Scala analysis: xen10-wilson-purvi-11a-02
Purvi modulation 2 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: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 14/9 764.915905 septimal minor sixth 6: 8/5 813.686286 minor sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 5/4 386.3137 major third 1: 9/8 203.9100 major whole tone 2: 28/27 62.9609 Archytas' 1/3-tone 3: 8/7 231.1741 septimal whole tone 4: 9/8 203.9100 major whole tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 5/4 386.3137 major third
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: 1 32/27 294.135 cents Pythagorean minor third 2: 2 9/7 435.084 cents septimal major third, BP third 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 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 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 266.9 498.0 702.0 764.9 813.7 1200.0 203.9 : 63.0 294.1 498.0 561.0 609.8 996.1 1200.0 266.9 : 231.2 435.1 498.0 546.8 933.1 1137.0 1200.0 498.0 : 203.9 266.9 315.6 702.0 905.9 968.8 1200.0 702.0 : 63.0 111.7 498.0 702.0 764.9 996.1 1200.0 764.9 : 48.8 435.1 639.0 702.0 933.1 1137.0 1200.0 813.7 : 386.3 590.2 653.2 884.4 1088.3 1151.2 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 : 158.18789 cents, oct.: 1107.31520 cents Scale is not proper Step pattern alph. order: ABCABDE Step pattern size order : CBDCBAE Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.605831 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 : 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 2 Length of longest subharmonic part : 1 at degree 0 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: 9 Scale harmonicity : 0.029983 Average absolute harmonicity : 0.263605 Specific harmonicity : 0.187374 Fundamental : 1/360, -8.4919 octaves, 0.7267 Hz. Guide tone : 504, 8.9773 octaves, 131859.285 Hz. Exponens Consonantiae : 1.814400E+05, 17.46913 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 40.5, average 5.78571 Mersenne's string divisions : 533715 Sum of van Prooijen's expressibility: 4.40680, average 0.62954 Sum of Tenney's harmonic distance : 9.34137, average 1.33448 Vogel's harmonic complexity : 15.14286 Wille's k value : 202 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 84.80960, average 3.02891 Lattice compactness (without 2's) : 48.64454, average 1.73731 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.28571 12 1 3: -2 .. 2 -0.14286 7 3 5: -1 .. 0 -0.14286 1 1 7: 0 .. 