Scala analysis: xen09-wilson-marwa-07-03
Marwa permutation 3 from Figure 7, Archytas 28/27 8/7 9/8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 7/6 266.870906 septimal minor third 3: 21/16 470.780907 narrow fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 9/8 203.9100 major whole tone 2: 28/27 62.9609 Archytas' 1/3-tone 3: 9/8 203.9100 major whole tone 4: 8/7 231.1741 septimal whole tone 5: 9/8 203.9100 major whole tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 8/7 231.1741 septimal 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 : 203.9 266.9 470.8 702.0 905.9 968.8 1200.0 203.9 : 63.0 266.9 498.0 702.0 764.9 996.1 1200.0 266.9 : 203.9 435.1 639.0 702.0 933.1 1137.0 1200.0 470.8 : 231.2 435.1 498.0 729.2 933.1 996.1 1200.0 702.0 : 203.9 266.9 498.0 702.0 764.9 968.8 1200.0 905.9 : 63.0 294.1 498.0 561.0 764.9 996.1 1200.0 968.8 : 231.2 435.1 498.0 702.0 933.1 1137.0 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 : 169.28639 cents, oct.: 1185.00475 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABACABC Step pattern size order : MSMLMSL 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 Hypolydian octave species of abstract tetrachord All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 2 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 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.038532 Average absolute harmonicity : 0.241159 Specific harmonicity : 0.194952 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 378, 8.5622 octaves, 98894.464 Hz. Exponens Consonantiae : 1.814400E+04, 14.14720 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 64.5, average 9.21429 Mersenne's string divisions : 58015815 Sum of van Prooijen's expressibility: 5.87514, average 0.83931 Sum of Tenney's harmonic distance : 11.16874, average 1.59553 Vogel's harmonic complexity : 10.57143 Wille's k value : 40 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 83.21960, average 2.97213 Lattice compactness (without 2's) : 48.64115, average 1.73718 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -2.00000 16 1 3: -1 .. 3 0.85714 8 3 7: 0 .. 1 0.42857 3 3 Average exponent except 2's : 9 / 7 = 1.28571 Average absolute exponent except 2's: 11 / 7 = 1.57143 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: 1 1 1 1 1 1 1 SP B ME I SD: 46.1809 c. M:-75.9862 c. Lebeng 8: 1 1 1 2 1 0 2 N D3 SD: 40.5593 c. M: 68.8259 c. 10: 2 0 2 2 2 0 2 N M DE I SD: 27.8866 c. M:-54.1350 c. 11: 2 0 2 2 2 1 2 N T3 SD: 32.2345 c. M: 48.6891 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 20.6212 c. M:-33.1291 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 16: 3 1 2 3 3 1 3 P SD: 19.9043 c. M:-33.1291 c. 17: 3 1 3 3 3 1 3 N M DE I SD: 14.0253 c. M:-23.3367 c. Supra-7 22: 4 1 4 4 4 1 4 N M DE I SD: 13.7380 c. M:-21.4077 c. Supra-7 24: 4 1 4 5 4 1 5 N T3 SD: 12.6739 c. M: 20.7809 c. 25: 4 2 4 5 4 1 5 N SD: 12.6176 c. M:-21.1291 c. 26: 4 2 4 5 5 1 5 N SD: 11.6388 c. M: 19.2946 c. 28: 5 1 5 5 5 2 5 N T3 SD: 10.5971 c. M:-16.8884 c. 31: 5 2 5 6 5 2 6 N T3 SD: 7.8647 c. M: 15.5424 c. 33: 6 1 6 6 6 2 6 N T3 SD: 9.7146 c. M:-14.2718 c. 36: 6 2 6 7 6 2 7 N T3 SD: 3.2763 c. M: 5.8650 c. 41: 7 2 7 8 7 2 8 N T3 SD: 2.0788 c. M: 3.4563 c. 77: 13 4 13 15 13 4 15 N T3 SD: 1.9658 c. M: 3.2484 c. 89: 15 5 15 17 15 5 17 N T3 SD: 1.7965 c. M:-2.7920 c. 94: 16 5 16 18 16 5 18 N T3 SD: 0.9447 c. M:-1.5595 c. 130: 22 7 22 25 22 7 25 N T3 SD: 0.6833 c. M: 1.2496 c. 135: 23 7 23 26 23 7 26 N T3 SD: 0.4061 c. M:-0.8017 c. 171: 29 9 29 33 29 9 33 N T3 SD: 0.4028 c. M: 0.6055 c. 265: 45 14 45 51 45 14 51 N T3 SD: 0.1829 c. M:-0.2989 c. 306: 52 16 52 59 52 16 59 N T3 SD: 0.1302 c. M: 0.2042 c. 400: 68 21 68 77 68 21 77 N T3 SD: 0.1327 c. M:-0.2191 c. 571: 97 30 97 110 97 30 110 N T3 SD: 0.0432 c. M: 0.0857 c. 706: 120 37 120 136 120 37 136 N T3 SD: 0.0431 c. M:-0.0840 c. 877: 149 46 149 169 149 46 169 N T3 SD: 0.0515 c. M: 0.0854 c. 971: 165 51 165 187 165 51 187 N T3 SD: 0.0473 c. M:-0.0739 c. 1012: 172 53 172 195 172 53 195 N T3 SD: 0.0465 c. M: 0.0725 c. 1277: 217 67 217 246 217 67 246 N T3 SD: 0.0063 c. M:-0.0100 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: 11.5751 cents 4 x x 5:6 x 7:8 S SD: 21.1168 cents 5 x 6:7 x 8:9:10 S SD: 32.0861 cents 6 x 7:8:9:10:11:12 S SD: 14.6174 cents 7:8 x 9:11:12 x 14 SD: 19.2324 cents 8:9 x 11:12 x 14:16 SD: 16.1074 cents 10:11:12:13:15:17:18:20 SD: 11.7007 cents 11:12:13:14:17 x 19:22 SD: 16.1230 cents 12 x 14:16:18:20:21:24 S SD: 5.7876 cents 13 x 15:17:20:22:23:26 SD: 8.6758 cents 14:16 x 18:21:24:25:28 SD: 10.5201 cents 16:18:19:21:24:27:28:32 SD: 4.3774 cents 20 x 23:26:30:34:35:40 SD: 5.4217 cents 22:25:26:29:33:37:39:44 SD: 5.3276 cents 23:26:27:30:35:39:40:46 SD: 4.7538 cents 25:28:29:33:38:42:44:50 SD: 4.3748 cents 30:34:35:39:45:51:53:60 SD: 4.2143 cents 31:35:36:41:47:52:54:62 SD: 4.0207 cents 32:36:37:42:48:54:56:64 SD: 2.2181 cents 48:54:56:63:72:81:84:96 S SD: 0.0000 cents