Scala analysis: xen10-wilson-purvi-11a-05
Purvi modulation 5 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: 9/8 203.910002 major whole tone 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: 9/8 203.9100 major whole tone 2: 280/243 245.3646 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: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 280/243 245.365 cents 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 32/27 294.135 cents Pythagorean minor 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 27/16 905.865 cents Pythagorean major sixth 5: 2 140/81 947.320 cents 5: 1 15/8 1088.269 cents classic major seventh 6: 1 8/5 813.686 cents minor sixth 6: 1 243/140 954.635 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 449.3 498.0 702.0 1088.3 1151.2 1200.0 203.9 : 245.4 294.1 498.0 884.4 947.3 996.1 1200.0 449.3 : 48.8 252.7 639.0 702.0 750.7 954.6 1200.0 498.0 : 203.9 590.2 653.2 702.0 905.9 1151.2 1200.0 702.0 : 386.3 449.3 498.0 702.0 947.3 996.1 1200.0 1088.3: 63.0 111.7 315.6 561.0 609.8 813.7 1200.0 1151.2: 48.8 252.7 498.0 546.8 750.7 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 186.80811 cents, oct.: 1307.65678 cents Scale is not proper Step pattern alph. order: ABCADEC Step pattern size order : CDACEBA Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.594117 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 19683/19600, 7.3158 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 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 n-1 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 : 243 (O: 243 U: 243) Highest odd numerator or denominator: 35 Scale harmonicity : 0.028556 Average absolute harmonicity : 0.253405 Specific harmonicity : 0.149615 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 1260, 10.2992 octaves, 329648.212 Hz. Exponens Consonantiae : 2.721600E+05, 18.05410 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 85.0, average 12.14286 Mersenne's string divisions : 134906730 Sum of van Prooijen's expressibility: 6.17271, average 0.88182 Sum of Tenney's harmonic distance : 11.86965, average 1.69566 Vogel's harmonic complexity : 14.57143 Wille's k value : 202 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 92.57356, average 3.30620 Lattice compactness (without 2's) : 62.47592, average 2.23128 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.71429 11 1 3: -3 .. 2 -0.28571 10 3 5: 0 .. 1 0.42857 3 1 7: 0 .. 1 0.28571 2 2 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 1 2 0 1 2 1 0 N T3 SD: 40.9727 c. M:-65.0111 c. 10: 2 2 0 2 3 1 0 N SD: 27.6320 c. M:-48.7704 c. 12: 2 3 0 2 4 1 0 N SD: 27.0242 c. M:-50.7254 c. 13: 2 3 0 3 4 0 1 N SD: 27.9308 c. M: 43.5373 c. 14: 2 3 1 2 5 0 1 N SD: 24.0622 c. M: 36.9439 c. 17: 3 3 1 3 5 1 1 N SD: 17.3139 c. M: 29.4452 c. 19: 3 4 1 3 6 1 1 N SD: 10.5811 c. M: 14.5845 c. 22: 4 4 1 4 7 1 1 N SD: 8.5569 c. M:-14.2718 c. 24: 4 5 1 4 8 1 1 N SD: 4.8195 c. M:-11.7313 c. 41: 7 8 2 7 13 2 2 N SD: 5.7369 c. M: 10.2502 c. 43: 7 9 2 7 14 2 2 N SD: 4.8873 c. M: 8.5612 c. 46: 8 9 2 8 15 2 2 N SD: 4.3761 c. M:-7.3835 c. 53: 9 11 2 9 17 3 2 N SD: 1.9644 c. M:-3.5556 c. 77: 13 16 3 13 25 4 3 N SD: 1.7226 c. M:-2.6734 c. 94: 16 19 4 16 30 5 4 N SD: 1.7534 c. M: 3.1623 c. 99: 17 20 4 17 32 5 4 N SD: 1.4449 c. M:-2.6404 c. 118: 20 24 5 20 38 6 5 N SD: 1.0717 c. M: 2.0771 c. 142: 24 29 6 24 46 7 6 N SD: 1.2514 c. M: 1.9338 c. 147: 25 30 6 25 47 8 6 N SD: 0.9783 c. M: 2.5544 c. 152: 26 31 6 26 49 8 6 N SD: 0.9776 c. M:-1.4020 c. 171: 29 35 7 29 55 9 7 N SD: 0.3141 c. M: 0.5494 c. 323: 55 66 13 55 104 17 13 N SD: 0.3020 c. M:-0.4732 c. 419: 71 86 17 71 135 22 17 N SD: 0.2996 c. M: 0.5687 c. 441: 75 90 18 75 142 23 18 N SD: 0.1702 c. M: 0.2950 c. 494: 84 101 20 84 159 26 20 N SD: 0.1055 c. M:-0.1874 c. 665: 113 136 27 113 214 35 27 N SD: 0.0618 c. M: 0.1484 c. 1106: 188 226 45 188 356 58 45 N SD: 0.0511 c. M: 0.0884 c. 1354: 230 277 55 230 436 71 55 N SD: 0.0470 c. M: 0.0695 c. 1600: 272 327 65 272 515 84 65 N SD: 0.0439 c. M:-0.0900 c. 1771: 301 362 72 301 570 93 72 N SD: 0.0363 c. M: 0.0700 c. 1966: 334 402 80 334 633 103 80 N SD: 0.0358 c. M: 0.0597 c. 2019: 343 413 82 343 650 106 82 N SD: 0.0331 c. M:-0.0567 c. 2289: 389 468 93 389 737 120 93 N SD: 0.0279 c. M:-0.0668 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 x 5 x 6 x x 8 S SD: 20.9870 cents 5:6 x 7:8:9 x 10 S SD: 38.5212 cents 6:7 x 8:9:11 x 12 SD: 14.8023 cents 7:8:9 x 11:13 x 14 SD: 17.5561 cents 8:9:10:11:12:15 x 16 S SD: 13.7458 cents 9:10 x 12:14:17 x 18 SD: 13.5497 cents 10:11:13 x 15:19 x 20 SD: 9.0860 cents 11:12:14:15:17:21 x 22 SD: 15.8157 cents 12:14 x 16:18 x 23:24 SD: 13.5419 cents 13:15:17 x 20:24:25:26 SD: 11.9703 cents 14:16:18:19:21:26:27:28 SD: 6.9392 cents 16:18:21 x 24:30:31:32 S SD: 3.7301 cents 19:21 x 25:29:36:37:38 SD: 8.6710 cents 20:23:26:27:30:38:39:40 SD: 7.1214 cents 21:24:27:28:32:39:41:42 SD: 6.4083 cents 22:25 x 29:33:41:43:44 SD: 4.9594 cents 24:27:31:32:36:45:47:48 SD: 1.9702 cents 40:45:52:53:60:75:78:80 SD: 1.8439 cents 48:54:62:64:72:90:93:96 SD: 1.2514 cents 54:61:70:72:81:101:105:108 SD: 1.1855 cents 72:81:93:96:108:135:140:144 SD: 0.8849 cents 88:99:114:117:132:165:171:176 SD: 0.7394 cents 104:117:135:139:156:195:202:208 SD: 0.7361 cents 112:126:145:149:168:210:218:224 SD: 0.6846 cents 128:144:166:171:192:240:249:256 SD: 0.5072 cents 144:162:187:192:216:270:280:288 SD: 0.4412 cents 162:182:210:216:243:304:315:324 SD: 0.3958 cents 168:189:218:224:252:315:327:336 SD: 0.3567 cents 192:216:249:256:288:360:373:384 SD: 0.2470 cents 216:243:280:288:324:405:420:432 SD: 0.0000 cents