Scala analysis: xen09-wilson-marwa-07-08
Marwa permutation 8 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: 14/9 764.915905 septimal minor 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: 28/27 62.9609 Archytas' 1/3-tone 6: 9/8 203.9100 major whole 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 : 203.9 266.9 498.0 702.0 764.9 968.8 1200.0 203.9 : 63.0 294.1 498.0 561.0 764.9 996.1 1200.0 266.9 : 231.2 435.1 498.0 702.0 933.1 1137.0 1200.0 498.0 : 203.9 266.9 470.8 702.0 905.9 968.8 1200.0 702.0 : 63.0 266.9 498.0 702.0 764.9 996.1 1200.0 764.9 : 203.9 435.1 639.0 702.0 933.1 1137.0 1200.0 968.8 : 231.2 435.1 498.0 729.2 933.1 996.1 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 : 164.83673 cents, oct.: 1153.85709 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : MSLMSML 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 Lydian octave species of abstract tetrachord 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 : 2 at degree 5 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 Limited inverse transpositions with margin 168.2132 cents: 6 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 9 Scale harmonicity : 0.038532 Average absolute harmonicity : 0.260036 Specific harmonicity : 0.199613 Fundamental : 1/72, -6.1699 octaves, 3.6337 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 1.814400E+04, 14.14720 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 39.5, average 5.64286 Mersenne's string divisions : 5870865 Sum of van Prooijen's expressibility: 4.55292, average 0.65042 Sum of Tenney's harmonic distance : 9.18647, average 1.31235 Vogel's harmonic complexity : 11.14286 Wille's k value : 40 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 78.35455, average 2.79838 Lattice compactness (without 2's) : 47.46300, average 1.69511 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.42857 11 1 3: -2 .. 2 -0.14286 7 3 7: 0 .. 1 0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 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 0 2 1 N T3 SD: 49.5680 c. M: 79.2016 c. 8: 1 1 1 1 1 1 2 P M ME S SD: 55.6346 c. M: 101.9550 c. 9: 2 0 2 1 1 1 2 N T3 SD: 35.6963 c. M:-62.7567 c. 10: 2 0 2 2 0 2 2 N M DE S SD: 26.1072 c. M: 44.9159 c. 12: 2 1 2 2 1 2 2 P M ME S SD: 21.7886 c. M:-35.0841 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 14: 2 1 3 2 1 2 3 P T3 SD: 18.4932 c. M: 32.4814 c. 17: 3 1 3 3 1 3 3 N M DE S SD: 10.9706 c. M:-19.4094 c. Seventeen-tone Natural Minor 22: 4 1 4 4 1 4 4 N M DE S SD: 8.5378 c. M:-14.2718 c. Twenty-two tone Minor, Superpyth-7 31: 5 2 6 5 2 5 6 N T3 SD: 6.1537 c. M: 10.3616 c. "Septimal" Natural Minor 36: 6 2 7 6 2 6 7 N T3 SD: 2.0943 c. M: 3.9100 c. 41: 7 2 8 7 2 7 8 N T3 SD: 2.3211 c. M: 3.9403 c. 58: 10 3 11 10 3 10 11 N T3 SD: 2.1045 c. M:-3.5879 c. 77: 13 4 15 13 4 13 15 N T3 SD: 1.4486 c. M: 2.5921 c. 94: 16 5 18 16 5 16 18 N T3 SD: 0.8160 c. M:-1.3869 c. 130: 22 7 25 22 7 22 25 N T3 SD: 0.6982 c. M:-1.2379 c. 135: 23 7 26 23 7 23 26 N T3 SD: 0.3154 c. M:-0.5344 c. 171: 29 9 33 29 9 29 33 N T3 SD: 0.2527 c. M: 0.4049 c. 265: 45 14 51 45 14 45 51 N T3 SD: 0.2088 c. M:-0.3671 c. 306: 52 16 59 52 16 52 59 N T3 SD: 0.1338 c. M: 0.2100 c. 400: 68 21 77 68 21 68 77 N T3 SD: 0.0972 c. M:-0.1741 c. 571: 97 30 110 97 30 97 110 N T3 SD: 0.0360 c. M:-0.0578 c. 706: 120 37 136 120 37 120 136 N T3 SD: 0.0316 c. M:-0.0560 c. 1277: 217 67 246 217 67 217 246 N T3 SD: 0.0042 c. M:-0.0073 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 x 5:6 S SD: 28.1557 cents 4 x x 5:6 x 7:8 S SD: 27.9328 cents 5 x 6:7 x 8:9:10 S SD: 23.8917 cents 6 x 7:8:9 x 11:12 SD: 16.1074 cents 7:8 x 9 x 11:12:14 SD: 15.8626 cents 8:9 x 11:12 x 14:16 SD: 10.6546 cents 9:10:11:12 x 14:16:18 S SD: 14.6174 cents 11:12:13:15 x 17:19:22 SD: 12.3491 cents 12 x 14:16:18:19:21:24 SD: 5.1070 cents 13 x 15:17 x 20:23:26 SD: 9.4234 cents 14:16 x 19:21:22:25:28 SD: 9.4494 cents 15:17:18:20 x 23:26:30 SD: 9.7707 cents 16:18:19:21:24:25:28:32 SD: 5.9620 cents 17:19:20:23 x 26:30:34 SD: 7.5433 cents 18:20:21:24:27:28:32:36 S SD: 4.9608 cents 20 x 23:27:30:31:35:40 SD: 5.5812 cents 23:26:27:31:35:36:40:46 SD: 5.3196 cents 24:27:28:32:36:37:42:48 SD: 2.2181 cents 48:54:56:64:72:75:84:96 SD: 1.1016 cents 72:81:84:96:108:112:126:144 S SD: 0.0000 cents