Scala analysis: xen15-gilson-didymus-chromatic
Didymus Chromatic
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: 10/9 182.403712 minor whole tone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 6: 5/3 884.358713 major sixth, BP sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 16/15 111.7313 minor diatonic semitone 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 6/5 315.6413 minor third 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 6/5 315.6413 minor third
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: 2 10/9 182.404 cents minor whole tone 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 32/25 427.373 cents classic diminished fourth 2: 1 27/20 519.551 cents acute 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: 1 40/27 680.449 cents grave fifth 5: 1 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: 2 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 : 111.7 182.4 498.0 702.0 813.7 884.4 1200.0 111.7 : 70.7 386.3 590.2 702.0 772.6 1088.3 1200.0 182.4 : 315.6 519.6 631.3 702.0 1017.6 1129.3 1200.0 498.0 : 203.9 315.6 386.3 702.0 813.7 884.4 1200.0 702.0 : 111.7 182.4 498.0 609.8 680.4 996.1 1200.0 813.7 : 70.7 386.3 498.0 568.7 884.4 1088.3 1200.0 884.4 : 315.6 427.4 498.0 813.7 1017.6 1129.3 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 .. 519.5513 cents 243/200, 337.1476 cents 25/27,-133.2376 cents 3: 386.3137 .. 631.2826 cents 144/125, 244.9689 cents 25/27,-133.2376 cents 4: 568.7174 .. 813.6863 cents 144/125, 244.9689 cents 625/648,-62.5651 cents 5: 680.4487 .. 1017.5963 cents 243/200, 337.1476 cents 25/27,-133.2376 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 : 161.09341 cents, oct.: 1127.65387 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : BADCBAD Scale is not a Constant Structure Scale diversity : 1.487547 Lumma stability : 0.117787 Lumma impropriety factor : 0.496263 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 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 n-1 differentially coherent in interval classes 2 and 3 combined 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 : 45 (O: 45 U: 45) Highest odd numerator or denominator: 15 Scale harmonicity : 0.038760 Average absolute harmonicity : 0.265536 Specific harmonicity : 0.220994 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 2.160000E+04, 14.39874 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 43.0, average 6.14286 Mersenne's string divisions : 6431880 Sum of van Prooijen's expressibility: 4.48252, average 0.64036 Sum of Tenney's harmonic distance : 9.27097, average 1.32442 Vogel's harmonic complexity : 11.71429 Wille's k value : 67 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 74.79078, average 2.67110 Lattice compactness (without 2's) : 43.30661, average 1.54666 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.42857 12 1 3: -2 .. 1 -0.57143 6 2 5: -1 .. 1 0.00000 4 4 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 10 / 7 = 1.42857
FIT/MODE
7: 1 0 2 1 1 0 2 N T3 SD: 31.2614 c. M:-59.6973 c. 9: 1 0 3 1 1 1 2 N SD: 33.7023 c. M: 49.0704 c. 10: 1 1 2 2 1 0 3 N SD: 30.9309 c. M:-57.5963 c. 12: 1 1 3 2 1 1 3 N SD: 11.2559 c. M:-17.5963 c. Chromatic Dorian, Mela Kanakangi, Raga Kanakambari 19: 2 1 5 3 2 1 5 N SD: 7.7568 c. M:-14.5845 c. 31: 3 2 8 5 3 2 8 N SD: 5.7744 c. M:-11.1447 c. 34: 3 2 9 6 3 2 9 N SD: 3.9275 c. M: 5.9331 c. 46: 4 3 12 8 4 3 12 N SD: 3.7352 c. M: 7.3835 c. 53: 5 3 14 9 5 3 14 N SD: 1.0408 c. M:-1.4763 c. 118: 11 7 31 20 11 7 31 N SD: 0.3246 c. M:-0.6471 c. 171: 16 10 45 29 16 10 45 N SD: 0.2748 c. M:-0.5494 c. 289: 27 17 76 49 27 17 76 N SD: 0.2271 c. M:-0.3794 c. 323: 30 19 85 55 30 19 85 N SD: 0.2146 c. M: 0.3604 c. 388: 36 23 102 66 36 23 102 N SD: 0.2046 c. M: 0.3911 c. 441: 41 26 116 75 41 26 116 N SD: 0.0905 c. M: 0.1667 c. 559: 52 33 147 95 52 33 147 N SD: 0.0649 c. M: 0.1034 c. 612: 57 36 161 104 57 36 161 N SD: 0.0323 c. M: 0.0508 c. 730: 68 43 192 124 68 43 192 N SD: 0.0375 c. M:-0.0620 c. 1171: 109 69 308 199 109 69 308 N SD: 0.0165 c. M: 0.0319 c. 1783: 166 105 469 303 166 105 469 N SD: 0.0082 c. M: 0.0145 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 x 5:6 S SD: 0.0000 cents 4 x x 5:6 x 7:8 S SD: 35.0166 cents 5 x 6:7 x 8 x 10 S SD: 39.4390 cents 6 x 7:8:9 x 10:12 S SD: 16.8934 cents 7 x 8:9 x 11:12:14 SD: 19.6919 cents 8 x 9:11:12:13 x 16 SD: 12.6822 cents 9 x 10:12 x 14:15:18 S SD: 9.7541 cents 10 x 11:13:15:16:17:20 SD: 9.7171 cents 11 x 12:15:17 x 18:22 SD: 15.7518 cents 12:13 x 16:18:19:20:24 SD: 5.3983 cents 13:14 x 17:20:21:22:26 SD: 10.9276 cents 14:15:16:19:21:22:23:28 SD: 10.0717 cents 15:16:17:20:23:24:25:30 SD: 7.3167 cents 16:17:18:21:24:26:27:32 SD: 7.0490 cents 18:19:20:24:27:29:30:36 SD: 3.1042 cents 30:32:33:40:45:48:50:60 SD: 2.4856 cents 42:45:47:56:63:67:70:84 SD: 2.2036 cents 45:48:50:60:68:72:75:90 SD: 1.8252 cents 60:64:67:80:90:96:100:120 SD: 1.2335 cents 72:77:80:96:108:115:120:144 SD: 0.7736 cents 90:96:100:120:135:144:150:180 S SD: 0.0000 cents