Scala analysis: xen10-wilson-purvi-11c-06
Purvi modulation 6 from Figure 11c, Archytas (28/27 5/4 36/35), (36/35 5/4 28/27)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 5/4 386.313714 major third 2: 9/7 435.084095 septimal major third, BP third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 12/7 933.129094 septimal major sixth 6: 27/14 1137.039096 septimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 5/4 386.3137 major third 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 9/8 203.9100 major whole tone 5: 8/7 231.1741 septimal whole tone 6: 9/8 203.9100 major whole tone 7: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 2 7/6 266.871 cents septimal minor third 2: 3 9/7 435.084 cents septimal major third, BP third 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 3: 1 6/5 315.641 cents minor third 3: 4 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 3: 1 35/24 653.185 cents septimal semi-diminished fifth 4: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 112/81 561.006 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 54/35 750.725 cents septimal semi-augmented fifth 5: 3 14/9 764.916 cents septimal minor sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 1 15/8 1088.269 cents classic major seventh 6: 1 8/5 813.686 cents minor sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh 6: 1 35/18 1151.230 cents septimal semi-diminished octave 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 : 386.3 435.1 498.0 702.0 933.1 1137.0 1200.0 386.3 : 48.8 111.7 315.6 546.8 750.7 813.7 1200.0 435.1 : 63.0 266.9 498.0 702.0 764.9 1151.2 1200.0 498.0 : 203.9 435.1 639.0 702.0 1088.3 1137.0 1200.0 702.0 : 231.2 435.1 498.0 884.4 933.1 996.1 1200.0 933.1 : 203.9 266.9 653.2 702.0 764.9 968.8 1200.0 1137.0: 63.0 449.3 498.0 561.0 764.9 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 386.3137 cents 175/144, 337.5433 cents 36/35, 48.7704 cents 2: 111.7313 .. 449.2746 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 750.7254 .. 1088.2687 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.515014 Largest / Average step : 2.253497 Largest / Smallest step : 7.921072 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 181.75941 cents, oct.: 1272.31585 cents Scale is not proper Step pattern alph. order: ABCDEDC Step pattern size order : EABCDCB Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.577632 Lumma stability : 0.081284 Lumma impropriety factor : 0.651213 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 : 245/243, 14.1905 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 Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 2 at degree 3 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 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.031896 Average absolute harmonicity : 0.255545 Specific harmonicity : 0.177735 Fundamental : 1/84, -6.3923 octaves, 3.1146 Hz. Guide tone : 540, 9.0768 octaves, 141277.805 Hz. Exponens Consonantiae : 4.536000E+04, 15.46913 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 50.0, average 7.14286 Mersenne's string divisions : 3926160 Sum of van Prooijen's expressibility: 4.88392, average 0.69770 Sum of Tenney's harmonic distance : 9.76050, average 1.39436 Vogel's harmonic complexity : 12.42857 Wille's k value : 52 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 75.65278, average 2.70189 Lattice compactness (without 2's) : 50.12344, average 1.79012 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.14286 9 1 3: -1 .. 