Scala analysis: xen10-wilson-purvi-09a-07
Purvi modulation 7 from Figure 9a, Hawkins (135/128 16/15 32/27), (32/27 135/128 16/15)
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: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 128/81 792.179997 Pythagorean minor sixth 5: 16/9 996.089998 Pythagorean minor seventh 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: 32/27 294.1350 Pythagorean minor third 2: 135/128 92.1787 major chroma, major limma 3: 16/15 111.7313 minor diatonic semitone 4: 32/27 294.1350 Pythagorean minor third 5: 9/8 203.9100 major whole tone 6: 135/128 92.1787 major chroma, major limma 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 135/128 92.179 cents major chroma, major limma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 32/27 294.135 cents Pythagorean minor third 2: 2 9/8 203.910 cents major whole tone 2: 1 1215/1024 296.089 cents wide augmented second 2: 1 5/4 386.314 cents major third 2: 2 512/405 405.866 cents narrow diminished fourth 2: 1 4/3 498.045 cents perfect 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: 1 3/2 701.955 cents perfect fifth 5: 2 405/256 794.134 cents wide augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 1 2048/1215 903.911 cents narrow diminished seventh 5: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/16 905.865 cents Pythagorean major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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 : 294.1 386.3 498.0 792.2 996.1 1088.3 1200.0 294.1 : 92.2 203.9 498.0 702.0 794.1 905.9 1200.0 386.3 : 111.7 405.9 609.8 702.0 813.7 1107.8 1200.0 498.0 : 294.1 498.0 590.2 702.0 996.1 1088.3 1200.0 792.2 : 203.9 296.1 407.8 702.0 794.1 905.9 1200.0 996.1 : 92.2 203.9 498.0 590.2 702.0 996.1 1200.0 1088.3: 111.7 405.9 498.0 609.8 903.9 1107.8 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 .. 498.0450 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 243/256,-90.2250 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 : 16/15, 111.7313 cents, amount: 2 Least squares average step : 183.14057 cents, oct.: 1281.98398 cents Scale is not proper Step pattern alph. order: ABCADBC Step pattern size order : DABDCAB Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.361761 Lumma stability : 0.153631 Lumma impropriety factor : 0.317044 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / 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 : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Phrygian octave species of abstract tetrachord Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 81 Scale harmonicity : 0.033632 Average absolute harmonicity : 0.236696 Specific harmonicity : 0.184544 Fundamental : 1/648, -9.3399 octaves, 0.4037 Hz. Guide tone : 1920, 10.9069 octaves, 502321.085 Hz. Exponens Consonantiae : 1.244160E+06, 20.24674 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 167.5, average 23.92857 Mersenne's string divisions : 446690475 Sum of van Prooijen's expressibility: 6.64627, average 0.94947 Sum of Tenney's harmonic distance : 13.87099, average 1.98157 Vogel's harmonic complexity : 14.57143 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 133.74226, average 4.77651 Lattice compactness (without 2's) : 61.38456, average 2.19231 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 7 2.00000 24 1 3: -4 .. 1 -1.28571 11 4 5: 0 .. 1 0.28571 2 2 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 17| Scale is weakly epimorphic with val: <7 11 18|
