Scala analysis: xen10-wilson-purvi-09c-07
Purvi modulation 7 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: 128/81 792.179997 Pythagorean minor sixth 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: 32/27 294.1350 Pythagorean minor third 5: 16/15 111.7313 minor diatonic semitone 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: 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: 1 9/8 203.910 cents major whole tone 2: 1 1215/1024 296.089 cents wide augmented second 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 2 512/405 405.866 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: 2 405/256 794.134 cents wide augmented fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 2048/1215 903.911 cents narrow diminished seventh 5: 1 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 : 294.1 405.9 498.0 792.2 903.9 1107.8 1200.0 294.1 : 111.7 203.9 498.0 609.8 813.7 905.9 1200.0 405.9 : 92.2 386.3 498.0 702.0 794.1 1088.3 1200.0 498.0 : 294.1 405.9 609.8 702.0 996.1 1107.8 1200.0 792.2 : 111.7 315.6 407.8 702.0 813.7 905.9 1200.0 903.9 : 203.9 296.1 590.2 702.0 794.1 1088.3 1200.0 1107.8: 92.2 386.3 498.0 590.2 884.4 996.1 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 : 16/15, 111.7313 cents, amount: 2 Least squares average step : 180.96576 cents, oct.: 1266.76033 cents Scale is not proper Step pattern alph. order: ABCABDC Step pattern size order : DBADBCA Scale is not a Constant Structure Scale diversity : 1.390463 Lumma stability : 0.156887 Lumma impropriety factor : 0.166669 Rothenberg efficiency : 0.448980 redundancy: 0.551020 Efficiency x scale size : 3.142857 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 : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord Best fifths form a closed circle Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 201.9563 cents: 4 -- Rational properties -- Prime limit : 5 Odd number limit : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 1215 Scale harmonicity : 0.032538 Average absolute harmonicity : 0.209050 Specific harmonicity : 0.158546 Fundamental : 1/1215, -10.2467 octaves, 0.2153 Hz. Guide tone : 2048, 11.0000 octaves, 535809.158 Hz. Exponens Consonantiae : 2.488320E+06, 21.24674 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 2424.5, average 346.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.63934, average 1.66276 Sum of Tenney's harmonic distance : 24.58362, average 3.51195 Vogel's harmonic complexity : 15.42857 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 154.21786, average 5.50778 Lattice compactness (without 2's) : 68.76897, average 2.45603 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 11 6.14286 43 1 3: -5 .. 0 -2.85714 20 3 5: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-23 / 7 =-3.28571 Average absolute exponent except 2's: 23 / 7 = 3.28571
FIT/MODE
7: 2 0 1 2 0 1 1 N T3 SD: 52.5027 c. M: 79.2499 c. 8: 2 1 0 2 1 1 1 N D3 SD: 36.7001 c. M: 57.8213 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 25.7868 c. M: 41.1546 c. 12: 3 1 1 3 1 2 1 N T3 S SD: 5.4806 c. M: 7.8213 c. 41: 10 4 3 10 4 7 3 N SD: 2.7243 c. M:-4.3738 c. 53: 13 5 4 13 5 9 4 N SD: 1.1088 c. M:-1.7491 c. 65: 16 6 5 16 6 11 5 N SD: 0.8541 c. M:-1.6662 c. 118: 29 11 9 29 11 20 9 N SD: 0.7925 c. M:-1.1735 c. 183: 45 17 14 45 17 31 14 N SD: 0.7767 c. M:-1.2626 c. 311: 76 29 24 76 29 53 24 N SD: 0.7571 c. M: 1.1832 c. 323: 79 30 25 79 30 55 25 N SD: 0.7329 c. M: 1.1249 c. 352: 86 33 27 86 33 60 27 N SD: 0.6468 c. M: 1.2709 c. 364: 89 34 28 89 34 62 28 N SD: 0.5432 c. M: 0.9712 c. 376: 92 35 29 92 35 64 29 N SD: 0.4975 c. M: 0.7198 c. 417: 102 39 32 102 39 71 32 N SD: 0.4130 c. M: 0.8131 c. 429: 105 40 33 105 40 73 33 N SD: 0.3367 c. M: 0.5716 c. 441: 108 41 34 108 41 75 34 N SD: 0.3264 c. M: 0.5099 c. 482: 118 45 37 118 45 82 37 N SD: 0.2423 c. M: 0.4788 c. 494: 121 46 38 121 46 84 38 N SD: 0.1899 c. M: 0.2772 c. 547: 134 51 42 134 51 93 42 N SD: 0.1124 c. M: 0.2239 c. 559: 137 52 43 137 52 95 43 N SD: 0.0963 c. M: 0.1546 c. 612: 150 57 47 150 57 104 47 N SD: 0.0156 c. M: 0.0231 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 x 5 x 6 S SD: 6.5175 cents 4 x 5 x 6:7 x 8 S SD: 28.2143 cents 5:6 x 7:8 x 9:10 S SD: 25.4561 cents 6:7 x 8:9:10:11:12 S SD: 18.7702 cents 7:8:9 x 11:12:13:14 SD: 14.0138 cents 8:9:10:11:13 x 15:16 SD: 19.7770 cents 9:11 x 12:14:15:17:18 SD: 10.5535 cents 10:12 x 13:16:17:19:20 SD: 9.2415 cents 12:14:15:16:19:20:23:24 SD: 6.1636 cents 21:25:27:28:33:35:40:42 SD: 5.4375 cents 22:26:28:29:35:37:42:44 SD: 4.1340 cents 26:31:33:35:41:44:49:52 SD: 3.5121 cents 31:37:39:41:49:52:59:62 SD: 3.2780 cents 33:39:42:44:52:56:63:66 SD: 3.0476 cents 38:45:48:51:60:64:72:76 SD: 1.6844 cents 48:57:61:64:76:81:91:96 SD: 1.4912 cents 60:71:76:80:95:101:114:120 SD: 0.9791 cents 76:90:96:101:120:128:144:152 SD: 0.9333 cents 98:116:124:131:155:165:186:196 SD: 0.8470 cents 102:121:129:136:161:172:193:204 SD: 0.6666 cents 114:135:144:152:180:192:216:228 SD: 0.4550 cents 162:192:205:216:256:273:307:324 SD: 0.2964 cents 276:327:349:368:436:465:523:552 SD: 0.2522 cents 318:377:402:424:503:536:603:636 SD: 0.2483 cents 357:423:451:476:564:602:677:714 SD: 0.2211 cents 378:448:478:504:597:637:717:756 SD: 0.1795 cents 405:480:512:540:640:683:768:810 SD: 0.1207 cents 519:615:656:692:820:875:984:1038 SD: 0.1022 cents 579:686:732:772:915:976:1098:1158 SD: 0.0826 cents