Scala analysis: xen09-wilson-marwa-06-06
Marwa permutation 6 from Figure 6, Didymus/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: 256/243 90.224996 limma, Pythagorean minor second 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 64/45 609.776284 2nd tritone 5: 128/81 792.179997 Pythagorean 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: 256/243 90.2250 limma, Pythagorean minor second 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 10/9 182.4037 minor whole tone 6: 9/8 203.9100 major whole tone 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 : 90.2 294.1 498.0 609.8 792.2 996.1 1200.0 90.2 : 203.9 407.8 519.6 702.0 905.9 1109.8 1200.0 294.1 : 203.9 315.6 498.0 702.0 905.9 996.1 1200.0 498.0 : 111.7 294.1 498.0 702.0 792.2 996.1 1200.0 609.8 : 182.4 386.3 590.2 680.4 884.4 1088.3 1200.0 792.2 : 203.9 407.8 498.0 702.0 905.9 1017.6 1200.0 996.1 : 203.9 294.1 498.0 702.0 813.7 996.1 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 : 163.92268 cents, oct.: 1147.45875 cents Scale is strictly proper Step pattern alph. order: ABBCDBB Step pattern size order : ADDBCDD 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 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 1 = 14.2857% 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: 4 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 243 Scale harmonicity : 0.036058 Average absolute harmonicity : 0.222603 Specific harmonicity : 0.208831 Fundamental : 1/1215, -10.2467 octaves, 0.2153 Hz. Guide tone : 256, 8.0000 octaves, 66976.145 Hz. Exponens Consonantiae : 3.110400E+05, 18.24674 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 455.5, average 65.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.81003, average 1.25858 Sum of Tenney's harmonic distance : 18.74402, average 2.67772 Vogel's harmonic complexity : 16.71429 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 119.31012, average 4.26108 Lattice compactness (without 2's) : 63.69891, average 2.27496 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 8 4.71429 33 1 3: -5 .. 0 -2.42857 17 5 5: -1 .. 0 -0.14286 1 1 Average exponent except 2's :-18 / 7 =-2.57143 Average absolute exponent except 2's: 18 / 7 = 2.57143 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 0 1 1 1 1 1 2 N T3 SD: 111.5094 c. M: 155.1879 c. 8: 1 1 1 1 1 2 1 P M ME S SD: 39.0911 c. M:-59.7750 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 41.6393 c. M:-70.5767 c. 11: 1 2 2 1 1 2 2 P D3 S SD: 30.9940 c. M:-47.4095 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 6.6094 c. M: 9.7763 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 29: 2 5 5 3 4 5 5 SP SD: 5.8766 c. M:-10.9134 c. 41: 3 7 7 4 6 7 7 SP SD: 2.2830 c. M:-4.8579 c. 53: 4 9 9 5 8 9 9 SP SD: 0.6143 c. M:-1.5445 c. 118: 9 20 20 11 18 20 20 SP SD: 0.7440 c. M:-1.3004 c. 171: 13 29 29 16 26 29 29 SP SD: 0.6298 c. M:-1.0031 c. 224: 17 38 38 21 34 38 38 SP SD: 0.5923 c. M:-0.9380 c. 277: 21 47 47 26 42 47 47 SP SD: 0.5791 c. M:-1.0540 c. 330: 25 56 56 31 50 56 56 SP SD: 0.5748 c. M:-1.1328 c. 335: 25 57 57 31 51 57 57 SP SD: 0.4884 c. M: 0.8211 c. 347: 26 59 59 32 53 59 59 SP SD: 0.4617 c. M: 1.1308 c. 388: 29 66 66 36 59 66 66 SP SD: 0.3537 c. M: 0.5343 c. 400: 30 68 68 37 61 68 68 SP SD: 0.3194 c. M: 0.7763 c. 441: 33 75 75 41 67 75 75 SP SD: 0.2588 c. M: 0.4291 c. 453: 34 77 77 42 69 77 77 SP SD: 0.2105 c. M: 0.5048 c. 494: 37 84 84 46 75 84 84 SP SD: 0.1955 c. M: 0.3465 c. 506: 38 86 86 47 77 86 86 SP SD: 0.1248 c. M: 0.2901 c. 547: 41 93 93 51 83 93 93 SP SD: 0.1610 c. M: 0.2798 c. 559: 42 95 95 52 85 95 95 SP SD: 0.0567 c. M: 0.1162 c. 612: 46 104 104 57 93 104 104 SP SD: 0.0193 c. M: 0.0289 c. 2395: 180 407 407 223 364 407 407 SP SD: 0.0209 c. M: 0.0371 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 45.1125 cents 3 x x 4 x 5 x 6 S SD: 30.7262 cents 4 x 5 x x 6:7:8 S SD: 32.9591 cents 5 x 6 x 7:8:9:10 S SD: 9.2323 cents 6 x 7:8 x 9:11:12 SD: 21.6535 cents 7 x 8:9:10:11:12:14 S SD: 18.2920 cents 8 x 9:11 x 13:14:16 SD: 23.7145 cents 9:10:11:12:13:14:16:18 S SD: 16.1616 cents 10:11:12:13:14:16:18:20 S SD: 14.0291 cents 12:13:14:16:17:19:21:24 SD: 8.9002 cents 14:15:17:19:20:22:25:28 SD: 8.7703 cents 15:16:18:20:21:24:27:30 S SD: 7.2751 cents 16:17:19:21:23:25:28:32 SD: 7.0560 cents 17:18:20:23:24:27:30:34 SD: 5.1128 cents 21:22:25:28:30:33:37:42 SD: 3.3434 cents 33:35:39:44:47:52:59:66 SD: 2.4172 cents 36:38:43:48:51:57:64:72 SD: 2.2599 cents 53:56:63:71:75:84:94:106 SD: 2.1977 cents 54:57:64:72:77:85:96:108 SD: 1.2584 cents 76:80:90:101:108:120:135:152 SD: 0.9333 cents 93:98:110:124:132:147:165:186 SD: 0.8690 cents 114:120:135:152:162:180:203:228 SD: 0.5751 cents 135:142:160:180:192:213:240:270 SD: 0.5469 cents 171:180:203:228:243:270:304:342 SD: 0.5380 cents 183:193:217:244:260:289:325:366 SD: 0.4920 cents 189:199:224:252:269:299:336:378 SD: 0.3592 cents 243:256:288:324:346:384:432:486 SD: 0.2861 cents 303:319:359:404:431:479:539:606 SD: 0.2576 cents 336:354:398:448:478:531:597:672 SD: 0.2085 cents 372:392:441:496:529:588:661:744 SD: 0.1678 cents 450:474:533:600:640:711:800:900 SD: 0.1640 cents 486:512:576:648:691:768:864:972 SD: 0.0716 cents