FIT/MODE
7: 2 0 1 2 1 0 1 N T3 SD: 43.6955 c. M:-64.9629 c. 8: 2 1 0 2 2 0 1 N S SD: 42.3398 c. M:-63.6863 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 30.8297 c. M: 62.7567 c. 11: 3 1 1 2 2 1 1 N D3 S SD: 31.3418 c. M:-50.0499 c. 12: 3 1 1 3 2 1 1 N SD: 7.9246 c. M:-13.6863 c. Chromatic Phrygian 29: 7 2 3 7 5 2 3 N SD: 7.6907 c. M: 13.8999 c. 40: 10 3 4 9 7 3 4 N SD: 7.9707 c. M: 12.1800 c. 41: 10 3 4 10 7 3 4 N SD: 3.1511 c. M: 5.8259 c. 53: 13 4 5 13 9 4 5 N SD: 0.7839 c. M: 1.4763 c. 118: 29 9 11 29 20 9 11 N SD: 0.5429 c. M:-1.0403 c. 171: 42 13 16 42 29 13 16 N SD: 0.4827 c. M:-0.8025 c. 224: 55 17 21 55 38 17 21 N SD: 0.5085 c. M: 0.7687 c. 289: 71 22 27 71 49 22 27 N SD: 0.4907 c. M:-0.8996 c. 323: 79 25 30 79 55 25 30 N SD: 0.4521 c. M: 0.8487 c. 335: 82 26 31 82 57 26 31 N SD: 0.4341 c. M:-0.6865 c. 376: 92 29 35 92 64 29 35 N SD: 0.3617 c. M: 0.6906 c. 388: 95 30 36 95 66 30 36 N SD: 0.2869 c. M: 0.4274 c. 429: 105 33 40 105 73 33 40 N SD: 0.3223 c. M: 0.5716 c. 441: 108 34 41 108 75 34 41 N SD: 0.1910 c. M: 0.3433 c. 494: 121 38 46 121 84 38 46 N SD: 0.1466 c. M: 0.2772 c. 506: 124 39 47 124 86 39 47 N SD: 0.1450 c. M:-0.2688 c. 547: 134 42 51 134 93 42 51 N SD: 0.1512 c. M: 0.2239 c. 559: 137 43 52 137 95 43 52 N SD: 0.0583 c. M:-0.1034 c. 612: 150 47 57 150 104 47 57 N SD: 0.0229 c. M: 0.0392 c. 1171: 287 90 109 287 199 90 109 N SD: 0.0240 c. M: 0.0365 c. 1783: 437 137 166 437 303 137 166 N SD: 0.0169 c. M: 0.0319 c. 1901: 466 146 177 466 323 146 177 N SD: 0.0183 c. M:-0.0346 c. 2395: 587 184 223 587 407 184 223 N SD: 0.0157 c. M: 0.0297 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: 45.1125 cents 3 x x 4:5 x x 6 S SD: 30.7262 cents 4 x 5 x 6:7 x 8 S SD: 23.5636 cents 5:6 x 7:8:9 x 10 S SD: 18.4632 cents 6:7 x 8:9 x 11:12 SD: 20.3937 cents 7:8:9 x 11:12:13:14 SD: 17.2200 cents 8:9:10:11:13:14:15:16 SD: 16.9389 cents 9 x 11:12:14:16:17:18 SD: 8.1993 cents 10:12 x 13:16:18:19:20 SD: 10.3206 cents 12:14:15:16:19:21:23:24 SD: 7.7538 cents 15:18:19:20:24:27:28:30 S SD: 6.3452 cents 16:19:20:21:25:28:30:32 SD: 6.1948 cents 17:20:21:23:27:30:32:34 SD: 5.5460 cents 21:25:26:28:33:37:39:42 SD: 4.3877 cents 24:28:30:32:38:43:45:48 SD: 4.3712 cents 27:32:34:36:43:48:51:54 SD: 3.2198 cents 31:37:39:41:49:55:58:62 SD: 3.1782 cents 32:38:40:43:51:57:60:64 SD: 2.9323 cents 33:39:41:44:52:59:62:66 SD: 2.3373 cents 45:53:56:60:71:80:84:90 SD: 2.2319 cents 48:57:60:64:76:85:90:96 SD: 1.1844 cents 72:85:90:96:114:128:135:144 SD: 1.0816 cents 81:96:101:108:128:144:152:162 SD: 0.6444 cents 129:153:161:172:204:229:242:258 SD: 0.5980 cents 135:160:169:180:213:240:253:270 SD: 0.5464 cents 152:180:190:203:240:270:285:304 SD: 0.5380 cents 167:198:209:223:264:297:313:334 SD: 0.5098 cents 183:217:229:244:289:325:343:366 SD: 0.4319 cents 184:218:230:245:291:327:345:368 SD: 0.4086 cents 216:256:270:288:341:384:405:432 SD: 0.2416 cents 264:313:330:352:417:469:495:528 SD: 0.2250 cents 312:370:390:416:493:555:585:624 SD: 0.2110 cents 324:384:405:432:512:576:608:648 SD: 0.2035 cents 336:398:420:448:531:597:630:672 SD: 0.1960 cents 384:455:480:512:607:683:720:768 SD: 0.1547 cents 432:512:540:576:683:768:810:864 SD: 0.1207 cents 567:672:709:756:896:1008:1063:1134 SD: 0.0919 cents