Scala analysis: xen10-wilson-purvi-11c-04
Purvi modulation 4 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: 54/35 750.725382 septimal semi-augmented fifth 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: 36/35 48.7704 septimal diesis, 1/4-tone 6: 5/4 386.3137 major third 7: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 7/6 266.871 cents septimal minor third 2: 2 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: 2 14/9 764.916 cents septimal minor sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 1 140/81 947.320 cents 5: 1 15/8 1088.269 cents classic major seventh 6: 2 8/5 813.686 cents minor sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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 : 48.8 435.1 498.0 702.0 750.7 1137.0 1200.0 48.8 : 386.3 449.3 653.2 702.0 1088.3 1151.2 1200.0 435.1 : 63.0 266.9 315.6 702.0 764.9 813.7 1200.0 498.0 : 203.9 252.7 639.0 702.0 750.7 1137.0 1200.0 702.0 : 48.8 435.1 498.0 546.8 933.1 996.1 1200.0 750.7 : 386.3 449.3 498.0 884.4 947.3 1151.2 1200.0 1137.0: 63.0 111.7 498.0 561.0 764.9 813.7 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 : 28/27, 62.9609 cents, amount: 2 Least squares average step : 172.83396 cents, oct.: 1209.83775 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : ADBCADB Scale is a Constant Structure, by a margin of 48.77038 cents Scale diversity : 1.569058 Lumma stability : 0.081284 Lumma impropriety factor : 0.651213 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 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 Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords 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 : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is 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 : 81 (O: 81 U: 81) Highest odd numerator or denominator: 35 Scale harmonicity : 0.032946 Average absolute harmonicity : 0.240493 Specific harmonicity : 0.154326 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 : 116.0, average 16.57143 Mersenne's string divisions : 435252720 Sum of van Prooijen's expressibility: 6.42798, average 0.91828 Sum of Tenney's harmonic distance : 12.91203, average 1.84458 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 : 75.69865, average 2.70352 Lattice compactness (without 2's) : 57.83382, average 2.06549 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -1 .. 3 1.42857 12 2 5: -1 .. 0 -0.28571 2 7: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 18 / 7 = 2.57143 Scale is weakly epimorphic with val: <7 10 15 21| 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 21|
FIT/MODE
7: 0 2 1 1 0 2 1 N T3 SD: 62.5683 c. M: 108.4677 c. 8: 0 3 0 2 0 3 0 N T3 I SD: 39.9683 c. M:-62.9609 c. 10: 0 3 1 2 0 3 1 N SD: 42.8701 c. M: 75.0841 c. 11: 0 4 0 2 1 3 1 N SD: 39.1465 c. M: 61.6814 c. 12: 0 4 1 2 0 4 1 N SD: 32.8678 c. M: 50.7254 c. 14: 1 4 1 2 1 4 1 N T3 I SD: 20.2877 c. M:-36.9439 c. 16: 1 5 1 2 1 5 1 N T3 I SD: 18.9325 c. M:-26.9550 c. 17: 1 5 1 3 1 5 1 N T3 I SD: 13.9457 c. M:-25.7452 c. 19: 1 6 1 3 1 6 1 N T3 I SD: 7.6713 c. M:-14.3875 c. 22: 1 7 1 4 1 7 1 N T3 I SD: 7.3128 c. M:-12.9110 c. 34: 1 11 2 6 1 11 2 N SD: 8.4120 c. M: 13.4763 c. 39: 2 12 2 7 1 13 2 N SD: 7.5583 c. M:-12.7681 c. 41: 2 13 2 7 2 13 2 N T3 I SD: 5.8066 c. M:-10.2502 