Scala analysis: xen10-wilson-purvi-07b-04
Purvi modulation 4 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: 16/15 111.731285 minor diatonic semitone 2: 16/13 359.472338 tridecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 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: 16/15 111.7313 minor diatonic semitone 2: 15/13 247.7411 tridecimal 5/4-tone 3: 13/12 138.5727 tridecimal 2/3-tone 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 10/9 182.4037 minor whole 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: 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 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 1 16/13 359.472 cents tridecimal neutral third 2: 2 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: 2 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 359.5 498.0 702.0 813.7 996.1 1200.0 111.7 : 247.7 386.3 590.2 702.0 884.4 1088.3 1200.0 359.5 : 138.6 342.5 454.2 636.6 840.5 952.3 1200.0 498.0 : 203.9 315.6 498.0 702.0 813.7 1061.4 1200.0 702.0 : 111.7 294.1 498.0 609.8 857.5 996.1 1200.0 813.7 : 182.4 386.3 498.0 745.8 884.4 1088.3 1200.0 996.1 : 203.9 315.6 563.4 702.0 905.9 1017.6 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: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 416/405, 46.3939 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 .. 905.8650 cents 135/128, 92.1787 cents 26/25, 67.9002 cents 6: 952.2589 .. 1088.2687 cents 225/208, 136.0098 cents 416/405, 46.3939 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 : 168.41145 cents, oct.: 1178.88012 cents Scale is strictly proper Step pattern alph. order: ABCDAED Step pattern size order : AEBDACD Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.575480 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.393003 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 512/507, 16.9897 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 Best major thirds form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 5 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 : 0.024065 Average absolute harmonicity : 0.259329 Specific harmonicity : 0.171026 Fundamental : 1/1170, -10.1923 octaves, 0.2236 Hz. Guide tone : 48, 5.5850 octaves, 12558.027 Hz. Exponens Consonantiae : 5.616000E+04, 15.77726 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 56.5, average 8.07143 Mersenne's string divisions : 6135675 Sum of van Prooijen's expressibility: 4.89749, average 0.69964 Sum of Tenney's harmonic distance : 10.61706, average 1.51672 Vogel's harmonic complexity : 22.85714 Wille's k value : 877 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 80.60553, average 2.87877 Lattice compactness (without 2's) : 39.75396, average 1.41978 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 2.42857 19 1 3: -2 .. 1 -0.42857 5 3 5: -1 .. 0 -0.28571 2 2 13: -1 .. 