1 0.28571 2 2 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 1 1 1 1 0 1 2 N T3 SD: 47.0833 c. M: 79.2016 c. 8: 1 1 1 1 1 0 3 N SD: 54.7532 c. M: 101.9550 c. 9: 2 0 2 1 1 0 3 N SD: 33.4817 c. M:-62.7567 c. 10: 2 0 2 2 0 1 3 N SD: 27.7376 c. M: 44.9159 c. 12: 2 1 2 2 1 0 4 N SD: 19.0438 c. M:-35.0841 c. 17: 3 1 3 3 1 1 5 N SD: 15.0213 c. M:-33.3725 c. 19: 3 1 4 3 1 1 6 N SD: 9.4031 c. M: 14.4363 c. 22: 4 1 4 4 1 1 7 N SD: 7.1880 c. M:-14.2718 c. 31: 5 2 6 5 2 1 10 N SD: 6.1472 c. M: 10.3616 c. 36: 6 2 7 6 2 1 12 N SD: 5.5208 c. M: 13.6863 c. 41: 7 2 8 7 2 2 13 N SD: 2.9957 c. M:-5.8259 c. 53: 9 3 10 9 3 2 17 N SD: 2.6532 c. M:-4.8954 c. 72: 12 4 14 12 4 3 23 N SD: 2.2336 c. M: 3.9100 c. 77: 13 4 15 13 4 3 25 N SD: 1.6404 c. M: 3.2967 c. 94: 16 5 18 16 5 4 30 N SD: 1.4071 c. M:-3.3350 c. 99: 17 5 19 17 5 4 32 N SD: 1.2573 c. M:-2.1506 c. 118: 20 6 23 20 6 5 38 N SD: 1.2734 c. M: 2.4641 c. 130: 22 7 25 22 7 5 42 N SD: 0.8576 c. M: 1.3786 c. 152: 26 8 29 26 8 6 49 N SD: 0.9405 c. M:-1.5501 c. 171: 29 9 33 29 9 7 55 N SD: 0.2405 c. M: 0.4012 c. 441: 75 23 85 75 23 18 142 N SD: 0.1588 c. M: 0.2901 c. 494: 84 26 95 84 26 20 159 N SD: 0.1767 c. M:-0.3356 c. 571: 97 30 110 97 30 23 184 N SD: 0.1467 c. M: 0.3763 c. 612: 104 32 118 104 32 25 197 N SD: 0.1118 c. M: 0.2100 c. 665: 113 35 128 113 35 27 214 N SD: 0.1192 c. M:-0.1969 c. 742: 126 39 143 126 39 30 239 N SD: 0.1029 c. M: 0.2092 c. 836: 142 44 161 142 44 34 269 N SD: 0.1092 c. M:-0.1893 c. 913: 155 48 176 155 48 37 294 N SD: 0.0982 c. M: 0.1860 c. 935: 159 49 180 159 49 38 301 N SD: 0.0777 c. M:-0.1542 c. 1106: 188 58 213 188 58 45 356 N SD: 0.0407 c. M:-0.0683 c. 1277: 217 67 246 217 67 52 411 N SD: 0.0364 c. M:-0.0960 c. 1848: 314 97 356 314 97 75 595 N SD: 0.0217 c. M: 0.0499 c. 2019: 343 106 389 343 106 82 650 N SD: 0.0235 c. M: 0.0467 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: 24.3840 cents 6 x 7:8:9 x 10:12 S SD: 14.1345 cents 7:8 x 9 x 11 x 14 SD: 17.7065 cents 8:9 x 11:12 x 13:16 SD: 11.9306 cents 9:10:11:12 x 14 x 18 SD: 16.6718 cents 10:11:12:13:15 x 16:20 SD: 12.7076 cents 11:12:13:15 x 17:18:22 SD: 13.4284 cents 12 x 14:16:18 x 19:24 SD: 3.6257 cents 13 x 15:17 x 20:21:26 SD: 9.2444 cents 14:16 x 19:21:22 x 28 SD: 8.9246 cents 15:17:18:20 x 23:24:30 SD: 9.3724 cents 16:18:19:21:24:25:26:32 SD: 7.0886 cents 17:19:20:23 x 26:27:34 SD: 7.4570 cents 18:20:21:24:27:28:29:36 SD: 3.5169 cents 19:21:22:25:29 x 30:38 SD: 9.2314 cents 20 x 23:27:30:31:32:40 SD: 5.5812 cents 22:25:26:29:33:34:35:44 SD: 5.3790 cents 23:26:27:31:35:36:37:46 SD: 5.2650 cents 24:27:28:32:36:37:38:48 SD: 3.4098 cents 30:34:35:40:45:47:48:60 SD: 2.5358 cents 40:45:47:53:60:62:64:80 SD: 2.5072 cents 42:47:49:56:63:65:67:84 SD: 1.9660 cents 48:54:56:64:72:75:77:96 SD: 1.2757 cents 72:81:84:96:108:112:115:144 SD: 0.4297 cents 162:182:189:216:243:252:259:324 SD: 0.3895 cents 168:189:196:224:252:261:269:336 SD: 0.3653 cents 192:216:224:256:288:299:307:384 SD: 0.3194 cents 198:223:231:264:297:308:317:396 SD: 0.3183 cents 216:243:252:288:324:336:346:432 SD: 0.2861 cents 240:270:280:320:360:373:384:480 SD: 0.2209 cents 270:304:315:360:405:420:432:540 SD: 0.2035 cents 288:324:336:384:432:448:461:576 SD: 0.1073 cents 360:405:420:480:540:560:576:720 S SD: 0.0000 cents