Scala analysis: xen09-wilson-marwa-04-06
Marwa permutation 6 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: 81/64 407.820003 Pythagorean major 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: 9/8 203.9100 major whole tone 3: 256/243 90.2250 limma, Pythagorean minor second 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: 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 : 203.9 407.8 498.0 702.0 905.9 1017.6 1200.0 203.9 : 203.9 294.1 498.0 702.0 813.7 996.1 1200.0 407.8 : 90.2 294.1 498.0 609.8 792.2 996.1 1200.0 498.0 : 203.9 407.8 519.6 702.0 905.9 1109.8 1200.0 702.0 : 203.9 315.6 498.0 702.0 905.9 996.1 1200.0 905.9 : 111.7 294.1 498.0 702.0 792.2 996.1 1200.0 1017.6: 182.4 386.3 590.2 680.4 884.4 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 : 173.97434 cents, oct.: 1217.82039 cents Scale is strictly proper Step pattern alph. order: AABAACD Step pattern size order : DDADDBC 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 major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 6 Formal octave complements present : 3 = 42.8571% 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 Limited inverse transpositions with margin 113.6850 cents: 1 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.036058 Average absolute harmonicity : 0.262224 Specific harmonicity : 0.222376 Fundamental : 1/960, -9.9069 octaves, 0.2725 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 3.110400E+05, 18.24674 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 117.0, average 16.71429 Mersenne's string divisions : 4451790 Sum of van Prooijen's expressibility: 6.20258, average 0.88608 Sum of Tenney's harmonic distance : 12.01906, average 1.71701 Vogel's harmonic complexity : 16.42857 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 111.45986, average 3.98071 Lattice compactness (without 2's) : 59.69891, average 2.13210 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 2 -1.57143 17 1 3: -1 .. 4 1.57143 13 5 5: -1 .. 0 -0.14286 1 1 Average exponent except 2's : 10 / 7 = 1.42857 Average absolute exponent except 2's: 14 / 7 = 2.00000 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: 34.4281 c. M: 64.9629 c. Lebeng 8: 1 2 0 2 1 1 1 P D3 S SD: 38.5199 c. M: 53.9100 c. 9: 2 1 1 1 2 1 1 P M ME S SD: 37.1339 c. M:-62.7567 c. 11: 2 2 1 1 2 1 2 N D3 SD: 33.5771 c. M:-47.4095 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 7.8204 c. M: 17.5963 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 29: 5 5 2 5 5 3 4 SP SD: 7.1142 c. M:-16.8865 c. 32: 5 6 2 6 5 3 5 P SD: 9.0550 c. M: 16.4100 c. 33: 6 5 3 5 6 3 5 SP T3 SD: 8.6157 c. M:-14.2718 c. 34: 6 6 2 6 6 3 5 P SD: 8.5636 c. M:-15.7094 c. 38: 6 7 3 6 7 3 6 P SD: 8.1802 c. M: 14.4363 c. 40: 7 7 3 6 7 4 6 P SD: 8.5479 c. M:-12.1800 c. 41: 7 7 3 7 7 4 6 SP SD: 2.7625 c. M:-6.7940 c. 53: 9 9 4 9 9 5 8 SP SD: 0.5016 c. M:-1.2716 c. 118: 20 20 9 20 20 11 18 SP SD: 0.5995 c. M: 1.0403 c. 171: 29 29 13 29 29 16 26 SP SD: 0.4226 c. M: 0.8025 c. 224: 38 38 17 38 38 21 34 SP SD: 0.3696 c. M: 0.6771 c. 277: 47 47 21 47 47 26 42 SP SD: 0.3592 c. M: 0.5998 c. 330: 56 56 25 56 56 31 50 SP SD: 0.3632 c. M:-0.5855 c. 335: 57 57 25 57 57 31 51 SP SD: 0.3027 c. M:-0.5382 c. 388: 66 66 29 66 66 36 59 SP SD: 0.2264 c. M:-0.4274 c. 441: 75 75 33 75 75 41 67 SP SD: 0.1838 c. M:-0.3433 c. 453: 77 77 34 77 77 42 69 SP SD: 0.1576 c. M: 0.3777 c. 494: 84 84 37 84 84 46 75 SP SD: 0.1674 c. M:-0.2772 c. 506: 86 86 38 86 86 47 77 SP SD: 0.0895 c. M: 0.2050 c. 559: 95 95 42 95 95 52 85 SP SD: 0.0365 c. M: 0.0650 c. 612: 104 104 46 104 104 57 93 SP SD: 0.0227 c. M:-0.0508 c. 1171: 199 199 88 199 199 109 178 SP SD: 0.0193 c. M:-0.0365 c. 1783: 303 303 134 303 303 166 271 SP SD: 0.0177 c. M:-0.0319 c. 2395: 407 407 180 407 407 223 364 SP SD: 0.0180 c. M:-0.0297 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: 13.3254 cents 5 x 6:7 x 8:9:10 S SD: 31.0667 cents 6:7 x 8:9:10:11:12 S SD: 12.2879 cents 7:8:9 x 11:12:13:14 SD: 17.9843 cents 8:9:10:11:12 x 14:16 S SD: 12.5599 cents 10:11 x 13:15:17:18:20 SD: 9.9973 cents 14:16:18:19:21:24:25:28 SD: 8.2798 cents 15:17:19:20:23:25:27:30 SD: 6.5085 cents 16:18:20:21:24:27:29:32 SD: 5.2477 cents 22:25:28:29:33:37:40:44 SD: 4.7914 cents 24:27:30:32:36:41:43:48 SD: 4.4683 cents 26:29:33:35:39:44:47:52 SD: 3.4944 cents 30:34:38:40:45:51:54:60 SD: 2.5893 cents 42:47:53:56:63:71:76:84 SD: 2.0359 cents 48:54:61:64:72:81:86:96 SD: 1.5326 cents 64:72:81:85:96:108:115:128 SD: 1.0591 cents 80:90:101:107:120:135:144:160 SD: 0.9845 cents 90:101:114:120:135:152:162:180 SD: 0.6757 cents 120:135:152:160:180:203:216:240 SD: 0.6430 cents 144:162:182:192:216:243:259:288 SD: 0.3895 cents 192:216:243:256:288:324:346:384 SD: 0.2861 cents 240:270:304:320:360:405:432:480 SD: 0.2035 cents 320:360:405:427:480:540:576:640 SD: 0.1931 cents 336:378:425:448:504:567:605:672 SD: 0.1669 cents 384:432:486:512:576:648:691:768 SD: 0.0716 cents 576:648:729:768:864:972:1037:1152 SD: 0.0477 cents