Scala analysis: xen09-wilson-marwa-03-13
Marwa permutation 13 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: 9/8 203.910002 major 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: 9/8 203.9100 major whole tone 2: 256/243 90.2250 limma, Pythagorean minor second 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: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 4 9/8 203.910 cents major whole tone 2: 3 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 2 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: 2 128/81 792.180 cents Pythagorean minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 3 27/16 905.865 cents Pythagorean major sixth 6: 4 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 15/8 1088.269 cents classic major seventh 6: 1 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.66667 = 11/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 294.1 498.0 702.0 884.4 996.1 1200.0 203.9 : 90.2 294.1 498.0 680.4 792.2 996.1 1200.0 294.1 : 203.9 407.8 590.2 702.0 905.9 1109.8 1200.0 498.0 : 203.9 386.3 498.0 702.0 905.9 996.1 1200.0 702.0 : 182.4 294.1 498.0 702.0 792.2 996.1 1200.0 884.4 : 111.7 315.6 519.6 609.8 813.7 1017.6 1200.0 996.1 : 203.9 407.8 498.0 702.0 905.9 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 203.9100 cents 2187/2048, 113.6850 cents 256/243, 90.2250 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 .. 1109.7750 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.900012 Largest / Average step : 1.189475 Largest / Smallest step : 2.260017 Median interval of one step : 9/8, 203.9100 cents, amount: 4 Most common interval of one step : 9/8, 203.9100 cents, amount: 4 Least squares average step : 170.66049 cents, oct.: 1194.62343 cents Scale is strictly proper Step pattern alph. order: ABAACDA Step pattern size order : DADDCBD Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.461397 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.467419 Rothenberg efficiency : 0.496599 redundancy: 0.503401 Efficiency x scale size : 3.476190 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.66667 = 11/3 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: 4 Number of recognisable fifths : 5, average 701.9550 cents 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 9 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 71.4286% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 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 : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.036058 Average absolute harmonicity : 0.271624 Specific harmonicity : 0.231213 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 1440, 10.4919 octaves, 376740.814 Hz. Exponens Consonantiae : 3.110400E+05, 18.24674 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 62.0, average 8.85714 Mersenne's string divisions : 4212600 Sum of van Prooijen's expressibility: 4.99306, average 0.71329 Sum of Tenney's harmonic distance : 10.28666, average 1.46952 Vogel's harmonic complexity : 12.14286 Wille's k value : 121 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 106.66417, average 3.80943 Lattice compactness (without 2's) : 56.87705, average 2.03132 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 1.14286 16 1 3: -3 .. 2 -0.57143 10 5 5: 0 .. 1 0.14286 1 1 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 11 / 7 = 1.57143 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: 28.6660 c. M:-48.7221 c. Lebeng 11: 2 1 2 1 2 1 2 P M ME I SD: 29.6072 c. M:-47.4095 c. Superkleismic-7 12: 2 1 2 2 2 1 2 P M ME I SD: 6.7323 c. M:-15.6413 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: 5 2 5 5 4 3 5 SP SD: 6.3168 c. M: 15.3932 c. 34: 6 2 6 6 5 3 6 P SD: 6.5146 c. M: 11.7821 c. 41: 7 3 7 7 6 4 7 SP SD: 2.5147 c. M: 6.3099 c. 53: 9 4 9 9 8 5 9 SP SD: 0.5187 c. M: 1.3398 c. 118: 20 9 20 20 18 11 20 SP SD: 0.4528 c. M:-0.7803 c. 171: 29 13 29 29 26 16 29 SP SD: 0.3352 c. M:-0.6018 c. 224: 38 17 38 38 34 21 38 SP SD: 0.3228 c. M:-0.5079 c. 335: 57 25 57 57 51 31 57 SP SD: 0.2721 c. M:-0.4174 c. 388: 66 29 66 66 59 36 66 SP SD: 0.1884 c. M: 0.3206 c. 441: 75 33 75 75 67 41 75 SP SD: 0.1414 c. M: 0.2574 c. 494: 84 37 84 84 75 46 84 SP SD: 0.1272 c. M: 0.2079 c. 506: 86 38 86 86 77 47 86 SP SD: 0.0924 c. M:-0.2263 c. 559: 95 42 95 95 85 52 95 SP SD: 0.0362 c. M:-0.0778 c. 612: 104 46 104 104 93 57 104 SP SD: 0.0195 c. M: 0.0450 c. 1171: 199 88 199 199 178 109 199 SP SD: 0.0159 c. M: 0.0274 c. 1783: 303 134 303 303 271 166 303 SP SD: 0.0134 c. M: 0.0239 c. 2395: 407 180 407 407 364 223 407 SP SD: 0.0137 c. M: 0.0223 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: 23.2999 cents 8:9 x 11:12:13:14:16 SD: 12.3631 cents 9:10:11:12:14:15:16:18 S SD: 12.1761 cents 10:11:12:13:15:17:18:20 SD: 10.6284 cents 12 x 14:16:18:20:21:24 S SD: 6.4262 cents 13:15 x 17:20:22:23:26 SD: 12.6279 cents 14:16:17:19:21:23:25:28 SD: 9.1761 cents 15:17:18:20:23:25:27:30 SD: 7.1943 cents 16:18:19:21:24:27:28:32 SD: 6.3255 cents 18:20:21:24:27:30:32:36 S SD: 4.9608 cents 22:25:26:29:33:37:39:44 SD: 4.4908 cents 24:27:28:32:36:40:43:48 SD: 4.3445 cents 26:29:31:35:39:43:46:52 SD: 4.1680 cents 30:34:36:40:45:50:53:60 SD: 3.8955 cents 32:36:38:43:48:53:57:64 SD: 2.5641 cents 42:47:50:56:63:70:75:84 SD: 2.0368 cents 48:54:57:64:72:80:85:96 SD: 1.0816 cents 54:61:64:72:81:90:96:108 SD: 1.0157 cents 72:81:85:96:108:120:128:144 SD: 0.9680 cents 96:108:114:128:144:160:171:192 SD: 0.6825 cents 114:128:135:152:171:190:203:228 SD: 0.6629 cents 120:135:142:160:180:200:213:240 SD: 0.5469 cents 144:162:171:192:216:240:256:288 SD: 0.4826 cents 162:182:192:216:243:270:288:324 SD: 0.3395 cents 168:189:199:224:252:280:299:336 SD: 0.3085 cents 216:243:256:288:324:360:384:432 SD: 0.0000 cents