Scala analysis: xen10-wilson-purvi-11b-05
Purvi modulation 5 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: 12/7 933.129094 septimal major sixth 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: 8/7 231.1741 septimal whole tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 5/4 386.314 cents major third 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 2 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 1 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: 1 54/35 750.725 cents septimal semi-augmented fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 1 140/81 947.320 cents 6: 1 8/5 813.686 cents minor sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh 6: 1 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 : 48.8 435.1 498.0 702.0 933.1 996.1 1200.0 48.8 : 386.3 449.3 653.2 884.4 947.3 1151.2 1200.0 435.1 : 63.0 266.9 498.0 561.0 764.9 813.7 1200.0 498.0 : 203.9 435.1 498.0 702.0 750.7 1137.0 1200.0 702.0 : 231.2 294.1 498.0 546.8 933.1 996.1 1200.0 933.1 : 63.0 266.9 315.6 702.0 764.9 968.8 1200.0 996.1 : 203.9 252.7 639.0 702.0 905.9 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: 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 : 173.30771 cents, oct.: 1213.15395 cents Scale is not proper Step pattern alph. order: ABCDECD Step pattern size order : AEBCDBC Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.477280 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 : 245/243, 14.1905 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 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 3 = 42.8571% Scale is 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 : 81 (O: 81 U: 81) Highest odd numerator or denominator: 35 Scale harmonicity : 0.030910 Average absolute harmonicity : 0.252384 Specific harmonicity : 0.170023 Fundamental : 1/630, -9.2992 octaves, 0.4153 Hz. Guide tone : 144, 7.1699 octaves, 37674.081 Hz. Exponens Consonantiae : 9.072000E+04, 16.46913 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 73.0, average 10.42857 Mersenne's string divisions : 11331600 Sum of van Prooijen's expressibility: 5.25189, average 0.75027 Sum of Tenney's harmonic distance : 11.14072, average 1.59153 Vogel's harmonic complexity : 18.00000 Wille's k value : 472 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 80.44171, average 2.87292 Lattice compactness (without 2's) : 54.00301, average 1.92868 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.42857 12 1 3: -2 .. 2 0.42857 9 3 5: -1 .. 0 -0.14286 1 7: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 18 18| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 0 3 0 1 1 1 1 N T3 S SD: 47.8210 c. M:-79.2016 c. 8: 0 3 0 2 1 1 1 N SD: 40.0384 c. M:-53.9100 c. 10: 0 4 0 2 2 0 2 N D3 SD: 31.7845 c. M: 48.7704 c. 12: 0 4 1 2 2 1 2 N SD: 25.9943 c. M: 48.7704 c. 14: 1 4 1 2 3 1 2 N SD: 20.9914 c. M:-36.9439 c. 16: 1 5 1 2 3 1 3 N SD: 23.6219 c. M: 33.1291 c. 17: 1 5 1 3 3 1 3 N D3 SD: 11.5991 c. M:-21.8179 c. 19: 1 6 1 3 4 1 3 N SD: 10.4994 c. M:-14.4363 c. 22: 1 7 1 4 4 1 4 N D3 SD: 7.3174 c. M: 14.2718 