Scala analysis: xen09-wilson-marwa-07-13
Marwa permutation 13 from Figure 7, Archytas 28/27 8/7 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: 14/9 764.915905 septimal 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: 28/27 62.9609 Archytas' 1/3-tone 6: 8/7 231.1741 septimal whole tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 4 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 3 32/27 294.135 cents Pythagorean minor third 2: 2 81/64 407.820 cents Pythagorean major third 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 21/16 470.781 cents narrow fourth 3: 5 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 4: 1 112/81 561.006 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 32/21 729.219 cents wide fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 2 128/81 792.180 cents Pythagorean minor sixth 5: 3 27/16 905.865 cents Pythagorean major sixth 5: 1 12/7 933.129 cents septimal major sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 4 16/9 996.090 cents Pythagorean minor seventh 6: 1 243/128 1109.775 cents Pythagorean major seventh 6: 1 27/14 1137.039 cents septimal 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 : 203.9 294.1 498.0 702.0 764.9 996.1 1200.0 203.9 : 90.2 294.1 498.0 561.0 792.2 996.1 1200.0 294.1 : 203.9 407.8 470.8 702.0 905.9 1109.8 1200.0 498.0 : 203.9 266.9 498.0 702.0 905.9 996.1 1200.0 702.0 : 63.0 294.1 498.0 702.0 792.2 996.1 1200.0 764.9 : 231.2 435.1 639.0 729.2 933.1 1137.0 1200.0 996.1 : 203.9 407.8 498.0 702.0 905.9 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 231.1741 cents 54/49, 168.2132 cents 28/27, 62.9609 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 3: 470.7809 .. 638.9941 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 4: 561.0059 .. 729.2191 cents 54/49, 168.2132 cents 6272/6561,-77.9882 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 6: 968.8259 .. 1137.0391 cents 54/49, 168.2132 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.722778 Largest / Average step : 1.348516 Largest / Smallest step : 3.671709 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 : 166.39468 cents, oct.: 1164.76273 cents Scale is not proper Step pattern alph. order: ABAACDA Step pattern size order : CBCCADC Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.447201 Lumma stability : 0.223924 Lumma impropriety factor : 0.064990 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 : 64/63, 27.2641 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 Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 2 at degree 5 Length of longest subharmonic part : 1 at degree 0 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 168.2132 cents: 6 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.031627 Average absolute harmonicity : 0.264464 Specific harmonicity : 0.205787 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 2016, 10.9773 octaves, 527437.140 Hz. Exponens Consonantiae : 4.354560E+05, 18.73217 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 69.5, average 9.92857 Mersenne's string divisions : 12111225 Sum of van Prooijen's expressibility: 5.24833, average 0.74976 Sum of Tenney's harmonic distance : 11.21094, average 1.60156 Vogel's harmonic complexity : 12.14286 Wille's k value : 121 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 108.06233, average 3.85937 Lattice compactness (without 2's) : 59.58595, average 2.12807 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 1.28571 17 1 3: -3 .. 2 -0.71429 11 5 7: 0 .. 1 0.14286 1 1 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 22| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 12 18|
FIT/MODE
7: 1 1 1 1 0 2 1 N T3 SD: 40.1503 c. M: 79.2016 c. 8: 1 1 1 2 0 2 1 P D3 S SD: 39.0716 c. M:-53.9100 c. 10: 1 1 2 2 0 2 2 P D3 S SD: 44.6297 c. M: 83.9100 c. 11: 2 1 2 1 1 2 2 N D3 SD: 29.2830 c. M:-47.4095 c. 12: 2 1 2 2 1 2 2 P M ME S SD: 13.6461 c. M:-35.0841 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 16: 3 1 3 2 1 3 3 N SD: 19.2710 c. M:-26.9550 c. 17: 3 1 3 3 1 3 3 N M DE S SD: 7.8063 c. M: 11.7821 c. Seventeen-tone Natural Minor 24: 4 2 4 4 1 5 4 N SD: 6.4929 c. M: 14.9159 c. 36: 6 3 6 6 2 7 6 N SD: 3.2882 c. M:-5.8650 c. 41: 7 3 7 7 2 8 7 N SD: 1.6893 c. M: 3.9403 c. 77: 13 6 13 13 4 15 13 N SD: 1.1845 c. M:-1.9689 c. 94: 16 7 16 16 5 18 16 N SD: 0.4857 c. M:-1.0415 c. 135: 23 10 23 23 7 26 23 N SD: 0.4749 c. M: 0.8017 c. 171: 29 13 29 29 9 33 29 N SD: 0.3305 c. M:-0.6018 c. 212: 36 16 36 36 11 41 36 N SD: 0.3102 c. M: 0.7650 c. 265: 45 20 45 45 14 51 45 N SD: 0.1786 c. M:-0.3671 c. 306: 52 23 52 52 16 59 52 N SD: 0.0800 c. M: 0.2100 c. 400: 68 30 68 68 21 77 68 N SD: 0.0807 c. M: 0.1350 c. 571: 97 43 97 97 30 110 97 N SD: 0.0519 c. M:-0.0857 c. 706: 120 53 120 120 37 136 120 N SD: 0.0490 c. M: 0.0840 c. 877: 149 66 149 149 46 169 149 N SD: 0.0304 c. M:-0.0497 c. 971: 165 73 165 165 51 187 165 N SD: 0.0261 c. M:-0.0686 c. 1277: 217 96 217 217 67 246 217 N SD: 0.0045 c. M: 0.0081 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 x 5:6 S SD: 37.2438 cents 4 x 5 x 6 x 7:8 S SD: 24.0316 cents 5 x 6:7 x 8:9:10 S SD: 20.4336 cents 6 x 7:8:9 x 11:12 SD: 11.9689 cents 7:8 x 9 x 11:12:14 SD: 18.9530 cents 8:9 x 11:12 x 14:16 SD: 11.9689 cents 9:10:11:12 x 14:16:18 S SD: 9.5750 cents 11:12:13:15 x 17:20:22 SD: 12.9280 cents 12 x 14:16:18:19:21:24 SD: 8.2084 cents 13:15 x 17 x 20:23:26 SD: 11.8099 cents 14:16:17:19:21:22:25:28 SD: 8.8227 cents 15:17:18:20 x 23:27:30 SD: 6.8896 cents 16:18:19:21:24:25:28:32 SD: 5.6380 cents 17:19:20:23 x 26:30:34 SD: 7.3696 cents 18:20:21:24:27:28:32:36 S SD: 4.9608 cents 22:25:26:29:33:34:39:44 SD: 4.2135 cents 31:35:37:41:47:48:55:62 SD: 4.0458 cents 32:36:38:43:48:50:57:64 SD: 2.3203 cents 48:54:57:64:72:75:85:96 SD: 1.5439 cents 54:61:64:72:81:84:96:108 SD: 1.0157 cents 72:81:85:96:108:112:128:144 SD: 0.9680 cents 96:108:114:128:144:149:171:192 SD: 0.8782 cents 104:117:123:139:156:162:185:208 SD: 0.8724 cents 112:126:133:149:168:174:199:224 SD: 0.8106 cents 114:128:135:152:171:177:203:228 SD: 0.8099 cents 120:135:142:160:180:187:213:240 SD: 0.7027 cents 135:152:160:180:203:210:240:270 SD: 0.6430 cents 144:162:171:192:216:224:256:288 SD: 0.4826 cents 162:182:192:216:243:252:288:324 SD: 0.3395 cents 216:243:256:288:324:336:384:432 SD: 0.0000 cents