Scala analysis: xen10-wilson-purvi-11a-06
Purvi modulation 6 from Figure 11a, Archytas (28/27 36/35 5/4), (5/4 28/27 36/35)
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: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 15/8 1088.268715 classic major seventh 6: 35/18 1151.229619 septimal semi-diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 5/4 386.3137 major third 2: 28/27 62.9609 Archytas' 1/3-tone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 9/8 203.9100 major whole tone 5: 5/4 386.3137 major third 6: 28/27 62.9609 Archytas' 1/3-tone 7: 36/35 48.7704 septimal diesis, 1/4-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: 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 : 386.3 449.3 498.0 702.0 1088.3 1151.2 1200.0 386.3 : 63.0 111.7 315.6 702.0 764.9 813.7 1200.0 449.3 : 48.8 252.7 639.0 702.0 750.7 1137.0 1200.0 498.0 : 203.9 590.2 653.2 702.0 1088.3 1151.2 1200.0 702.0 : 386.3 449.3 498.0 884.4 947.3 996.1 1200.0 1088.3: 63.0 111.7 498.0 561.0 609.8 813.7 1200.0 1151.2: 48.8 435.1 498.0 546.8 750.7 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 : 188.11099 cents, oct.: 1316.77696 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : DBACDBA 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 : 0.253269 Specific harmonicity : 0.159008 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 420, 8.7142 octaves, 109882.737 Hz. Exponens Consonantiae : 9.072000E+04, 16.46913 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 81.0, average 11.57143 Mersenne's string divisions : 23807070 Sum of van Prooijen's expressibility: 5.91744, average 0.84535 Sum of Tenney's harmonic distance : 11.31335, average 1.61619 Vogel's harmonic complexity : 14.57143 Wille's k value : 202 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: -3 .. 2 -0.57143 10 1 3: -3 .. 1 -0.57143 8 2 5: 0 .. 1 0.57143 4 2 7: 0 .. 1 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: 2 1 0 1 2 1 0 N T3 SD: 42.4007 c. M:-65.0111 c. 9: 3 0 1 1 3 1 0 N SD: 33.7026 c. M: 49.2746 c. 10: 3 1 0 2 3 1 0 N SD: 26.0072 c. M:-48.7704 c. 12: 4 1 0 2 4 1 0 N SD: 27.4752 c. M:-50.7254 c. 13: 4 1 0 3 4 0 1 N SD: 27.7243 c. M: 43.5373 c. 16: 5 1 0 3 5 1 1 N SD: 27.5575 c. M: 48.0450 c. 17: 5 1 1 3 5 1 1 N SD: 21.2146 c. M: 33.3725 c. 19: 6 1 1 3 6 1 1 N SD: 9.4836 c. M: 14.5845 c. 22: 7 1 1 4 7 1 1 N SD: 6.8564 c. M: 12.9110 c. 24: 8 1 1 4 8 1 1 N SD: 6.9140 c. M:-13.6863 c. 32: 10 2 1 6 10 2 1 N SD: 8.2681 c. M: 11.3137 c. 34: 11 2 1 6 11 2 1 N SD: 6.9851 c. M:-13.4763 c. 41: 13 2 2 7 13 2 2 N SD: 6.1341 c. M: 10.2502 c. 43: 14 2 2 7 14 2 2 N SD: 4.0200 c. M: 7.0436 c. 53: 17 3 2 9 17 3 2 N SD: 2.0345 c. M:-3.5556 c. 75: 24 4 3 13 24 4 3 N SD: 1.5122 c. M: 2.3137 c. 96: 31 5 4 16 31 5 4 N SD: 1.2918 c. M: 1.9550 c. 99: 32 5 4 17 32 5 4 N SD: 1.3330 c. M:-2.6404 c. 118: 38 6 5 20 38 6 5 N SD: 1.0546 c. M: 2.0771 c. 128: 41 7 5 22 41 7 5 N SD: 1.2652 c. M: 1.9387 c. 149: 48 8 6 25 48 8 6 N SD: 1.0425 c. M:-1.7321 c. 152: 49 8 6 26 49 8 6 N SD: 0.8568 c. M:-1.4020 c. 171: 55 9 7 29 55 9 7 N SD: 0.3050 c. M: 0.5494 c. 323: 104 17 13 55 104 17 13 N SD: 0.2570 c. M:-0.4732 c. 419: 135 22 17 71 135 22 17 N SD: 0.2414 c. M:-0.3674 c. 441: 142 23 18 75 142 23 18 N SD: 0.1603 c. M: 0.2950 c. 494: 159 26 20 84 159 26 20 N SD: 0.0963 c. M:-0.1874 c. 665: 214 35 27 113 214 35 27 N SD: 0.0835 c. M: 0.1484 c. 935: 301 49 38 159 301 49 38 N SD: 0.0576 c. M:-0.0771 c. 1106: 356 58 45 188 356 58 45 N SD: 0.0490 c. M: 0.0884 c. 1429: 460 75 58 243 460 75 58 N SD: 0.0511 c. M:-0.0744 c. 1525: 491 80 62 259 491 80 62 N SD: 0.0370 c. M:-0.0534 c. 1600: 515 84 65 272 515 84 65 N SD: 0.0368 c. M: 0.0637 c. 2019: 650 106 82 343 650 106 82 N SD: 0.0286 c. M:-0.0567 c. 2190: 705 115 89 372 705 115 89 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 4:5 x x 6 S SD: 60.8012 cents 4:5 x x 6 x x 8 S SD: 0.0000 cents 5:6 x 7:8:9 x 10 S SD: 34.4138 cents 6 x x 8:9:11 x 12 SD: 9.7264 cents 7 x 9 x 11:13 x 14 SD: 20.8597 cents 8:10 x 11:12:15 x 16 S SD: 10.6546 cents 9:11 x 12:14:17 x 18 SD: 15.0213 cents 10 x 13 x 15:19 x 20 SD: 5.8641 cents 11:14 x 15:17:21 x 22 SD: 15.6600 cents 12:15 x 16:18 x 23:24 SD: 4.9821 cents 13:16:17 x 20:24:25:26 SD: 10.4850 cents 14 x 18:19:21:26:27:28 SD: 6.7002 cents 15:19 x 20:23:28:29:30 SD: 7.6948 cents 16:20:21 x 24:30:31:32 S SD: 3.7301 cents 18 x 23:24:27:34:35:36 SD: 4.6660 cents 19:24 x 25:29:36:37:38 SD: 7.6311 cents 20:25:26:27:30:38:39:40 SD: 4.6006 cents 22:28 x 29:33:41:43:44 SD: 6.5739 cents 23:29:30:31:35:43:45:46 SD: 5.4409 cents 24:30:31:32:36:45:47:48 SD: 1.9702 cents 40:50:52:53:60:75:78:80 SD: 1.8439 cents 48:60:62:64:72:90:93:96 S SD: 1.2514 cents 72:90:93:96:108:135:140:144 S SD: 0.8849 cents 88:110:114:117:132:165:171:176 SD: 0.7394 cents 104:130:135:139:156:195:202:208 SD: 0.7361 cents 108:135:140:144:162:203:210:216 SD: 0.6099 cents 128:160:166:171:192:240:249:256 SD: 0.5072 cents 144:180:187:192:216:270:280:288 SD: 0.4412 cents 168:210:218:224:252:315:327:336 SD: 0.3567 cents 192:240:249:256:288:360:373:384 SD: 0.2470 cents 216:270:280:288:324:405:420:432 S SD: 0.0000 cents