Scala analysis: xen10-wilson-purvi-08c-06
Purvi modulation 6 from Figure 8c, Ptolemy (22/21 7/6 12/11), (12/11 7/6 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: 56/33 915.552963 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: 112/99 213.5980 6: 9/8 203.9100 major whole 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: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 112/99 213.598 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 2 33/28 284.447 cents undecimal minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 3 14/11 417.508 cents undecimal diminished fourth or major third 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: 3 11/7 782.492 cents undecimal augmented fifth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 2 56/33 915.553 cents 5: 1 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 1 99/56 986.402 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 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 : 266.9 417.5 498.0 702.0 915.6 1119.5 1200.0 266.9 : 150.6 231.2 435.1 648.7 852.6 933.1 1200.0 417.5 : 80.5 284.4 498.0 702.0 782.5 1049.4 1200.0 498.0 : 203.9 417.5 621.4 702.0 968.8 1119.5 1200.0 702.0 : 213.6 417.5 498.0 764.9 915.6 996.1 1200.0 915.6 : 203.9 284.4 551.3 702.0 782.5 986.4 1200.0 1119.5: 80.5 347.4 498.0 578.6 782.5 996.1 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 .. 417.5080 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 968.8259 cents 49/44, 186.3339 cents 99/98, 17.5761 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 179.27417 cents, oct.: 1254.91922 cents Scale is not proper Step pattern alph. order: ABCDEDC Step pattern size order : EBACDCA Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.570782 Lumma stability : 0.163522 Lumma impropriety factor : 0.095191 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 : 896/891, 9.6880 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 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 n-1 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 : 99 (O: 99 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.026454 Average absolute harmonicity : 0.236290 Specific harmonicity : 0.115046 Fundamental : 1/66, -6.0444 octaves, 3.9640 Hz. Guide tone : 168, 7.3923 octaves, 43953.095 Hz. Exponens Consonantiae : 1.108800E+04, 13.43671 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 87.0, average 12.42857 Mersenne's string divisions : 19437600 Sum of van Prooijen's expressibility: 5.68147, average 0.81164 Sum of Tenney's harmonic distance : 11.59945, average 1.65706 Vogel's harmonic complexity : 14.57143 Wille's k value : 49 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 66.71463, average 2.38267 Lattice compactness (without 2's) : 41.66292, average 1.48796 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 0.71429 9 1 3: -1 .. 1 -0.14286 5 2 7: 0 .. 1 0.57143 4 1 11: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 18 23| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 0 2 1 1 1 N T3 SD: 85.1067 c. M: 155.1879 c. 8: 2 1 0 2 1 1 1 N D3 SD: 41.1216 c. M: 69.4630 c. 9: 2 1 1 1 2 1 1 P M ME S SD: 29.0337 c. M: 52.7963 c. 12: 3 1 1 2 2 2 1 N T3 SD: 17.0395 c. M:-33.1291 c. Mela Sulini, Raga Sailadesakshi, Raga Trishuli, Houzam: Greece 14: 3 2 1 2 3 2 1 P T3 SD: 14.7206 c. M:-27.3042 c. 17: 4 2 1 3 3 3 1 N SD: 7.6547 c. M:-15.4820 c. 26: 6 3 2 4 5 4 2 N SD: 8.3397 c. M: 11.7707 c. 29: 6 4 2 5 5 5 2 N SD: 7.5223 c. M: 18.5950 c. 31: 7 4 2 5 6 5 2 N SD: 6.8738 c. M:-13.4793 c. 41: 9 5 3 7 7 7 3 N SD: 5.2530 c. M: 8.2359 c. 46: 10 6 3 8 8 8 3 N SD: 2.9022 c. M: 6.0013 c. 58: 13 7 4 10 10 10 4 N SD: 2.7956 c. M: 5.2081 c. 63: 14 8 4 11 11 11 4 N SD: 2.3503 c. M:-4.3466 c. 72: 16 9 5 12 13 12 5 N SD: 1.5790 c. M: 2.7963 c. 89: 20 11 6 15 16 15 6 N SD: 1.2661 c. M:-2.7920 c. 118: 26 15 8 20 21 20 8 N SD: 1.0198 c. M: 2.4641 c. 135: 30 17 9 23 24 23 9 N SD: 0.2792 c. M:-0.5370 c. 342: 76 43 23 58 61 58 23 N SD: 0.1718 c. M:-0.2365 c. 477: 106 60 32 81 85 81 32 N SD: 0.1144 c. M: 0.2042 c. 877: 195 110 59 149 156 149 59 N SD: 0.1177 c. M: 0.1927 c. 894: 199 112 60 152 159 152 60 N SD: 0.1089 c. M:-0.2432 c. 1012: 225 127 68 172 180 172 68 N SD: 0.0827 c. M: 0.1379 c. 1147: 255 144 77 195 204 195 77 N SD: 0.0687 c. M: 0.1214 c. 1236: 275 155 83 210 220 210 83 N SD: 0.0508 c. M:-0.1194 c. 1282: 285 161 86 218 228 218 86 N SD: 0.0709 c. M: 0.1083 c. 1354: 301 170 91 230 241 230 91 N SD: 0.0700 c. M: 0.1129 c. 1371: 305 172 92 233 244 233 92 N SD: 0.0349 c. M:-0.0875 c. 1506: 335 189 101 256 268 256 101 N SD: 0.0391 c. M:-0.0614 c. 1713: 381 215 115 291 305 291 115 N SD: 0.0245 c. M:-0.0337 c. 1848: 411 232 124 314 329 314 124 N SD: 0.0175 c. M:-0.0315 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: 10.3981 cents 4 x 5 x 6:7 x 8 S SD: 15.4335 cents 5:6 x 7 x 8 x 10 S SD: 35.2580 cents 6:7 x 8:9:10:11:12 S SD: 12.7879 cents 7:8:9 x 11:12:13:14 SD: 17.2074 cents 8:9:10:11:12:14:15:16 S SD: 15.3771 cents 9 x 11:12:14:15:17:18 SD: 16.8246 cents 10:12:13 x 15:17:19:20 SD: 10.2790 cents 12:14:15:16:18:20:23:24 SD: 6.3779 cents 13:15 x 17:20:22:25:26 SD: 9.9994 cents 14:16:18:19:21:24:27:28 SD: 8.0051 cents 18:21:23:24:27:31:34:36 SD: 4.6074 cents 24:28:31:32:36:41:46:48 SD: 4.1268 cents 30:35:38:40:45:51:57:60 SD: 1.7268 cents 36:42:46:48:54:61:69:72 SD: 1.4333 cents 54:63:69:72:81:92:103:108 SD: 1.4023 cents 66:77:84:88:99:112:126:132 SD: 0.0000 cents