Scala analysis: xen10-wilson-purvi-08a-06
Purvi modulation 6 from Figure 8a, Ptolemy (12/11 22/21 7/6), (7/6 12/11 22/21)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 14/11 417.507964 undecimal diminished fourth or major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 7/4 968.825906 harmonic seventh 6: 21/11 1119.462965 undecimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 7/6 266.8709 septimal minor third 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 22/21 80.5370 undecimal minor semitone 4: 9/8 203.9100 major whole tone 5: 7/6 266.8709 septimal minor third 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 7/6 266.871 cents septimal minor third 2: 2 8/7 231.174 cents septimal whole tone 2: 1 33/28 284.447 cents undecimal minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 21/16 470.781 cents narrow fourth 3: 1 9/7 435.084 cents septimal major third, BP third 3: 4 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 1 32/21 729.219 cents wide fifth 5: 2 11/7 782.492 cents undecimal augmented fifth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 56/33 915.553 cents 5: 2 7/4 968.826 cents harmonic seventh 6: 2 12/7 933.129 cents septimal major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 21/11 1119.463 cents undecimal major seventh 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 : 266.9 417.5 498.0 702.0 968.8 1119.5 1200.0 266.9 : 150.6 231.2 435.1 702.0 852.6 933.1 1200.0 417.5 : 80.5 284.4 551.3 702.0 782.5 1049.4 1200.0 498.0 : 203.9 470.8 621.4 702.0 968.8 1119.5 1200.0 702.0 : 266.9 417.5 498.0 764.9 915.6 996.1 1200.0 968.8 : 150.6 231.2 498.0 648.7 729.2 933.1 1200.0 1119.5: 80.5 347.4 498.0 578.6 782.5 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 266.8709 cents 49/44, 186.3339 cents 22/21, 80.5370 cents 2: 231.1741 .. 470.7809 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 6: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.128568 Largest / Average step : 1.556747 Largest / Smallest step : 3.313642 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Least squares average step : 181.17678 cents, oct.: 1268.23746 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : DBACDBA Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.595742 Lumma stability : 0.134228 Lumma impropriety factor : 0.154686 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 : 99/98, 17.5761 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 n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.026454 Average absolute harmonicity : 0.243733 Specific harmonicity : 0.130411 Fundamental : 1/132, -7.0444 octaves, 1.9820 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 1.108800E+04, 13.43671 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 48.0, average 6.85714 Mersenne's string divisions : 2402400 Sum of van Prooijen's expressibility: 5.00805, average 0.71544 Sum of Tenney's harmonic distance : 9.77990, average 1.39713 Vogel's harmonic complexity : 16.85714 Wille's k value : 115 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 62.61661, average 2.23631 Lattice compactness (without 2's) : 38.57775, average 1.37778 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 8 1 3: -1 .. 1 0.00000 4 2 7: 0 .. 