Scala analysis: mavchrome4
Fourth 25/24&135/128 scale inverse mavchrome5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 6/5 315.641287 minor 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: 9/8 203.9100 major whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 10/9 182.4037 minor whole tone 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: 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 32/27 294.135 cents Pythagorean minor third 2: 3 6/5 315.641 cents minor third 2: 3 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: 3 8/5 813.686 cents minor sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major 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 : 203.9 315.6 498.0 702.0 813.7 1088.3 1200.0 203.9 : 111.7 294.1 498.0 609.8 884.4 996.1 1200.0 315.6 : 182.4 386.3 498.0 772.6 884.4 1088.3 1200.0 498.0 : 203.9 315.6 590.2 702.0 905.9 1017.6 1200.0 702.0 : 111.7 386.3 498.0 702.0 813.7 996.1 1200.0 813.7 : 274.6 386.3 590.2 702.0 884.4 1088.3 1200.0 1088.3: 111.7 315.6 427.4 609.8 813.7 925.4 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: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 2048/2025, 19.5526 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 .. 905.8650 cents 135/128, 92.1787 cents 128/125, 41.0589 cents 6: 925.4176 .. 1088.2687 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 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 : 172.39422 cents, oct.: 1206.75956 cents Scale is strictly proper Step pattern alph. order: ABCABDB Step pattern size order : CABCADA Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.434704 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.303532 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 3.266667 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 intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 3 = 42.8571% 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 Scale is differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 15 Scale harmonicity : 0.037313 Average absolute harmonicity : 0.270800 Specific harmonicity : 0.232220 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 4.320000E+04, 15.39874 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 39.5, average 5.64286 Mersenne's string divisions : 5870865 Sum of van Prooijen's expressibility: 4.48252, average 0.64036 Sum of Tenney's harmonic distance : 9.17406, average 1.31058 Vogel's harmonic complexity : 12.00000 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 87.69955, average 3.13213 Lattice compactness (without 2's) : 41.25798, average 1.47350 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.00000 14 1 3: -1 .. 2 0.57143 6 3 5: -1 .. 1 -0.14286 3 3 Average exponent except 2's : 3 / 7 = 0.42857 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: 33.3285 c. M: 59.6973 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 25.8629 c. M:-44.3587 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 1 2 2 1 3 1 P D3 SD: 9.2003 c. M: 15.6413 c. Harmonic Minor, Mischung 4, Pilu That, Mela Kiravani, Raga Kiranavali, Kirvani (Kirwani), Kalyana Vasantha, Deshi(3), Maqam Bayat-e-Esfahan, Sultani Yakah, Zhalibny Minor, Armoniko minore: Greece 19: 3 2 3 3 2 4 2 SP D3 SD: 9.0995 c. M: 14.5845 c. Nineteen-tone Harmonic Minor 22: 4 2 3 4 2 5 2 P SD: 8.1766 c. M:-14.2718 c. Twenty-two tone Harmonic Minor 31: 5 3 5 5 3 7 3 SP D3 SD: 5.5622 c. M: 10.3616 c. Thirty-one tone Harmonic Minor 34: 6 3 5 6 3 8 3 P SD: 4.3829 c. M:-7.8547 c. Thirty-four tone Harmonic Minor 41: 7 4 6 7 4 9 4 SP SD: 3.8489 c. M:-6.3099 c. Forty-one tone Harmonic Minor 53: 9 5 8 9 5 12 5 SP SD: 0.9247 c. M: 1.4763 c. Fifty-three tone Harmonic Minor 65: 11 6 10 11 6 15 6 SP SD: 1.0064 c. M: 1.7951 c. 118: 20 11 18 20 11 27 11 SP SD: 0.2902 c. M: 0.5202 c. 289: 49 27 44 49 27 66 27 SP SD: 0.2608 c. M: 0.4498 c. 323: 55 30 49 55 30 74 30 SP SD: 0.2307 c. M:-0.4244 c. 376: 64 35 57 64 35 86 35 SP SD: 0.2071 c. M:-0.3453 c. 441: 75 41 67 75 41 101 41 SP SD: 0.1059 c. M:-0.1716 c. 494: 84 46 75 84 46 113 46 SP SD: 0.0903 c. M:-0.1482 c. 559: 95 52 85 95 52 128 52 SP SD: 0.0609 c. M:-0.1034 c. 612: 104 57 93 104 57 140 57 SP SD: 0.0264 c. M:-0.0450 c. 1171: 199 109 178 199 109 268 109 SP SD: 0.0178 c. M:-0.0319 c. 1783: 303 166 271 303 166 408 166 SP SD: 0.0086 c. M:-0.0160 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: 23.5575 cents 5 x 6:7 x 8:9:10 S SD: 22.0266 cents 6 x 7:8:9:10:11:12 S SD: 15.7116 cents 7:8 x 9 x 11:13:14 SD: 15.4337 cents 8:9:10:11:12:13:15:16 SD: 13.2118 cents 9:10:11:12 x 14:17:18 SD: 10.5586 cents 10:11:12:13:15:16:19:20 SD: 8.9905 cents 12 x 14:16:18:19:23:24 SD: 10.7433 cents 14:16:17:19:21:22:26:28 SD: 8.2679 cents 15:17:18:20:23:24:28:30 SD: 5.8389 cents 22:25:26:29:33:35:41:44 SD: 5.7159 cents 24:27:29:32:36:38:45:48 SD: 3.1042 cents 30:34:36:40:45:48:56:60 SD: 2.1319 cents 40:45:48:53:60:64:75:80 SD: 1.5506 cents 64:72:77:85:96:102:120:128 SD: 1.5125 cents 66:74:79:88:99:106:124:132 SD: 1.4867 cents 70:79:84:93:105:112:131:140 SD: 1.2727 cents 72:81:86:96:108:115:135:144 SD: 1.2255 cents 80:90:96:107:120:128:150:160 SD: 0.7717 cents 90:101:108:120:135:144:169:180 SD: 0.7127 cents 120:135:144:160:180:192:225:240 SD: 0.0000 cents