Scala analysis: xen09-wilson-marwa-04-01
Marwa permutation 1 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: 27/20 519.551289 acute fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 243/128 1109.775004 Pythagorean major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 1: 9/8 203.9100 major whole tone 2: 9/8 203.9100 major whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 10/9 182.4037 minor whole tone 5: 9/8 203.9100 major whole tone 6: 9/8 203.9100 major whole tone 7: 256/243 90.2250 limma, Pythagorean minor second
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 : 203.9 407.8 519.6 702.0 905.9 1109.8 1200.0 203.9 : 203.9 315.6 498.0 702.0 905.9 996.1 1200.0 407.8 : 111.7 294.1 498.0 702.0 792.2 996.1 1200.0 519.6 : 182.4 386.3 590.2 680.4 884.4 1088.3 1200.0 702.0 : 203.9 407.8 498.0 702.0 905.9 1017.6 1200.0 905.9 : 203.9 294.1 498.0 702.0 813.7 996.1 1200.0 1109.8: 90.2 294.1 498.0 609.8 792.2 996.1 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 : 178.38571 cents, oct.: 1248.69995 cents Scale is strictly proper Step pattern alph. order: AABCAAD Step pattern size order : DDBCDDA 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 harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 3 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: 2 -- 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 : 0.235173 Specific harmonicity : 0.209059 Fundamental : 1/640, -9.3219 octaves, 0.4088 Hz. Guide tone : 486, 8.9248 octaves, 127150.025 Hz. Exponens Consonantiae : 3.110400E+05, 18.24674 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 315.5, average 45.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.58818, average 1.22688 Sum of Tenney's harmonic distance : 16.51187, average 2.35884 Vogel's harmonic complexity : 15.85714 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 117.26589, average 4.18807 Lattice compactness (without 2's) : 64.62512, average 2.30804 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 1 -3.14286 24 1 3: 0 .. 5 2.57143 18 5 5: -1 .. 0 -0.14286 1 1 Average exponent except 2's : 17 / 7 = 2.42857 Average absolute exponent except 2's: 19 / 7 = 2.71429 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: 45.5672 c. M: 81.2036 c. Lebeng 8: 1 2 0 2 1 1 1 P D3 S SD: 46.9629 c. M: 69.5513 c. 9: 2 1 1 1 2 1 1 P M ME S SD: 33.9066 c. M:-62.7567 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 36.4424 c. M:-54.1350 c. Pseudo Rast 11: 2 2 1 1 2 2 1 P D3 S SD: 27.7517 c. M: 47.4095 c. 12: 2 2 1 2 2 2 1 P M ME S SD: 9.1999 c. M: 19.5513 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 27: 5 4 3 4 4 5 2 SP SD: 11.7123 c. M:-18.3122 c. 28: 5 5 2 4 5 5 2 P SD: 11.2409 c. M:-20.7514 c. 29: 5 5 3 4 5 5 2 SP SD: 8.1105 c. M:-18.3797 c. 30: 5 5 3 5 5 5 2 P T3 SD: 10.0471 c. M:-18.0450 c. 32: 5 6 3 5 5 6 2 P SD: 9.9877 c. M: 16.4100 c. 35: 6 6 3 5 6 6 3 SP SD: 9.8252 c. M: 16.2407 c. 37: 6 7 3 6 6 6 3 SP SD: 8.1618 c. M:-13.8016 c. 39: 7 6 4 6 6 7 3 SP SD: 7.8039 c. M: 13.5573 c. 41: 7 7 4 6 7 7 3 SP SD: 3.0672 c. M:-7.2780 c. 53: 9 9 5 8 9 9 4 SP SD: 0.4934 c. M:-1.2034 c. 171: 29 29 16 26 29 29 13 SP SD: 0.5704 c. M: 1.0031 c. 224: 38 38 21 34 38 38 17 SP SD: 0.4758 c. M: 0.8464 c. 277: 47 47 26 42 47 47 21 SP SD: 0.4358 c. M: 0.7497 c. 330: 56 56 31 50 56 56 25 SP SD: 0.4193 c. M: 0.6841 c. 335: 57 57 31 51 57 57 25 SP SD: 0.3813 c. M:-0.6728 c. 347: 59 59 32 53 59 59 26 SP SD: 0.3555 c. M: 0.8193 c. 383: 65 65 36 58 65 65 29 SP SD: 0.4136 c. M: 0.6366 c. 388: 66 66 36 59 66 66 29 SP SD: 0.2998 c. M:-0.5343 c. 400: 68 68 37 61 68 68 30 SP SD: 0.2436 c. M: 0.5513 c. 441: 75 75 41 67 75 75 33 SP SD: 0.2496 c. M:-0.4291 c. 453: 77 77 42 69 77 77 34 SP SD: 0.1582 c. M: 0.3460 c. 506: 86 86 47 77 86 86 38 SP SD: 0.0915 c. M: 0.1837 c. 559: 95 95 52 85 95 95 42 SP SD: 0.0409 c. M:-0.0640 c. 612: 104 104 57 93 104 104 46 SP SD: 0.0268 c. M:-0.0566 c. 1171: 199 199 109 178 199 199 88 SP SD: 0.0257 c. M:-0.0457 c. 1783: 303 303 166 271 303 303 134 SP SD: 0.0239 c. M:-0.0399 c. 2395: 407 407 223 364 407 407 180 SP SD: 0.0239 c. M:-0.0371 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: 10.1382 cents 4 x 5 x 6:7 x 8 S SD: 16.6332 cents 5 x 6:7 x 8 x 10 S SD: 36.1921 cents 6:7 x 8:9:10:11:12 S SD: 15.4009 cents 7:8:9 x 11:12:13:14 SD: 16.8042 cents 8:9:10:11:12:14:15:16 S SD: 10.9714 cents 12:14:15:16:18:20:23:24 SD: 10.7146 cents 14:16:18:19:21:24:27:28 SD: 7.8983 cents 16:18:20:22:24:27:30:32 S SD: 6.2827 cents 18:20:23:24:27:30:34:36 SD: 5.9547 cents 22:25:28:30:33:37:42:44 SD: 4.1090 cents 26:29:33:35:39:44:49:52 SD: 3.0432 cents 34:38:43:46:51:57:65:68 SD: 2.9284 cents 38:43:48:51:57:64:72:76 SD: 2.2096 cents 42:47:53:57:63:71:80:84 SD: 2.1958 cents 46:52:58:62:69:78:87:92 SD: 2.1757 cents 48:54:61:65:72:81:91:96 SD: 1.3144 cents 72:81:91:97:108:122:137:144 SD: 1.3135 cents 80:90:101:108:120:135:152:160 SD: 0.6444 cents 128:144:162:173:192:216:243:256 SD: 0.2861 cents 286:322:362:386:429:483:543:572 SD: 0.2807 cents 294:331:372:397:441:496:558:588 SD: 0.2246 cents 320:360:405:432:480:540:608:640 SD: 0.2035 cents 346:389:438:467:519:584:657:692 SD: 0.1909 cents 384:432:486:518:576:648:729:768 SD: 0.1909 cents 400:450:506:540:600:675:759:800 SD: 0.1728 cents 432:486:547:583:648:729:820:864 SD: 0.1463 cents 474:533:600:640:711:800:900:948 SD: 0.1394 cents 512:576:648:691:768:864:972:1024 SD: 0.0716 cents