Scala analysis: xen09-wilson-marwa-04-15
Marwa permutation 15 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: 16/15 111.731285 minor diatonic semitone 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 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: 16/15 111.7313 minor diatonic semitone 2: 10/9 182.4037 minor whole tone 3: 9/8 203.9100 major whole tone 4: 9/8 203.9100 major whole tone 5: 256/243 90.2250 limma, Pythagorean minor second 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 : 111.7 294.1 498.0 702.0 792.2 996.1 1200.0 111.7 : 182.4 386.3 590.2 680.4 884.4 1088.3 1200.0 294.1 : 203.9 407.8 498.0 702.0 905.9 1017.6 1200.0 498.0 : 203.9 294.1 498.0 702.0 813.7 996.1 1200.0 702.0 : 90.2 294.1 498.0 609.8 792.2 996.1 1200.0 792.2 : 203.9 407.8 519.6 702.0 905.9 1109.8 1200.0 996.1 : 203.9 315.6 498.0 702.0 905.9 996.1 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 : 166.70997 cents, oct.: 1166.96981 cents Scale is strictly proper Step pattern alph. order: ABCCDCC Step pattern size order : BCDDADD 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 1 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: 5 -- 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 : 0.257744 Specific harmonicity : 0.223671 Fundamental : 1/810, -9.6618 octaves, 0.3230 Hz. Guide tone : 384, 8.5850 octaves, 100464.217 Hz. Exponens Consonantiae : 3.110400E+05, 18.24674 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 169.5, average 24.21429 Mersenne's string divisions : 200687025 Sum of van Prooijen's expressibility: 6.42443, average 0.91778 Sum of Tenney's harmonic distance : 13.64914, average 1.94988 Vogel's harmonic complexity : 16.14286 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 110.98771, average 3.96385 Lattice compactness (without 2's) : 58.87705, average 2.10275 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 7 3.14286 24 1 3: -4 .. 1 -1.42857 12 5 5: -1 .. 0 -0.14286 1 1 Average exponent except 2's :-11 / 7 =-1.57143 Average absolute exponent except 2's: 13 / 7 = 1.85714 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: 40.9535 c. M:-64.9629 c. Lebeng 8: 1 1 1 2 0 2 1 P D3 S SD: 39.2810 c. M:-53.9100 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 33.1905 c. M: 62.7567 c. Pseudo Pelog, Pelogic-7, Antiionian 11: 1 2 2 1 1 2 2 P D3 S SD: 30.7498 c. M:-47.4095 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 6.0487 c. M: 11.7313 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 29: 3 4 5 5 2 5 5 SP SD: 5.6449 c. M:-12.4066 c. 41: 4 6 7 7 3 7 7 SP SD: 2.2614 c. M:-5.3419 c. 53: 5 8 9 9 4 9 9 SP SD: 0.5761 c. M:-1.4763 c. 118: 11 18 20 20 9 20 20 SP SD: 0.5496 c. M:-1.0403 c. 171: 16 26 29 29 13 29 29 SP SD: 0.4705 c. M:-0.8025 c. 224: 21 34 38 38 17 38 38 SP SD: 0.4597 c. M:-0.7687 c. 323: 30 49 55 55 24 55 55 SP SD: 0.4586 c. M: 0.8487 c. 335: 31 51 57 57 25 57 57 SP SD: 0.3841 c. M: 0.6865 c. 376: 35 57 64 64 28 64 64 SP SD: 0.3635 c. M: 0.6906 c. 388: 36 59 66 66 29 66 66 SP SD: 0.2691 c. M: 0.4274 c. 441: 41 67 75 75 33 75 75 SP SD: 0.1913 c. M: 0.3433 c. 453: 42 69 77 77 34 77 77 SP SD: 0.1909 c. M: 0.4730 c. 494: 46 75 84 84 37 84 84 SP SD: 0.1459 c. M: 0.2772 c. 506: 47 77 86 86 38 86 86 SP SD: 0.1110 c. M: 0.2688 c. 547: 51 83 93 93 41 93 93 SP SD: 0.1310 c. M: 0.2239 c. 559: 52 85 95 95 42 95 95 SP SD: 0.0475 c. M: 0.1034 c. 612: 57 93 104 104 46 104 104 SP SD: 0.0175 c. M:-0.0334 c. 1783: 166 271 303 303 134 303 303 SP SD: 0.0172 c. M: 0.0319 c. 2395: 223 364 407 407 180 407 407 SP SD: 0.0156 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: 30.7262 cents 4 x 5 x 6 x 7:8 S SD: 24.0316 cents 5 x 6:7 x 8:9:10 S SD: 18.4632 cents 6 x 7:8:9 x 11:12 SD: 11.9689 cents 7 x 8:9 x 11:12:14 SD: 21.8962 cents 8 x 9:11:12:13:14:16 SD: 19.7620 cents 9:10:11:12 x 14:16:18 S SD: 15.4344 cents 10:11:12:13:15:16:18:20 SD: 11.2002 cents 11:12:13:15 x 17:20:22 SD: 12.9644 cents 12:13:14:16:18:19:21:24 SD: 6.7288 cents 16:17:19:21:24:25:28:32 SD: 6.2699 cents 18:19:21:24:27:28:32:36 SD: 6.0866 cents 22:23:26:29:33:35:39:44 SD: 6.0353 cents 24:26:28:32:36:38:43:48 SD: 5.8147 cents 26:28:31:35:39:41:46:52 SD: 3.8846 cents 28:30:33:37:42:44:50:56 SD: 3.3434 cents 32:34:38:43:48:51:57:64 SD: 3.0879 cents 42:45:50:56:63:66:75:84 SD: 2.3572 cents 48:51:57:64:72:76:85:96 SD: 1.5296 cents 60:64:71:80:90:95:107:120 SD: 0.9889 cents 76:81:90:101:114:120:135:152 SD: 0.9109 cents 90:96:107:120:135:142:160:180 SD: 0.8632 cents 102:109:121:136:153:161:181:204 SD: 0.7388 cents 108:115:128:144:162:171:192:216 SD: 0.6462 cents 136:145:161:181:204:215:242:272 SD: 0.6019 cents 150:160:178:200:225:237:267:300 SD: 0.4386 cents 162:173:192:216:243:256:288:324 SD: 0.2861 cents 210:224:249:280:315:332:373:420 SD: 0.2705 cents 270:288:320:360:405:427:480:540 SD: 0.1931 cents 378:403:448:504:567:597:672:756 SD: 0.1847 cents 432:461:512:576:648:683:768:864 SD: 0.1615 cents 450:480:533:600:675:711:800:900 SD: 0.1594 cents 540:576:640:720:810:853:960:1080 SD: 0.0966 cents 600:640:711:800:900:948:1067:1200 SD: 0.0946 cents