Scala analysis: xen10-wilson-purvi-11c-02
Purvi modulation 2 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: 36/35 48.770381 septimal diesis, 1/4-tone 2: 81/70 252.680383 Al-Hwarizmi's lute middle finger 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: 9/8 203.9100 major whole tone 3: 280/243 245.3646 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: 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 9/7 435.084 cents septimal major third, BP third 2: 3 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: 3 54/35 750.725 cents septimal semi-augmented fifth 5: 1 14/9 764.916 cents septimal minor 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 48.8 252.7 498.0 702.0 750.7 813.7 1200.0 48.8 : 203.9 449.3 653.2 702.0 764.9 1151.2 1200.0 252.7 : 245.4 449.3 498.0 561.0 947.3 996.1 1200.0 498.0 : 203.9 252.7 315.6 702.0 750.7 954.6 1200.0 702.0 : 48.8 111.7 498.0 546.8 750.7 996.1 1200.0 750.7 : 63.0 449.3 498.0 702.0 947.3 1151.2 1200.0 813.7 : 386.3 435.1 639.0 884.4 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 .. 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 : 156.37022 cents, oct.: 1094.59154 cents Scale is not proper Step pattern alph. order: ABCBADE Step pattern size order : ACDCABE Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.557433 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 : 19683/19600, 7.3158 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 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 n-1 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: 81 Scale harmonicity : 0.029395 Average absolute harmonicity : 0.244176 Specific harmonicity : 0.139833 Fundamental : 1/210, -7.7142 octaves, 1.2458 Hz. Guide tone : 648, 9.3399 octaves, 169533.366 Hz. Exponens Consonantiae : 1.360800E+05, 17.05410 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 169.5, average 24.21429 Mersenne's string divisions : 1302440685 Sum of van Prooijen's expressibility: 6.64983, average 0.94998 Sum of Tenney's harmonic distance : 13.89084, average 1.98441 Vogel's harmonic complexity : 15.00000 Wille's k value : 157 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 87.72729, average 3.13312 Lattice compactness (without 2's) : 64.62097, average 2.30789 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.00000 11 1 3: -1 .. 4 1.28571 11 2 5: -1 .. 0 -0.57143 4 1 7: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 18 / 7 = 2.57143 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 19|
FIT/MODE
7: 0 1 2 1 0 1 2 N T3 SD: 47.2423 c. M: 81.2518 c. 9: 0 2 2 1 1 0 3 N SD: 33.1232 c. M:-49.2746 c. 10: 0 2 2 2 0 1 3 N SD: 26.2598 c. M: 48.7704 c. 14: 1 2 3 2 1 1 4 N SD: 24.5804 c. M:-43.4566 c. 16: 1 2 4 2 1 1 5 N SD: 20.8254 c. M: 27.6804 c. 17: 1 3 3 3 1 1 5 N T3 SD: 21.2599 c. M:-33.3725 c. 19: 1 3 4 3 1 1 6 N SD: 7.7170 c. M:-14.3875 c. 24: 1 4 5 4 1 1 8 N SD: 5.4008 c. M: 13.6863 c. 32: 1 6 6 6 1 2 10 N SD: 9.0583 c. M:-11.3137 c. 34: 1 6 7 6 1 2 11 N SD: 6.9584 c. M: 13.4763 c. 41: 2 7 8 7 2 2 13 N SD: 7.0719 c. M:-10.7343 c. 43: 2 7 9 7 2 2 14 N SD: 4.0605 c. M:-7.0436 c. 53: 2 9 11 9 2 3 17 N SD: 