Scala analysis: xen07-london-didymus
Scale for 'Solo in Didymus's Chromatic'
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 25/16 772.627428 classic augmented fifth 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: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 6/5 315.6413 minor third 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 6/5 315.6413 minor third 7: 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: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 75/64 274.582 cents classic augmented second 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 2 32/25 427.373 cents classic diminished fourth 3: 1 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 36/25 631.283 cents classic diminished fifth 4: 1 25/18 568.717 cents classic augmented fourth 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 8/5 813.686 cents minor sixth 5: 2 25/16 772.627 cents classic augmented fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 128/75 925.418 cents diminished seventh 5: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 2 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 70.7 386.3 498.0 702.0 772.6 1088.3 1200.0 70.7 : 315.6 427.4 631.3 702.0 1017.6 1129.3 1200.0 386.3 : 111.7 315.6 386.3 702.0 813.7 884.4 1200.0 498.0 : 203.9 274.6 590.2 702.0 772.6 1088.3 1200.0 702.0 : 70.7 386.3 498.0 568.7 884.4 996.1 1200.0 772.6 : 315.6 427.4 498.0 813.7 925.4 1129.3 1200.0 1088.3: 111.7 182.4 498.0 609.8 813.7 884.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 315.6413 cents 144/125, 244.9689 cents 25/24, 70.6724 cents 2: 182.4037 .. 427.3726 cents 144/125, 244.9689 cents 25/27,-133.2376 cents 3: 386.3137 .. 631.2826 cents 144/125, 244.9689 cents 125/128,-41.0589 cents 4: 568.7174 .. 813.6863 cents 144/125, 244.9689 cents 625/648,-62.5651 cents 5: 772.6274 .. 1017.5963 cents 144/125, 244.9689 cents 125/128,-41.0589 cents 6: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 2.425678 Largest / Average step : 1.841241 Largest / Smallest step : 4.466258 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Least squares average step : 170.98574 cents, oct.: 1196.90021 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : ADBCADB Scale is not a Constant Structure Scale diversity : 1.537490 Lumma stability : 0.117787 Lumma impropriety factor : 0.342632 Rothenberg efficiency : 0.451701 redundancy: 0.548299 Efficiency x scale size : 3.161905 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 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 contains a complete diamond : 1 3 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 : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 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: 25 Scale harmonicity : 0.041436 Average absolute harmonicity : 0.257515 Specific harmonicity : 0.203045 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 300, 8.2288 octaves, 78487.670 Hz. Exponens Consonantiae : 1.440000E+04, 13.81378 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 68.5, average 9.78571 Mersenne's string divisions : 2079315 Sum of van Prooijen's expressibility: 5.62518, average 0.80360 Sum of Tenney's harmonic distance : 10.91878, average 1.55983 Vogel's harmonic complexity : 9.85714 Wille's k value : 37 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 86.49196, average 3.08900 Lattice compactness (without 2's) : 42.73012, average 1.52608 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.42857 16 1 3: -1 .. 1 0.00000 4 2 5: 0 .. 2 0.85714 6 4 Average exponent except 2's : 6 / 7 = 0.85714 Average absolute exponent except 2's: 10 / 7 = 1.42857
FIT/MODE
7: 0 2 1 1 0 2 1 N T3 SD: 51.4480 c. M: 86.9131 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 33.4240 c. M:-62.6609 c. 10: 0 3 1 2 0 3 1 N SD: 36.2063 c. M: 70.6724 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 16.6560 c. M:-29.3276 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: 1 5 2 3 1 5 2 N SD: 9.5968 c. M: 14.7327 c. 22: 1 6 2 4 1 6 2 N SD: 8.1936 c. M: 16.1270 c. 29: 2 7 3 5 2 7 3 N SD: 9.8711 c. M: 13.8999 c. 31: 2 8 3 5 2 8 3 N SD: 4.1681 c. M:-6.7469 c. 34: 2 9 3 6 2 9 3 N SD: 3.4543 c. M:-5.8489 c. 53: 3 14 5 9 3 14 5 N SD: 1.6756 c. M: 2.8161 c. 84: 5 22 8 14 5 22 8 N SD: 1.5370 c. M: 2.5544 c. 87: 5 23 8 15 5 23 8 N SD: 1.1559 c. M: 1.7069 c. 118: 7 31 11 20 7 31 11 N SD: 0.2667 c. M:-0.5140 c. 205: 12 54 19 35 12 54 19 N SD: 0.3621 c. M:-0.5118 c. 289: 17 76 27 49 17 76 27 N SD: 0.2304 c. M: 0.3794 c. 323: 19 85 30 55 19 85 30 N SD: 0.1664 c. M:-0.2762 c. 441: 26 116 41 75 26 116 41 N SD: 0.1075 c. M:-0.1667 c. 559: 33 147 52 95 33 147 52 N SD: 0.1072 c. M:-0.1812 c. 612: 36 161 57 104 36 161 57 N SD: 0.0477 c. M: 0.0842 c. 730: 43 192 68 124 43 192 68 N SD: 0.0296 c. M: 0.0495 c. 1171: 69 308 109 199 69 308 109 N SD: 0.0270 c. M:-0.0455 c. 1665: 98 438 155 283 98 438 155 N SD: 0.0235 c. M: 0.0418 c. 1783: 105 469 166 303 105 469 166 N SD: 0.0060 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: 37.2438 cents 4 x 5 x 6 x x 8 S SD: 0.0000 cents 5 x 6:7 x 8:9:10 S SD: 27.4297 cents 6 x x 8:9 x 11:12 SD: 9.7264 cents 7 x 9 x x 11:13:14 SD: 13.1109 cents 9:10:11:12 x 14:17:18 SD: 19.8748 cents 10:11 x 13:15:16:19:20 SD: 19.0258 cents 11:12:14:15 x 17:21:22 SD: 16.8447 cents 12:13:15:16:18:19:23:24 SD: 11.5918 cents 13:14:16:17 x 20:24:26 SD: 13.5526 cents 14:15:18:19:21:22:26:28 SD: 11.1280 cents 15:16:19:20 x 23:28:30 SD: 9.6253 cents 16:17:20:21:24:25:30:32 SD: 6.2575 cents 20:21:25:27:30:31:38:40 SD: 5.2915 cents 23:24:29:31:35:36:43:46 SD: 5.0282 cents 24:25:30:32:36:38:45:48 SD: 3.2758 cents 32:33:40:43:48:50:60:64 SD: 3.1437 cents 44:46:55:59:66:69:83:88 SD: 2.4101 cents 48:50:60:64:72:75:90:96 S SD: 0.0000 cents