Scala analysis: xen10-wilson-purvi-10a-03
Purvi modulation 3 from Figure 10a, Didymus (16/15 25/24 6/5), (6/5 16/15 25/24)
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: 48/25 1129.327573 classic diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 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: 6/5 315.6413 minor third 7: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 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 6/5 315.641 cents minor third 2: 1 75/64 274.582 cents classic augmented second 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 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 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 25/16 772.627 cents classic augmented fifth 5: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 128/75 925.418 cents diminished seventh 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 1 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 315.6 498.0 702.0 813.7 1129.3 1200.0 203.9 : 111.7 294.1 498.0 609.8 925.4 996.1 1200.0 315.6 : 182.4 386.3 498.0 813.7 884.4 1088.3 1200.0 498.0 : 203.9 315.6 631.3 702.0 905.9 1017.6 1200.0 702.0 : 111.7 427.4 498.0 702.0 813.7 996.1 1200.0 813.7 : 315.6 386.3 590.2 702.0 884.4 1088.3 1200.0 1129.3: 70.7 274.6 386.3 568.7 772.6 884.4 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: 274.5824 .. 427.3726 cents 2048/1875, 152.7901 cents 125/128,-41.0589 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 .. 925.4176 cents 2048/1875, 152.7901 cents 125/128,-41.0589 cents 6: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 125/128,-41.0589 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 174.15389 cents, oct.: 1219.07722 cents Scale is not proper Step pattern alph. order: ABCABDE Step pattern size order : DBCDBEA Scale is not a Constant Structure Scale diversity : 1.549589 Lumma stability : 0.117787 Lumma impropriety factor : 0.189000 Rothenberg efficiency : 0.425850 redundancy: 0.574150 Efficiency x scale size : 2.980952 Number of different interval sizes : 24 = 4.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 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 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents 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 : 2 at degree 2 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 25 Scale harmonicity : 0.035971 Average absolute harmonicity : 0.266300 Specific harmonicity : 0.216362 Fundamental : 1/600, -9.2288 octaves, 0.4360 Hz. Guide tone : 144, 7.1699 octaves, 37674.081 Hz. Exponens Consonantiae : 8.640000E+04, 16.39874 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 64.5, average 9.21429 Mersenne's string divisions : 18633615 Sum of van Prooijen's expressibility: 4.70437, average 0.67205 Sum of Tenney's harmonic distance : 10.17406, average 1.45344 Vogel's harmonic complexity : 15.85714 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 89.55381, average 3.19835 Lattice compactness (without 2's) : 43.49405, average 1.55336 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 1.00000 15 1 3: -1 .. 2 0.57143 6 3 5: -2 .. 0 -0.57143 4 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 10 / 7 = 1.42857
FIT/MODE
7: 1 1 1 1 1 2 0 N T3 SD: 36.2656 c. M:-70.6724 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 44.6955 c. M: 70.5767 c. 10: 2 1 1 2 1 2 1 P M ME S SD: 31.7289 c. M: 49.3276 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 1 2 2 1 3 1 P D3 SD: 13.7061 c. M: 29.3276 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 16: 3 1 3 2 2 4 1 N SD: 18.0844 c. M:-26.9550 c. 19: 3 2 3 3 2 5 1 N SD: 7.7769 c. M: 14.4363 c. 31: 5 3 5 5 3 8 2 N SD: 5.8888 c. M: 10.3616 c. 34: 6 3 5 6 3 9 2 N SD: 3.7847 c. M:-7.8547 c. 46: 8 4 7 8 4 12 3 N SD: 4.2019 c. M: 7.5884 c. 53: 9 5 8 9 5 14 3 N SD: 1.2737 c. M:-2.7479 c. 99: 17 9 15 17 9 26 6 N SD: 1.4066 c. M:-2.1506 c. 118: 20 11 18 20 11 31 7 N SD: 0.3456 c. M: 0.5202 c. 171: 29 16 26 29 16 45 10 N SD: 0.3005 c. M:-0.4970 c. 289: 49 27 44 49 27 76 17 N SD: 0.2202 c. M: 0.4498 c. 323: 55 30 49 55 30 85 19 N SD: 0.2081 c. M:-0.4244 c. 441: 75 41 67 75 41 116 26 N SD: 0.0898 c. M:-0.1716 c. 559: 95 52 85 95 52 147 33 N SD: 0.0789 c. M: 0.1684 c. 612: 104 57 93 104 57 161 36 N SD: 0.0394 c. M:-0.0842 c. 730: 124 68 111 124 68 192 43 N SD: 0.0363 c. M: 0.0744 c. 1171: 199 109 178 199 109 308 69 N SD: 0.0190 c. M: 0.0364 c. 1342: 228 125 204 228 125 353 79 N SD: 0.0224 c. M: 0.0352 c. 1783: 303 166 271 303 166 469 105 N SD: 0.0080 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 x 10 S SD: 21.1168 cents 6 x 7:8:9:10 x 12 S SD: 17.1734 cents 7:8 x 9 x 11:13:14 SD: 18.9750 cents 8:9:10:11:12:13:15:16 SD: 14.4553 cents 9:10:11:12 x 14:17:18 SD: 11.3652 cents 10:11:12:13:15:16:19:20 SD: 8.7639 cents 12 x 14:16:18:19:23:24 SD: 8.6862 cents 14:16:17:19:21:22:27:28 SD: 7.9982 cents 15:17:18:20:23:24:29:30 SD: 5.9841 cents 22:25:26:29:33:35:42:44 SD: 5.6919 cents 24:27:29:32:36:38:46:48 SD: 3.1338 cents 30:34:36:40:45:48:58:60 SD: 2.5022 cents 40:45:48:53:60:64:77:80 SD: 1.6787 cents 50:56:60:67:75:80:96:100 SD: 1.6538 cents 64:72:77:85:96:102:123:128 SD: 1.5317 cents 66:74:79:88:99:106:127:132 SD: 1.5030 cents 70:79:84:93:105:112:134:140 SD: 1.3932 cents 72:81:86:96:108:115:138:144 SD: 1.2986 cents 80:90:96:107:120:128:154:160 SD: 1.0046 cents 90:101:108:120:135:144:173:180 SD: 0.6750 cents 120:135:144:160:180:192:230:240 SD: 0.4297 cents 150:169:180:200:225:240:288:300 SD: 0.3661 cents 200:225:240:267:300:320:384:400 SD: 0.3090 cents 210:236:252:280:315:336:403:420 SD: 0.2892 cents 240:270:288:320:360:384:461:480 SD: 0.1073 cents 360:405:432:480:540:576:691:720 SD: 0.0716 cents 600:675:720:800:900:960:1152:1200 S SD: 0.0000 cents