Scala analysis: xen10-wilson-purvi-11b-04
Purvi modulation 4 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: 9/7 435.084095 septimal major third, BP third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 54/35 750.725382 septimal semi-augmented fifth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 5/4 386.3137 major third 3: 28/27 62.9609 Archytas' 1/3-tone 4: 9/8 203.9100 major whole tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 280/243 245.3646 7: 9/8 203.9100 major whole 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: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 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 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: 1 14/9 764.916 cents septimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 2 140/81 947.320 cents 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 : 48.8 435.1 498.0 702.0 750.7 996.1 1200.0 48.8 : 386.3 449.3 653.2 702.0 947.3 1151.2 1200.0 435.1 : 63.0 266.9 315.6 561.0 764.9 813.7 1200.0 498.0 : 203.9 252.7 498.0 702.0 750.7 1137.0 1200.0 702.0 : 48.8 294.1 498.0 546.8 933.1 996.1 1200.0 750.7 : 245.4 449.3 498.0 884.4 947.3 1151.2 1200.0 996.1 : 203.9 252.7 639.0 702.0 905.9 954.6 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: 252.6804 .. 449.2746 cents 2450/2187, 196.5942 cents 162/175,-133.6333 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 .. 947.3196 cents 2450/2187, 196.5942 cents 162/175,-133.6333 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 162/175,-133.6333 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 : 166.79329 cents, oct.: 1167.55302 cents Scale is not proper Step pattern alph. order: ABCDAED Step pattern size order : AEBCADC Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.470169 Lumma stability : 0.081284 Lumma impropriety factor : 0.416298 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 : 0.248392 Specific harmonicity : 0.147436 Fundamental : 1/630, -9.2992 octaves, 0.4153 Hz. Guide tone : 432, 8.7549 octaves, 113022.244 Hz. Exponens Consonantiae : 2.721600E+05, 18.05410 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 108.0, average 15.42857 Mersenne's string divisions : 53079600 Sum of van Prooijen's expressibility: 5.95086, average 0.85012 Sum of Tenney's harmonic distance : 12.49290, average 1.78470 Vogel's harmonic complexity : 18.00000 Wille's k value : 472 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 86.91806, average 3.10422 Lattice compactness (without 2's) : 63.29777, average 2.26063 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.28571 11 1 3: -2 .. 3 0.71429 11 3 5: -1 .. 0 -0.28571 2 7: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 18 21| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 12 16 21| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 0 2 1 1 0 2 1 N T3 SD: 48.8341 c. M: 92.2270 c. 8: 0 3 0 2 0 2 1 N SD: 38.0310 c. M:-53.9100 c. 10: 0 3 1 2 0 2 2 N SD: 39.4859 c. M: 75.0841 c. 11: 0 4 0 2 1 2 2 N G SD: 35.4619 c. M: 61.6814 c. 12: 0 4 1 2 0 3 2 N SD: 29.7740 c. M: 50.7254 c. 14: 1 4 1 2 1 3 2 N SD: 22.0987 c. M:-36.9439 c. 16: 1 5 1 2 1 3 3 N SD: 20.0319 c. M:-26.9550 c. 17: 1 5 1 3 1 3 3 N D3 SD: 13.9637 c. M:-25.7452 c. 19: 1 6 1 3 1 4 3 N SD: 9.4136 c. M:-14.4363 c. 22: 1 7 1 4 1 4 4 N D3 SD: 8.5123 c. M: 14.2718 c. 24: 1 8 1 4 1 5 4 N SD: 5.9456 c. M:-14.9159 c. 34: 1 11 2 6 1 7 6 