c. 24: 1 8 1 4 5 1 4 N SD: 8.7142 c. M:-16.8709 c. 31: 1 10 2 5 6 2 5 N SD: 7.2222 c. M:-10.3616 c. 36: 1 12 2 6 7 2 6 N SD: 6.1452 c. M: 15.4370 c. 41: 2 13 2 7 8 2 7 N SD: 4.2132 c. M:-9.7662 c. 45: 2 14 3 7 9 2 8 N SD: 6.8575 c. M: 9.4233 c. 46: 2 15 2 8 9 2 8 N SD: 4.6662 c. M:-8.3942 c. 49: 2 16 2 9 9 3 8 N SD: 5.8456 c. M: 8.2491 c. 50: 2 16 3 8 10 3 8 N SD: 5.7460 c. M:-11.9100 c. 53: 2 17 3 9 10 3 9 N SD: 2.9144 c. M: 4.8954 c. 72: 3 23 4 12 14 4 12 N SD: 1.9839 c. M:-3.9100 c. 77: 3 25 4 13 15 4 13 N SD: 1.3114 c. M: 2.0171 c. 94: 4 30 5 16 18 5 16 N SD: 1.0689 c. M:-2.2934 c. 152: 6 49 8 26 29 8 26 N SD: 1.0609 c. M: 1.5501 c. 171: 7 55 9 29 33 9 29 N SD: 0.2412 c. M:-0.4012 c. 441: 18 142 23 75 85 23 75 N SD: 0.1748 c. M:-0.2901 c. 494: 20 159 26 84 95 26 84 N SD: 0.1880 c. M: 0.3356 c. 571: 23 184 30 97 110 30 97 N SD: 0.1680 c. M: 0.4341 c. 612: 25 197 32 104 118 32 104 N SD: 0.1455 c. M:-0.2492 c. 665: 27 214 35 113 128 35 113 N SD: 0.1068 c. M: 0.1969 c. 836: 34 269 44 142 161 44 142 N SD: 0.0834 c. M: 0.1559 c. 935: 38 301 49 159 180 49 159 N SD: 0.0777 c. M: 0.1542 c. 1007: 41 324 53 171 194 53 171 N SD: 0.0893 c. M:-0.1364 c. 1012: 41 326 53 172 195 53 172 N SD: 0.0760 c. M: 0.1538 c. 1106: 45 356 58 188 213 58 188 N SD: 0.0402 c. M: 0.0683 c. 1277: 52 411 67 217 246 67 217 N SD: 0.0357 c. M:-0.0941 c. 1848: 75 595 97 314 356 97 314 N SD: 0.0282 c. M: 0.0691 c. 2019: 82 650 106 343 389 106 343 N SD: 0.0260 c. M:-0.0467 c. 2289: 93 737 120 389 441 120 389 N SD: 0.0222 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 5 x 6 S SD: 16.2568 cents 4 x 5 x 6 x 7:8 S SD: 13.9684 cents 5 x 6:7:8 x 9:10 S SD: 37.0663 cents 6 x x 8:9:10:11:12 S SD: 14.4451 cents 7:8:9 x 11:12 x 14 SD: 39.8785 cents 8:9:10:11:12 x 14:16 S SD: 28.8811 cents 9:10 x 12:14:15:16:18 S SD: 25.9275 cents 10:11:13 x 15:17:18:20 SD: 20.1030 cents 11:12:14:15:17:19:20:22 SD: 18.3808 cents 12:13:15:16:18 x 21:24 SD: 17.6276 cents 13:14:17 x 20:22:23:26 SD: 16.3940 cents 14:15:18:19:21:24:25:28 SD: 11.0592 cents 16:17 x 21:24:27:28:32 SD: 12.2324 cents 17:18:22:23:26:29:30:34 SD: 9.7417 cents 18:19:23:24:27:31:32:36 SD: 6.6835 cents 21:22:27:28:32:36:37:42 SD: 6.3784 cents 22:23:28:29:33:38:39:44 SD: 5.8725 cents 24:25:31:32:36:41:43:48 SD: 3.9420 cents 28:29:36:37:42:48:50:56 SD: 3.0105 cents 32:33:41:43:48:55:57:64 SD: 2.3462 cents 36:37:46:48:54:62:64:72 SD: 1.9200 cents 42:43:54:56:63:72:75:84 SD: 1.5908 cents 60:62:77:80:90:103:107:120 SD: 1.4928 cents 66:68:85:88:99:113:117:132 SD: 0.9689 cents 98:101:126:131:147:168:174:196 SD: 0.8585 cents 102:105:131:136:153:175:181:204 SD: 0.6011 cents 108:111:139:144:162:185:192:216 SD: 0.3709 cents 144:148:185:192:216:247:256:288 SD: 0.3056 cents 210:216:270:280:315:360:373:420 SD: 0.2209 cents 252:259:324:336:378:432:448:504 SD: 0.1909 cents 354:364:455:472:531:607:629:708 SD: 0.1806 cents 378:389:486:504:567:648:672:756 SD: 0.1272 cents 420:432:540:560:630:720:747:840 SD: 0.1104 cents 486:500:625:648:729:833:864:972 SD: 0.0905 cents 522:537:671:696:783:895:928:1044 SD: 0.0767 cents