Scala analysis: xen10-wilson-purvi-09c-06
Purvi modulation 6 from Figure 9c, Hawkins (135/128 32/27 16/15) (16/15 32/27 135/128)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 32/27 294.134997 Pythagorean minor third 2: 512/405 405.866283 narrow diminished fourth 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 2048/1215 903.911282 narrow diminished seventh 6: 256/135 1107.821284 octave - major chroma 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 135/128 92.1787 major chroma, major limma 1: 32/27 294.1350 Pythagorean minor third 2: 16/15 111.7313 minor diatonic semitone 3: 135/128 92.1787 major chroma, major limma 4: 9/8 203.9100 major whole tone 5: 4096/3645 201.9563 narrow diminished third 6: 9/8 203.9100 major whole tone 7: 135/128 92.1787 major chroma, major limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 135/128 92.179 cents major chroma, major limma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 4096/3645 201.956 cents narrow diminished third 1: 2 9/8 203.910 cents major whole tone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 2 1215/1024 296.089 cents wide augmented second 2: 1 5/4 386.314 cents major third 2: 3 512/405 405.866 cents narrow diminished fourth 3: 1 81/64 407.820 cents Pythagorean major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 64/45 609.776 cents 2nd tritone 4: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 128/81 792.180 cents Pythagorean minor sixth 5: 3 405/256 794.134 cents wide augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 2 2048/1215 903.911 cents narrow diminished seventh 5: 1 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 3645/2048 998.044 cents wide augmented sixth 6: 1 15/8 1088.269 cents classic major seventh 6: 2 256/135 1107.821 cents octave - major chroma 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 : 294.1 405.9 498.0 702.0 903.9 1107.8 1200.0 294.1 : 111.7 203.9 407.8 609.8 813.7 905.9 1200.0 405.9 : 92.2 296.1 498.0 702.0 794.1 1088.3 1200.0 498.0 : 203.9 405.9 609.8 702.0 996.1 1107.8 1200.0 702.0 : 202.0 405.9 498.0 792.2 903.9 996.1 1200.0 903.9 : 203.9 296.1 590.2 702.0 794.1 998.0 1200.0 1107.8: 92.2 386.3 498.0 590.2 794.1 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 294.1350 cents 4096/3645, 201.9563 cents 135/128, 92.1787 cents 2: 203.9100 .. 405.8663 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 32805/32768, 1.9537 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 794.1337 .. 996.0900 cents 4096/3645, 201.9563 cents 32805/32768, 1.9537 cents 6: 905.8650 .. 1107.8213 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.859741 Largest / Average step : 1.715787 Largest / Smallest step : 3.190921 Median interval of one step : 4096/3645, 201.9563 cents, amount: 1 Least squares average step : 178.38790 cents, oct.: 1248.71533 cents Scale is not proper Step pattern alph. order: ABCDEDC Step pattern size order : EBADCDA Scale is not a Constant Structure Scale diversity : 1.365334 Lumma stability : 0.156887 Lumma impropriety factor : 0.166669 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 : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 32805/32768, 1.9537 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 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 3645 (O: 3645 U: 3645) Highest odd numerator or denominator: 1215 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.239925 Specific harmonicity : 0.144252 