Scala analysis: xen10-wilson-purvi-04-06
Purvi modulation 6 from Figure 4, Archytas (8/7 9/8 28/27) all 6 permutations
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 14/9 764.915905 septimal 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: 28/27 62.9609 Archytas' 1/3-tone 2: 8/7 231.1741 septimal whole tone 3: 9/8 203.9100 major whole tone 4: 9/8 203.9100 major whole tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 8/7 231.1741 septimal whole tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 3 9/8 203.910 cents major whole tone 1: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 81/64 407.820 cents Pythagorean major third 2: 2 9/7 435.084 cents septimal major third, BP third 3: 1 21/16 470.781 cents narrow fourth 3: 5 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 4: 1 112/81 561.006 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 32/21 729.219 cents wide fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 5: 2 12/7 933.129 cents septimal major sixth 6: 2 7/4 968.826 cents harmonic seventh 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 63.0 294.1 498.0 702.0 764.9 996.1 1200.0 63.0 : 231.2 435.1 639.0 702.0 933.1 1137.0 1200.0 294.1 : 203.9 407.8 470.8 702.0 905.9 968.8 1200.0 498.0 : 203.9 266.9 498.0 702.0 764.9 996.1 1200.0 702.0 : 63.0 294.1 498.0 561.0 792.2 996.1 1200.0 764.9 : 231.2 435.1 498.0 729.2 933.1 1137.0 1200.0 996.1 : 203.9 266.9 498.0 702.0 905.9 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 231.1741 cents 54/49, 168.2132 cents 28/27, 62.9609 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 3: 470.7809 .. 638.9941 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 4: 561.0059 .. 729.2191 cents 54/49, 168.2132 cents 6272/6561,-77.9882 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 6: 968.8259 .. 1137.0391 cents 54/49, 168.2132 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.722778 Largest / Average step : 1.348516 Largest / Smallest step : 3.671709 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 165.38790 cents, oct.: 1157.71527 cents Scale is not proper Step pattern alph. order: ABCCABC Step pattern size order : SLMMSLM Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.378117 Lumma stability : 0.223924 Lumma impropriety factor : 0.064990 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 64/63, 27.2641 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale is Hypolydian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 168.2132 cents: 5 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.037102 Average absolute harmonicity : 0.254363 Specific harmonicity : 0.198288 Fundamental : 1/54, -5.7549 octaves, 4.8449 Hz. Guide tone : 672, 9.3923 octaves, 175812.380 Hz. Exponens Consonantiae : 3.628800E+04, 15.14720 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 88.5, average 12.64286 Mersenne's string divisions : 7836675 Sum of van Prooijen's expressibility: 5.72546, average 0.81792 Sum of Tenney's harmonic distance : 12.23213, average 1.74745 Vogel's harmonic complexity : 9.71429 Wille's k value : 40 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 90.09618, average 3.21772 Lattice compactness (without 2's) : 54.56078, average 1.94860 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 5 2.00000 16 1 3: -3 .. 1 -1.42857 12 4 7: 0 .. 1 0.28571 2 2 Average exponent except 2's :-8 / 7 =-1.14286 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 10 22| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 12 18|
FIT/MODE
7: 0 2 1 1 0 2 1 N T3 SD: 45.0292 c. M: 79.2016 c. 9: 0 2 2 1 1 1 2 N T3 SD: 42.0517 c. M: 62.9609 c. 10: 0 2 2 2 0 2 2 N M DE S SD: 39.3988 c. M: 62.9609 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 19.4940 c. M:-37.0391 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 14: 1 2 3 2 1 3 2 P T3 SD: 22.3962 c. M: 36.9921 c. 16: 1 3 3 2 1 3 3 P SD: 18.1256 c. M:-26.9550 c. Gorgo-Pelog 17: 1 3 3 3 1 3 3 N M DE S SD: 7.7740 c. M: 11.7821 c. 24: 1 5 4 4 1 5 4 N SD: 7.9982 c. M: 14.9159 c. Diatonic + Enharmonic Diesis Dorian 36: 2 7 6 6 2 7 6 N SD: 3.2542 c. M:-5.8650 c. Diatonic + Soft Chromatic Diesis Dorian 41: 2 8 7 7 2 8 7 N SD: 2.3487 c. M: 4.4243 c. 58: 3 11 10 10 3 11 10 N SD: 2.2234 c. M: 4.4798 c. 77: 4 15 13 13 4 15 13 N SD: 1.1011 c. M:-1.9689 c. 94: 5 18 16 16 5 18 16 N SD: 0.5716 c. M:-1.0415 c. 135: 7 26 23 23 7 26 23 N SD: 0.5126 c. M: 0.8017 c. 171: 9 33 29 29 9 33 29 N SD: 0.3030 c. M:-0.6018 c. 265: 14 51 45 45 14 51 45 N SD: 0.2373 c. M:-0.4353 c. 306: 16 59 52 52 16 59 52 N SD: 0.1141 c. M: 0.2158 c. 400: 21 77 68 68 21 77 68 N SD: 0.0746 c. M: 0.1350 c. 571: 30 110 97 97 30 110 97 N SD: 0.0574 c. M:-0.0864 c. 706: 37 136 120 120 37 136 120 N SD: 0.0517 c. M: 0.0840 c. 877: 46 169 149 149 46 169 149 N SD: 0.0287 c. M:-0.0497 c. 1277: 67 246 217 217 67 246 217 N SD: 0.0040 c. M: 0.0081 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 x 5:6 S SD: 37.2438 cents 4 x 5 x 6 x 7:8 S SD: 24.0316 cents 5 x 6:7 x 8:9:10 S SD: 20.4336 cents 6 x 7:8:9 x 11:12 SD: 11.9689 cents 7 x 8:9 x 11:12:14 SD: 22.0918 cents 8 x 9:11:12 x 14:16 SD: 21.6535 cents 9 x 11:12 x 14:16:18 SD: 10.6546 cents 11:12:13:15 x 17:20:22 SD: 17.3733 cents 12:13:14:16:18:19:21:24 SD: 12.8910 cents 13:14:15:17 x 20:23:26 SD: 14.8950 cents 14:15:17:19:21:22:25:28 SD: 11.3038 cents 15:16:18:20 x 23:27:30 SD: 10.4405 cents 16:17:19:21:24:25:28:32 SD: 8.2327 cents 17:18:20:23 x 26:30:34 SD: 9.3123 cents 18:19:21:24:27:28:32:36 SD: 5.8594 cents 21:22:25:28:32:33:37:42 SD: 5.8235 cents 22:23:26:29:33:34:39:44 SD: 3.9462 cents 27:28:32:36:41:42:48:54 SD: 3.0346 cents 32:33:38:43:48:50:57:64 SD: 2.7017 cents 48:50:57:64:72:75:85:96 SD: 1.8966 cents 54:56:64:72:81:84:96:108 S SD: 0.0000 cents