Scala analysis: xen10-wilson-purvi-11c-07
Purvi modulation 7 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: 5/3 884.358713 major sixth, BP sixth 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: 5/4 386.3137 major third 5: 36/35 48.7704 septimal diesis, 1/4-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: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 7/6 266.871 cents septimal minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 2 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: 2 54/35 750.725 cents septimal semi-augmented fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 1 140/81 947.320 cents 5: 1 15/8 1088.269 cents classic major seventh 6: 2 8/5 813.686 cents minor sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh 6: 2 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 : 386.3 435.1 498.0 884.4 933.1 1137.0 1200.0 386.3 : 48.8 111.7 498.0 546.8 750.7 813.7 1200.0 435.1 : 63.0 449.3 498.0 702.0 764.9 1151.2 1200.0 498.0 : 386.3 435.1 639.0 702.0 1088.3 1137.0 1200.0 884.4 : 48.8 252.7 315.6 702.0 750.7 813.7 1200.0 933.1 : 203.9 266.9 653.2 702.0 764.9 1151.2 1200.0 1137.0: 63.0 449.3 498.0 561.0 947.3 996.1 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 : 28/27, 62.9609 cents, amount: 2 Least squares average step : 186.97094 cents, oct.: 1308.79659 cents Scale is not proper Step pattern alph. order: ABCABDC Step pattern size order : DABDACB Scale is a Constant Structure, by a margin of 48.77038 cents Scale diversity : 1.569058 Lumma stability : 0.081284 Lumma impropriety factor : 0.651213 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 : 245/243, 14.1905 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 701.955 1151.230 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% 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 337.5433 cents: 4 -- 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 : 0.232340 Specific harmonicity : 0.160099 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 : 51.5, average 7.35714 Mersenne's string divisions : 785232 Sum of van Prooijen's expressibility: 5.10577, average 0.72940 Sum of Tenney's harmonic distance : 10.15844, average 1.45121 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 : 77.99071, average 2.78538 Lattice compactness (without 2's) : 54.89613, average 1.96058 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.28571 8 1 3: -1 .. 3 0.57143 8 1 5: 0 .. 1 0.28571 2 2 7: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 15 21| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18| Scale is weakly epimorphic with val: <7 12 18 21|
FIT/MODE
