Scala analysis: xen10-wilson-purvi-07a-01
Purvi modulation 1 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: 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: 9/8 203.9100 major whole tone 2: 13/12 138.5727 tridecimal 2/3-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: 2 52/45 250.304 cents 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: 1 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: 1 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: 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 : 203.9 342.5 454.2 702.0 840.5 952.3 1200.0 203.9 : 138.6 250.3 498.0 636.6 748.3 996.1 1200.0 342.5 : 111.7 359.5 498.0 609.8 857.5 1061.4 1200.0 454.2 : 247.7 386.3 498.0 745.8 949.7 1088.3 1200.0 702.0 : 138.6 250.3 498.0 702.0 840.5 952.3 1200.0 840.5 : 111.7 359.5 563.4 702.0 813.7 1061.4 1200.0 952.3 : 247.7 451.7 590.2 702.0 949.7 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 .. 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 : 166.96807 cents, oct.: 1168.77646 cents Scale is strictly proper Step pattern alph. order: ABCDBCD Step pattern size order : CBADBAD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.481717 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 Hypodorian octave species of abstract tetrachord 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 n-1 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: 39 Scale harmonicity : 0.023500 Average absolute harmonicity : 0.218698 Specific harmonicity : 0.110422 Fundamental : 1/480, -8.9069 octaves, 0.5451 Hz. Guide tone : 234, 7.8704 octaves, 61220.382 Hz. Exponens Consonantiae : 1.123200E+05, 16.77726 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 90.5, average 12.92857 Mersenne's string divisions : 119511105 Sum of van Prooijen's expressibility: 6.42641, average 0.91806 Sum of Tenney's harmonic distance : 12.75477, average 1.82211 Vogel's harmonic complexity : 18.71429 Wille's k value : 292 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 87.63110, average 3.12968 Lattice compactness (without 2's) : 42.19760, average 1.50706 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -1.57143 15 1 3: -1 .. 2 0.42857 5 2 5: -1 .. 0 -0.28571 2 13: 0 .. 1 0.57143 4 4 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 10 17 29| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 11 18 27|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 39.6903 c. M:-76.3125 c. Lebeng 9: 1 1 1 2 1 1 2 P M ME S SD: 49.1560 c. M: 75.8160 c. 10: 2 1 1 2 1 1 2 P D3 I SD: 19.4939 c. M:-36.0900 c. 14: 2 2 1 3 2 1 3 P T3 SD: 18.2872 c. M: 32.4814 c. 18: 3 2 2 4 2 1 4 N SD: 18.0479 c. M:-31.3783 c. 19: 3 2 2 4 2 2 4 P SD: 14.7496 c. M: 26.6932 c. 21: 4 2 2 4 3 2 4 P SD: 14.7561 c. M:-24.6614 c. 23: 4 3 2 4 3 2 5 N SD: 14.8430 c. M: 23.6941 c. 24: 4 3 2 5 3 2 5 P SD: 5.1852 c. M:-9.4723 c. 34: 6 4 3 7 4 3 7 P SD: 5.9865 c. M:-10.4585 c. 43: 7 5 4 9 5 4 9 P SD: 5.7496 c. M: 8.5612 c. 53: 9 6 5 11 6 5 11 P SD: 1.6751 c. M: 2.8600 c. 77: 13 9 7 16 9 7 16 P SD: 1.2582 c. M: 2.2659 c. 130: 22 15 12 27 15 12 27 P SD: 1.0617 c. M: 1.9063 c. 140: 24 16 13 29 16 13 29 P SD: 0.8605 c. M:-1.8043 c. 164: 28 19 15 34 19 15 34 P SD: 0.8825 c. M:-1.4198 c. 193: 33 22 18 40 22 18 40 P SD: 0.8143 c. M:-1.2713 c. 217: 37 25 20 45 25 20 45 P SD: 0.6035 c. M: 1.1069 c. 224: 38 26 21 46 26 21 46 SP SD: 0.7180 c. M:-1.3125 c. 270: 46 31 25 56 31 25 56 P SD: 0.6320 c. M: 1.1478 c. 277: 47 32 26 57 32 26 57 SP SD: 0.4262 c. M:-0.8096 c. 301: 51 35 28 62 35 28 62 SP SD: 0.4490 c. M:-0.6684 c. 330: 56 38 31 68 38 31 68 SP SD: 0.4040 c. M: 0.6645 c. 354: 60 41 33 73 41 33 73 SP SD: 0.2546 c. M: 0.5202 c. 407: 69 47 38 84 47 38 84 SP SD: 0.2880 c. M: 0.4702 c. 417: 71 48 39 86 48 39 86 SP SD: 0.2794 c. M:-0.4623 c. 441: 75 51 41 91 51 41 91 SP SD: 0.2133 c. M:-0.3745 c. 494: 84 57 46 102 57 46 102 SP SD: 0.0643 c. M:-0.1386 c. 848: 144 98 79 175 98 79 175 SP SD: 0.0722 c. M: 0.1364 c. 1289: 219 149 120 266 149 120 266 SP SD: 0.0830 c. M:-0.1240 c. 1342: 228 155 125 277 155 125 277 SP SD: 0.0278 c. M:-0.0510 c. 1836: 312 212 171 379 212 171 379 SP SD: 0.0177 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 6:7 x 8:9:10 x 12 S SD: 17.6708 cents 7:8 x 9 x 11:12:14 SD: 13.9189 cents 8:9:10 x 12:13:14:16 S SD: 7.8096 cents 14:16:17:18:21:23:24:28 SD: 6.1836 cents 18:20:22:23:27:29:31:36 SD: 5.9291 cents 22:25:27:29:33:36:38:44 SD: 4.9668 cents 23:26:28:30:35:37:40:46 SD: 4.6631 cents 24:27:29:31:36:39:42:48 SD: 3.5550 cents 32:36:39:42:48:52:55:64 SD: 3.1572 cents 40:45:49:52:60:65:69:80 SD: 1.7381 cents 50:56:61:65:75:81:87:100 SD: 1.6614 cents 56:63:68:73:84:91:97:112 SD: 1.1459 cents 64:72:78:83:96:104:111:128 SD: 0.6135 cents 120:135:146:156:180:195:208:240 SD: 0.4231 cents 160:180:195:208:240:260:277:320 SD: 0.2974 cents 224:252:273:291:336:364:388:448 SD: 0.2403 cents 256:288:312:333:384:416:444:512 SD: 0.2101 cents 320:360:390:416:480:520:555:640 SD: 0.1486 cents 360:405:439:468:540:585:624:720 SD: 0.1409 cents 416:468:507:541:624:676:721:832 SD: 0.0943 cents 480:540:585:624:720:780:832:960 SD: 0.0000 cents