N SD: 8.4418 c. M: 13.4763 c. 41: 2 13 2 7 2 8 7 N SD: 5.5726 c. M:-10.2502 c. 45: 2 14 3 7 2 9 8 N SD: 7.0266 c. M: 9.4233 c. 46: 2 15 2 8 2 9 8 N SD: 4.6291 c. M:-8.3942 c. 48: 2 15 3 8 2 10 8 N SD: 4.2537 c. M: 10.0841 c. 53: 2 17 3 9 2 11 9 N SD: 2.6403 c. M: 4.8954 c. 72: 3 23 4 12 3 15 12 N SD: 2.0013 c. M:-3.9100 c. 77: 3 25 4 13 3 16 13 N SD: 1.4851 c. M: 2.6734 c. 94: 4 30 5 16 4 19 16 N SD: 1.3419 c. M:-2.4661 c. 99: 4 32 5 17 4 20 17 N SD: 1.1514 c. M: 2.1506 c. 118: 5 38 6 20 5 24 20 N SD: 1.3564 c. M:-2.2040 c. 147: 6 47 8 25 6 30 25 N SD: 0.9323 c. M: 2.4310 c. 152: 6 49 8 26 6 31 26 N SD: 0.9259 c. M: 1.4020 c. 171: 7 55 9 29 7 35 29 N SD: 0.2357 c. M:-0.4012 c. 441: 18 142 23 75 18 90 75 N SD: 0.1924 c. M:-0.2950 c. 494: 20 159 26 84 20 101 84 N SD: 0.1458 c. M: 0.2663 c. 612: 25 197 32 104 25 125 104 N SD: 0.1565 c. M:-0.2550 c. 665: 27 214 35 113 27 136 113 N SD: 0.0788 c. M: 0.1969 c. 836: 34 269 44 142 34 171 142 N SD: 0.0713 c. M: 0.1559 c. 935: 38 301 49 159 38 191 159 N SD: 0.0771 c. M: 0.1542 c. 1007: 41 324 53 171 41 206 171 N SD: 0.0866 c. M:-0.1364 c. 1106: 45 356 58 188 45 226 188 N SD: 0.0504 c. M:-0.0884 c. 1277: 52 411 67 217 52 261 217 N SD: 0.0511 c. M:-0.0969 c. 1354: 55 436 71 230 55 277 230 N SD: 0.0488 c. M:-0.0710 c. 1771: 72 570 93 301 72 362 301 N SD: 0.0379 c. M: 0.0756 c. 1848: 75 595 97 314 75 378 314 N SD: 0.0400 c. M: 0.0760 c. 1942: 79 625 102 330 79 397 330 N SD: 0.0358 c. M: 0.0686 c. 2019: 82 650 106 343 82 413 343 N SD: 0.0336 c. M: 0.0567 c. 2118: 86 682 111 360 86 433 360 N SD: 0.0357 c. M: 0.0560 c. 2289: 93 737 120 389 93 468 389 N SD: 0.0193 c. M:-0.0404 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: 37.2438 cents 4 x 5 x 6 x 7:8 S SD: 13.9684 cents 5 x 6:7 x 8:9:10 S SD: 32.1421 cents 6 x x 8:9 x 11:12 SD: 13.3182 cents 7:8:9 x x 11:12:14 SD: 39.1123 cents 8:9:10:11:12 x 14:16 S SD: 28.8811 cents 9:10 x 12 x 14:16:18 S SD: 26.8769 cents 10:11:13 x 15 x 18:20 SD: 23.9489 cents 11:12:14:15 x 17:20:22 SD: 19.5232 cents 12:13:15:16:18:19:21:24 SD: 16.4107 cents 13:14:17 x x 20:23:26 SD: 17.0643 cents 14:15:18:19:21:22:25:28 SD: 11.9541 cents 15:16:19:20 x 23:27:30 SD: 12.0291 cents 16:17 x 21:24:25:28:32 SD: 11.9293 cents 17:18:22:23 x 26:30:34 SD: 10.1068 cents 18:19:23:24:27:28:32:36 SD: 6.8902 cents 19:20:24:25 x 29:34:38 SD: 9.9223 cents 20:21:26:27:30:31:36:40 SD: 7.3251 cents 21:22:27:28 x 32:37:42 SD: 6.8975 cents 22:23:28:29:33:34:39:44 SD: 5.5835 cents 23:24:30:31 x 35:41:46 SD: 7.7866 cents 24:25:31:32:36:37:43:48 SD: 3.8517 cents 28:29:36:37:42:43:50:56 SD: 3.2218 cents 32:33:41:43:48:49:57:64 SD: 2.9290 cents 36:37:46:48:54:56:64:72 SD: 2.5478 cents 42:43:54:56:63:65:75:84 SD: 1.7640 cents 63:65:81:84:95:97:112:126 SD: 1.5949 cents 66:68:85:88:99:102:117:132 SD: 1.0071 cents 98:101:126:131:147:151:174:196 SD: 0.9188 cents 102:105:131:136:153:157:181:204 SD: 0.8137 cents 108:111:139:144:162:167:192:216 SD: 0.6359 cents 136:140:175:181:204:210:242:272 SD: 0.6173 cents 140:144:180:187:210:216:249:280 SD: 0.4548 cents 144:148:185:192:216:222:256:288 SD: 0.3307 cents 210:216:270:280:315:324:373:420 SD: 0.2209 cents 350:360:450:467:525:540:622:700 SD: 0.1975 cents 354:364:455:472:531:546:629:708 SD: 0.1878 cents 378:389:486:504:567:583:672:756 SD: 0.1529 cents 420:432:540:560:630:648:747:840 SD: 0.1104 cents 486:500:625:648:729:750:864:972 SD: 0.0979 cents