Scala analysis: xen09-wilson-marwa-04-12
Marwa permutation 12 from Figure 4, Didymus 16/15 10/9 9/8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 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: 16/15 111.7313 minor diatonic semitone 2: 9/8 203.9100 major whole tone 3: 10/9 182.4037 minor whole tone 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 10/9 182.4037 minor whole tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 6/5 315.641 cents minor third 2: 3 5/4 386.314 cents major third 3: 5 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 40/27 680.449 cents grave fifth 4: 5 3/2 701.955 cents perfect fifth 5: 3 8/5 813.686 cents minor sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 15/8 1088.269 cents classic 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 : 111.7 315.6 498.0 702.0 813.7 996.1 1200.0 111.7 : 203.9 386.3 590.2 702.0 884.4 1088.3 1200.0 315.6 : 182.4 386.3 498.0 680.4 884.4 996.1 1200.0 498.0 : 203.9 315.6 498.0 702.0 813.7 1017.6 1200.0 702.0 : 111.7 294.1 498.0 609.8 813.7 996.1 1200.0 813.7 : 182.4 386.3 498.0 702.0 884.4 1088.3 1200.0 996.1 : 203.9 315.6 519.6 702.0 905.9 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 2: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 256/243, 90.2250 cents 3: 498.0450 .. 590.2237 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 4: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 905.8650 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 256/243, 90.2250 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 : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 167.78529 cents, oct.: 1174.49701 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : SLMLSML Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.374079 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.539106 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 : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 315.641 701.955 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 Hypophrygian octave species of abstract tetrachord Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 92.1787 cents: 5 -- Rational properties -- Prime limit : 5 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 15 Scale harmonicity : 0.051546 Average absolute harmonicity : 0.268058 Specific harmonicity : 0.257372 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 48, 5.5850 octaves, 12558.027 Hz. Exponens Consonantiae : 4.320000E+03, 12.07682 octaves Euler's gradus suavitatis : 16 Sum of Mann's harmonic distance : 47.5, average 6.78571 Mersenne's string divisions : 2327325 Sum of van Prooijen's expressibility: 4.48252, average 0.64036 Sum of Tenney's harmonic distance : 9.77612, average 1.39659 Vogel's harmonic complexity : 11.00000 Wille's k value : 67 Wilson's harmonic complexity : 14 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 78.00667, average 2.78595 Lattice compactness (without 2's) : 41.76998, average 1.49178 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 2.00000 16 1 3: -2 .. 1 -0.28571 6 3 5: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.3285 c. M:-59.6973 c. Lebeng 10: 1 2 1 2 1 1 2 P M ME S SD: 25.8629 c. M:-44.3587 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 9.2003 c. M: 15.6413 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 19: 2 3 3 3 2 3 3 SP M ME S SD: 9.0995 c. M:-14.5845 c. Nineteen-tone Phrygian 22: 2 4 3 4 2 3 4 P T3 SD: 8.1766 c. M: 14.2718 c. 29: 3 5 4 5 3 4 5 SP T3 SD: 9.2386 c. M:-15.3932 c. 31: 3 5 5 5 3 5 5 SP M DE S SD: 5.5622 c. M:-10.3616 c. Intense Diatonic Dorian, M.Phrygian 34: 3 6 5 6 3 5 6 P T3 SD: 4.3829 c. M: 7.8547 c. 41: 4 7 6 7 4 6 7 SP T3 SD: 3.8489 c. M:-6.3099 c. 46: 4 8 7 8 4 7 8 P T3 SD: 4.1494 c. M: 7.3835 c. 53: 5 9 8 9 5 8 9 SP T3 SD: 0.9247 c. M:-1.4763 c. 118: 11 20 18 20 11 18 20 SP T3 SD: 0.2902 c. M:-0.5202 c. 171: 16 29 26 29 16 26 29 SP T3 SD: 0.3133 c. M:-0.5494 c. 289: 27 49 44 49 27 44 49 SP T3 SD: 0.2608 c. M:-0.4498 c. 323: 30 55 49 55 30 49 55 SP T3 SD: 0.2307 c. M: 0.4244 c. 376: 35 64 57 64 35 57 64 SP T3 SD: 0.2071 c. M: 0.3453 c. 388: 36 66 59 66 36 59 66 SP T3 SD: 0.2183 c. M: 0.3911 c. 441: 41 75 67 75 41 67 75 SP T3 SD: 0.1059 c. M: 0.1716 c. 494: 46 84 75 84 46 75 84 SP T3 SD: 0.0903 c. M:-0.1482 c. 559: 52 95 85 95 52 85 95 SP T3 SD: 0.0609 c. M: 0.1034 c. 612: 57 104 93 104 57 93 104 SP T3 SD: 0.0264 c. M:-0.0450 c. 1171: 109 199 178 199 109 178 199 SP T3 SD: 0.0178 c. M: 0.0319 c. 1783: 166 303 271 303 166 271 303 SP T3 SD: 0.0086 c. M: 0.0160 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: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 18.9373 cents 5 x 6:7 x 8:9:10 S SD: 17.4324 cents 6 x 7:8:9:10:11:12 S SD: 16.8417 cents 7 x 8:9 x 11:12:14 SD: 25.3266 cents 8:9:10:11:12:13:14:16 S SD: 19.0559 cents 9:10:11:12 x 14:16:18 S SD: 15.2591 cents 10:11:12:13:15:16:18:20 SD: 10.3230 cents 12:13:14:16:18:19:21:24 SD: 9.2262 cents 14:15:17:19:21:22:25:28 SD: 7.0721 cents 15:16:18:20:23:24:27:30 SD: 6.2440 cents 18:19:22:24:27:29:32:36 SD: 5.4982 cents 24:26:29:32:36:38:43:48 SD: 5.2956 cents 26:28:31:35:39:42:46:52 SD: 4.5557 cents 28:30:34:37:42:45:50:56 SD: 4.1386 cents 30:32:36:40:45:48:53:60 SD: 1.5506 cents 60:64:72:80:90:96:107:120 SD: 0.7717 cents 90:96:108:120:135:144:160:180 S SD: 0.0000 cents