Scala analysis: xen10-wilson-purvi-11b-02
Purvi modulation 2 from Figure 11b, Archytas (5/4 36/35 28/27), (36/35 28/27 5/4)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 16/15 111.731285 minor diatonic semitone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 54/35 750.725382 septimal semi-augmented fifth 6: 8/5 813.686286 minor sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 5/4 386.3137 major third 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 28/27 62.9609 Archytas' 1/3-tone 3: 5/4 386.3137 major third 4: 9/8 203.9100 major whole tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 5/4 386.3137 major third
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: 2 16/15 111.731 cents minor diatonic semitone 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 9/7 435.084 cents septimal major third, BP third 2: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 45/32 590.224 cents diatonic tritone 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 64/45 609.776 cents 2nd tritone 5: 2 54/35 750.725 cents septimal semi-augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 140/81 947.320 cents 5: 2 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 : 48.8 111.7 498.0 702.0 750.7 813.7 1200.0 48.8 : 63.0 449.3 653.2 702.0 764.9 1151.2 1200.0 111.7 : 386.3 590.2 639.0 702.0 1088.3 1137.0 1200.0 498.0 : 203.9 252.7 315.6 702.0 750.7 813.7 1200.0 702.0 : 48.8 111.7 498.0 546.8 609.8 996.1 1200.0 750.7 : 63.0 449.3 498.0 561.0 947.3 1151.2 1200.0 813.7 : 386.3 435.1 498.0 884.4 1088.3 1137.0 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 .. 590.2237 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 609.7763 .. 1088.2687 cents 675/512, 478.4924 cents 64/75,-274.5824 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 : 154.35666 cents, oct.: 1080.49663 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : ABDCABD Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.578397 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 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 Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian 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 : 1 at degree 0 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 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: 35 Scale harmonicity : 0.030910 Average absolute harmonicity : 0.250070 Specific harmonicity : 0.159008 Fundamental : 1/210, -7.7142 octaves, 1.2458 Hz. Guide tone : 432, 8.7549 octaves, 113022.244 Hz. Exponens Consonantiae : 9.072000E+04, 16.46913 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 109.5, average 15.64286 Mersenne's string divisions : 267388485 Sum of van Prooijen's expressibility: 5.91744, average 0.84535 Sum of Tenney's harmonic distance : 12.51747, average 1.78821 Vogel's harmonic complexity : 14.57143 Wille's k value : 157 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 83.30262, average 2.97509 Lattice compactness (without 2's) : 54.84969, average 1.95892 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.71429 14 1 3: -1 .. 3 0.57143 8 2 5: -1 .. 