Scala analysis: xen10-wilson-purvi-07c-02
Purvi modulation 2 from Figure 7c, Kathleen Schlesinger (16/15 15/13 13/12), (13/12 15/13 16/15)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-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: 13/12 138.5727 tridecimal 2/3-tone 2: 9/8 203.9100 major whole 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: 2 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 3 16/13 359.472 cents tridecimal neutral third 2: 1 5/4 386.314 cents major third 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 8/5 813.686 cents minor sixth 5: 3 13/8 840.528 cents tridecimal neutral sixth 5: 2 64/39 857.517 cents 39th subharmonic 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 138.6 342.5 498.0 702.0 840.5 952.3 1200.0 138.6 : 203.9 359.5 563.4 702.0 813.7 1061.4 1200.0 342.5 : 155.6 359.5 498.0 609.8 857.5 996.1 1200.0 498.0 : 203.9 342.5 454.2 702.0 840.5 1044.4 1200.0 702.0 : 138.6 250.3 498.0 636.6 840.5 996.1 1200.0 840.5 : 111.7 359.5 498.0 702.0 857.5 1061.4 1200.0 952.3 : 247.7 386.3 590.2 745.8 949.7 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 .. 386.3137 cents 225/208, 136.0098 cents 676/675, 2.5629 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 26/25, 67.9002 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 949.6961 cents 225/208, 136.0098 cents 26/25, 67.9002 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 : 167.44061 cents, oct.: 1172.08425 cents Scale is strictly proper Step pattern alph. order: ABCBADE Step pattern size order : BDCDBAE Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.498679 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.319951 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / 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 : 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 Best fifths form a closed circle 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 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 117 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.024458 Average absolute harmonicity : 0.232660 Specific harmonicity : 0.116308 Fundamental : 1/480, -8.9069 octaves, 0.5451 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 7.488000E+04, 16.19229 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 86.5, average 12.35714 Mersenne's string divisions : 1528275 Sum of van Prooijen's expressibility: 5.94929, average 0.84990 Sum of Tenney's harmonic distance : 12.05580, average 1.72226 Vogel's harmonic complexity : 18.28571 Wille's k value : 292 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 91.69825, average 3.27494 Lattice compactness (without 2's) : 38.93550, average 1.39055 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.00000 15 1 3: -1 .. 1 -0.14286 5 2 5: -1 .. 0 -0.14286 1 13: 0 .. 1 0.57143 4 4 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 10 17 26| 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: 33.1810 c. M:-76.3125 c. Lebeng 9: 1 2 1 1 1 1 2 N D3 S SD: 33.4384 c. M:-57.5173 c. 10: 1 2 1 2 1 1 2 P M ME S SD: 13.9553 c. M: 18.5727 c. 17: 2 3 2 3 2 1 4 N SD: 14.0796 c. M: 34.6119 c. 19: 2 3 3 3 2 2 4 P T3 SD: 13.9906 c. M: 26.6932 c. 24: 3 4 3 4 3 2 5 P SD: 6.4317 c. M:-11.4273 c. 34: 4 6 4 6 4 3 7 P SD: 5.2117 c. M:-10.4585 c. 43: 5 7 6 7 5 4 9 P SD: 4.1064 c. M: 7.5989 c. 53: 6 9 7 9 6 5 11 P SD: 1.8948 c. M: 2.8600 c. 77: 9 13 10 13 9 7 16 P SD: 1.0352 c. M:-1.6871 c. 130: 15 22 17 22 15 12 27 P SD: 0.7318 c. M: 1.4897 c. 140: 16 24 18 24 16 13 29 P SD: 0.8264 c. M: 1.4298 c. 164: 19 28 21 28 19 15 34 P SD: 0.8145 c. M:-1.4198 c. 200: 23 34 26 34 23 19 41 SP SD: 0.7440 c. M:-1.7411 c. 207: 24 35 27 35 24 19 43 P SD: 0.6954 c. M: 1.5343 c. 217: 25 37 28 37 25 20 45 P SD: 0.4949 c. M: 1.1069 c. 253: 29 43 33 43 29 24 52 SP SD: 0.7769 c. M:-1.1007 c. 267: 31 45 35 45 31 25 55 SP SD: 0.6640 c. M: 0.9096 c. 270: 31 46 35 46 31 25 56 P SD: 0.5902 c. M: 1.1478 c. 277: 32 47 36 47 32 26 57 SP SD: 0.3321 c. M:-0.8096 c. 330: 38 56 43 56 38 31 68 SP SD: 0.4017 c. M: 0.6645 c. 354: 41 60 46 60 41 33 73 SP SD: 0.2446 c. M:-0.4104 c. 407: 47 69 53 69 47 38 84 SP SD: 0.2358 c. M: 0.4679 c. 441: 51 75 57 75 51 41 91 SP SD: 0.2051 c. M:-0.3745 c. 484: 56 82 63 82 56 45 100 SP SD: 0.2406 c. M: 0.3339 c. 494: 57 84 64 84 57 46 102 SP SD: 0.0603 c. M: 0.1111 c. 848: 98 144 110 144 98 79 175 SP SD: 0.0686 c. M:-0.1066 c. 1065: 123 181 138 181 123 99 220 SP SD: 0.0614 c. M: 0.1463 c. 1342: 155 228 174 228 155 125 277 SP SD: 0.0241 c. M:-0.0510 c. 1836: 212 312 238 312 212 171 379 SP SD: 0.0121 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 x 7:8:9:10 x 12 S SD: 17.4795 cents 7:8 x 9 x 11:12:14 SD: 25.5133 cents 8:9:10:11:12:13:14:16 S SD: 13.7786 cents 10:11:12:13:15:16:17:20 SD: 10.2925 cents 12:13:15:16:18:20:21:24 SD: 9.1660 cents 14:15:17:19:21:23:24:28 SD: 6.4984 cents 22:24:27:29:33:36:38:44 SD: 4.2013 cents 24:26:29:32:36:39:42:48 SD: 3.1793 cents 36:39:44:48:54:59:62:72 SD: 2.7304 cents 45:49:55:60:68:73:78:90 SD: 2.3677 cents 46:50:56:61:69:75:80:92 SD: 1.9845 cents 50:54:61:67:75:81:87:100 SD: 1.9102 cents 60:65:73:80:90:98:104:120 SD: 1.3339 cents 72:78:88:96:108:117:125:144 SD: 0.8074 cents 96:104:117:128:144:156:166:192 SD: 0.5952 cents 120:130:146:160:180:195:208:240 SD: 0.4231 cents 168:182:205:224:252:273:291:336 SD: 0.3463 cents 192:208:234:256:288:312:333:384 SD: 0.1486 cents 288:312:351:384:432:468:499:576 SD: 0.0991 cents 480:520:585:640:720:780:832:960 SD: 0.0000 cents