3 0.85714 8 2 5: 0 .. 1 0.14286 1 1 7: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 15 18| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 2 0 0 2 1 1 1 N T3 S SD: 86.4213 c. M: 155.1879 c. 8: 2 0 1 1 2 1 1 N T3 SD: 82.0054 c. M: 135.0841 c. 9: 3 0 1 1 2 2 0 N SD: 33.5365 c. M:-62.9609 c. 10: 3 1 0 2 2 1 1 N SD: 32.3741 c. M: 57.0391 c. 12: 4 0 1 2 2 2 1 N SD: 23.5896 c. M: 37.0391 c. 14: 5 0 1 2 3 2 1 N SD: 20.5913 c. M:-42.2577 c. 15: 5 0 1 3 3 2 1 N SD: 20.9824 c. M: 35.0841 c. 17: 5 1 1 3 3 3 1 N T3 SD: 15.0045 c. M: 33.3725 c. 19: 6 1 1 3 4 3 1 N SD: 7.6584 c. M:-14.2393 c. 22: 7 1 1 4 4 4 1 N T3 SD: 5.7172 c. M:-8.4154 c. 36: 12 1 2 6 7 6 2 N SD: 5.5006 c. M:-13.6863 c. 41: 13 2 2 7 8 7 2 N SD: 3.4112 c. M: 5.8259 c. 53: 17 2 3 9 10 9 3 N SD: 3.2491 c. M: 4.9636 c. 58: 19 2 3 10 11 10 3 N SD: 2.8311 c. M:-6.7897 c. 72: 23 3 4 12 14 12 4 N SD: 2.1833 c. M: 3.7058 c. 77: 25 3 4 13 15 13 4 N SD: 1.5813 c. M:-3.2967 c. 94: 30 4 5 16 18 16 5 N SD: 1.4390 c. M: 3.3350 c. 99: 32 4 5 17 19 17 5 N SD: 1.3086 c. M:-2.3548 c. 130: 42 5 7 22 25 22 7 N SD: 1.0136 c. M: 1.6545 c. 149: 48 6 8 25 29 25 8 N SD: 0.9831 c. M: 1.4686 c. 152: 49 6 8 26 29 26 8 N SD: 0.7928 c. M: 1.5501 c. 171: 55 7 9 29 33 29 9 N SD: 0.2010 c. M: 0.3488 c. 441: 142 18 23 75 85 75 23 N SD: 0.2030 c. M:-0.3759 c. 494: 159 20 26 84 95 84 26 N SD: 0.1844 c. M: 0.3356 c. 571: 184 23 30 97 110 97 30 N SD: 0.1488 c. M:-0.3763 c. 593: 191 24 31 101 114 101 31 N SD: 0.1940 c. M: 0.2455 c. 612: 197 25 32 104 118 104 32 N SD: 0.1384 c. M:-0.2158 c. 665: 214 27 35 113 128 113 35 N SD: 0.1405 c. M: 0.1970 c. 742: 239 30 39 126 143 126 39 N SD: 0.0986 c. M:-0.2092 c. 764: 246 31 40 130 147 130 40 N SD: 0.1089 c. M: 0.1448 c. 836: 269 34 44 142 161 142 44 N SD: 0.1284 c. M: 0.1970 c. 913: 294 37 48 155 176 155 48 N SD: 0.0838 c. M: 0.1278 c. 935: 301 38 49 159 180 159 49 N SD: 0.0583 c. M: 0.0810 c. 1106: 356 45 58 188 213 188 58 N SD: 0.0337 c. M: 0.0569 c. 1848: 595 75 97 314 356 314 97 N SD: 0.0233 c. M:-0.0499 c. 2019: 650 82 106 343 389 343 106 N SD: 0.0218 c. M: 0.0406 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: 16.2568 cents 4:5 x x 6:7 x 8 S SD: 8.9242 cents 5:6 x 7:8:9 x 10 S SD: 35.6359 cents 6 x x 8:9:10 x 12 S SD: 12.1926 cents 7 x 9 x 11:12 x 14 SD: 20.1343 cents 8:10 x 11:12:14:15:16 S SD: 13.4276 cents 9:11 x 12:14:15:17:18 SD: 15.9442 cents 10 x 13 x 15:17:19:20 SD: 7.0527 cents 11 x 14:15:17:19:21:22 SD: 11.7536 cents 12:15 x 16:18:21:23:24 SD: 6.2119 cents 13:16:17 x 20:22:25:26 SD: 10.5752 cents 14 x 18:19:21:24:27:28 SD: 5.1070 cents 15:19 x 20:23:26:29:30 SD: 8.0929 cents 16:20 x 21:24:27:31:32 SD: 6.5630 cents 18 x 23:24:27:31:35:36 SD: 3.2499 cents 19:24 x 25:29:33:37:38 SD: 8.4247 cents 20:25:26:27:30:34:39:40 SD: 5.3534 cents 22 x 28:29:33:38:42:44 SD: 5.7253 cents 24:30:31:32:36:41:46:48 SD: 2.0953 cents 26 x 33:35:39:45:50:52 SD: 5.4578 cents 27:34:35:36:41:46:52:54 SD: 4.3716 cents 28:35:36:37:42:48:54:56 SD: 2.2181 cents 48:60:62:64:72:82:93:96 SD: 1.8303 cents 52:65:67:69:78:89:100:104 SD: 1.5345 cents 56:70:72:75:84:96:108:112 SD: 1.1016 cents 60:75:77:80:90:103:116:120 SD: 0.8366 cents 84:105:108:112:126:144:162:168 S SD: 0.0000 cents