0 -0.57143 4 2 7: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 18| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 0 1 2 1 0 1 2 N T3 SD: 42.4007 c. M: 65.0111 c. 9: 0 1 3 1 1 0 3 N SD: 33.7026 c. M:-49.2746 c. 10: 0 1 3 2 0 1 3 N SD: 26.0072 c. M: 48.7704 c. 12: 0 1 4 2 0 1 4 N SD: 27.4752 c. M: 50.7254 c. 16: 1 0 6 2 1 1 5 N SD: 22.7372 c. M: 36.7313 c. 17: 1 1 5 3 1 1 5 N SD: 21.2146 c. M:-33.3725 c. 19: 1 1 6 3 1 1 6 N SD: 9.4836 c. M:-14.5845 c. 22: 1 1 7 4 1 1 7 N SD: 6.8564 c. M:-12.9110 c. 24: 1 1 8 4 1 1 8 N SD: 6.9140 c. M: 13.6863 c. Enharmonic Dorian 32: 1 2 10 6 1 2 10 N SD: 8.2681 c. M:-11.3137 c. 34: 1 2 11 6 1 2 11 N SD: 6.9851 c. M: 13.4763 c. 41: 2 2 13 7 2 2 13 N SD: 6.1341 c. M:-10.2502 c. 43: 2 2 14 7 2 2 14 N SD: 4.0200 c. M:-7.0436 c. 53: 2 3 17 9 2 3 17 N SD: 2.0345 c. M: 3.5556 c. 75: 3 4 24 13 3 4 24 N SD: 1.5122 c. M:-2.3137 c. 96: 4 5 31 16 4 5 31 N SD: 1.2918 c. M: 1.9550 c. 99: 4 5 32 17 4 5 32 N SD: 1.3330 c. M: 2.6404 c. 118: 5 6 38 20 5 6 38 N SD: 1.0546 c. M:-2.0771 c. 128: 5 7 41 22 5 7 41 N SD: 1.2652 c. M:-1.9387 c. 149: 6 8 48 25 6 8 48 N SD: 1.0425 c. M: 1.7321 c. 152: 6 8 49 26 6 8 49 N SD: 0.8568 c. M: 1.4020 c. 171: 7 9 55 29 7 9 55 N SD: 0.3050 c. M:-0.5494 c. 323: 13 17 104 55 13 17 104 N SD: 0.2570 c. M: 0.4732 c. 419: 17 22 135 71 17 22 135 N SD: 0.2414 c. M: 0.3674 c. 441: 18 23 142 75 18 23 142 N SD: 0.1603 c. M:-0.2950 c. 494: 20 26 159 84 20 26 159 N SD: 0.0963 c. M: 0.1874 c. 665: 27 35 214 113 27 35 214 N SD: 0.0835 c. M:-0.1484 c. 935: 38 49 301 159 38 49 301 N SD: 0.0576 c. M:-0.0771 c. 1106: 45 58 356 188 45 58 356 N SD: 0.0490 c. M:-0.0884 c. 1429: 58 75 460 243 58 75 460 N SD: 0.0511 c. M:-0.0744 c. 1525: 62 80 491 259 62 80 491 N SD: 0.0370 c. M:-0.0534 c. 1600: 65 84 515 272 65 84 515 N SD: 0.0368 c. M:-0.0637 c. 2019: 82 106 650 343 82 106 650 N SD: 0.0286 c. M: 0.0567 c. 2190: 89 115 705 372 89 115 705 N SD: 0.0317 c. M:-0.0495 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: 23.5575 cents 4 x x 5:6 x x 8 S SD: 37.2438 cents 5 x x 7 x x 8:10 SD: 28.1557 cents 6 x 7:8:9 x 10:12 S SD: 34.0957 cents 7 x 8:9 x x 11:14 SD: 34.6444 cents 8 x 9:11:12 x 13:16 SD: 21.9594 cents 9 x 10:12 x 14 x 18 SD: 18.0208 cents 10 x 11:13:15 x 16:20 SD: 13.7973 cents 11 x 12:15 x 17:18:22 SD: 13.4899 cents 12 x 13:16:18 x 19:24 SD: 6.4779 cents 13 x 14:17 x 20:21:26 SD: 8.2546 cents 14 x 15:19:21 x 22:28 SD: 8.8803 cents 15 x 16:20 x 23:24:30 SD: 2.1439 cents 16 x 17:21:24:25:26:32 SD: 7.4338 cents 17 x 18:23 x 26:27:34 SD: 6.9134 cents 18 x 19:24:27:28:29:36 SD: 4.3255 cents 19 x 20:25 x 29:30:38 SD: 8.7765 cents 20 x 21:27:30:31:32:40 SD: 5.9390 cents 21 x 22:28 x 32:34:42 SD: 8.6148 cents 22:23 x 29:33:34:35:44 SD: 5.9901 cents 23:24:25:31 x 35:37:46 SD: 8.6480 cents 24:25:26:32:36:37:38:48 SD: 5.5889 cents 26:27:28:35:39:40:42:52 SD: 4.7857 cents 27:28:29:36:41:42:43:54 SD: 4.6556 cents 28:29:30:37:42:43:45:56 SD: 3.4050 cents 30:31:32:40:45:46:48:60 S SD: 1.9105 cents 60:62:64:80:90:93:96:120 S SD: 1.6155 cents 70:72:75:93:105:108:112:140 SD: 1.4130 cents 72:74:77:96:108:111:115:144 SD: 0.8193 cents 105:108:112:140:158:162:168:210 SD: 0.7839 cents 108:111:115:144:162:167:173:216 SD: 0.7786 cents 132:136:141:176:198:204:211:264 SD: 0.7241 cents 136:140:145:181:204:210:218:272 SD: 0.7127 cents 138:142:147:184:207:213:221:276 SD: 0.4278 cents 180:185:192:240:270:278:288:360 SD: 0.3180 cents 210:216:224:280:315:324:336:420 S SD: 0.0000 cents