Scala analysis: xen09-wilson-marwa-04-07
Marwa permutation 7 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: 9/8 203.910002 major whole tone 2: 6/5 315.641287 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: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 9/8 203.9100 major whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 10/9 182.4037 minor whole tone 4: 9/8 203.9100 major whole tone 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 10/9 182.4037 minor 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 : 203.9 315.6 498.0 702.0 905.9 1017.6 1200.0 203.9 : 111.7 294.1 498.0 702.0 813.7 996.1 1200.0 315.6 : 182.4 386.3 590.2 702.0 884.4 1088.3 1200.0 498.0 : 203.9 407.8 519.6 702.0 905.9 1017.6 1200.0 702.0 : 203.9 315.6 498.0 702.0 813.7 996.1 1200.0 905.9 : 111.7 294.1 498.0 609.8 792.2 996.1 1200.0 1017.6: 182.4 386.3 498.0 680.4 884.4 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 : 172.65750 cents, oct.: 1208.60252 cents Scale is strictly proper Step pattern alph. order: ABCAABC Step pattern size order : LSMLLSM 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 Phrygian octave species of abstract tetrachord Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords 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 : 1 at degree 0 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 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 : 0.267844 Specific harmonicity : 0.244150 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 2.592000E+04, 14.66178 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 50.0, average 7.14286 Mersenne's string divisions : 1688610 Sum of van Prooijen's expressibility: 4.99306, average 0.71329 Sum of Tenney's harmonic distance : 9.78151, average 1.39736 Vogel's harmonic complexity : 13.42857 Wille's k value : 202 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: -4 .. 2 -0.57143 12 1 3: -1 .. 3 1.14286 10 4 5: -1 .. 0 -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 28: 5 2 5 4 5 3 4 P SD: 12.1578 c. M:-16.2407 c. 29: 5 3 4 5 5 3 4 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: 6 3 5 5 6 3 5 SP SD: 9.2098 c. M:-14.2718 c. 34: 6 3 5 6 6 3 5 P SD: 6.2173 c. M:-11.7821 c. 41: 7 4 6 7 7 4 6 SP SD: 3.5755 c. M:-6.7940 c. 53: 9 5 8 9 9 5 8 SP SD: 0.7053 c. M:-1.3398 c. 118: 20 11 18 20 20 11 18 SP SD: 0.4756 c. M: 0.7803 c. 171: 29 16 26 29 29 16 26 SP SD: 0.2996 c. M: 0.6018 c. 224: 38 21 34 38 38 21 34 SP SD: 0.3123 c. M: 0.5079 c. 323: 55 30 49 55 55 30 49 SP SD: 0.3437 c. M:-0.6365 c. 335: 57 31 51 57 57 31 51 SP SD: 0.2741 c. M: 0.4174 c. 388: 66 36 59 66 66 36 59 SP SD: 0.1723 c. M:-0.3206 c. 441: 75 41 67 75 75 41 67 SP SD: 0.1302 c. M:-0.2574 c. 494: 84 46 75 84 84 46 75 SP SD: 0.1421 c. M:-0.2175 c. 506: 86 47 77 86 86 47 77 SP SD: 0.1195 c. M: 0.2263 c. 559: 95 52 85 95 95 52 85 SP SD: 0.0426 c. M: 0.0778 c. 612: 104 57 93 104 104 57 93 SP SD: 0.0270 c. M:-0.0508 c. 1171: 199 109 178 199 199 109 178 SP SD: 0.0144 c. M:-0.0274 c. 1783: 303 166 271 303 303 166 271 SP SD: 0.0131 c. M:-0.0239 c. 2395: 407 223 364 407 407 223 364 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: 7.1688 cents 4 x 5 x 6 x 7:8 S SD: 21.4668 cents 5 x 6:7 x 8:9:10 S SD: 25.0053 cents 6 x 7:8:9:10:11:12 S SD: 10.3417 cents 7:8 x 9:11:12:13:14 SD: 20.3199 cents 8:9:10:11:12 x 14:16 S SD: 16.8417 cents 9:10:11:12:14:15:16:18 S SD: 11.3935 cents 10:11:12:13:15:17:18:20 SD: 8.5691 cents 12 x 14:16:18:20:22:24 S SD: 10.3417 cents 14:16:17:19:21:24:25:28 SD: 7.8710 cents 15:17:18:20:23:25:27:30 SD: 6.5053 cents 16:18:19:21:24:27:29:32 SD: 4.9806 cents 24:27:29:32:36:41:43:48 SD: 3.6682 cents 30:34:36:40:45:51:54:60 SD: 2.5813 cents 40:45:48:53:60:68:72:80 SD: 2.3950 cents 48:54:58:64:72:81:86:96 SD: 2.0607 cents 50:56:60:67:75:84:90:100 SD: 1.9872 cents 54:61:65:72:81:91:97:108 SD: 1.4097 cents 64:72:77:85:96:108:115:128 SD: 1.2391 cents 70:79:84:93:105:118:126:140 SD: 1.2108 cents 80:90:96:107:120:135:144:160 SD: 0.7717 cents 90:101:108:120:135:152:162:180 SD: 0.6444 cents 96:108:115:128:144:162:173:192 SD: 0.5163 cents 144:162:173:192:216:243:259:288 SD: 0.3439 cents 234:263:281:312:351:395:421:468 SD: 0.3258 cents 240:270:288:320:360:405:432:480 S SD: 0.0000 cents