Scala analysis: xen10-wilson-purvi-09b-06
Purvi modulation 6 from Figure 9b, Hawkins (32/27 16/15 135/128), (16/15 135/128 32/27)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 32/27 294.134997 Pythagorean minor third 2: 512/405 405.866283 narrow diminished fourth 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 2048/1215 903.911282 narrow diminished seventh 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: 32/27 294.1350 Pythagorean minor third 2: 16/15 111.7313 minor diatonic semitone 3: 135/128 92.1787 major chroma, major limma 4: 9/8 203.9100 major whole tone 5: 4096/3645 201.9563 narrow diminished third 6: 135/128 92.1787 major chroma, major limma 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 135/128 92.179 cents major chroma, major limma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 4096/3645 201.956 cents narrow diminished third 1: 2 9/8 203.910 cents major whole tone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 1215/1024 296.089 cents wide augmented second 2: 2 512/405 405.866 cents narrow diminished fourth 2: 1 4/3 498.045 cents perfect fourth 3: 1 81/64 407.820 cents Pythagorean major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 64/45 609.776 cents 2nd tritone 4: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 3/2 701.955 cents perfect fifth 5: 2 405/256 794.134 cents wide augmented fifth 5: 2 2048/1215 903.911 cents narrow diminished seventh 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 3645/2048 998.044 cents wide augmented sixth 6: 1 15/8 1088.269 cents classic major seventh 6: 2 256/135 1107.821 cents octave - major chroma 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 : 294.1 405.9 498.0 702.0 903.9 996.1 1200.0 294.1 : 111.7 203.9 407.8 609.8 702.0 905.9 1200.0 405.9 : 92.2 296.1 498.0 590.2 794.1 1088.3 1200.0 498.0 : 203.9 405.9 498.0 702.0 996.1 1107.8 1200.0 702.0 : 202.0 294.1 498.0 792.2 903.9 996.1 1200.0 903.9 : 92.2 296.1 590.2 702.0 794.1 998.0 1200.0 996.1 : 203.9 498.0 609.8 702.0 905.9 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 294.1350 cents 4096/3645, 201.9563 cents 135/128, 92.1787 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 6: 905.8650 .. 1107.8213 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.859741 Largest / Average step : 1.715787 Largest / Smallest step : 3.190921 Median interval of one step : 4096/3645, 201.9563 cents, amount: 1 Least squares average step : 173.59942 cents, oct.: 1215.19595 cents Scale is not proper Step pattern alph. order: ABCDECD Step pattern size order : EBADCAD Scale is not a Constant Structure Scale diversity : 1.330644 Lumma stability : 0.153631 Lumma impropriety factor : 0.317044 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / 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 : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 3645 (O: 3645 U: 3645) Highest odd numerator or denominator: 1215 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.248854 Specific harmonicity : 0.155415 Fundamental : 1/2430, -11.2467 octaves, 0.1077 Hz. Guide tone : 6144, 12.5850 octaves, 1607427.473 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 2139.5, average 305.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.03188, average 1.29027 Sum of Tenney's harmonic distance : 18.96587, average 2.70941 Vogel's harmonic complexity : 18.00000 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 161.66090, average 5.77360 Lattice compactness (without 2's) : 73.96004, average 2.64143 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 11 4.42857 33 1 3: -5 .. 1 -2.00000 16 4 5: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-16 / 7 =-2.28571 Average absolute exponent except 2's: 18 / 7 = 2.57143
