Scala analysis: xen09-wilson-marwa-04-13
Marwa permutation 13 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: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 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: 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: 16/15 111.7313 minor diatonic semitone 6: 10/9 182.4037 minor 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 : 203.9 294.1 498.0 702.0 813.7 996.1 1200.0 203.9 : 90.2 294.1 498.0 609.8 792.2 996.1 1200.0 294.1 : 203.9 407.8 519.6 702.0 905.9 1109.8 1200.0 498.0 : 203.9 315.6 498.0 702.0 905.9 996.1 1200.0 702.0 : 111.7 294.1 498.0 702.0 792.2 996.1 1200.0 813.7 : 182.4 386.3 590.2 680.4 884.4 1088.3 1200.0 996.1 : 203.9 407.8 498.0 702.0 905.9 1017.6 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 : 168.13647 cents, oct.: 1176.95532 cents Scale is strictly proper Step pattern alph. order: ABAACDA Step pattern size order : DADDBCD 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 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 5 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 Limited inverse transpositions with margin 113.6850 cents: 6 -- 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 : 0.271066 Specific harmonicity : 0.230935 Fundamental : 1/1080, -10.0768 octaves, 0.2422 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 3.110400E+05, 18.24674 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 64.5, average 9.21429 Mersenne's string divisions : 6845475 Sum of van Prooijen's expressibility: 4.99306, average 0.71329 Sum of Tenney's harmonic distance : 10.71263, average 1.53038 Vogel's harmonic complexity : 16.57143 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 108.72090, average 3.88289 Lattice compactness (without 2's) : 56.46284, average 2.01653 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 1.57143 19 1 3: -3 .. 2 -0.42857 9 5 5: -1 .. 0 -0.14286 1 1 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 10 / 7 = 1.42857 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: 31.3959 c. M:-48.7221 c. Lebeng 10: 2 0 2 2 1 1 2 P D3 S SD: 31.3488 c. M: 54.1350 c. 12: 2 1 2 2 1 2 2 P M ME S SD: 6.0937 c. M: 13.6863 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 29: 5 2 5 5 3 4 5 SP SD: 5.8012 c. M:-13.8999 c. 34: 6 2 6 6 3 5 6 P SD: 6.5110 c. M: 11.7821 c. 37: 6 3 6 7 3 6 6 SP SD: 8.0539 c. M:-11.5585 c. 40: 7 3 7 6 4 6 7 P SD: 7.6346 c. M:-11.9550 c. 41: 7 3 7 7 4 6 7 SP SD: 2.3419 c. M:-5.8259 c. 53: 9 4 9 9 5 8 9 SP SD: 0.5439 c. M:-1.4081 c. 65: 11 5 11 11 6 10 11 SP SD: 0.8617 c. M: 1.3786 c. 118: 20 9 20 20 11 18 20 SP SD: 0.4312 c. M:-0.7803 c. 171: 29 13 29 29 16 26 29 SP SD: 0.3558 c. M:-0.6018 c. 224: 38 17 38 38 21 34 38 SP SD: 0.3593 c. M:-0.5994 c. 323: 55 24 55 55 30 49 55 SP SD: 0.3504 c. M: 0.6365 c. 335: 57 25 57 57 31 51 57 SP SD: 0.3044 c. M: 0.5520 c. 376: 64 28 64 64 35 57 64 SP SD: 0.2896 c. M: 0.5180 c. 388: 66 29 66 66 36 59 66 SP SD: 0.2062 c. M: 0.3206 c. 441: 75 33 75 75 41 67 75 SP SD: 0.1446 c. M: 0.2574 c. 494: 84 37 84 84 46 75 84 SP SD: 0.1180 c. M: 0.2079 c. 506: 86 38 86 86 47 77 86 SP SD: 0.0999 c. M: 0.2476 c. 547: 93 41 93 93 51 83 93 SP SD: 0.1211 c. M:-0.2077 c. 559: 95 42 95 95 52 85 95 SP SD: 0.0402 c. M: 0.0906 c. 612: 104 46 104 104 57 93 104 SP SD: 0.0176 c. M:-0.0392 c. 1171: 199 88 199 199 109 178 199 SP SD: 0.0173 c. M: 0.0274 c. 1783: 303 134 303 303 166 271 303 SP SD: 0.0132 c. M: 0.0239 c. 2395: 407 180 407 407 223 364 407 SP SD: 0.0127 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: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 24.0316 cents 5 x 6:7 x 8:9:10 S SD: 17.9552 cents 6 x 7:8:9:10:11:12 S SD: 15.4344 cents 7:8 x 9 x 11:12:14 SD: 19.6413 cents 8:9 x 11:12:13:14:16 SD: 10.9313 cents 9:10:11:12 x 14:16:18 S SD: 12.5599 cents 10:11:12:13:15:16:18:20 SD: 9.4327 cents 12 x 14:16:18:19:21:24 SD: 7.1010 cents 13:15 x 17:20:21:23:26 SD: 12.1524 cents 14:16:17:19:21:22:25:28 SD: 9.5601 cents 15:17:18:20:23:24:27:30 SD: 7.1943 cents 16:18:19:21:24:26:28:32 SD: 6.7288 cents 18:20:21:24:27:29:32:36 SD: 5.2477 cents 22:25:26:29:33:35:39:44 SD: 4.1405 cents 30:34:36:40:45:48:53:60 SD: 3.8955 cents 32:36:38:43:48:51:57:64 SD: 2.2599 cents 42:47:50:56:63:67:75:84 SD: 2.1661 cents 48:54:57:64:72:77:85:96 SD: 1.2584 cents 72:81:85:96:108:115:128:144 SD: 1.0591 cents 80:90:95:107:120:128:142:160 SD: 0.9889 cents 90:101:107:120:135:144:160:180 SD: 0.9845 cents 96:108:114:128:144:154:171:192 SD: 0.9378 cents 102:115:121:136:153:163:181:204 SD: 0.8002 cents 112:126:133:149:168:179:199:224 SD: 0.7960 cents 120:135:142:160:180:192:213:240 SD: 0.5469 cents 152:171:180:203:228:243:270:304 SD: 0.5380 cents 162:182:192:216:243:259:288:324 SD: 0.3895 cents 168:189:199:224:252:269:299:336 SD: 0.3592 cents 216:243:256:288:324:346:384:432 SD: 0.2861 cents 270:304:320:360:405:432:480:540 SD: 0.2035 cents 360:405:427:480:540:576:640:720 SD: 0.1931 cents 378:425:448:504:567:605:672:756 SD: 0.1669 cents 400:450:474:533:600:640:711:800 SD: 0.1640 cents 432:486:512:576:648:691:768:864 SD: 0.0716 cents