7: 2 0 1 2 0 1 1 N T3 SD: 64.2961 c. M: 108.4677 c. 8: 3 0 0 3 0 2 0 N T3 S SD: 41.2189 c. M:-63.6863 c. 9: 3 0 1 3 0 2 0 N SD: 35.9088 c. M:-62.9609 c. 11: 3 1 0 4 0 2 1 N SD: 43.4309 c. M: 61.6814 c. 12: 4 0 1 4 0 2 1 N SD: 24.3079 c. M: 37.0391 c. 14: 5 0 1 4 1 2 1 N SD: 22.1841 c. M:-42.2577 c. 15: 5 0 1 5 1 2 1 N SD: 19.9112 c. M: 35.0841 c. 16: 5 1 1 5 0 3 1 N SD: 19.1393 c. M: 33.1291 c. 17: 5 1 1 5 1 3 1 N T3 S SD: 20.5350 c. M: 37.2999 c. 18: 6 0 1 6 1 3 1 N SD: 19.7469 c. M: 35.0841 c. 19: 6 1 1 6 1 3 1 N T3 S SD: 7.1562 c. M:-14.2393 c. 22: 7 1 1 7 1 4 1 N T3 S SD: 6.6887 c. M: 11.6314 c. 41: 13 2 2 13 2 7 2 N T3 S SD: 4.1582 c. M: 6.3099 c. 53: 17 2 3 17 2 9 3 N SD: 3.2882 c. M: 4.9636 c. 72: 23 3 4 23 3 12 4 N SD: 2.0906 c. M: 3.7058 c. 77: 25 3 4 25 3 13 4 N SD: 2.1613 c. M:-3.9530 c. 80: 26 3 4 26 3 14 4 N SD: 2.4447 c. M:-3.6863 c. 94: 30 4 5 30 4 16 5 N SD: 1.9556 c. M: 3.5076 c. 99: 32 4 5 32 4 17 5 N SD: 1.2575 c. M:-2.3548 c. 118: 38 5 6 38 5 20 6 N SD: 1.4610 c. M:-2.4641 c. 130: 42 5 7 42 5 22 7 N SD: 1.2095 c. M:-1.7951 c. 149: 48 6 8 48 6 25 8 N SD: 1.0359 c. M:-1.5473 c. 152: 49 6 8 49 6 26 8 N SD: 0.7525 c. M: 1.5501 c. 171: 55 7 9 55 7 29 9 N SD: 0.1943 c. M: 0.3488 c. 441: 142 18 23 142 18 75 23 N SD: 0.2004 c. M:-0.3759 c. 494: 159 20 26 159 20 84 26 N SD: 0.1910 c. M: 0.3356 c. 593: 191 24 31 191 24 101 31 N SD: 0.1728 c. M: 0.2455 c. 612: 197 25 32 197 25 104 32 N SD: 0.1394 c. M:-0.2158 c. 665: 214 27 35 214 27 113 35 N SD: 0.1513 c. M: 0.1970 c. 742: 239 30 39 239 30 126 39 N SD: 0.1416 c. M:-0.2774 c. 764: 246 31 40 246 31 130 40 N SD: 0.0985 c. M: 0.1448 c. 935: 301 38 49 301 38 159 49 N SD: 0.0590 c. M: 0.0810 c. 1106: 356 45 58 356 45 188 58 N SD: 0.0464 c. M: 0.0911 c. 1848: 595 75 97 595 75 314 97 N SD: 0.0316 c. M:-0.0569 c. 2019: 650 82 106 650 82 343 106 N SD: 0.0249 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: 91.2019 cents 3 x x 4:5 x x 6 S SD: 0.0000 cents 4:5 x x x 7 x 8 SD: 11.8989 cents 5:6 x 7:8:9 x 10 S SD: 31.1503 cents 6 x x 8:10 x x 12 S SD: 0.0000 cents 7 x 9 x x 12 x 14 SD: 0.0000 cents 8:10 x 11:13:14:15:16 SD: 15.2861 cents 9:11 x 12:15 x 17:18 SD: 10.6004 cents 10 x 13 x x 17:19:20 SD: 8.8159 cents 11 x 14:15:18:19:21:22 SD: 9.5907 cents 12:15 x 16:20:21:23:24 SD: 6.2119 cents 13:16:17 x x 22:25:26 SD: 9.1759 cents 14 x 18:19:23:24:27:28 SD: 6.5817 cents 15:19 x 20:25:26:29:30 SD: 5.0277 cents 16:20 x 21:27 x 31:32 SD: 7.1268 cents 17:21:22:23:28:29:33:34 SD: 6.0695 cents 18 x 23:24:30:31:35:36 SD: 3.2499 cents 19:24 x 25:32:33:37:38 SD: 7.4110 cents 20:25:26:27:33:34:39:40 SD: 5.9024 cents 21:26:27:28:35:36:41:42 SD: 3.8484 cents 22 x 28:29:37:38:42:44 SD: 6.2926 cents 24:30:31:32:40:41:46:48 SD: 2.0953 cents 26 x 33:35:43:45:50:52 SD: 5.8951 cents 27:34:35:36:45:46:52:54 SD: 3.1467 cents 28:35:36:37:47:48:54:56 SD: 2.8317 cents 36:45:46:48:60:62:69:72 SD: 2.4485 cents 39:49:50:52:65:67:75:78 SD: 1.6955 cents 45:56:58:60:75:77:87:90 SD: 1.4723 cents 56:70:72:75:93:96:108:112 SD: 1.4130 cents 60:75:77:80:100:103:116:120 SD: 0.8366 cents 81:101:104:108:135:139:156:162 SD: 0.8179 cents 84:105:108:112:140:144:162:168 S SD: 0.0000 cents