2.3883 c. M: 3.6238 c. 72: 3 12 15 12 3 4 23 N SD: 1.9179 c. M:-2.9804 c. 75: 3 13 15 13 3 4 24 N SD: 1.9623 c. M:-3.3196 c. 77: 3 13 16 13 3 4 25 N SD: 2.2050 c. M: 3.3297 c. 94: 4 16 19 16 4 5 30 N SD: 2.0524 c. M:-3.3350 c. 96: 4 16 20 16 4 5 31 N SD: 1.6157 c. M: 2.6804 c. 99: 4 17 20 17 4 5 32 N SD: 1.1305 c. M:-1.8651 c. 118: 5 20 24 20 5 6 38 N SD: 1.2066 c. M:-2.0771 c. 147: 6 25 30 25 6 8 47 N SD: 1.0185 c. M:-2.6402 c. 152: 6 26 31 26 6 8 49 N SD: 0.7259 c. M: 1.4020 c. 171: 7 29 35 29 7 9 55 N SD: 0.2242 c. M:-0.3524 c. 441: 18 75 90 75 18 23 142 N SD: 0.2060 c. M:-0.3808 c. 494: 20 84 101 84 20 26 159 N SD: 0.0980 c. M: 0.1874 c. 665: 27 113 136 113 27 35 214 N SD: 0.0645 c. M:-0.1483 c. 1031: 42 175 211 175 42 54 332 N SD: 0.0940 c. M:-0.1142 c. 1106: 45 188 226 188 45 58 356 N SD: 0.0669 c. M:-0.1225 c. 1277: 52 217 261 217 52 67 411 N SD: 0.0731 c. M:-0.0996 c. 1354: 55 230 277 230 55 71 436 N SD: 0.0601 c. M: 0.0969 c. 1429: 58 243 292 243 58 75 460 N SD: 0.0577 c. M:-0.0838 c. 1525: 62 259 312 259 62 80 491 N SD: 0.0502 c. M: 0.0902 c. 1600: 65 272 327 272 65 84 515 N SD: 0.0447 c. M:-0.0696 c. 1771: 72 301 362 301 72 93 570 N SD: 0.0451 c. M:-0.0912 c. 1795: 73 305 367 305 73 94 578 N SD: 0.0394 c. M: 0.0930 c. 1966: 80 334 402 334 80 103 633 N SD: 0.0362 c. M:-0.0597 c. 2019: 82 343 413 343 82 106 650 N SD: 0.0416 c. M: 0.0801 c. 2118: 86 360 433 360 86 111 682 N SD: 0.0412 c. M: 0.0886 c. 2190: 89 372 448 372 89 115 705 N SD: 0.0389 c. M: 0.0776 c. 2289: 93 389 468 389 93 120 737 N SD: 0.0229 c. M: 0.0559 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 6:7 x x 8:10 S SD: 26.3377 cents 6 x 7:8:9 x 10:12 S SD: 14.4166 cents 7 x 8:9 x x 11:14 SD: 18.3706 cents 8 x 9:11:12 x 13:16 SD: 15.4104 cents 9 x 10:12 x 14 x 18 SD: 17.9238 cents 10 x 12:13:15 x 16:20 SD: 15.3431 cents 11:12:13:15 x 17:18:22 SD: 20.2395 cents 12:13:14:16:18 x 19:24 SD: 15.4510 cents 13:14:15:17 x 20:21:26 SD: 14.6989 cents 14:15:16:19:21 x 22:28 SD: 14.3073 cents 15:16:17:20 x 23:24:30 SD: 12.2185 cents 16:17:19:21:24:25:26:32 SD: 12.0460 cents 17:18:20:23 x 26:27:34 SD: 11.0208 cents 18:19:21:24:27:28:29:36 SD: 7.2228 cents 19:20:22:25 x 29:30:38 SD: 9.1341 cents 20:21:23:27:30:31:32:40 SD: 6.2526 cents 21:22:24:28 x 32:34:42 SD: 8.0862 cents 22:23:25:29:33:34:35:44 SD: 6.8151 cents 23:24:27:31 x 35:37:46 SD: 7.9034 cents 24:25:28:32:36:37:38:48 SD: 4.5434 cents 26:27:30:35:39:40:42:52 SD: 4.2190 cents 30:31:35:40:45:46:48:60 SD: 2.7856 cents 38:39:44:51:57:59:61:76 SD: 2.4597 cents 57:59:66:76:86:88:91:114 SD: 2.2058 cents 62:64:72:83:93:96:99:124 SD: 1.8944 cents 63:65:73:84:95:97:101:126 SD: 1.7026 cents 64:66:74:85:96:99:102:128 SD: 1.6547 cents 66:68:76:88:99:102:106:132 SD: 1.6353 cents 68:70:79:91:102:105:109:136 SD: 1.4435 cents 70:72:81:93:105:108:112:140 SD: 0.8849 cents 102:105:118:136:153:157:163:204 SD: 0.6913 cents 108:111:125:144:162:167:173:216 SD: 0.6517 cents 138:142:160:184:207:213:221:276 SD: 0.5536 cents 140:144:162:187:210:216:224:280 SD: 0.4412 cents 204:210:236:272:306:315:326:408 SD: 0.4209 cents 210:216:243:280:315:324:336:420 SD: 0.0000 cents