Scala analysis: xen10-wilson-purvi-08c-04
Purvi modulation 4 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: 12/11 150.637059 undecimal neutral second, 3/4-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: 18/11 852.592059 undecimal neutral sixth 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: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 7/6 266.8709 septimal minor third 3: 22/21 80.5370 undecimal minor semitone 4: 9/8 203.9100 major whole tone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 7/6 266.8709 septimal minor third 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: 1 8/7 231.174 cents septimal whole tone 2: 1 33/28 284.447 cents undecimal minor third 2: 2 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 2 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: 2 11/7 782.492 cents undecimal augmented fifth 5: 1 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 56/33 915.553 cents 5: 1 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 : 150.6 417.5 498.0 702.0 852.6 1119.5 1200.0 150.6 : 266.9 347.4 551.3 702.0 968.8 1049.4 1200.0 417.5 : 80.5 284.4 435.1 702.0 782.5 933.1 1200.0 498.0 : 203.9 354.5 621.4 702.0 852.6 1119.5 1200.0 702.0 : 150.6 417.5 498.0 648.7 915.6 996.1 1200.0 852.6 : 266.9 347.4 498.0 764.9 845.5 1049.4 1200.0 1119.5: 80.5 231.2 498.0 578.6 782.5 933.1 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 : 12/11, 150.6371 cents, amount: 2 Least squares average step : 176.19533 cents, oct.: 1233.36730 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : BDACBDA Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.579325 Lumma stability : 0.163522 Lumma impropriety factor : 0.095191 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 : 243/242, 7.1391 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 Best minor thirds form a closed circle 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 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.025337 Average absolute harmonicity : 0.233946 Specific harmonicity : 0.121134 Fundamental : 1/66, -6.0444 octaves, 3.9640 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 1.663200E+04, 14.02167 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 62.0, average 8.85714 Mersenne's string divisions : 11205600 Sum of van Prooijen's expressibility: 5.40064, average 0.77152 Sum of Tenney's harmonic distance : 11.12673, average 1.58953 Vogel's harmonic complexity : 13.28571 Wille's k value : 49 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 59.12073, average 2.11145 Lattice compactness (without 2's) : 42.79795, average 1.52850 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.85714 8 1 3: -1 .. 2 0.57143 6 2 7: 0 .. 1 0.28571 2 11: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 18 26| 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 1 1 1 2 0 N T3 SD: 43.1600 c. M:-80.5370 c. 8: 1 2 0 2 1 1 1 P D3 S SD: 42.6705 c. M: 69.4630 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 35.1524 c. M: 52.7963 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 30.7360 c. M: 57.5080 c. 11: 1 3 1 1 2 2 1 N D3 S SD: 33.3760 c. M:-47.4095 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 29.3331 c. M: 52.5921 c. Double Harmonic Major, Major Gipsy, Bhairav That, Mela Mayamalavagaula, Raga Paraj, Kalingada, Gaulipantu, Lalitapancamam, Gandhakriya, Kalingda, Manjiri, Chromatic 2nd Byzantine Liturgical, Hitzazkiar: Greece, Maqam Zengule, Hijaz Kar, Suzidil 14: 2 3 1 2 2 3 1 P T3 SD: 12.7039 c. M:-20.7915 c. 17: 2 4 1 3 2 4 1 N SD: 6.3942 c. M:-9.9488 c. Dastgah-e Chahargah 31: 4 7 2 5 4 7 2 N SD: 4.6426 c. M:-8.2985 c. 41: 5 9 3 7 5 9 3 N SD: 4.5726 c. M: 7.7519 c. 46: 6 10 3 8 6 10 3 N SD: 4.1368 c. M:-8.2775 c. 48: 6 11 3 8 6 11 3 N SD: 3.8090 c. M:-7.4920 c. 55: 7 12 4 9 7 12 4 N SD: 3.5821 c. M: 6.7357 c. 58: 7 13 4 10 7 13 4 N SD: 3.2858 c. M: 5.8095 c. 63: 8 14 4 11 8 14 4 N SD: 2.9465 c. M:-4.5508 c. 72: 9 16 5 12 9 16 5 N SD: 1.8243 c. M: 2.7963 c. 89: 11 20 6 15 11 20 6 N SD: 1.5618 c. M: 3.1539 c. 104: 13 23 7 18 13 23 7 N SD: 1.3987 c. M: 2.1233 c. 118: 15 26 8 20 15 26 8 N SD: 1.0320 c. M:-1.9053 c. 135: 17 30 9 23 17 30 9 N SD: 0.4273 c. M:-0.7413 c. 207: 26 46 14 35 26 46 14 N SD: 0.3955 c. M: 0.6224 c. 311: 39 69 21 53 39 69 21 N SD: 0.3930 c. M: 0.7877 c. 342: 43 76 23 58 43 76 23 N SD: 0.1550 c. M:-0.2401 c. 477: 60 106 32 81 60 106 32 N SD: 0.1565 c. M:-0.3063 c. 670: 84 149 45 114 84 149 45 N SD: 0.1290 c. M: 0.1945 c. 701: 88 156 47 119 88 156 47 N SD: 0.0990 c. M:-0.1811 c. 805: 101 179 54 137 101 179 54 N SD: 0.1047 c. M:-0.1568 c. 836: 105 186 56 142 105 186 56 N SD: 0.1024 c. M:-0.1954 c. 1012: 127 225 68 172 127 225 68 N SD: 0.0610 c. M: 0.1167 c. 1147: 144 255 77 195 144 255 77 N SD: 0.0468 c. M: 0.0712 c. 1371: 172 305 92 233 172 305 92 N SD: 0.0453 c. M: 0.0900 c. 1489: 187 331 100 253 187 331 100 N SD: 0.0439 c. M:-0.0681 c. 1506: 189 335 101 256 189 335 101 N SD: 0.0344 c. M:-0.0589 c. 1713: 215 381 115 291 215 381 115 N SD: 0.0282 c. M: 0.0527 c. 1848: 232 411 124 314 232 411 124 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: 10.5889 cents 4 x 5 x 6:7 x 8 S SD: 30.0867 cents 5 x 6:7 x 8 x 10 S SD: 34.4830 cents 6:7 x 8:9:10:11:12 S SD: 23.2340 cents 7:8:9 x x 11:13:14 SD: 23.6561 cents 8:9:10:11:12:13:15:16 SD: 12.5907 cents 10:11:13 x 15:16:19:20 SD: 9.3329 cents 11:12:14:15:17:18:21:22 SD: 9.2414 cents 12:13:15:16:18:20:23:24 SD: 6.6620 cents 13:14 x 17:20:21:25:26 SD: 10.8128 cents 14:15:18:19:21:23:27:28 SD: 7.2518 cents 18:20:23:24:27:29:34:36 SD: 6.5781 cents 20:22:25:27:30:33:38:40 SD: 6.2543 cents 21:23:27:28:32:34:40:42 SD: 5.4472 cents 22:24:28:29:33:36:42:44 SD: 2.8265 cents 30:33:38:40:45:49:57:60 SD: 2.6851 cents 33:36:42:44:50:54:63:66 SD: 2.4856 cents 36:39:46:48:54:59:69:72 SD: 2.2438 cents 44:48:56:59:66:72:84:88 SD: 1.4012 cents 66:72:84:88:99:108:126:132 S SD: 0.0000 cents