Scala analysis: xen10-wilson-purvi-07b-06
Purvi modulation 6 from Figure 7b, Kathleen Schlesinger (15/13 16/15 13/12), (16/15 13/12 15/13)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/13 247.741053 tridecimal 5/4-tone 2: 16/13 359.472338 tridecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 64/39 857.517337 39th subharmonic 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: 15/13 247.7411 tridecimal 5/4-tone 2: 16/15 111.7313 minor diatonic semitone 3: 13/12 138.5727 tridecimal 2/3-tone 4: 9/8 203.9100 major whole tone 5: 128/117 155.5623 6: 13/12 138.5727 tridecimal 2/3-tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 128/117 155.562 cents 1: 2 9/8 203.910 cents major whole tone 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 16/13 359.472 cents tridecimal neutral third 2: 1 135/104 451.651 cents 3: 1 13/10 454.214 cents tridecimal semi-diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 18/13 563.382 cents tridecimal augmented fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 13/9 636.618 cents tridecimal diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 20/13 745.786 cents tridecimal semi-augmented fifth 5: 1 208/135 748.349 cents 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 2 64/39 857.517 cents 39th subharmonic 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 45/26 949.696 cents 6: 1 26/15 952.259 cents tridecimal semi-augmented sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 117/64 1044.438 cents 6: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 1 15/8 1088.269 cents classic 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 : 247.7 359.5 498.0 702.0 857.5 996.1 1200.0 247.7 : 111.7 250.3 454.2 609.8 748.3 952.3 1200.0 359.5 : 138.6 342.5 498.0 636.6 840.5 1088.3 1200.0 498.0 : 203.9 359.5 498.0 702.0 949.7 1061.4 1200.0 702.0 : 155.6 294.1 498.0 745.8 857.5 996.1 1200.0 857.5 : 138.6 342.5 590.2 702.0 840.5 1044.4 1200.0 996.1 : 203.9 451.7 563.4 702.0 905.9 1061.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 247.7411 cents 225/208, 136.0098 cents 16/15, 111.7313 cents 2: 250.3039 .. 451.6511 cents 6075/5408, 201.3471 cents 676/675, 2.5629 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 676/675, 2.5629 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 748.3489 .. 949.6961 cents 6075/5408, 201.3471 cents 676/675, 2.5629 cents 6: 952.2589 .. 1088.2687 cents 225/208, 136.0098 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 1.534293 Largest / Average step : 1.445156 Largest / Smallest step : 2.217294 Median interval of one step : 128/117, 155.5623 cents, amount: 1 Least squares average step : 170.94834 cents, oct.: 1196.63837 cents Scale is strictly proper Step pattern alph. order: ABCDECD Step pattern size order : EABDCBD Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.512925 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.211056 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 : 676/675, 2.5629 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 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 : 13 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 39 Scale harmonicity : 0.022960 Average absolute harmonicity : 0.242409 Specific harmonicity : 0.116411 Fundamental : 1/234, -7.8704 octaves, 1.1181 Hz. Guide tone : 960, 9.9069 octaves, 251160.543 Hz. Exponens Consonantiae : 2.246400E+05, 17.77726 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 100.0, average 14.28571 Mersenne's string divisions : 6272700 Sum of van Prooijen's expressibility: 5.78958, average 0.82708 Sum of Tenney's harmonic distance : 12.32207, average 1.76030 Vogel's harmonic complexity : 16.57143 Wille's k value : 175 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 97.20391, average 3.47157 Lattice compactness (without 2's) : 43.83792, average 1.56564 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 6 2.28571 18 1 3: -2 .. 