Scala analysis: xen10-wilson-purvi-08a-05
Purvi modulation 5 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: 9/8 203.910002 major whole tone 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: 9/8 203.9100 major whole tone 2: 112/99 213.5980 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: 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 32/27 294.135 cents Pythagorean minor 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 27/16 905.865 cents Pythagorean major 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 417.5 498.0 702.0 968.8 1119.5 1200.0 203.9 : 213.6 294.1 498.0 764.9 915.6 996.1 1200.0 417.5 : 80.5 284.4 551.3 702.0 782.5 986.4 1200.0 498.0 : 203.9 470.8 621.4 702.0 905.9 1119.5 1200.0 702.0 : 266.9 417.5 498.0 702.0 915.6 996.1 1200.0 968.8 : 150.6 231.2 435.1 648.7 729.2 933.1 1200.0 1119.5: 80.5 284.4 498.0 578.6 782.5 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 180.72706 cents, oct.: 1265.08941 cents Scale is not proper Step pattern alph. order: ABCADEC Step pattern size order : CDACEBA Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.506814 Lumma stability : 0.134228 Lumma impropriety factor : 0.154686 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 : 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: 21 Scale harmonicity : 0.024115 Average absolute harmonicity : 0.250637 Specific harmonicity : 0.126532 Fundamental : 1/264, -8.0444 octaves, 0.9910 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 6.652800E+04, 16.02167 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 50.0, average 7.14286 Mersenne's string divisions : 3141600 Sum of van Prooijen's expressibility: 5.11720, average 0.73103 Sum of Tenney's harmonic distance : 10.01399, average 1.43057 Vogel's harmonic complexity : 17.85714 Wille's k value : 148 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 73.47224, average 2.62401 Lattice compactness (without 2's) : 42.28058, average 1.51002 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.28571 10 1 3: -1 .. 2 0.42857 5 3 7: 0 .. 1 0.42857 3 1 11: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 20 22| Scale is weakly epimorphic with val: <7 12 18 24| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 1 2 1 0 N T3 SD: 49.5855 c. M:-80.5370 c. 8: 1 2 0 2 1 1 1 P D3 S SD: 50.9072 c. M: 69.4630 c. 9: 1 2 0 2 2 1 1 N T3 SD: 53.7093 c. M: 98.0450 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 31.3873 c. M: 57.5080 c. Pseudo Rast 11: 2 2 1 1 3 1 1 N D3 S SD: 29.3712 c. M:-47.4095 c. 12: 2 2 1 2 3 1 1 N SD: 15.4924 c. M:-31.1741 c. Mela Naganandini, Raga Nagabharanam, Nupur, Samanta 17: 3 3 1 3 4 2 1 N SD: 9.2929 c. M:-19.4094 c. 26: 4 5 2 4 6 3 2 N SD: 10.0117 c. M: 19.2946 c. 27: 5 4 2 5 6 3 2 N SD: 11.7073 c. M:-18.3122 c. 29: 5 5 2 5 6 4 2 N SD: 6.8095 c. M: 17.1018 c. 31: 5 6 2 5 7 4 2 N SD: 5.8652 c. M: 10.3616 c. 41: 7 7 3 7 9 5 3 N SD: 4.1944 c. M: 7.7519 c. 46: 8 8 3 8 10 6 3 N SD: 2.7404 c. M:-4.7857 c. 58: 10 10 4 10 13 7 4 N SD: 2.5351 c. M: 3.7149 c. 72: 12 13 5 12 16 9 5 N SD: 2.2716 c. M: 3.9100 c. 77: 13 14 5 13 17 10 5 N SD: 1.9582 c. M:-3.2713 c. 89: 15 16 6 15 20 11 6 N SD: 1.0917 c. M:-1.9606 c. 118: 20 21 8 20 26 15 8 N SD: 1.1219 c. M: 2.7242 c. 135: 23 24 9 23 30 17 9 N SD: 0.3367 c. M:-0.5370 c. 342: 58 61 23 58 76 43 23 N SD: 0.2489 c. M: 0.4049 c. 359: 61 64 24 61 80 45 24 N SD: 0.2633 c. M:-0.5334 c. 477: 81 85 32 81 106 60 32 N SD: 0.1275 c. M: 0.2724 c. 612: 104 109 41 104 136 77 41 N SD: 0.1069 c. M: 0.1985 c. 836: 142 149 56 142 186 105 56 N SD: 0.1052 c. M:-0.1954 c. 877: 149 156 59 149 195 110 59 N SD: 0.1032 c. M: 0.1927 c. 1012: 172 180 68 172 225 127 68 N SD: 0.0633 c. M: 0.1167 c. 1147: 195 204 77 195 255 144 77 N SD: 0.0561 c. M:-0.1005 c. 1236: 210 220 83 210 275 155 83 N SD: 0.0469 c. M:-0.1061 c. 1371: 233 244 92 233 305 172 92 N SD: 0.0410 c. M:-0.1019 c. 1506: 256 268 101 256 335 189 101 N SD: 0.0559 c. M:-0.0984 c. 1624: 276 289 109 276 361 204 109 N SD: 0.0435 c. M: 0.1067 c. 1713: 291 305 115 291 381 215 115 N SD: 0.0279 c. M: 0.0571 c. 1848: 314 329 124 314 411 232 124 N SD: 0.0132 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 x 6:7:8:9 x 10 S SD: 35.9855 cents 6:7 x 8:9 x 11:12 SD: 18.8447 cents 7:8:9 x 11:12:13:14 SD: 17.5546 cents 8:9:10:11:12:14:15:16 S SD: 9.8811 cents 10:11:13 x 15:18:19:20 SD: 12.1425 cents 12:14:15:16:18:21:23:24 SD: 10.0855 cents 13:15 x 17:20:23:25:26 SD: 12.3492 cents 14:16:18:19:21:25:27:28 SD: 8.4798 cents 15:17:19:20:23:26:29:30 SD: 7.0437 cents 16:18:20:21:24:28:31:32 SD: 6.9552 cents 18:20:23:24:27:32:34:36 SD: 5.7001 cents 22:25:28:29:33:39:42:44 SD: 4.9348 cents 24:27:31:32:36:42:46:48 SD: 3.7823 cents 30:34:38:40:45:53:57:60 SD: 3.4080 cents 32:36:41:43:48:56:61:64 SD: 2.5621 cents 40:45:51:53:60:70:76:80 SD: 1.9982 cents 48:54:61:64:72:84:92:96 SD: 1.0464 cents 80:90:102:107:120:140:153:160 SD: 0.9924 cents 88:99:112:117:132:154:168:176 SD: 0.7036 cents 96:108:122:128:144:168:183:192 SD: 0.5209 cents 120:135:153:160:180:210:229:240 SD: 0.4520 cents 144:162:183:192:216:252:275:288 SD: 0.3773 cents 168:189:214:224:252:294:321:336 SD: 0.2973 cents 216:243:275:288:324:378:412:432 SD: 0.2330 cents 264:297:336:352:396:462:504:528 SD: 0.0000 cents