Scala analysis: xen10-wilson-purvi-07c-06
Purvi modulation 6 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: 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: 5/3 884.358713 major sixth, BP sixth 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: 10/9 182.4037 minor whole tone 6: 9/8 203.9100 major whole 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: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 2 6/5 315.641 cents minor third 2: 1 16/13 359.472 cents tridecimal neutral third 2: 3 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: 3 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 45/26 949.696 cents 6: 1 26/15 952.259 cents tridecimal semi-augmented sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 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 : 247.7 386.3 498.0 702.0 884.4 1088.3 1200.0 247.7 : 138.6 250.3 454.2 636.6 840.5 952.3 1200.0 386.3 : 111.7 315.6 498.0 702.0 813.7 1061.4 1200.0 498.0 : 203.9 386.3 590.2 702.0 949.7 1088.3 1200.0 702.0 : 182.4 386.3 498.0 745.8 884.4 996.1 1200.0 884.4 : 203.9 315.6 563.4 702.0 813.7 1017.6 1200.0 1088.3: 111.7 359.5 498.0 609.8 813.7 996.1 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 176.24092 cents, oct.: 1233.68647 cents Scale is strictly proper Step pattern alph. order: ABCDEDC Step pattern size order : EBADCDA Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.537528 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.319951 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 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 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 15 Scale harmonicity : 0.025715 Average absolute harmonicity : 0.261608 Specific harmonicity : 0.167330 Fundamental : 1/312, -8.2854 octaves, 0.8385 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 1.872000E+04, 14.19229 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 41.5, average 5.92857 Mersenne's string divisions : 57960 Sum of van Prooijen's expressibility: 4.70437, average 0.67205 Sum of Tenney's harmonic distance : 9.00470, average 1.28639 Vogel's harmonic complexity : 20.00000 Wille's k value : 292 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 70.11358, average 2.50406 Lattice compactness (without 2's) : 38.93550, average 1.39055 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.42857 9 1 3: -1 .. 1 0.14286 5 2 5: 0 .. 1 0.57143 4 3 13: -1 .. 0 -0.14286 1 1 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 10 16 25| 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: 42.3321 c. M: 76.3125 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 29.0349 c. M:-48.9746 c. 10: 2 1 1 2 1 2 1 P M ME S SD: 22.1670 c. M: 44.3587 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 2 1 2 2 2 1 P M ME S SD: 20.2006 c. M: 47.7411 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 14: 3 2 1 2 2 3 1 P T3 SD: 23.3581 c. M:-42.2577 c. 15: 3 2 1 3 2 3 1 N T3 SD: 16.5803 c. M:-31.7313 c. Fifteen-tone "Major" 19: 4 2 2 3 3 3 2 P T3 SD: 7.5130 c. M: 14.5845 c. 31: 6 4 3 5 5 5 3 SP SD: 7.0602 c. M: 15.4830 c. 33: 7 4 3 5 5 6 3 P SD: 9.4105 c. M:-13.6863 c. 34: 7 4 3 6 5 6 3 P SD: 3.2346 c. M:-5.8489 c. 53: 11 6 5 9 8 9 5 P SD: 1.0486 c. M: 1.4763 c. 130: 27 15 12 22 20 22 12 P SD: 1.1094 c. M:-1.7951 c. 140: 29 16 13 24 21 24 13 P SD: 0.8471 c. M: 1.5016 c. 171: 35 20 16 29 26 29 16 SP SD: 0.8494 c. M: 2.1270 c. 183: 38 21 17 31 28 31 17 P SD: 0.7020 c. M:-1.4393 c. 217: 45 25 20 37 33 37 20 P SD: 0.7124 c. M:-1.1322 c. 224: 46 26 21 38 34 38 21 SP SD: 0.6453 c. M: 1.3125 c. 236: 49 27 22 40 36 40 22 P SD: 0.5746 c. M:-1.4115 c. 248: 51 29 23 42 38 42 23 SP SD: 0.6806 c. M:-1.1252 c. 258: 53 30 24 44 39 44 24 SP SD: 0.5701 c. M: 1.2294 c. 267: 55 31 25 45 41 45 25 SP SD: 0.6752 c. M:-1.0345 c. 270: 56 31 25 46 41 46 25 P SD: 0.5314 c. M:-1.1478 c. 277: 57 32 26 47 42 47 26 SP SD: 0.5918 c. M: 0.9041 c. 289: 60 33 27 49 44 49 27 P SD: 0.5628 c. M:-1.3939 c. 301: 62 35 28 51 46 51 28 SP SD: 0.4032 c. M:-0.6911 c. 311: 64 36 29 53 47 53 29 SP SD: 0.4814 c. M: 0.7957 c. 323: 67 37 30 55 49 55 30 P SD: 0.4742 c. M:-1.1754 c. 335: 69 39 31 57 51 57 31 SP SD: 0.4341 c. M:-0.6865 c. 354: 73 41 33 60 54 60 33 SP SD: 0.2388 c. M:-0.3870 c. 388: 80 45 36 66 59 66 36 SP SD: 0.2359 c. M:-0.3911 c. 407: 84 47 38 69 62 69 38 SP SD: 0.1862 c. M: 0.3080 c. 441: 91 51 41 75 67 75 41 SP SD: 0.0956 c. M:-0.1667 c. 494: 102 57 46 84 75 84 46 SP SD: 0.0746 c. M: 0.1482 c. 848: 175 98 79 144 129 144 79 SP SD: 0.0640 c. M: 0.0995 c. 901: 186 104 84 153 137 153 84 SP SD: 0.0720 c. M: 0.1444 c. 935: 193 108 87 159 142 159 87 SP SD: 0.0603 c. M: 0.0806 c. 1289: 266 149 120 219 196 219 120 SP SD: 0.0472 c. M: 0.1072 c. 1342: 277 155 125 228 204 228 125 SP SD: 0.0284 c. M: 0.0510 c. 1783: 368 206 166 303 271 303 166 SP SD: 0.0266 c. M: 0.0686 c. 1836: 379 212 171 312 279 312 171 SP SD: 0.0282 c. M: 0.0450 c. 2277: 470 263 212 387 346 387 212 SP SD: 0.0261 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: 0.0000 cents 4 x 5 x 6:7 x 8 S SD: 21.1168 cents 5:6 x 7 x 8:9:10 S SD: 29.4851 cents 6:7 x 8:9:10:11:12 S SD: 7.2257 cents 7:8:9 x 11:12:13:14 SD: 18.0987 cents 8:9:10:11:12:13:15:16 SD: 11.6762 cents 10:12 x 13:15:17:19:20 SD: 15.1224 cents 11:13:14:15:17:18:21:22 SD: 13.4465 cents 12:14:15:16:18:20:23:24 SD: 6.0841 cents 20:23:25:27:30:33:38:40 SD: 5.1991 cents 24:28:30:32:36:40:45:48 S SD: 2.7328 cents 32:37:40:43:48:53:60:64 SD: 2.5246 cents 39:45:49:52:59:65:73:78 SD: 2.4920 cents 40:46:50:53:60:67:75:80 SD: 2.1466 cents 48:55:60:64:72:80:90:96 SD: 1.7235 cents 60:69:75:80:90:100:113:120 SD: 1.3729 cents 64:74:80:85:96:107:120:128 SD: 1.3407 cents 72:83:90:96:108:120:135:144 SD: 0.2291 cents 168:194:210:224:252:280:315:336 SD: 0.1962 cents 240:277:300:320:360:400:450:480 SD: 0.0687 cents 312:360:390:416:468:520:585:624 SD: 0.0000 cents