Scala analysis: xen10-wilson-purvi-11c-05
Purvi modulation 5 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: 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: 27/14 1137.039096 septimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-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: 9/8 203.9100 major whole tone 7: 28/27 62.9609 Archytas' 1/3-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 16/15 111.731 cents minor diatonic semitone 2: 2 7/6 266.871 cents septimal minor third 2: 3 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: 3 14/9 764.916 cents septimal minor sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 1 15/8 1088.269 cents classic major seventh 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 48.8 435.1 498.0 702.0 933.1 1137.0 1200.0 48.8 : 386.3 449.3 653.2 884.4 1088.3 1151.2 1200.0 435.1 : 63.0 266.9 498.0 702.0 764.9 813.7 1200.0 498.0 : 203.9 435.1 639.0 702.0 750.7 1137.0 1200.0 702.0 : 231.2 435.1 498.0 546.8 933.1 996.1 1200.0 933.1 : 203.9 266.9 315.6 702.0 764.9 968.8 1200.0 1137.0: 63.0 111.7 498.0 561.0 764.9 996.1 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 : 179.34838 cents, oct.: 1255.43868 cents Scale is not proper Step pattern alph. order: ABCDEDC Step pattern size order : AEBCDCB Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.577632 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 : 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 : 2 at degree 4 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 : 0.032946 Average absolute harmonicity : 0.244486 Specific harmonicity : 0.173111 Fundamental : 1/210, -7.7142 octaves, 1.2458 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 2.268000E+04, 14.46913 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 81.0, average 11.57143 Mersenne's string divisions : 92919120 Sum of van Prooijen's expressibility: 5.72901, average 0.81843 Sum of Tenney's harmonic distance : 11.55984, average 1.65141 Vogel's harmonic complexity : 15.42857 Wille's k value : 202 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 72.85013, average 2.60179 Lattice compactness (without 2's) : 51.57293, average 1.84189 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.71429 9 1 3: -1 .. 3 1.14286 10 2 5: -1 .. 0 -0.14286 1 7: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 15 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 2 0 2 1 1 1 N T3 SD: 86.8254 c. M: 155.1879 c. 8: 0 3 0 2 1 2 0 N SD: 41.8830 c. M:-62.9609 c. 10: 0 4 0 2 2 1 1 N SD: 35.9021 c. M: 57.0391 c. 12: 0 4 1 2 2 2 1 N SD: 29.4873 c. M: 48.7704 c. 14: 1 4 1 2 3 2 1 N SD: 19.0756 c. M:-36.9439 c. 16: 1 5 1 2 3 3 1 N SD: 22.6971 c. M: 33.1291 c. 17: 1 5 1 3 3 3 1 N T3 SD: 11.5774 c. M:-21.8179 c. 19: 1 6 1 3 4 3 1 N SD: 8.9706 c. M:-14.3875 c. 22: 1 7 1 4 4 4 1 N T3 SD: 5.8791 c. M:-8.4154 c. 36: 1 12 2 6 7 6 2 N SD: 6.1271 c. M: 15.4370 c. 41: 2 13 2 7 8 7 2 N SD: 4.5181 c. M:-9.7662 c. 53: 2 17 3 9 10 9 3 N SD: 3.4657 c. M: 4.9636 c. 58: 2 19 3 10 11 10 3 N SD: 3.0386 c. M: 7.3911 c. 72: 3 23 4 12 14 12 4 N SD: 1.9271 c. M: 3.7058 c. 77: 3 25 4 13 15 13 4 N SD: 1.2366 c. M: 2.0171 c. 94: 4 30 5 16 18 16 5 N SD: 1.1106 c. M:-2.2934 c. 99: 4 32 5 17 19 17 5 N SD: 1.1722 c. M:-2.3548 c. 130: 5 42 7 22 25 22 7 N SD: 1.3168 c. M: 2.6165 c. 149: 6 48 8 25 29 25 8 N SD: 0.9926 c. M: 1.4686 c. 152: 6 49 8 26 29 26 8 N SD: 0.9324 c. M: 1.5501 c. 171: 7 55 9 29 33 29 9 N SD: 0.2019 c. M:-0.3524 c. 441: 18 142 23 75 85 75 23 N SD: 0.2157 c. M:-0.3759 c. 494: 20 159 26 84 95 84 26 N SD: 0.1953 c. M: 0.3356 c. 571: 23 184 30 97 110 97 30 N SD: 0.1698 c. M: 0.4341 c. 593: 24 191 31 101 114 101 31 N SD: 0.1953 c. M: 0.2455 c. 612: 25 197 32 104 118 104 32 N SD: 0.1667 c. M:-0.2492 c. 665: 27 214 35 113 128 113 35 N SD: 0.1302 c. M: 0.1970 c. 742: 30 239 39 126 143 126 39 N SD: 0.1123 c. M: 0.2529 c. 764: 31 246 40 130 147 130 40 N SD: 0.1095 c. M: 0.1448 c. 836: 34 269 44 142 161 142 44 N SD: 0.1074 c. M: 0.1970 c. 913: 37 294 48 155 176 155 48 N SD: 0.0908 c. M: 0.1395 c. 935: 38 301 49 159 180 159 49 N SD: 0.0583 c. M: 0.0810 c. 1106: 45 356 58 188 213 188 58 N SD: 0.0330 c. M:-0.0542 c. 1848: 75 595 97 314 356 314 97 N SD: 0.0294 c. M: 0.0691 c. 2019: 82 650 106 343 389 343 106 N SD: 0.0245 c. M: 0.0406 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 6:7 x 8 S SD: 15.1096 cents 5 x 6:7:8:9 x 10 S SD: 40.5067 cents 6 x x 8:9:10 x 12 S SD: 12.1926 cents 7:8:9 x 11:12 x 14 SD: 39.8785 cents 8:9:10:11:12:14:15:16 S SD: 25.9268 cents 9:10 x 12:14:15:17:18 SD: 26.6125 cents 10:11:13 x 15:17:19:20 SD: 20.2442 cents 11:12:14:15:17:19:21:22 SD: 17.6994 cents 12:13:15:16:18:21:23:24 SD: 15.5394 cents 13:14:17 x 20:22:25:26 SD: 16.3557 cents 14:15:18:19:21:24:27:28 SD: 11.0042 cents 16:17 x 21:24:27:31:32 SD: 11.4350 cents 17:18:22:23:26:29:33:34 SD: 9.7039 cents 18:19:23:24:27:31:35:36 SD: 6.9842 cents 21:22:27:28:32:36:41:42 SD: 6.7062 cents 22:23:28:29:33:38:42:44 SD: 6.3479 cents 24:25:31:32:36:41:46:48 SD: 3.7656 cents 28:29:36:37:42:48:54:56 SD: 2.8017 cents 32:33:41:43:48:55:62:64 SD: 2.5645 cents 36:37:46:48:54:62:69:72 SD: 2.4560 cents 38:39:49:51:57:65:73:76 SD: 2.1621 cents 42:43:54:56:63:72:81:84 SD: 1.1477 cents 66:68:85:88:99:113:127:132 SD: 0.8676 cents 98:101:126:131:147:168:189:196 SD: 0.7984 cents 102:105:131:136:153:175:197:204 SD: 0.5321 cents 108:111:139:144:162:185:208:216 SD: 0.5028 cents 140:144:180:187:210:240:270:280 SD: 0.4412 cents 144:148:185:192:216:247:278:288 SD: 0.3975 cents 168:173:216:224:252:288:324:336 SD: 0.2861 cents 210:216:270:280:315:360:405:420 S SD: 0.0000 cents