Scala analysis: xen10-wilson-purvi-07a-02
Purvi modulation 2 from Figure 7a, Kathleen Schlesinger (13/12 16/15 15/13), (15/13 13/12 16/15)
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: 39/32 342.482663 39th harmonic, Zalzal wosta of Ibn Sina 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 13/8 840.527662 tridecimal neutral sixth 6: 26/15 952.258947 tridecimal semi-augmented sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/13 247.7411 tridecimal 5/4-tone 1: 9/8 203.9100 major whole tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 128/117 155.5623 4: 9/8 203.9100 major whole tone 5: 13/12 138.5727 tridecimal 2/3-tone 6: 16/15 111.7313 minor diatonic semitone 7: 15/13 247.7411 tridecimal 5/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 128/117 155.562 cents 1: 2 9/8 203.910 cents major whole tone 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 16/13 359.472 cents tridecimal neutral third 2: 1 135/104 451.651 cents 3: 1 13/10 454.214 cents tridecimal semi-diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 18/13 563.382 cents tridecimal augmented fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 13/9 636.618 cents tridecimal diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 20/13 745.786 cents tridecimal semi-augmented fifth 5: 1 208/135 748.349 cents 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 2 64/39 857.517 cents 39th subharmonic 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 45/26 949.696 cents 6: 1 26/15 952.259 cents tridecimal semi-augmented sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 117/64 1044.438 cents 6: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 1 15/8 1088.269 cents classic major seventh 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 : 203.9 342.5 498.0 702.0 840.5 952.3 1200.0 203.9 : 138.6 294.1 498.0 636.6 748.3 996.1 1200.0 342.5 : 155.6 359.5 498.0 609.8 857.5 1061.4 1200.0 498.0 : 203.9 342.5 454.2 702.0 905.9 1044.4 1200.0 702.0 : 138.6 250.3 498.0 702.0 840.5 996.1 1200.0 840.5 : 111.7 359.5 563.4 702.0 857.5 1061.4 1200.0 952.3 : 247.7 451.7 590.2 745.8 949.7 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 247.7411 cents 225/208, 136.0098 cents 16/15, 111.7313 cents 2: 250.3039 .. 451.6511 cents 6075/5408, 201.3471 cents 676/675, 2.5629 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 676/675, 2.5629 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 748.3489 .. 949.6961 cents 6075/5408, 201.3471 cents 676/675, 2.5629 cents 6: 952.2589 .. 1088.2687 cents 225/208, 136.0098 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 1.534293 Largest / Average step : 1.445156 Largest / Smallest step : 2.217294 Median interval of one step : 128/117, 155.5623 cents, amount: 1 Least squares average step : 167.90730 cents, oct.: 1175.35112 cents Scale is strictly proper Step pattern alph. order: ABCABDE Step pattern size order : DBCDBAE Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.512925 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.211056 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / 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 : 676/675, 2.5629 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 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 n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 39 Scale harmonicity : 0.022960 Average absolute harmonicity : 0.244476 Specific harmonicity : 0.116411 Fundamental : 1/480, -8.9069 octaves, 0.5451 Hz. Guide tone : 468, 8.8704 octaves, 122440.765 Hz. Exponens Consonantiae : 2.246400E+05, 17.77726 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 82.5, average 11.78571 Mersenne's string divisions : 5196135 Sum of van Prooijen's expressibility: 5.78958, average 0.82708 Sum of Tenney's harmonic distance : 11.72001, average 1.67429 Vogel's harmonic complexity : 17.57143 Wille's k value : 292 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 97.20391, average 3.47157 Lattice compactness (without 2's) : 43.83792, average 1.56564 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.14286 16 1 3: -1 .. 