Scala analysis: xen09-wilson-marwa-07-07
Marwa permutation 7 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: 4/3 498.044999 perfect 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: 8/7 231.1741 septimal whole tone 4: 9/8 203.9100 major 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: 2 7/6 266.871 cents septimal minor third 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 81/64 407.820 cents Pythagorean major third 2: 2 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: 2 14/9 764.916 cents septimal minor sixth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 5: 2 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: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 266.9 498.0 702.0 905.9 968.8 1200.0 203.9 : 63.0 294.1 498.0 702.0 764.9 996.1 1200.0 266.9 : 231.2 435.1 639.0 702.0 933.1 1137.0 1200.0 498.0 : 203.9 407.8 470.8 702.0 905.9 968.8 1200.0 702.0 : 203.9 266.9 498.0 702.0 764.9 996.1 1200.0 905.9 : 63.0 294.1 498.0 561.0 792.2 996.1 1200.0 968.8 : 231.2 435.1 498.0 729.2 933.1 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 : 169.87062 cents, oct.: 1189.09436 cents Scale is not proper Step pattern alph. order: ABCAABC Step pattern size order : MSLMMSL Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.378117 Lumma stability : 0.223924 Lumma impropriety factor : 0.064990 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 : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 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 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 Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 2 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 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 : 0.037102 Average absolute harmonicity : 0.263344 Specific harmonicity : 0.203759 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 756, 9.5622 octaves, 197788.927 Hz. Exponens Consonantiae : 3.628800E+04, 15.14720 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 49.5, average 7.07143 Mersenne's string divisions : 10975965 Sum of van Prooijen's expressibility: 5.03004, average 0.71858 Sum of Tenney's harmonic distance : 9.72159, average 1.38880 Vogel's harmonic complexity : 9.57143 Wille's k value : 40 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 88.51160, average 3.16113 Lattice compactness (without 2's) : 51.57665, average 1.84202 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.14286 14 1 3: -1 .. 3 0.57143 8 4 7: 0 .. 1 0.28571 2 2 Average exponent except 2's : 6 / 7 = 0.85714 Average absolute exponent except 2's: 10 / 7 = 1.42857 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: 43.5887 c. M:-75.9862 c. Lebeng 9: 2 0 2 1 2 0 2 N T3 I SD: 34.7300 c. M:-62.7567 c. 10: 2 0 2 2 2 0 2 N M DE I SD: 28.4963 c. M:-54.1350 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 17.4302 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 17: 3 1 3 3 3 1 3 N M DE I SD: 11.0051 c. M:-19.4094 c. Supra-7 24: 4 1 5 4 4 1 5 N SD: 9.9741 c. M: 18.8259 c. Diatonic + Enharmonic Diesis Phrygian 27: 5 1 5 5 4 2 5 N SD: 11.1571 c. M:-18.3122 c. 29: 5 1 6 5 5 1 6 N SD: 9.7957 c. M: 18.5950 c. 31: 5 2 6 5 5 2 6 N SD: 7.7512 c. M: 15.5424 c. 36: 6 2 7 6 6 2 7 N SD: 2.9769 c. M: 5.8650 c. Diatonic + Soft Chromatic Diesis Phrygian 41: 7 2 8 7 7 2 8 N SD: 1.8630 c. M: 3.4563 c. 77: 13 4 15 13 13 4 15 N SD: 1.5551 c. M: 2.5921 c. 94: 16 5 18 16 16 5 18 N SD: 0.7411 c. M:-1.3869 c. 130: 22 7 25 22 22 7 25 N SD: 0.7011 c. M: 1.2496 c. 135: 23 7 26 23 23 7 26 N SD: 0.3994 c. M:-0.8017 c. 171: 29 9 33 29 29 9 33 N SD: 0.3400 c. M: 0.6018 c. 265: 45 14 51 45 45 14 51 N SD: 0.1742 c. M:-0.2989 c. 306: 52 16 59 52 52 16 59 N SD: 0.1080 c. M: 0.2042 c. 400: 68 21 77 68 68 21 77 N SD: 0.1051 c. M:-0.1741 c. 571: 97 30 110 97 97 30 110 N SD: 0.0432 c. M: 0.0857 c. 706: 120 37 136 120 120 37 136 N SD: 0.0417 c. M:-0.0840 c. 877: 149 46 169 149 149 46 169 N SD: 0.0407 c. M: 0.0688 c. 971: 165 51 187 165 165 51 187 N SD: 0.0382 c. M:-0.0721 c. 1277: 217 67 246 217 217 67 246 N SD: 0.0051 c. M:-0.0081 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: 7.1688 cents 4 x x 5:6 x 7:8 S SD: 27.9328 cents 5 x 6:7 x 8:9:10 S SD: 28.5578 cents 6 x 7:8:9:10:11:12 S SD: 13.8932 cents 7:8 x 9:11:12 x 14 SD: 21.8513 cents 8:9 x 11:12 x 14:16 SD: 10.6546 cents 11:12:13:15:17 x 19:22 SD: 14.9387 cents 12 x 14:16:18:20:21:24 S SD: 3.5844 cents 13 x 15:17:20:22:23:26 SD: 10.2733 cents 14:16 x 19:21:24:25:28 SD: 10.0677 cents 15:17:18:20:23:25:26:30 SD: 9.8215 cents 16:18:19:21:24:27:28:32 SD: 5.8594 cents 18:20:21:24:27:30:32:36 S SD: 5.8351 cents 20 x 23:27:30:34:35:40 SD: 5.8838 cents 23:26:27:31:35:39:40:46 SD: 5.2320 cents 24:27:28:32:36:41:42:48 SD: 3.0346 cents 32:36:37:43:48:54:56:64 SD: 2.9367 cents 42:47:49:56:63:71:74:84 SD: 2.1732 cents 48:54:56:64:72:81:84:96 S SD: 0.0000 cents