Scala analysis: xen10-wilson-purvi-07c-01
Purvi modulation 1 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: 13/10 454.213948 tridecimal semi-diminished 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: 16/15 111.7313 minor diatonic semitone 4: 15/13 247.7411 tridecimal 5/4-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: 2 16/15 111.731 cents minor diatonic semitone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 6/5 315.641 cents minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 16/13 359.472 cents tridecimal neutral third 2: 2 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: 2 8/5 813.686 cents minor sixth 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 45/26 949.696 cents 6: 2 26/15 952.259 cents tridecimal semi-augmented sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 2 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 : 138.6 342.5 454.2 702.0 840.5 952.3 1200.0 138.6 : 203.9 315.6 563.4 702.0 813.7 1061.4 1200.0 342.5 : 111.7 359.5 498.0 609.8 857.5 996.1 1200.0 454.2 : 247.7 386.3 498.0 745.8 884.4 1088.3 1200.0 702.0 : 138.6 250.3 498.0 636.6 840.5 952.3 1200.0 840.5 : 111.7 359.5 498.0 702.0 813.7 1061.4 1200.0 952.3 : 247.7 386.3 590.2 702.0 949.7 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 : 13/12, 138.5727 cents, amount: 2 Least squares average step : 166.50137 cents, oct.: 1165.50959 cents Scale is strictly proper Step pattern alph. order: ABCDACD Step pattern size order : BCADBAD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.523872 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.319951 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / 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 : 676/675, 2.5629 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypophrygian octave species of abstract tetrachord Best fifths form a closed circle Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 136.0098 cents: 3 -- Rational properties -- Prime limit : 13 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 39 Scale harmonicity : 0.025071 Average absolute harmonicity : 0.206882 Specific harmonicity : 0.118275 Fundamental : 1/480, -8.9069 octaves, 0.5451 Hz. Guide tone : 78, 6.2854 octaves, 20406.794 Hz. Exponens Consonantiae : 3.744000E+04, 15.19229 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 94.5, average 13.50000 Mersenne's string divisions : 35150325 Sum of van Prooijen's expressibility: 6.58611, average 0.94087 Sum of Tenney's harmonic distance : 13.09056, average 1.87008 Vogel's harmonic complexity : 19.42857 Wille's k value : 292 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 82.40305, average 2.94297 Lattice compactness (without 2's) : 38.25991, average 1.36643 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -1.42857 14 1 3: -1 .. 1 0.00000 4 1 5: -1 .. 0 -0.28571 2 13: 0 .. 1 0.71429 5 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 11 15 27| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 17 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 39.7343 c. M:-76.3125 c. Lebeng 8: 1 1 1 2 1 0 2 N D3 SD: 38.7840 c. M:-59.4723 c. 9: 1 1 1 2 1 1 2 P M ME S SD: 41.3359 c. M: 75.8160 c. 10: 1 2 1 2 1 1 2 P M ME S SD: 15.5955 c. M:-25.7861 c. 19: 2 3 2 4 2 2 4 P T3 S SD: 14.4651 c. M: 26.6932 c. 21: 2 4 2 4 3 2 4 SP T3 SD: 14.6671 c. M: 24.2869 c. 24: 3 4 2 5 3 2 5 P SD: 6.5846 c. M:-11.4273 c. 34: 4 6 3 7 4 3 7 P SD: 5.2909 c. M:-10.4585 c. 43: 5 7 4 9 5 4 9 P SD: 4.7665 c. M: 7.7023 c. 53: 6 9 5 11 6 5 11 P SD: 1.9655 c. M: 2.8600 c. 77: 9 13 7 16 9 7 16 P SD: 1.3204 c. M: 2.2659 c. 87: 10 15 8 18 10 8 18 P SD: 1.1994 c. M:-2.3449 c. 130: 15 22 12 27 15 12 27 P SD: 1.0148 c. M: 1.9063 c. 140: 16 24 13 29 16 13 29 P SD: 0.7532 c. M: 1.4298 c. 164: 19 28 15 34 19 15 34 P SD: 0.8210 c. M:-1.4198 c. 217: 25 37 20 45 25 20 45 P SD: 0.5564 c. M: 1.1069 c. 267: 31 45 25 55 31 25 55 SP SD: 0.5945 c. M: 0.9096 c. 270: 31 46 25 56 31 25 56 P SD: 0.6700 c. M: 1.1478 c. 277: 32 47 26 57 32 26 57 SP SD: 0.4114 c. M:-0.8096 c. 330: 38 56 31 68 38 31 68 SP SD: 0.4176 c. M: 0.6645 c. 354: 41 60 33 73 41 33 73 SP SD: 0.2241 c. M:-0.4104 c. 407: 47 69 38 84 47 38 84 SP SD: 0.2267 c. M: 0.4679 c. 441: 51 75 41 91 51 41 91 SP SD: 0.2172 c. M:-0.3745 c. 494: 57 84 46 102 57 46 102 SP SD: 0.0561 c. M: 0.1111 c. 848: 98 144 79 175 98 79 175 SP SD: 0.0647 c. M:-0.1066 c. 1342: 155 228 125 277 155 125 277 SP SD: 0.0264 c. M:-0.0510 c. 1836: 212 312 171 379 212 171 379 SP SD: 0.0176 c. M:-0.0344 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: 20.6622 cents 4 x 5 x 6 x 7:8 S SD: 11.7144 cents 5 x 6 x x 8:9:10 S SD: 18.8909 cents 6 x 7:8:9:10 x 12 S SD: 19.5545 cents 7:8 x 9 x 11:12:14 SD: 22.5167 cents 8:9:10 x 12:13:14:16 S SD: 13.4004 cents 10:11:12:13:15:16:17:20 SD: 8.1687 cents 14:15:17:18:21:23:24:28 SD: 5.5258 cents 22:24:27:29:33:36:38:44 SD: 4.6326 cents 23:25:28:30:35:37:40:46 SD: 4.5832 cents 24:26:29:31:36:39:42:48 SD: 3.5550 cents 26:28:32:34:39:42:45:52 SD: 3.5302 cents 34:37:41:44:51:55:59:68 SD: 3.2760 cents 36:39:44:47:54:59:62:72 SD: 2.9270 cents 37:40:45:48:56:60:64:74 SD: 2.4989 cents 46:50:56:60:69:75:80:92 SD: 1.6744 cents 50:54:61:65:75:81:87:100 SD: 1.4586 cents 60:65:73:78:90:98:104:120 SD: 1.3339 cents 72:78:88:94:108:117:125:144 SD: 1.3282 cents 74:80:90:96:111:120:128:148 SD: 1.1509 cents 86:93:105:112:129:140:149:172 SD: 0.8914 cents 96:104:117:125:144:156:166:192 SD: 0.7149 cents 110:119:134:143:165:179:191:220 SD: 0.6627 cents 120:130:146:156:180:195:208:240 SD: 0.4231 cents 192:208:234:250:288:312:333:384 SD: 0.4230 cents 206:223:251:268:309:335:357:412 SD: 0.3290 cents 264:286:322:343:396:429:458:528 SD: 0.3231 cents 266:288:324:346:399:432:461:532 SD: 0.2884 cents 274:297:334:356:411:445:475:548 SD: 0.2474 cents 334:362:407:434:501:543:579:668 SD: 0.2029 cents 360:390:439:468:540:585:624:720 SD: 0.1409 cents 480:520:585:624:720:780:832:960 SD: 0.0000 cents