0 -0.14286 1 1 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is weakly epimorphic with val: <7 10 16 29| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 15 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.3173 c. M:-59.6973 c. Lebeng 10: 1 2 1 2 1 1 2 P M ME S SD: 19.6933 c. M: 36.0900 c. 12: 1 3 1 2 1 2 2 P D3 SD: 16.8623 c. M:-40.5277 c. Phrygian Dominant, Phrygian Major, Mela Vakulabharanam, Raga Ahiri, Basant Mukhari, Jogiya, Vativasantabhairavi, Zilof, Ahava Rabba, Freygish: Jewish, Maqam Hijaz-Nahawand, Humayun, Spanish Gipsy, Dorico Flamenco: Spain, Hitzaz: Greece, Harmonic Major inverse, Mixolydian flat 2 flat 6 17: 2 3 2 3 2 2 3 SP M ME S SD: 17.3861 c. M:-33.3725 c. 19: 2 4 2 3 2 3 3 SP D3 SD: 11.7038 c. M:-19.4750 c. 22: 2 5 2 4 2 3 4 P SD: 10.9025 c. M:-22.3458 c. 24: 2 5 3 4 2 4 4 P SD: 7.9066 c. M: 13.6863 c. 31: 3 6 4 5 3 5 5 SP SD: 6.5887 c. M: 11.0852 c. 34: 3 7 4 6 3 5 6 P SD: 4.9728 c. M: 7.8547 c. 41: 4 8 5 7 4 6 7 SP SD: 4.3423 c. M: 8.2528 c. 46: 4 10 5 8 4 7 8 P SD: 4.5792 c. M: 7.3835 c. 53: 5 11 6 9 5 8 9 SP SD: 1.3084 c. M:-2.7918 c. 130: 12 27 15 22 12 20 22 SP SD: 0.7696 c. M: 1.3786 c. 171: 16 35 20 29 16 26 29 SP SD: 0.6712 c. M: 1.5776 c. 183: 17 38 21 31 17 28 31 SP SD: 0.5844 c. M:-1.1834 c. 217: 20 45 25 37 20 33 37 SP SD: 0.6126 c. M: 1.1322 c. 224: 21 46 26 38 21 34 38 SP SD: 0.4501 c. M:-0.7687 c. 270: 25 56 31 46 25 41 46 SP SD: 0.4168 c. M: 0.6202 c. 277: 26 57 32 47 26 42 47 SP SD: 0.4675 c. M:-0.9041 c. 301: 28 62 35 51 28 46 51 SP SD: 0.4024 c. M: 0.6684 c. 354: 33 73 41 60 33 54 60 SP SD: 0.2570 c. M:-0.5202 c. 407: 38 84 47 69 38 62 69 SP SD: 0.2635 c. M:-0.4702 c. 441: 41 91 51 75 41 67 75 SP SD: 0.1520 c. M: 0.2887 c. 494: 46 102 57 84 46 75 84 SP SD: 0.0726 c. M: 0.1386 c. 848: 79 175 98 144 79 129 144 SP SD: 0.0688 c. M:-0.1364 c. 1118: 104 231 129 190 104 170 190 SP SD: 0.0650 c. M: 0.1034 c. 1289: 120 266 149 219 120 196 219 SP SD: 0.0509 c. M: 0.1240 c. 1342: 125 277 155 228 125 204 228 SP SD: 0.0248 c. M:-0.0422 c. 1836: 171 379 212 312 171 279 312 SP SD: 0.0203 c. M:-0.0392 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: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 9.5649 cents 5 x 6:7 x 8:9:10 S SD: 19.5124 cents 6 x 7:8:9:10:11:12 S SD: 21.3487 cents 7:8 x 9 x 11:12:14 SD: 30.4420 cents 8:9:10:11:12:13:14:16 S SD: 16.6103 cents 9:10:11:12 x 14:16:18 S SD: 14.4517 cents 10:11:12:13:15:16:18:20 SD: 12.0736 cents 12:13:15:16:18:19:21:24 SD: 7.1612 cents 17:18:21:23:26:27:30:34 SD: 6.8497 cents 18:19:22:24:27:29:32:36 SD: 3.5506 cents 30:32:37:40:45:48:53:60 SD: 1.6338 cents 48:51:59:64:72:77:85:96 SD: 1.5465 cents 60:64:74:80:90:96:107:120 SD: 0.9276 cents 90:96:111:120:135:144:160:180 SD: 0.5147 cents 168:179:207:224:252:269:299:336 SD: 0.5122 cents 192:205:236:256:288:307:341:384 SD: 0.4964 cents 195:208:240:260:293:312:347:390 SD: 0.4847 cents 198:211:244:264:297:317:352:396 SD: 0.4203 cents 208:222:256:277:312:333:370:416 SD: 0.3933 cents 212:226:261:283:318:339:377:424 SD: 0.3717 cents 238:254:293:317:357:381:423:476 SD: 0.3312 cents 252:269:310:336:378:403:448:504 SD: 0.2529 cents 270:288:332:360:405:432:480:540 SD: 0.2291 cents 300:320:369:400:450:480:533:600 SD: 0.2187 cents 330:352:406:440:495:528:587:660 SD: 0.1689 cents 360:384:443:480:540:576:640:720 SD: 0.0429 cents