Scala analysis: xen10-wilson-purvi-07a-06
Purvi modulation 6 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: 15/13 247.741053 tridecimal 5/4-tone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 45/26 949.696054 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: 15/13 247.7411 tridecimal 5/4-tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 15/13 247.7411 tridecimal 5/4-tone 6: 13/12 138.5727 tridecimal 2/3-tone 7: 16/15 111.7313 minor diatonic semitone
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: 2 52/45 250.304 cents 2: 1 6/5 315.641 cents minor third 2: 1 16/13 359.472 cents tridecimal neutral third 2: 2 5/4 386.314 cents major 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 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 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 : 247.7 386.3 498.0 702.0 949.7 1088.3 1200.0 247.7 : 138.6 250.3 454.2 702.0 840.5 952.3 1200.0 386.3 : 111.7 315.6 563.4 702.0 813.7 1061.4 1200.0 498.0 : 203.9 451.7 590.2 702.0 949.7 1088.3 1200.0 702.0 : 247.7 386.3 498.0 745.8 884.4 996.1 1200.0 949.7 : 138.6 250.3 498.0 636.6 748.3 952.3 1200.0 1088.3: 111.7 359.5 498.0 609.8 813.7 1061.4 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 : 13/12, 138.5727 cents, amount: 2 Least squares average step : 178.57440 cents, oct.: 1250.02080 cents Scale is strictly proper Step pattern alph. order: ABCDABC Step pattern size order : DBACDBA Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.515941 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.211056 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 Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 42.8571% 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 : 13 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.024065 Average absolute harmonicity : 0.249946 Specific harmonicity : 0.127427 Fundamental : 1/312, -8.2854 octaves, 0.8385 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 5.616000E+04, 15.77726 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 73.0, average 10.42857 Mersenne's string divisions : 2057580 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 10.89679, average 1.55668 Vogel's harmonic complexity : 19.28571 Wille's k value : 292 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 72.52948, average 2.59034 Lattice compactness (without 2's) : 42.23288, average 1.50832 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.57143 10 1 3: -1 .. 2 0.57143 6 2 5: 0 .. 1 0.57143 4 2 13: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 6 / 7 = 0.85714 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 11 15 24| 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: 53.9437 c. M: 92.5532 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 23.2084 c. M:-35.2883 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 15.0149 c. M: 26.3137 c. Pseudo Rast 19: 4 2 2 3 4 2 2 P SD: 7.5641 c. M: 14.5845 c. 24: 5 3 2 4 5 3 2 P SD: 6.9465 c. M:-13.6863 c. 34: 7 4 3 6 7 4 3 P SD: 3.3753 c. M:-5.8489 c. 43: 9 5 4 7 9 5 4 P SD: 3.1242 c. M:-4.3840 c. 53: 11 6 5 9 11 6 5 P SD: 1.0322 c. M: 1.4763 c. 130: 27 15 12 22 27 15 12 P SD: 0.9669 c. M:-1.4897 c. 140: 29 16 13 24 29 16 13 P SD: 0.9079 c. M:-1.7325 c. 183: 38 21 17 31 38 21 17 P SD: 0.7488 c. M:-1.4393 c. 236: 49 27 22 40 49 27 22 P SD: 0.7058 c. M:-1.4115 c. 248: 51 29 23 42 51 29 23 SP SD: 0.7260 c. M: 1.3090 c. 258: 53 30 24 44 53 30 24 SP SD: 0.6101 c. M: 1.2294 c. 277: 57 32 26 47 57 32 26 SP SD: 0.6555 c. M: 0.9596 c. 301: 62 35 28 51 62 35 28 SP SD: 0.4469 c. M: 0.8588 c. 311: 64 36 29 53 64 36 29 SP SD: 0.4307 c. M: 0.7957 c. 335: 69 39 31 57 69 39 31 SP SD: 0.4376 c. M:-0.6865 c. 354: 73 41 33 60 73 41 33 SP SD: 0.2790 c. M: 0.5435 c. 388: 80 45 36 66 80 45 36 SP SD: 0.2398 c. M:-0.3911 c. 407: 84 47 38 69 84 47 38 SP SD: 0.2114 c. M: 0.3103 c. 441: 91 51 41 75 91 51 41 SP SD: 0.0965 c. M:-0.1667 c. 494: 102 57 46 84 102 57 46 SP SD: 0.0624 c. M:-0.1015 c. 935: 193 108 87 159 193 108 87 SP SD: 0.0538 c. M:-0.0771 c. 1342: 277 155 125 228 277 155 125 SP SD: 0.0384 c. M: 0.0686 c. 1783: 368 206 166 303 368 206 166 SP SD: 0.0350 c. M: 0.0686 c. 1836: 379 212 171 312 379 212 171 SP SD: 0.0241 c. M: 0.0392 c. 2277: 470 263 212 387 470 263 212 SP SD: 0.0240 c. M: 0.0467 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: 21.7791 cents 4 x 5 x 6:7 x 8 S SD: 4.7825 cents 5:6 x 7:8:9 x 10 S SD: 33.9644 cents 6:7 x 8:9:10:11:12 S SD: 13.0688 cents 7:8:9 x 11:12:13:14 SD: 16.4047 cents 8:9:10:11:12:14:15:16 S SD: 10.2271 cents 10:12 x 13:15:17:19:20 SD: 14.9274 cents 11:13:14:15:17:19:21:22 SD: 12.6675 cents 12:14:15:16:18:21:23:24 SD: 6.6697 cents 18:21:23:24:27:31:34:36 SD: 6.4689 cents 20:23:25:27:30:35:38:40 SD: 5.3217 cents 24:28:30:32:36:42:45:48 S SD: 3.8648 cents 32:37:40:43:48:55:60:64 SD: 2.6343 cents 40:46:50:53:60:69:75:80 SD: 1.9412 cents 48:55:60:64:72:83:90:96 SD: 1.7386 cents 52:60:65:69:78:90:98:104 SD: 1.7381 cents 60:69:75:80:90:104:113:120 SD: 1.4209 cents 64:74:80:85:96:111:120:128 SD: 1.2111 cents 72:83:90:96:108:125:135:144 SD: 0.7958 cents 96:111:120:128:144:166:180:192 SD: 0.5634 cents 144:166:180:192:216:249:270:288 SD: 0.3240 cents 168:194:210:224:252:291:315:336 SD: 0.2775 cents 216:249:270:288:324:374:405:432 SD: 0.2507 cents 240:277:300:320:360:415:450:480 SD: 0.2392 cents 312:360:390:416:468:540:585:624 SD: 0.0000 cents