289: 27 49 17 27 49 27 17 49 27 N I SD: 0.2228 c. M:-0.3794 c. 323: 30 55 19 30 55 30 19 55 30 N I SD: 0.1810 c. M:-0.2762 c. 441: 41 75 26 41 75 41 26 75 41 N I SD: 0.0963 c. M:-0.1667 c. 494: 46 84 29 46 84 46 29 84 46 N I SD: 0.0857 c. M: 0.1482 c. 559: 52 95 33 52 95 52 33 95 52 N I SD: 0.0747 c. M:-0.1034 c. 612: 57 104 36 57 104 57 36 104 57 N I SD: 0.0324 c. M:-0.0450 c. 730: 68 124 43 68 124 68 43 124 68 N I SD: 0.0320 c. M:-0.0495 c. 1171: 109 199 69 109 199 109 69 199 109 N I SD: 0.0200 c. M:-0.0319 c. 1783: 166 303 105 166 303 166 105 303 166 N I SD: 0.0066 c. M:-0.0095 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x x 4 x x 5 x 6 S SD: 0.0000 cents 4 x x 5 x 6 x 7 x 8 S SD: 21.1168 cents 5 x 6 x 7 x 8 x 9:10 S SD: 22.0266 cents 6 x 7 x 8:9 x 10:11:12 S SD: 10.3979 cents 7 x 8:9 x x 11:12:13:14 SD: 19.1045 cents 8:9 x 10:11:12:13 x 15:16 SD: 15.6853 cents 9:10:11 x 12 x 14:15:17:18 SD: 13.2060 cents 10:11:12 x 13:15:16:17:19:20 SD: 10.0470 cents 11:12:13:14:15:17 x 18:21:22 SD: 12.0884 cents 12:13:14:15:16:18:19:20:23:24 SD: 7.7583 cents 13:14 x 16:17:20:21:22:24:26 SD: 9.4701 cents 14:15:17:18:19:21:22:23:26:28 SD: 8.3628 cents 15:16:18:19:20:23:24:25:28:30 SD: 5.0100 cents 24:26:29:30:32:36:38:40:45:48 SD: 3.8372 cents 30:32:36:38:40:45:48:50:56:60 SD: 2.6881 cents 40:43:48:50:53:60:64:67:75:80 SD: 2.1485 cents 45:48:54:56:60:68:72:75:84:90 SD: 1.8665 cents 48:51:58:60:64:72:77:80:90:96 SD: 1.6091 cents 60:64:72:75:80:90:96:100:113:120 SD: 0.8530 cents 104:111:125:130:139:156:166:173:195:208 SD: 0.8203 cents 105:112:126:131:140:158:168:175:197:210 SD: 0.7219 cents 120:128:144:150:160:180:192:200:225:240 S SD: 0.0000 cents