1 -0.28571 6 3 5: 0 .. 1 0.14286 1 13: -1 .. 0 -0.42857 3 3 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 16 26| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.1282 c. M: 76.3125 c. Lebeng 9: 2 1 1 1 1 1 2 N D3 I SD: 40.9492 c. M: 62.7567 c. 10: 2 1 1 2 1 1 2 P D3 I SD: 18.2083 c. M: 36.0900 c. 14: 3 1 2 2 2 2 2 P T3 SD: 16.6783 c. M:-32.4814 c. 17: 3 2 2 3 2 2 3 SP D3 I SD: 14.8270 c. M: 35.9763 c. Safi al-Din's maqam Rast 19: 4 2 2 3 3 2 3 P SD: 14.2845 c. M:-26.6932 c. 20: 4 2 2 4 2 3 3 P SD: 15.0712 c. M:-23.9100 c. 23: 5 2 3 3 3 3 4 N SD: 16.3356 c. M:-23.6941 c. 24: 5 2 3 4 3 3 4 P SD: 4.9896 c. M: 9.4723 c. 34: 7 3 4 6 4 4 6 P SD: 5.9166 c. M: 10.4585 c. 43: 9 4 5 7 6 5 7 P SD: 5.2154 c. M:-8.5612 c. 49: 10 5 5 9 6 6 8 P SD: 6.2128 c. M: 8.2491 c. 53: 11 5 6 9 7 6 9 P SD: 1.5916 c. M:-2.8600 c. 77: 16 7 9 13 10 9 13 P SD: 0.9545 c. M:-1.6096 c. 130: 27 12 15 22 17 15 22 P SD: 0.7955 c. M:-1.4897 c. 164: 34 15 19 28 21 19 28 P SD: 0.8765 c. M: 1.4198 c. 193: 40 18 22 33 25 22 33 P SD: 0.8399 c. M: 1.2713 c. 200: 41 19 23 34 26 23 34 SP SD: 0.7126 c. M: 1.7411 c. 217: 45 20 25 37 28 25 37 P SD: 0.5474 c. M:-1.1069 c. 224: 46 21 26 38 29 26 38 SP SD: 0.5770 c. M: 1.3125 c. 253: 52 24 29 43 33 29 43 SP SD: 0.6740 c. M: 1.1007 c. 270: 56 25 31 46 35 31 46 P SD: 0.5467 c. M:-1.1478 c. 277: 57 26 32 47 36 32 47 SP SD: 0.3503 c. M: 0.8096 c. 301: 62 28 35 51 39 35 51 SP SD: 0.4511 c. M: 0.6684 c. 330: 68 31 38 56 43 38 56 SP SD: 0.3876 c. M:-0.6645 c. 354: 73 33 41 60 46 41 60 SP SD: 0.2728 c. M:-0.5202 c. 364: 75 34 42 62 47 42 62 SP SD: 0.3273 c. M: 0.4883 c. 407: 84 38 47 69 53 47 69 SP SD: 0.2953 c. M:-0.4702 c. 417: 86 39 48 71 54 48 71 SP SD: 0.2311 c. M: 0.4065 c. 441: 91 41 51 75 57 51 75 SP SD: 0.2009 c. M: 0.3745 c. 494: 102 46 57 84 64 57 84 SP SD: 0.0680 c. M: 0.1386 c. 848: 175 79 98 144 110 98 144 SP SD: 0.0758 c. M:-0.1364 c. 1065: 220 99 123 181 138 123 181 SP SD: 0.0623 c. M:-0.1463 c. 1289: 266 120 149 219 167 149 219 SP SD: 0.0757 c. M: 0.1240 c. 1342: 277 125 155 228 174 155 228 SP SD: 0.0257 c. M: 0.0510 c. 1836: 379 171 212 312 238 212 312 SP SD: 0.0122 c. M: 0.0286 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: 8.9471 cents 4 x 5 x 6 x 7:8 S SD: 9.5649 cents 5 x 6:7 x 8:9:10 S SD: 21.3912 cents 6:7 x 8:9:10:11:12 S SD: 10.4409 cents 7:8 x 9 x 11:12:14 SD: 23.5214 cents 8:9:10:11:12:13:14:16 S SD: 11.5278 cents 10 x 12:13:15:16:18:20 SD: 13.1508 cents 12:14:15:16:18:20:21:24 S SD: 7.2142 cents 14:16:17:19:21:23:25:28 SD: 6.0970 cents 18:21:22:24:27:30:32:36 S SD: 5.0142 cents 22:25:27:29:33:36:39:44 SD: 4.8716 cents 26:30:32:35:39:43:46:52 SD: 3.2751 cents 34:39:42:45:51:56:60:68 SD: 3.2310 cents 38:44:47:51:57:62:68:76 SD: 3.0873 cents 39:45:48:52:59:64:69:78 SD: 2.4189 cents 44:51:54:59:66:72:78:88 SD: 2.1695 cents 48:55:59:64:72:79:85:96 SD: 2.1295 cents 52:60:64:69:78:85:92:104 SD: 1.9438 cents 58:67:71:77:87:95:103:116 SD: 1.8156 cents 60:69:74:80:90:98:107:120 SD: 1.7008 cents 64:74:79:85:96:105:114:128 SD: 1.4007 cents 66:76:81:88:99:108:117:132 SD: 1.3173 cents 72:83:89:96:108:118:128:144 SD: 1.1418 cents 78:90:96:104:117:128:139:156 SD: 0.5938 cents 144:166:177:192:216:236:256:288 SD: 0.5101 cents 156:180:192:208:234:256:277:312 SD: 0.2974 cents 234:270:288:312:351:384:416:468 SD: 0.0000 cents