Fundamental : 1/2430, -11.2467 octaves, 0.1077 Hz. Guide tone : 6144, 12.5850 octaves, 1607427.473 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 2322.5, average 331.78571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.20797, average 1.45828 Sum of Tenney's harmonic distance : 21.34608, average 3.04944 Vogel's harmonic complexity : 17.42857 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 171.71175, average 6.13256 Lattice compactness (without 2's) : 76.24543, average 2.72305 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 11 5.00000 37 1 3: -5 .. 1 -2.14286 17 3 5: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-18 / 7 =-2.57143 Average absolute exponent except 2's: 20 / 7 = 2.85714
FIT/MODE
7: 2 0 1 1 1 1 1 N T3 SD: 46.8117 c. M: 79.2499 c. 8: 2 1 0 2 1 1 1 N D3 SD: 37.7159 c. M: 57.8213 c. 9: 2 1 1 1 2 1 1 P M ME S SD: 28.8811 c. M: 41.1546 c. 12: 3 1 1 2 2 2 1 N T3 SD: 4.6740 c. M: 7.8213 c. Mela Sulini, Raga Sailadesakshi, Raga Trishuli, Houzam: Greece 41: 10 4 3 7 7 7 3 N SD: 2.6305 c. M:-4.3738 c. 53: 13 5 4 9 9 9 4 N SD: 1.1043 c. M:-1.7491 c. 65: 16 6 5 11 11 11 5 N SD: 0.5980 c. M:-1.2496 c. 118: 29 11 9 20 20 20 9 N SD: 0.6951 c. M:-1.1735 c. 183: 45 17 14 31 31 31 14 N SD: 0.6243 c. M:-1.0068 c. 248: 61 23 19 42 42 42 19 N SD: 0.6035 c. M:-1.0263 c. 311: 76 29 24 53 52 53 24 N SD: 0.6210 c. M: 1.0174 c. 313: 77 29 24 53 53 53 24 N SD: 0.5957 c. M:-1.0727 c. 340: 83 32 26 58 57 58 26 N SD: 0.5424 c. M: 1.1938 c. 352: 86 33 27 60 59 60 27 N SD: 0.4495 c. M: 0.9532 c. 364: 89 34 28 62 61 62 28 N SD: 0.4108 c. M: 0.7284 c. 376: 92 35 29 64 63 64 29 N SD: 0.4286 c. M: 0.7198 c. 405: 99 38 31 69 68 69 31 N SD: 0.3662 c. M: 0.8017 c. 417: 102 39 32 71 70 71 32 N SD: 0.2864 c. M: 0.6098 c. 429: 105 40 33 73 72 73 33 N SD: 0.2638 c. M: 0.4287 c. 470: 115 44 36 80 79 80 36 N SD: 0.2427 c. M: 0.5180 c. 482: 118 45 37 82 81 82 37 N SD: 0.1673 c. M: 0.3591 c. 494: 121 46 38 84 83 84 38 N SD: 0.1605 c. M: 0.2676 c. 535: 131 50 41 91 90 91 41 N SD: 0.1570 c. M: 0.3032 c. 547: 134 51 42 93 92 93 42 N SD: 0.0770 c. M: 0.1679 c. 559: 137 52 43 95 94 95 43 N SD: 0.0944 c. M: 0.1546 c. 612: 150 57 47 104 103 104 47 N SD: 0.0131 c. M:-0.0219 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: 6.5175 cents 4 x 5 x 6:7 x 8 S SD: 16.9488 cents 5:6 x 7 x 8:9:10 S SD: 30.9052 cents 6:7 x 8:9:10:11:12 S SD: 11.2336 cents 7:8:9 x 11:12:13:14 SD: 19.3378 cents 8:9:10:11:12:13:15:16 SD: 17.9345 cents 9:11 x 12:14:15:17:18 SD: 14.1719 cents 10:12 x 13:15:17:19:20 SD: 8.5181 cents 12:14:15:16:18:20:23:24 SD: 6.1447 cents 16:19:20:21:24:27:30:32 SD: 5.5754 cents 18:21:23:24:27:30:34:36 SD: 5.5581 cents 22:26:28:29:33:37:42:44 SD: 3.7847 cents 26:31:33:35:39:44:49:52 SD: 3.4733 cents 34:40:43:45:51:57:64:68 SD: 3.4362 cents 38:45:48:51:57:64:72:76 SD: 1.6720 cents 48:57:61:64:72:81:91:96 SD: 1.4110 cents 54:64:68:72:81:91:102:108 SD: 1.3703 cents 60:71:76:80:90:101:114:120 SD: 0.8519 cents 98:116:124:131:147:165:186:196 SD: 0.8188 cents 102:121:129:136:153:172:193:204 SD: 0.6029 cents 114:135:144:152:171:192:216:228 SD: 0.4069 cents 156:185:197:208:234:263:296:312 SD: 0.3446 cents 162:192:205:216:243:273:307:324 SD: 0.2964 cents 204:242:258:272:306:344:387:408 SD: 0.2851 cents 216:256:273:288:324:364:410:432 SD: 0.2561 cents 270:320:341:360:405:455:512:540 SD: 0.2491 cents 276:327:349:368:414:465:523:552 SD: 0.2378 cents 318:377:402:424:477:536:603:636 SD: 0.0746 cents