2 0.28571 6 3 5: -1 .. 0 -0.14286 1 13: 0 .. 1 0.42857 3 3 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is JI-epimorphic with val: <7 11 16 26| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.1282 c. M:-76.3125 c. Lebeng 8: 1 1 1 2 1 0 2 N D3 SD: 47.2012 c. M:-59.4723 c. 10: 2 1 1 2 1 1 2 P D3 I SD: 18.2083 c. M:-36.0900 c. 14: 2 2 2 2 2 1 3 P T3 SD: 16.6783 c. M: 32.4814 c. 17: 3 2 2 3 2 1 4 N SD: 14.3555 c. M: 34.6119 c. 19: 3 2 3 3 2 2 4 P SD: 14.2845 c. M: 26.6932 c. 20: 3 3 2 4 2 2 4 P SD: 15.0712 c. M: 23.9100 c. 24: 4 3 3 4 3 2 5 P SD: 4.9896 c. M:-9.4723 c. 34: 6 4 4 6 4 3 7 P SD: 5.9166 c. M:-10.4585 c. 43: 7 5 6 7 5 4 9 P SD: 5.2154 c. M: 8.5612 c. 49: 8 6 6 9 5 5 10 P SD: 6.2128 c. M: 8.2491 c. 53: 9 6 7 9 6 5 11 P SD: 1.5916 c. M: 2.8600 c. 77: 13 9 10 13 9 7 16 P SD: 0.9545 c. M: 1.6096 c. 130: 22 15 17 22 15 12 27 P SD: 0.7955 c. M: 1.4897 c. 164: 28 19 21 28 19 15 34 P SD: 0.8765 c. M:-1.4198 c. 193: 33 22 25 33 22 18 40 P SD: 0.8399 c. M:-1.2713 c. 200: 34 23 26 34 23 19 41 SP SD: 0.7126 c. M:-1.7411 c. 217: 37 25 28 37 25 20 45 P SD: 0.5474 c. M: 1.1069 c. 224: 38 26 29 38 26 21 46 SP SD: 0.5770 c. M:-1.3125 c. 253: 43 29 33 43 29 24 52 SP SD: 0.6740 c. M:-1.1007 c. 270: 46 31 35 46 31 25 56 P SD: 0.5467 c. M: 1.1478 c. 277: 47 32 36 47 32 26 57 SP SD: 0.3503 c. M:-0.8096 c. 301: 51 35 39 51 35 28 62 SP SD: 0.4511 c. M:-0.6684 c. 330: 56 38 43 56 38 31 68 SP SD: 0.3876 c. M: 0.6645 c. 354: 60 41 46 60 41 33 73 SP SD: 0.2728 c. M: 0.5202 c. 364: 62 42 47 62 42 34 75 SP SD: 0.3273 c. M:-0.4883 c. 407: 69 47 53 69 47 38 84 SP SD: 0.2953 c. M: 0.4702 c. 417: 71 48 54 71 48 39 86 SP SD: 0.2311 c. M:-0.4065 c. 441: 75 51 57 75 51 41 91 SP SD: 0.2009 c. M:-0.3745 c. 494: 84 57 64 84 57 46 102 SP SD: 0.0680 c. M:-0.1386 c. 848: 144 98 110 144 98 79 175 SP SD: 0.0758 c. M: 0.1364 c. 1065: 181 123 138 181 123 99 220 SP SD: 0.0623 c. M: 0.1463 c. 1289: 219 149 167 219 149 120 266 SP SD: 0.0757 c. M:-0.1240 c. 1342: 228 155 174 228 155 125 277 SP SD: 0.0257 c. M:-0.0510 c. 1836: 312 212 238 312 212 171 379 SP SD: 0.0122 c. M:-0.0286 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: 14.6104 cents 4 x 5 x 6 x 7:8 S SD: 11.7144 cents 5 x 6:7 x 8:9:10 S SD: 22.6668 cents 6:7 x 8:9:10 x 12 S SD: 15.3431 cents 7:8 x 9 x 11:12:14 SD: 18.3755 cents 8:9:10:11:12:13:14:16 S SD: 10.1354 cents 14:16:17:19:21:23:24:28 SD: 7.0661 cents 18:20:22:24:27:29:31:36 SD: 4.1196 cents 24:27:29:32:36:39:42:48 SD: 3.1793 cents 32:36:39:43:48:52:55:64 SD: 2.8409 cents 40:45:49:53:60:65:69:80 SD: 2.3292 cents 42:47:51:56:63:68:73:84 SD: 1.9569 cents 54:61:66:72:81:88:94:108 SD: 1.7703 cents 56:63:68:75:84:91:97:112 SD: 1.4374 cents 64:72:78:85:96:104:111:128 SD: 0.9793 cents 72:81:88:96:108:117:125:144 SD: 0.8074 cents 96:108:117:128:144:156:166:192 SD: 0.5952 cents 120:135:146:160:180:195:208:240 SD: 0.4231 cents 168:189:205:224:252:273:291:336 SD: 0.3463 cents 192:216:234:256:288:312:333:384 SD: 0.1486 cents 288:324:351:384:432:468:499:576 SD: 0.0991 cents 480:540:585:640:720:780:832:960 SD: 0.0000 cents