c. 45: 2 14 3 7 2 15 2 N SD: 7.0660 c. M:-9.6276 c. 46: 2 15 2 8 2 15 2 N T3 I SD: 5.8974 c. M:-10.7870 c. 50: 2 16 3 8 2 16 3 N SD: 5.4506 c. M: 9.0391 c. 53: 2 17 3 9 2 17 3 N SD: 3.2385 c. M: 4.9636 c. 72: 3 23 4 12 3 23 4 N SD: 1.9450 c. M: 3.7058 c. 75: 3 24 4 13 3 24 4 N SD: 1.7392 c. M: 3.0841 c. 77: 3 25 4 13 3 25 4 N SD: 1.4194 c. M: 2.6734 c. 94: 4 30 5 16 4 30 5 N SD: 1.3753 c. M:-2.4661 c. 96: 4 31 5 16 4 31 5 N SD: 1.4991 c. M:-2.4159 c. 99: 4 32 5 17 4 32 5 N SD: 1.2071 c. M:-2.3548 c. 118: 5 38 6 20 5 38 6 N SD: 1.5301 c. M:-2.2040 c. 147: 6 47 8 25 6 47 8 N SD: 1.2848 c. M: 2.4310 c. 149: 6 48 8 25 6 48 8 N SD: 1.1141 c. M: 1.7321 c. 152: 6 49 8 26 6 49 8 N SD: 0.7754 c. M: 1.4020 c. 171: 7 55 9 29 7 55 9 N SD: 0.1951 c. M:-0.3524 c. 441: 18 142 23 75 18 142 23 N SD: 0.2302 c. M:-0.3759 c. 494: 20 159 26 84 20 159 26 N SD: 0.1551 c. M: 0.2663 c. 590: 24 190 31 100 24 190 31 N SD: 0.1778 c. M:-0.2601 c. 593: 24 191 31 101 24 191 31 N SD: 0.1723 c. M: 0.2372 c. 665: 27 214 35 113 27 214 35 N SD: 0.1084 c. M: 0.1970 c. 764: 31 246 40 130 31 246 40 N SD: 0.0975 c. M:-0.1392 c. 935: 38 301 49 159 38 301 49 N SD: 0.0575 c. M:-0.0771 c. 1106: 45 356 58 188 45 356 58 N SD: 0.0448 c. M:-0.0884 c. 1354: 55 436 71 230 55 436 71 N SD: 0.0433 c. M:-0.0710 c. 1525: 62 491 80 259 62 491 80 N SD: 0.0404 c. M:-0.0634 c. 1771: 72 570 93 301 72 570 93 N SD: 0.0400 c. M: 0.0756 c. 1848: 75 595 97 314 75 595 97 N SD: 0.0409 c. M: 0.0760 c. 2019: 82 650 106 343 82 650 106 N SD: 0.0324 c. M: 0.0567 c. 2190: 89 705 115 372 89 705 115 N SD: 0.0326 c. M: 0.0528 c. 2289: 93 737 120 389 93 737 120 N SD: 0.0261 c. M:-0.0513 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: 44.5444 cents 4 x 5 x 6 x x 8 S SD: 16.2568 cents 5 x 6:7 x 8 x 10 S SD: 39.8163 cents 6 x x 8:9 x x 12 S SD: 0.0000 cents 7:8:9 x x 11 x 14 SD: 46.2873 cents 8:9:10:11:12 x 15:16 S SD: 29.6570 cents 9:10 x 12 x 14:17:18 SD: 27.8243 cents 10:11:13 x 15 x 19:20 SD: 24.1197 cents 11:12:14:15 x 17:21:22 SD: 18.6464 cents 12:13:15:16:18:19:23:24 SD: 16.0152 cents 13:14:17 x x 20:25:26 SD: 17.0112 cents 14:15:18:19:21:22:27:28 SD: 11.9032 cents 15:16:19:20 x 23:29:30 SD: 11.5047 cents 16:17 x 21:24:25:31:32 SD: 11.1102 cents 17:18:22:23 x 26:33:34 SD: 10.0571 cents 18:19:23:24:27:28:35:36 SD: 7.1822 cents 19:20:24:25 x 29:37:38 SD: 10.1344 cents 20:21:26:27:30:31:39:40 SD: 7.1893 cents 21:22:27:28 x 32:41:42 SD: 7.3084 cents 22:23:28:29:33:34:42:44 SD: 6.0815 cents 23:24:30:31 x 35:44:46 SD: 8.0907 cents 24:25:31:32:36:37:46:48 SD: 3.6710 cents 28:29:36:37:42:43:54:56 SD: 3.0276 cents 36:37:46:48:54:56:69:72 SD: 2.9726 cents 38:39:49:51:57:59:73:76 SD: 2.6114 cents 39:40:50:52:59:60:75:78 SD: 2.5342 cents 42:43:54:56:63:65:81:84 SD: 1.3777 cents 66:68:85:88:99:102:127:132 SD: 0.9100 cents 70:72:90:93:105:108:135:140 SD: 0.8849 cents 98:101:126:131:147:151:189:196 SD: 0.8629 cents 102:105:131:136:153:157:197:204 SD: 0.7641 cents 108:111:139:144:162:167:208:216 SD: 0.7208 cents 136:140:175:181:204:210:262:272 SD: 0.6341 cents 138:142:177:184:207:213:266:276 SD: 0.6286 cents 140:144:180:187:210:216:270:280 SD: 0.4412 cents 144:148:185:192:216:222:278:288 SD: 0.4171 cents 168:173:216:224:252:259:324:336 SD: 0.3439 cents 210:216:270:280:315:324:405:420 S SD: 0.0000 cents