Scala analysis: xen10-wilson-purvi-07b-07
Purvi modulation 7 from Figure 7b, Kathleen Schlesinger (15/13 16/15 13/12), (16/15 13/12 15/13)
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: 16/13 359.472338 tridecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 20/13 745.786052 tridecimal semi-augmented fifth 5: 64/39 857.517337 39th subharmonic 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 15/13 247.7411 tridecimal 5/4-tone 2: 16/15 111.7313 minor diatonic semitone 3: 13/12 138.5727 tridecimal 2/3-tone 4: 15/13 247.7411 tridecimal 5/4-tone 5: 16/15 111.7313 minor diatonic semitone 6: 13/12 138.5727 tridecimal 2/3-tone 7: 9/8 203.9100 major whole 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 : 247.7 359.5 498.0 745.8 857.5 996.1 1200.0 247.7 : 111.7 250.3 498.0 609.8 748.3 952.3 1200.0 359.5 : 138.6 386.3 498.0 636.6 840.5 1088.3 1200.0 498.0 : 247.7 359.5 498.0 702.0 949.7 1061.4 1200.0 745.8 : 111.7 250.3 454.2 702.0 813.7 952.3 1200.0 857.5 : 138.6 342.5 590.2 702.0 840.5 1088.3 1200.0 996.1 : 203.9 451.7 563.4 702.0 949.7 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 : 172.20065 cents, oct.: 1205.40458 cents Scale is strictly proper Step pattern alph. order: ABCABCD Step pattern size order : DABDABC 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 Mixolydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 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 : 0.208124 Specific harmonicity : 0.110422 Fundamental : 1/117, -6.8704 octaves, 2.2361 Hz. Guide tone : 960, 9.9069 octaves, 251160.543 Hz. Exponens Consonantiae : 1.123200E+05, 16.77726 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 114.0, average 16.28571 Mersenne's string divisions : 68999700 Sum of van Prooijen's expressibility: 6.42641, average 0.91806 Sum of Tenney's harmonic distance : 13.95889, average 1.99413 Vogel's harmonic complexity : 14.42857 Wille's k value : 67 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: 0 .. 6 2.71429 19 1 3: -2 .. 1 -0.42857 5 2 5: 0 .. 1 0.28571 2 13: -1 .. 0 -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 8: 2 0 1 2 1 1 1 N D3 SD: 43.5973 c. M: 59.4723 c. 10: 2 1 1 2 1 1 2 P D3 I SD: 19.4939 c. M: 36.0900 c. 14: 3 1 2 3 1 2 2 P T3 SD: 18.2872 c. M:-32.4814 c. 18: 4 1 2 4 2 2 3 N SD: 18.0479 c. M: 31.3783 c. 19: 4 2 2 4 2 2 3 P SD: 14.7496 c. M:-26.6932 c. 21: 4 2 3 4 2 2 4 P SD: 14.7561 c. M: 24.6614 c. 23: 5 2 3 4 2 3 4 N SD: 14.8430 c. M:-23.6941 c. 24: 5 2 3 5 2 3 4 P SD: 5.1852 c. M: 9.4723 c. 34: 7 3 4 7 3 4 6 P SD: 5.9865 c. M: 10.4585 c. 43: 9 4 5 9 4 5 7 P SD: 5.7496 c. M:-8.5612 c. 53: 11 5 6 11 5 6 9 P SD: 1.6751 c. M:-2.8600 c. 77: 16 7 9 16 7 9 13 P SD: 1.2582 c. M:-2.2659 c. 130: 27 12 15 27 12 15 22 P SD: 1.0617 c. M:-1.9063 c. 140: 29 13 16 29 13 16 24 P SD: 0.8605 c. M: 1.8043 c. 164: 34 15 19 34 15 19 28 P SD: 0.8825 c. M: 1.4198 c. 193: 40 18 22 40 18 22 33 P SD: 0.8143 c. M: 1.2713 c. 217: 45 20 25 45 20 25 37 P SD: 0.6035 c. M:-1.1069 c. 224: 46 21 26 46 21 26 38 SP SD: 0.7180 c. M: 1.3125 c. 270: 56 25 31 56 25 31 46 P SD: 0.6320 c. M:-1.1478 c. 277: 57 26 32 57 26 32 47 SP SD: 0.4262 c. M: 0.8096 c. 301: 62 28 35 62 28 35 51 SP SD: 0.4490 c. M: 0.6684 c. 330: 68 31 38 68 31 38 56 SP SD: 0.4040 c. M:-0.6645 c. 354: 73 33 41 73 33 41 60 SP SD: 0.2546 c. M:-0.5202 c. 407: 84 38 47 84 38 47 69 SP SD: 0.2880 c. M:-0.4702 c. 417: 86 39 48 86 39 48 71 SP SD: 0.2794 c. M: 0.4623 c. 441: 91 41 51 91 41 51 75 SP SD: 0.2133 c. M: 0.3745 c. 494: 102 46 57 102 46 57 84 SP SD: 0.0643 c. M: 0.1386 c. 848: 175 79 98 175 79 98 144 SP SD: 0.0722 c. M:-0.1364 c. 1289: 266 120 149 266 120 149 219 SP SD: 0.0830 c. M: 0.1240 c. 1342: 277 125 155 277 125 155 228 SP SD: 0.0278 c. M: 0.0510 c. 1836: 379 171 212 379 171 212 312 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: 21.9155 cents 3 x x 4 x 5 x 6 S SD: 8.9471 cents 4 x 5 x 6 x 7:8 S SD: 14.5451 cents 5 x 6:7 x 8:9:10 S SD: 21.3912 cents 6:7 x 8:9:10:11:12 S SD: 12.7427 cents 7:8 x 9:11 x 12:14 SD: 19.5448 cents 8:9:10:11:12:13:14:16 S SD: 13.1186 cents 9:10:11:12:14:15:16:18 S SD: 10.5955 cents 10 x 12:13:15:16:18:20 SD: 15.0436 cents 11:13:14:15:17:18:20:22 SD: 12.9371 cents 12:14:15:16:18:20:21:24 S SD: 9.5526 cents 13:15:16:17:20:21:23:26 SD: 6.2972 cents 18:21:22:24:28:30:32:36 S SD: 5.7106 cents 21:24:26:28:32:34:37:42 SD: 5.4219 cents 22:25:27:29:34:36:39:44 SD: 4.9990 cents 26:30:32:35:40:43:46:52 SD: 3.2751 cents 31:36:38:41:48:51:55:62 SD: 3.2718 cents 33:38:41:44:51:54:59:66 SD: 3.0660 cents 39:45:48:52:60:64:69:78 SD: 1.1919 cents 78:90:96:104:120:128:139:156 SD: 0.5938 cents 117:135:144:156:180:192:208:234 SD: 0.0000 cents