Scala analysis: xen10-wilson-purvi-04-07
Purvi modulation 7 from Figure 4, Archytas (8/7 9/8 28/27) all 6 permutations
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 112/81 561.005903 5: 14/9 764.915905 septimal minor sixth 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: 28/27 62.9609 Archytas' 1/3-tone 2: 8/7 231.1741 septimal whole tone 3: 9/8 203.9100 major whole tone 4: 28/27 62.9609 Archytas' 1/3-tone 5: 9/8 203.9100 major whole tone 6: 8/7 231.1741 septimal whole tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 3 9/8 203.910 cents major whole tone 1: 2 8/7 231.174 cents septimal whole tone 2: 3 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 9/7 435.084 cents septimal major third, BP third 3: 1 21/16 470.781 cents narrow fourth 3: 5 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 4: 1 112/81 561.006 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 32/21 729.219 cents wide fifth 5: 3 14/9 764.916 cents septimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 3 12/7 933.129 cents septimal major sixth 6: 2 7/4 968.826 cents harmonic seventh 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 63.0 294.1 498.0 561.0 764.9 996.1 1200.0 63.0 : 231.2 435.1 498.0 702.0 933.1 1137.0 1200.0 294.1 : 203.9 266.9 470.8 702.0 905.9 968.8 1200.0 498.0 : 63.0 266.9 498.0 702.0 764.9 996.1 1200.0 561.0 : 203.9 435.1 639.0 702.0 933.1 1137.0 1200.0 764.9 : 231.2 435.1 498.0 729.2 933.1 996.1 1200.0 996.1 : 203.9 266.9 498.0 702.0 764.9 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 231.1741 cents 54/49, 168.2132 cents 28/27, 62.9609 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 3: 470.7809 .. 638.9941 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 4: 561.0059 .. 729.2191 cents 54/49, 168.2132 cents 6272/6561,-77.9882 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 6: 968.8259 .. 1137.0391 cents 54/49, 168.2132 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.722778 Largest / Average step : 1.348516 Largest / Smallest step : 3.671709 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 161.36078 cents, oct.: 1129.52545 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCACBC Step pattern size order : SLMSMLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.317229 Lumma stability : 0.223924 Lumma impropriety factor : 0.064990 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 64/63, 27.2641 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 266.871 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Phrygian octave species of abstract tetrachord All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 168.2132 cents: 4 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.038532 Average absolute harmonicity : 0.221128 Specific harmonicity : 0.186072 Fundamental : 1/81, -6.3399 octaves, 3.2299 Hz. Guide tone : 224, 7.8074 octaves, 58604.127 Hz. Exponens Consonantiae : 1.814400E+04, 14.14720 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 182.5, average 26.07143 Mersenne's string divisions : 1512478275 Sum of van Prooijen's expressibility: 7.15682, average 1.02240 Sum of Tenney's harmonic distance : 15.41168, average 2.20167 Vogel's harmonic complexity : 11.28571 Wille's k value : 40 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 85.35259, average 3.04831 Lattice compactness (without 2's) : 54.33417, average 1.94051 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 5 2.71429 19 1 3: -4 .. 0 -2.14286 15 3 7: 0 .. 1 0.42857 3 3 Average exponent except 2's :-12 / 7 =-1.71429 Average absolute exponent except 2's: 18 / 7 = 2.57143 Scale is weakly epimorphic with val: <7 10 22| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 12 18|
FIT/MODE
7: 0 2 1 0 1 2 1 N T3 SD: 47.9768 c. M: 79.2016 c. 8: 0 2 1 1 1 2 1 N D3 SD: 39.5621 c. M: 62.9609 c. 9: 0 2 2 0 2 1 2 N T3 S SD: 41.2292 c. M: 62.9609 c. 10: 0 2 2 0 2 2 2 N M DE S SD: 49.4284 c. M: 81.0059 c. 11: 1 2 2 0 2 2 2 N T3 SD: 29.0834 c. M:-47.4095 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 24.4273 c. M:-38.9941 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 13: 1 2 2 1 2 3 2 N G T3 S SD: 22.7206 c. M: 36.5065 c. 15: 1 3 2 1 3 2 3 N T3 SD: 23.3585 c. M: 36.0900 c. 16: 1 3 3 0 3 3 3 N T3 SD: 20.2471 c. M: 36.0059 c. 17: 1 3 3 1 3 3 3 N M DE S SD: 7.7581 c. M: 11.7821 c. Safi al-Din's maqam Abu Salik 36: 2 7 6 2 6 7 6 N T3 SD: 3.8238 c. M:-5.8650 c. 41: 2 8 7 2 7 8 7 N T3 SD: 2.9874 c. M: 4.9083 c. 58: 3 11 10 3 10 11 10 N T3 SD: 2.3319 c. M: 4.4798 c. 77: 4 15 13 4 13 15 13 N T3 SD: 1.0728 c. M:-1.9689 c. 94: 5 18 16 5 16 18 16 N T3 SD: 0.6259 c. M:-1.0415 c. 135: 7 26 23 7 23 26 23 N T3 SD: 0.6301 c. M: 1.0059 c. 171: 9 33 29 9 29 33 29 N T3 SD: 0.3296 c. M:-0.6018 c. 265: 14 51 45 14 45 51 45 N T3 SD: 0.3031 c. M:-0.5035 c. 306: 16 59 52 16 52 59 52 N T3 SD: 0.1415 c. M: 0.2216 c. 400: 21 77 68 21 68 77 68 N T3 SD: 0.0727 c. M: 0.1350 c. 571: 30 110 97 30 97 110 97 N T3 SD: 0.0711 c. M:-0.1149 c. 706: 37 136 120 37 120 136 120 N T3 SD: 0.0631 c. M: 0.0994 c. 877: 46 169 149 46 149 169 149 N T3 SD: 0.0280 c. M:-0.0497 c. 1277: 67 246 217 67 217 246 217 N T3 SD: 0.0041 c. M: 0.0081 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 31.4805 cents 3 x x 4 x x 5:6 S SD: 37.2438 cents 4 x 5 x x 6:7:8 S SD: 28.7275 cents 5 x 6 x 7:8:9:10 S SD: 12.2737 cents 6 x 7:8 x 9:11:12 SD: 17.3729 cents 7 x 8:9:10:11:12:14 S SD: 20.6770 cents 8 x 9 x 11:12:14:16 SD: 22.7524 cents 9 x 11:12 x 14:16:18 SD: 10.6546 cents 11:12:13 x 15:17:20:22 SD: 16.6090 cents 12:13:14:16:17:19:21:24 SD: 14.2186 cents 13:14:15:17:18:20:23:26 SD: 12.7717 cents 14:15:17:19 x 22:25:28 SD: 13.1878 cents 15:16:18:20:21:23:27:30 SD: 9.4617 cents 16:17:19:21:22:25:28:32 SD: 8.3482 cents 18:19:21:24:25:28:32:36 SD: 5.9620 cents 21:22:25:28:29:33:37:42 SD: 4.3408 cents 26:27:31:35:36:40:46:52 SD: 4.1130 cents 27:28:32:36:37:42:48:54 SD: 2.2181 cents 49:51:58:65:68:76:87:98 SD: 1.9849 cents 54:56:64:72:75:84:96:108 SD: 1.1016 cents 81:84:96:108:112:126:144:162 S SD: 0.0000 cents