Scala analysis: xen09-wilson-marwa-03-06
Marwa permutation 6 from Figure 3, 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: 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: 15/8 1088.268715 classic major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 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: 10/9 182.4037 minor whole tone 7: 16/15 111.7313 minor diatonic semitone
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 1088.3 1200.0 203.9 : 203.9 294.1 498.0 702.0 884.4 996.1 1200.0 407.8 : 90.2 294.1 498.0 680.4 792.2 996.1 1200.0 498.0 : 203.9 407.8 590.2 702.0 905.9 1109.8 1200.0 702.0 : 203.9 386.3 498.0 702.0 905.9 996.1 1200.0 905.9 : 182.4 294.1 498.0 702.0 792.2 996.1 1200.0 1088.3: 111.7 315.6 519.6 609.8 813.7 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 : 177.00316 cents, oct.: 1239.02212 cents Scale is strictly proper Step pattern alph. order: AABAACD Step pattern size order : DDADDCB 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 fifths form a closed circle 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 : 2 at degree 4 Length of longest subharmonic part : 1 at degree 0 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 Scale is n-1 differentially coherent in interval classes 4 and 5 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: 81 Scale harmonicity : 0.036058 Average absolute harmonicity : 0.261888 Specific harmonicity : 0.223671 Fundamental : 1/192, -7.5850 octaves, 1.3626 Hz. Guide tone : 1620, 10.6618 octaves, 423833.416 Hz. Exponens Consonantiae : 3.110400E+05, 18.24674 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 121.5, average 17.35714 Mersenne's string divisions : 51195585 Sum of van Prooijen's expressibility: 6.42443, average 0.91778 Sum of Tenney's harmonic distance : 12.44502, average 1.77786 Vogel's harmonic complexity : 12.00000 Wille's k value : 121 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: -6 .. 2 -2.00000 20 1 3: -1 .. 4 1.42857 12 5 5: 0 .. 1 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 2 0 2 1 1 1 P D3 S SD: 39.2810 c. M: 53.9100 c. 9: 2 1 1 1 2 1 1 P M ME S SD: 33.1905 c. M:-62.7567 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 32.1591 c. M:-54.1350 c. Pseudo Rast 11: 2 2 1 1 2 2 1 P D3 S SD: 30.7498 c. M:-47.4095 c. 12: 2 2 1 2 2 2 1 P M ME S SD: 6.0487 c. M:-11.7313 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 29: 5 5 2 5 5 4 3 SP SD: 5.6449 c. M: 12.4066 c. 41: 7 7 3 7 7 6 4 SP SD: 2.2614 c. M: 5.3419 c. 53: 9 9 4 9 9 8 5 SP SD: 0.5761 c. M: 1.4763 c. 118: 20 20 9 20 20 18 11 SP SD: 0.5496 c. M: 1.0403 c. 171: 29 29 13 29 29 26 16 SP SD: 0.4705 c. M: 0.8025 c. 224: 38 38 17 38 38 34 21 SP SD: 0.4597 c. M: 0.7687 c. 323: 55 55 24 55 55 49 30 SP SD: 0.4586 c. M:-0.8487 c. 335: 57 57 25 57 57 51 31 SP SD: 0.3841 c. M:-0.6865 c. 376: 64 64 28 64 64 57 35 SP SD: 0.3635 c. M:-0.6906 c. 388: 66 66 29 66 66 59 36 SP SD: 0.2691 c. M:-0.4274 c. 441: 75 75 33 75 75 67 41 SP SD: 0.1913 c. M:-0.3433 c. 453: 77 77 34 77 77 69 42 SP SD: 0.1909 c. M:-0.4730 c. 494: 84 84 37 84 84 75 46 SP SD: 0.1459 c. M:-0.2772 c. 506: 86 86 38 86 86 77 47 SP SD: 0.1110 c. M:-0.2688 c. 547: 93 93 41 93 93 83 51 SP SD: 0.1310 c. M:-0.2239 c. 559: 95 95 42 95 95 85 52 SP SD: 0.0475 c. M:-0.1034 c. 612: 104 104 46 104 104 93 57 SP SD: 0.0175 c. M: 0.0334 c. 1783: 303 303 134 303 303 271 166 SP SD: 0.0172 c. M:-0.0319 c. 2395: 407 407 180 407 407 364 223 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: 7.1688 cents 4 x 5 x 6:7 x 8 S SD: 16.6332 cents 5 x 6:7 x 8:9:10 S SD: 34.1310 cents 6:7 x 8:9:10:11:12 S SD: 12.8455 cents 7:8:9 x 11:12:13:14 SD: 15.8032 cents 8:9:10:11:12:14:15:16 S SD: 12.1761 cents 10:11 x 13:15:17:19:20 SD: 10.7029 cents 14:16:18:19:21:24:26:28 SD: 8.3829 cents 15:17:19:20:23:25:28:30 SD: 6.6010 cents 16:18:20:21:24:27:30:32 S SD: 4.9608 cents 22:25:28:29:33:37:41:44 SD: 4.3634 cents 24:27:30:32:36:41:45:48 SD: 4.3184 cents 26:29:33:35:39:44:49:52 SD: 3.5635 cents 30:34:38:40:45:51:56:60 SD: 2.8139 cents 38:43:48:51:57:64:71:76 SD: 2.4354 cents 42:47:53:56:63:71:79:84 SD: 1.7481 cents 48:54:61:64:72:81:90:96 SD: 1.0157 cents 64:72:81:85:96:108:120:128 SD: 0.9680 cents 90:101:114:120:135:152:169:180 SD: 0.7686 cents 102:115:129:136:153:172:191:204 SD: 0.6774 cents 120:135:152:160:180:203:225:240 SD: 0.6430 cents 128:144:162:171:192:216:240:256 SD: 0.4826 cents 144:162:182:192:216:243:270:288 SD: 0.3395 cents 192:216:243:256:288:324:360:384 SD: 0.0000 cents