FIT/MODE
7: 2 0 1 1 1 1 1 N T3 SD: 38.0110 c. M: 63.0091 c. 8: 2 1 0 2 1 1 1 N D3 SD: 36.8790 c. M:-53.9100 c. 9: 2 1 1 1 2 0 2 N T3 SD: 33.9822 c. M: 62.7567 c. 10: 2 1 1 2 1 1 2 P D3 I SD: 39.7720 c. M: 63.9113 c. 12: 3 1 1 2 2 1 2 N SD: 3.9105 c. M: 5.8663 c. Mela Vagadhisvari, Raga Bhogachayanata, Nandkauns, Ganavaridhi, Chayanata, Bluesy Rock 'n Roll 41: 10 4 3 7 7 3 7 N SD: 2.0786 c. M:-3.8898 c. 53: 13 5 4 9 9 4 9 N SD: 0.9223 c. M:-1.7491 c. 65: 16 6 5 11 11 5 11 N SD: 0.6741 c. M:-1.2496 c. 118: 29 11 9 20 20 9 20 N SD: 0.6789 c. M:-1.1735 c. 183: 45 17 14 31 31 14 31 N SD: 0.6531 c. M:-1.0068 c. 248: 61 23 19 42 42 19 42 N SD: 0.6501 c. M:-1.0263 c. 311: 76 29 24 53 52 24 53 N SD: 0.6401 c. M: 1.0174 c. 323: 79 30 25 55 54 25 55 N SD: 0.6295 c. M: 1.1249 c. 340: 83 32 26 58 57 26 58 N SD: 0.6002 c. M: 1.1938 c. 352: 86 33 27 60 59 27 60 N SD: 0.5072 c. M: 0.9532 c. 364: 89 34 28 62 61 28 62 N SD: 0.4472 c. M: 0.7284 c. 376: 92 35 29 64 63 29 64 N SD: 0.4250 c. M: 0.7198 c. 405: 99 38 31 69 68 31 69 N SD: 0.3996 c. M: 0.8017 c. 417: 102 39 32 71 70 32 71 N SD: 0.3231 c. M: 0.6098 c. 429: 105 40 33 73 72 33 73 N SD: 0.2809 c. M: 0.4287 c. 441: 108 41 34 75 74 34 75 N SD: 0.2804 c. M: 0.5099 c. 470: 115 44 36 80 79 36 80 N SD: 0.2569 c. M: 0.5180 c. 482: 118 45 37 82 81 37 82 N SD: 0.1888 c. M: 0.3591 c. 494: 121 46 38 84 83 38 84 N SD: 0.1616 c. M: 0.2676 c. 535: 131 50 41 91 90 41 91 N SD: 0.1543 c. M: 0.3032 c. 547: 134 51 42 93 92 42 93 N SD: 0.0866 c. M: 0.1679 c. 559: 137 52 43 95 94 43 95 N SD: 0.0815 c. M: 0.1546 c. 600: 147 56 46 102 101 46 102 N SD: 0.0895 c. M: 0.1350 c. 612: 150 57 47 104 103 47 104 N SD: 0.0111 c. M: 0.0174 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: 6.5175 cents 4 x 5 x 6 x 7:8 S SD: 8.3876 cents 5:6 x 7 x 8:9:10 S SD: 25.4561 cents 6:7 x 8:9:10:11:12 S SD: 10.4929 cents 7:8:9 x 11:12 x 14 SD: 22.0523 cents 8:9:10:11:12:13:14:16 S SD: 18.1387 cents 9:11 x 12:14:15:16:18 SD: 14.1268 cents 10:12 x 13:15:17:18:20 SD: 9.2243 cents 12:14:15:16:18:20:21:24 S SD: 6.7782 cents 16:19:20:21:24:27:28:32 SD: 6.2010 cents 18:21:23:24:27:30:32:36 SD: 5.4731 cents 22:26:28:29:33:37:39:44 SD: 3.4718 cents 26:31:33:35:39:44:46:52 SD: 3.3391 cents 38:45:48:51:57:64:68:76 SD: 2.3204 cents 42:50:53:56:63:71:75:84 SD: 1.7720 cents 48:57:61:64:72:81:85:96 SD: 1.7100 cents 54:64:68:72:81:91:96:108 SD: 0.9699 cents 76:90:96:101:114:128:135:152 SD: 0.9109 cents 98:116:124:131:147:165:174:196 SD: 0.8503 cents 102:121:129:136:153:172:181:204 SD: 0.5277 cents 140:166:177:187:210:236:249:280 SD: 0.4687 cents 156:185:197:208:234:263:277:312 SD: 0.4303 cents 162:192:205:216:243:273:288:324 SD: 0.2488 cents 216:256:273:288:324:364:384:432 SD: 0.0854 cents 594:704:751:792:891:1001:1056:1188 SD: 0.0643 cents