Scala analysis: xen10-wilson-purvi-08b-03
Purvi modulation 3 from Figure 8b, Ptolemy (7/6 22/21 12/11), (22/21 12/11 7/6)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 11/7 782.492036 undecimal augmented fifth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 22/21 80.5370 undecimal minor semitone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 7/6 266.8709 septimal minor third 4: 9/8 203.9100 major whole tone 5: 22/21 80.5370 undecimal minor semitone 6: 112/99 213.5980 7: 9/8 203.9100 major whole tone
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 : 80.5 231.2 498.0 702.0 782.5 996.1 1200.0 80.5 : 150.6 417.5 621.4 702.0 915.6 1119.5 1200.0 231.2 : 266.9 470.8 551.3 764.9 968.8 1049.4 1200.0 498.0 : 203.9 284.4 498.0 702.0 782.5 933.1 1200.0 702.0 : 80.5 294.1 498.0 578.6 729.2 996.1 1200.0 782.5 : 213.6 417.5 498.0 648.7 915.6 1119.5 1200.0 996.1 : 203.9 284.4 435.1 702.0 905.9 986.4 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 : 165.24172 cents, oct.: 1156.69202 cents Scale is not proper Step pattern alph. order: ABCDAED Step pattern size order : ABECADC 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 3 and 4 combined -- 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 : 0.247953 Specific harmonicity : 0.126532 Fundamental : 1/126, -6.9773 octaves, 2.0764 Hz. Guide tone : 528, 9.0444 octaves, 138138.298 Hz. Exponens Consonantiae : 6.652800E+04, 16.02167 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 58.0, average 8.28571 Mersenne's string divisions : 135450 Sum of van Prooijen's expressibility: 5.11720, average 0.73103 Sum of Tenney's harmonic distance : 10.61605, average 1.51658 Vogel's harmonic complexity : 14.28571 Wille's k value : 94 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: -1 .. 4 1.42857 12 1 3: -2 .. 1 -0.42857 5 3 7: -1 .. 0 -0.42857 3 1 11: 0 .. 1 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: 0 1 2 1 0 2 1 N T3 SD: 54.7778 c. M: 96.7778 c. 10: 1 1 2 2 1 1 2 P D3 S SD: 31.3873 c. M:-57.5080 c. 11: 1 1 3 1 1 2 2 N D3 S SD: 29.3712 c. M:-47.4095 c. 12: 1 1 3 2 1 2 2 N SD: 15.4924 c. M: 31.1741 c. Mela Ratnangi, Raga Phenadyuti 17: 1 2 4 3 1 3 3 N SD: 9.2929 c. M: 19.4094 c. 26: 2 3 6 4 2 5 4 N SD: 10.0117 c. M:-19.2946 c. 27: 2 3 6 5 2 4 5 N SD: 11.7073 c. M: 18.3122 c. 29: 2 4 6 5 2 5 5 N SD: 6.8095 c. M:-17.1018 c. 31: 2 4 7 5 2 6 5 N SD: 5.8652 c. M:-10.3616 c. 41: 3 5 9 7 3 7 7 N SD: 4.1944 c. M:-7.7519 c. 46: 3 6 10 8 3 8 8 N SD: 2.7404 c. M: 4.7857 c. 58: 4 7 13 10 4 10 10 N SD: 2.5351 c. M:-3.7149 c. 72: 5 9 16 12 5 13 12 N SD: 2.2716 c. M:-3.9100 c. 77: 5 10 17 13 5 14 13 N SD: 1.9582 c. M: 3.2713 c. 89: 6 11 20 15 6 16 15 N SD: 1.0917 c. M: 1.9606 c. 118: 8 15 26 20 8 21 20 N SD: 1.1219 c. M:-2.7242 c. 135: 9 17 30 23 9 24 23 N SD: 0.3367 c. M: 0.5370 c. 342: 23 43 76 58 23 61 58 N SD: 0.2489 c. M:-0.4049 c. 359: 24 45 80 61 24 64 61 N SD: 0.2633 c. M: 0.5334 c. 477: 32 60 106 81 32 85 81 N SD: 0.1275 c. M:-0.2724 c. 612: 41 77 136 104 41 109 104 N SD: 0.1069 c. M:-0.1985 c. 836: 56 105 186 142 56 149 142 N SD: 0.1052 c. M: 0.1954 c. 877: 59 110 195 149 59 156 149 N SD: 0.1032 c. M:-0.1927 c. 1012: 68 127 225 172 68 180 172 N SD: 0.0633 c. M:-0.1167 c. 1147: 77 144 255 195 77 204 195 N SD: 0.0561 c. M: 0.1005 c. 1236: 83 155 275 210 83 220 210 N SD: 0.0469 c. M: 0.1061 c. 1371: 92 172 305 233 92 244 233 N SD: 0.0410 c. M: 0.1019 c. 1506: 101 189 335 256 101 268 256 N SD: 0.0559 c. M: 0.0984 c. 1624: 109 204 361 276 109 289 276 N SD: 0.0435 c. M:-0.1067 c. 1713: 115 215 381 291 115 305 291 N SD: 0.0279 c. M:-0.0571 c. 1848: 124 232 411 314 124 329 314 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: 33.9556 cents 4 x x 5:6 x 7:8 S SD: 28.7524 cents 5 x 6:7 x 8:9:10 S SD: 25.0639 cents 6 x 7:8:9 x 11:12 SD: 12.8254 cents 7 x 8:9 x 11:12:14 SD: 17.8080 cents 8 x 9:11:12:13:14:16 SD: 14.6181 cents 9 x 10:12 x 14:16:18 S SD: 10.3682 cents 10 x 11:13:15:16:18:20 SD: 14.6583 cents 11:12:13:15 x 17:20:22 SD: 18.3652 cents 12:13:14:16:18:19:21:24 SD: 10.6488 cents 13:14:15:17 x 20:23:26 SD: 11.9055 cents 14:15:16:19:21:22:25:28 SD: 7.1601 cents 18:19:21:24:27:28:32:36 SD: 5.9828 cents 20:21:23:27:30:31:36:40 SD: 5.7532 cents 21:22:24:28:32:33:37:42 SD: 4.4822 cents 22:23:25:29:33:35:39:44 SD: 4.4740 cents 26:27:30:35:39:41:46:52 SD: 4.2525 cents 28:29:32:37:42:44:50:56 SD: 3.7581 cents 36:38:41:48:54:57:64:72 SD: 2.7764 cents 40:42:46:53:60:63:71:80 SD: 2.3577 cents 42:44:48:56:63:66:75:84 SD: 1.1016 cents 84:88:96:112:126:132:149:168 SD: 0.5527 cents 126:132:144:168:189:198:224:252 SD: 0.0000 cents