1 0.57143 4 2 11: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 10 22 23| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 20 26| Scale is weakly epimorphic with val: <7 12 18 22| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 0 2 1 1 1 N T3 SD: 92.3993 c. M: 155.1879 c. 8: 2 1 0 2 2 1 0 N SD: 53.2452 c. M:-81.1741 c. 9: 2 1 1 1 2 1 1 P M ME S SD: 31.2691 c. M: 52.7963 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 30.0373 c. M: 57.5080 c. Pseudo Rast 11: 2 2 1 1 3 1 1 N D3 S SD: 34.2379 c. M: 48.6891 c. 12: 3 1 1 2 3 1 1 N SD: 19.8650 c. M:-33.1291 c. Mela Calanata, Raga None, Chromatic Dorian inverse 14: 3 2 1 2 3 2 1 P T3 SD: 14.3713 c. M: 25.9688 c. 17: 4 2 1 3 4 2 1 N SD: 10.5729 c. M:-19.4094 c. 26: 6 3 2 4 6 3 2 N SD: 7.8414 c. M: 11.7707 c. 31: 7 4 2 5 7 4 2 N SD: 4.6326 c. M:-8.2985 c. 41: 9 5 3 7 9 5 3 N SD: 4.3779 c. M: 7.7519 c. 46: 10 6 3 8 10 6 3 N SD: 3.0632 c. M: 6.0013 c. 58: 13 7 4 10 13 7 4 N SD: 2.4040 c. M: 3.7149 c. 63: 14 8 4 11 14 8 4 N SD: 2.5025 c. M:-4.3466 c. 72: 16 9 5 12 16 9 5 N SD: 1.7269 c. M: 2.7963 c. 89: 20 11 6 15 20 11 6 N SD: 1.3822 c. M:-2.7920 c. 104: 23 13 7 18 23 13 7 N SD: 1.4187 c. M: 2.1233 c. 118: 26 15 8 20 26 15 8 N SD: 1.4448 c. M: 2.7242 c. 130: 29 16 9 22 29 16 9 N SD: 1.3172 c. M: 2.5399 c. 135: 30 17 9 23 30 17 9 N SD: 0.2802 c. M:-0.5370 c. 342: 76 43 23 58 76 43 23 N SD: 0.2120 c. M: 0.4049 c. 477: 106 60 32 81 106 60 32 N SD: 0.1398 c. M: 0.2724 c. 566: 126 71 38 96 126 71 38 N SD: 0.1580 c. M:-0.2669 c. 612: 136 77 41 104 136 77 41 N SD: 0.1317 c. M: 0.2042 c. 670: 149 84 45 114 149 84 45 N SD: 0.1161 c. M: 0.1945 c. 701: 156 88 47 119 156 88 47 N SD: 0.1172 c. M:-0.1811 c. 805: 179 101 54 137 179 101 54 N SD: 0.1068 c. M:-0.1568 c. 836: 186 105 56 142 186 105 56 N SD: 0.1095 c. M:-0.1954 c. 877: 195 110 59 149 195 110 59 N SD: 0.1043 c. M: 0.1927 c. 1012: 225 127 68 172 225 127 68 N SD: 0.0671 c. M: 0.1167 c. 1147: 255 144 77 195 255 144 77 N SD: 0.0531 c. M: 0.0880 c. 1371: 305 172 92 233 305 172 92 N SD: 0.0515 c. M:-0.1019 c. 1506: 335 189 101 256 335 189 101 N SD: 0.0536 c. M:-0.0984 c. 1578: 351 198 106 268 351 198 106 N SD: 0.0441 c. M: 0.0713 c. 1713: 381 215 115 291 381 215 115 N SD: 0.0209 c. M:-0.0293 c. 1848: 411 232 124 314 411 232 124 N SD: 0.0130 c. M:-0.0245 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: 28.1557 cents 4 x 5 x 6:7 x 8 S SD: 7.7986 cents 5:6 x 7:8:9 x 10 S SD: 31.2254 cents 6:7 x 8:9 x 11:12 SD: 14.0200 cents 7:8:9 x 11:12:13:14 SD: 17.9697 cents 8:9:10:11:12:14:15:16 S SD: 13.3617 cents 9 x 11:12:14:16:17:18 SD: 16.6338 cents 10:12:13 x 15:18:19:20 SD: 13.0944 cents 11:13:14:15:17:19:21:22 SD: 10.2975 cents 12:14:15:16:18:21:23:24 SD: 4.5627 cents 13:15 x 17:20:23:25:26 SD: 10.4548 cents 14:16:18:19:21:25:27:28 SD: 9.0962 cents 16:19:20:21:24:28:31:32 SD: 8.2181 cents 18:21:23:24:27:32:34:36 SD: 4.8012 cents 24:28:31:32:36:42:46:48 SD: 3.7823 cents 30:35:38:40:45:53:57:60 SD: 2.8780 cents 36:42:46:48:54:63:69:72 SD: 1.3852 cents 48:56:61:64:72:84:92:96 SD: 1.0464 cents 84:98:107:112:126:147:160:168 SD: 0.5995 cents 96:112:122:128:144:168:183:192 SD: 0.5209 cents 120:140:153:160:180:210:229:240 SD: 0.4520 cents 132:154:168:176:198:231:252:264 S SD: 0.0000 cents