Scala analysis: xen09-wilson-marwa-03-14
Marwa permutation 14 from Figure 3, Ptolemy 16/15 9/8 10/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP 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: 10/9 182.4037 minor whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 16/15 111.7313 minor diatonic semitone 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: 2 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 81/64 407.820 cents Pythagorean 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: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 2 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: 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 : 182.4 294.1 498.0 702.0 884.4 996.1 1200.0 182.4 : 111.7 315.6 519.6 702.0 813.7 1017.6 1200.0 294.1 : 203.9 407.8 590.2 702.0 905.9 1088.3 1200.0 498.0 : 203.9 386.3 498.0 702.0 884.4 996.1 1200.0 702.0 : 182.4 294.1 498.0 680.4 792.2 996.1 1200.0 884.4 : 111.7 315.6 498.0 609.8 813.7 1017.6 1200.0 996.1 : 203.9 386.3 498.0 702.0 905.9 1088.3 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 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 590.2237 cents 135/128, 92.1787 cents 256/243, 90.2250 cents 4: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 2048/2025, 19.5526 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 256/243, 90.2250 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 : 170.50687 cents, oct.: 1193.54811 cents Scale is strictly proper Step pattern alph. order: ABCCABC Step pattern size order : MSLLMSL Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.415885 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.503263 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 : 2048/2025, 19.5526 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 Dorian octave species of abstract tetrachord Scale is Hypolydian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 3 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 Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.043353 Average absolute harmonicity : 0.265701 Specific harmonicity : 0.244150 Fundamental : 1/54, -5.7549 octaves, 4.8449 Hz. Guide tone : 480, 8.9069 octaves, 125580.271 Hz. Exponens Consonantiae : 2.592000E+04, 14.66178 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 63.0, average 9.00000 Mersenne's string divisions : 4708200 Sum of van Prooijen's expressibility: 4.99306, average 0.71329 Sum of Tenney's harmonic distance : 10.38357, average 1.48337 Vogel's harmonic complexity : 9.71429 Wille's k value : 40 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 87.64273, average 3.13010 Lattice compactness (without 2's) : 49.17762, average 1.75634 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 5 1.71429 14 1 3: -3 .. 1 -1.14286 10 4 5: 0 .. 1 0.28571 2 2 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 12 / 7 = 1.71429 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: 26.2340 c. M:-48.7221 c. Lebeng 12: 2 1 2 2 2 1 2 P M ME I SD: 9.3473 c. M:-17.5963 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 29: 4 3 5 5 4 3 5 SP SD: 8.9087 c. M: 16.8865 c. 31: 5 3 5 5 5 3 5 SP M DE I SD: 8.9633 c. M:-15.5424 c. Intense Diatonic Phrygian, M.Dorian 33: 5 3 6 5 5 3 6 SP SD: 9.2098 c. M: 14.2718 c. 34: 5 3 6 6 5 3 6 P SD: 6.2173 c. M: 11.7821 c. 41: 6 4 7 7 6 4 7 SP SD: 3.5755 c. M: 6.7940 c. 53: 8 5 9 9 8 5 9 SP SD: 0.7053 c. M: 1.3398 c. 118: 18 11 20 20 18 11 20 SP SD: 0.4756 c. M:-0.7803 c. 171: 26 16 29 29 26 16 29 SP SD: 0.2996 c. M:-0.6018 c. 224: 34 21 38 38 34 21 38 SP SD: 0.3123 c. M:-0.5079 c. 323: 49 30 55 55 49 30 55 SP SD: 0.3437 c. M: 0.6365 c. 335: 51 31 57 57 51 31 57 SP SD: 0.2741 c. M:-0.4174 c. 388: 59 36 66 66 59 36 66 SP SD: 0.1723 c. M: 0.3206 c. 441: 67 41 75 75 67 41 75 SP SD: 0.1302 c. M: 0.2574 c. 494: 75 46 84 84 75 46 84 SP SD: 0.1421 c. M: 0.2175 c. 506: 77 47 86 86 77 47 86 SP SD: 0.1195 c. M:-0.2263 c. 559: 85 52 95 95 85 52 95 SP SD: 0.0426 c. M:-0.0778 c. 612: 93 57 104 104 93 57 104 SP SD: 0.0270 c. M: 0.0508 c. 1171: 178 109 199 199 178 109 199 SP SD: 0.0144 c. M: 0.0274 c. 1783: 271 166 303 303 271 166 303 SP SD: 0.0131 c. M: 0.0239 c. 2395: 364 223 407 407 364 223 407 SP SD: 0.0154 c. M: 0.0238 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: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 24.0316 cents 5 x 6:7 x 8:9:10 S SD: 22.8511 cents 6 x 7:8:9:10:11:12 S SD: 9.9740 cents 7:8 x 9:11:12 x 14 SD: 24.6636 cents 8:9 x 11:12:13:14:16 SD: 12.8723 cents 9:10:11:12:14:15:16:18 S SD: 11.7821 cents 10:11:12:13:15:17:18:20 SD: 9.3942 cents 12:13:14:16:18:20:21:24 S SD: 8.3395 cents 16:18:19:21:24:27:28:32 SD: 7.0322 cents 18:20:21:24:27:30:32:36 S SD: 3.8949 cents 26:29:31:35:39:43:46:52 SD: 3.7103 cents 27:30:32:36:41:45:48:54 SD: 3.0346 cents 36:40:43:48:54:60:64:72 SD: 1.9247 cents 48:53:57:64:72:80:85:96 SD: 1.8906 cents 54:60:64:72:81:90:96:108 S SD: 0.0000 cents