Scala analysis: xen10-wilson-purvi-07a-07
Purvi modulation 7 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: 20/13 745.786052 tridecimal semi-augmented 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: 15/13 247.7411 tridecimal 5/4-tone 5: 9/8 203.9100 major whole 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 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 : 247.7 386.3 498.0 745.8 949.7 1088.3 1200.0 247.7 : 138.6 250.3 498.0 702.0 840.5 952.3 1200.0 386.3 : 111.7 359.5 563.4 702.0 813.7 1061.4 1200.0 498.0 : 247.7 451.7 590.2 702.0 949.7 1088.3 1200.0 745.8 : 203.9 342.5 454.2 702.0 840.5 952.3 1200.0 949.7 : 138.6 250.3 498.0 636.6 748.3 996.1 1200.0 1088.3: 111.7 359.5 498.0 609.8 857.5 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 : 179.82672 cents, oct.: 1258.78701 cents Scale is strictly proper Step pattern alph. order: ABCADBC Step pattern size order : DBADCBA 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 Phrygian octave species of abstract tetrachord 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: 45 Scale harmonicity : 0.024065 Average absolute harmonicity : 0.215661 Specific harmonicity : 0.112946 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 : 87.0, average 12.42857 Mersenne's string divisions : 4526676 Sum of van Prooijen's expressibility: 6.29543, average 0.89935 Sum of Tenney's harmonic distance : 12.53362, average 1.79052 Vogel's harmonic complexity : 18.14286 Wille's k value : 292 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 78.91589, average 2.81842 Lattice compactness (without 2's) : 42.64709, average 1.52311 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.14286 11 1 3: -1 .. 2 0.42857 5 1 5: 0 .. 1 0.71429 5 2 13: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714 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: 58.2045 c. M: 92.5532 c. Lebeng 8: 2 1 0 2 1 1 1 N D3 SD: 43.1728 c. M:-63.6863 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 27.9395 c. M:-54.2139 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 16.5504 c. M: 26.3137 c. Pseudo Rast 19: 4 2 2 4 3 2 2 P SD: 8.4094 c. M: 14.5845 c. 24: 5 3 2 5 4 3 2 P SD: 7.0883 c. M:-13.6863 c. 34: 7 4 3 7 6 4 3 P SD: 3.4963 c. M:-5.8489 c. 43: 9 5 4 9 7 5 4 P SD: 3.9519 c. M:-7.7023 c. 53: 11 6 5 11 9 6 5 P SD: 1.1568 c. M: 1.4763 c. 130: 27 15 12 27 22 15 12 P SD: 1.1955 c. M:-1.9063 c. 140: 29 16 13 29 24 16 13 P SD: 0.8419 c. M:-1.7325 c. 193: 40 22 18 40 33 22 18 P SD: 0.8200 c. M:-1.5993 c. 217: 45 25 20 45 37 25 20 P SD: 0.9209 c. M:-1.4560 c. 224: 46 26 21 46 38 26 21 SP SD: 0.9414 c. M: 1.4818 c. 227: 47 26 21 47 39 26 21 P SD: 0.9296 c. M:-1.8458 c. 246: 51 28 23 51 42 28 23 P SD: 0.8500 c. M:-1.5235 c. 248: 51 29 23 51 42 29 23 SP SD: 0.7524 c. M: 1.3090 c. 267: 55 31 25 55 45 31 25 SP SD: 0.6987 c. M: 1.3814 c. 270: 56 31 25 56 46 31 25 P SD: 0.8173 c. M:-1.4151 c. 277: 57 32 26 57 47 32 26 SP SD: 0.6990 c. M: 0.9596 c. 301: 62 35 28 62 51 35 28 SP SD: 0.4448 c. M: 0.8588 c. 335: 69 39 31 69 57 39 31 SP SD: 0.5111 c. M: 0.7114 c. 354: 73 41 33 73 60 41 33 SP SD: 0.2613 c. M: 0.5435 c. 388: 80 45 36 80 66 45 36 SP SD: 0.2859 c. M: 0.4252 c. 407: 84 47 38 84 69 47 38 SP SD: 0.2011 c. M: 0.3103 c. 441: 91 51 41 91 75 51 41 SP SD: 0.1202 c. M: 0.2078 c. 494: 102 57 46 102 84 57 46 SP SD: 0.0584 c. M:-0.1015 c. 1342: 277 155 125 277 228 155 125 SP SD: 0.0399 c. M: 0.0686 c. 1836: 379 212 171 379 312 212 171 SP SD: 0.0273 c. M: 0.0392 c. 2330: 481 269 217 481 396 269 217 SP SD: 0.0265 c. M: 0.0476 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: 21.7791 cents 4 x 5 x 6:7 x 8 S SD: 11.9559 cents 5:6 x 7:8:9 x 10 S SD: 28.9593 cents 6:7 x 8:9:10:11:12 S SD: 14.9720 cents 7:8:9 x 11:12:13:14 SD: 11.2414 cents 10:12 x 13:15:17:19:20 SD: 16.6191 cents 11:13:14:15:17:19:21:22 SD: 10.3543 cents 12:14:15:16:18:21:23:24 SD: 9.1483 cents 13:15:16:17:20:23:24:26 SD: 9.0564 cents 15:17:19:20:23:26:28:30 SD: 5.6957 cents 19:22:24:25:29:33:36:38 SD: 5.4303 cents 21:24:26:28:32:36:39:42 S SD: 5.2921 cents 24:28:30:32:37:42:45:48 SD: 3.8989 cents 31:36:39:41:48:54:58:62 SD: 3.7964 cents 32:37:40:43:49:55:60:64 SD: 2.8792 cents 33:38:41:44:51:57:62:66 SD: 2.0659 cents 45:52:56:60:69:78:84:90 SD: 1.8377 cents 48:55:60:64:74:83:90:96 SD: 1.8132 cents 52:60:65:69:80:90:98:104 SD: 1.7381 cents 60:69:75:80:92:104:113:120 SD: 1.6434 cents 63:73:79:84:97:109:118:126 SD: 1.3492 cents 71:82:89:95:109:123:133:142 SD: 1.2942 cents 72:83:90:96:111:125:135:144 SD: 0.9478 cents 96:111:120:128:148:166:180:192 SD: 0.7631 cents 104:120:130:139:160:180:195:208 SD: 0.5938 cents 156:180:195:208:240:270:293:312 SD: 0.4224 cents 201:232:251:268:309:348:377:402 SD: 0.3390 cents 208:240:260:277:320:360:390:416 SD: 0.2974 cents 240:277:300:320:369:415:450:480 SD: 0.2848 cents 279:322:349:372:429:483:523:558 SD: 0.2441 cents 312:360:390:416:480:540:585:624 SD: 0.0000 cents