Scala analysis: xen09-wilson-marwa-08-03
Marwa permutation 3 from Figure 8, 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: 28/27 62.960904 Archytas' 1/3-tone 2: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth 4: 112/81 561.005903 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: 28/27 62.9609 Archytas' 1/3-tone 2: 9/8 203.9100 major whole tone 3: 8/7 231.1741 septimal whole tone 4: 28/27 62.9609 Archytas' 1/3-tone 5: 9/8 203.9100 major whole 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: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 3 9/8 203.910 cents major whole tone 1: 2 8/7 231.174 cents septimal whole tone 2: 3 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 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: 3 14/9 764.916 cents septimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 3 12/7 933.129 cents septimal major sixth 6: 2 7/4 968.826 cents harmonic seventh 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 63.0 266.9 498.0 561.0 764.9 996.1 1200.0 63.0 : 203.9 435.1 498.0 702.0 933.1 1137.0 1200.0 266.9 : 231.2 294.1 498.0 729.2 933.1 996.1 1200.0 498.0 : 63.0 266.9 498.0 702.0 764.9 968.8 1200.0 561.0 : 203.9 435.1 639.0 702.0 905.9 1137.0 1200.0 764.9 : 231.2 435.1 498.0 702.0 933.1 996.1 1200.0 996.1 : 203.9 266.9 470.8 702.0 764.9 968.8 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: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 160.97129 cents, oct.: 1126.79904 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1277-tone equal temperament with octave 2/1 degrees: 67 284 530 597 814 1060 1277 Least number of segments generator : 639 of 600.470 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 747 of 701.958 cents and inv. generated superset size: 72 = 65 more = 1028.571% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCABCB Step pattern size order : SMLSMLM Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.317229 Lumma stability : 0.223924 Lumma impropriety factor : 0.064990 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 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 Scale is a chain of 3 triads 0.0 435.084 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Mixolydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 5 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 168.2132 cents: 4 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.038532 Average absolute harmonicity : 0.220377 Specific harmonicity : 0.183431 Fundamental : 1/162, -7.3399 octaves, 1.6150 Hz. Guide tone : 112, 6.8074 octaves, 29302.063 Hz. Exponens Consonantiae : 1.814400E+04, 14.14720 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 159.5, average 22.78571 Mersenne's string divisions : 333257925 Sum of van Prooijen's expressibility: 6.57055, average 0.93865 Sum of Tenney's harmonic distance : 14.09842, average 2.01406 Vogel's harmonic complexity : 13.28571 Wille's k value : 94 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 84.57744, average 3.02062 Lattice compactness (without 2's) : 52.74838, average 1.88387 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.85714 15 1 3: -4 .. 0 -1.85714 13 2 7: 0 .. 1 0.57143 4 4 Average exponent except 2's :-9 / 7 =-1.28571 Average absolute exponent except 2's: 17 / 7 = 2.42857 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: 0 2 1 0 1 2 1 N T3 SD: 52.7967 c. M: 79.2016 c. 8: 0 2 1 1 1 2 1 N D3 SD: 41.4371 c. M: 62.9609 c. 9: 0 2 2 0 2 1 2 N T3 S SD: 39.9007 c. M: 62.9609 c. 10: 0 2 2 0 2 2 2 N M DE S SD: 46.1266 c. M: 81.0059 c. 11: 0 2 2 1 2 2 2 N T3 SD: 38.8890 c. M: 62.9609 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 27.3600 c. M:-38.9941 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 13: 1 2 2 1 2 3 2 N G T3 S SD: 22.0984 c. M: 36.5065 c. 14: 1 2 3 1 2 3 2 P T3 SD: 22.3419 c. M:-38.9941 c. 17: 1 3 3 1 3 3 3 N M DE S SD: 8.6371 c. M:-15.4820 c. Safi al-Din's maqam Abu Salik 19: 1 3 4 1 3 4 3 N T3 SD: 9.0047 c. M:-14.4363 c. 22: 1 4 4 1 4 4 4 N M DE S SD: 9.2829 c. M: 15.5514 c. 31: 2 5 6 2 5 6 5 N T3 SD: 10.9009 c. M:-19.6393 c. Soft Diatonic Mixolydian 33: 2 5 7 1 6 6 6 N SD: 10.8000 c. M: 15.5514 c. 35: 2 6 7 1 6 7 6 N SD: 9.4195 c. M:-16.2407 c. 36: 2 6 7 2 6 7 6 N T3 SD: 3.1166 c. M:-5.6608 c. 41: 2 7 8 2 7 8 7 N T3 SD: 3.2140 c. M: 4.9083 c. 58: 3 10 11 3 10 11 10 N T3 SD: 1.7882 c. M: 2.9865 c. 77: 4 13 15 4 13 15 13 N T3 SD: 1.0642 c. M: 1.9358 c. 94: 5 16 18 5 16 18 16 N T3 SD: 0.7510 c. M:-1.2142 c. 135: 7 23 26 7 23 26 23 N T3 SD: 0.5579 c. M: 1.0059 c. 171: 9 29 33 9 29 33 29 N T3 SD: 0.2507 c. M:-0.4012 c. 306: 16 52 59 16 52 59 52 N T3 SD: 0.1611 c. M: 0.2216 c. 400: 21 68 77 21 68 77 68 N T3 SD: 0.0711 c. M:-0.1291 c. 571: 30 97 110 30 97 110 97 N T3 SD: 0.0643 c. M:-0.1149 c. 706: 37 120 136 37 120 136 120 N T3 SD: 0.0548 c. M: 0.0994 c. 877: 46 149 169 46 149 169 149 N T3 SD: 0.0286 c. M: 0.0522 c. 1277: 67 217 246 67 217 246 217 N T3 SD: 0.0033 c. M: 0.0054 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 31.4805 cents 3 x x 4 x x 5:6 S SD: 37.2438 cents 4 x x 5 x 6:7:8 S SD: 32.7789 cents 5 x 6 x 7:8:9:10 S SD: 15.0760 cents 6 x 7:8 x 9:11:12 SD: 16.4949 cents 7 x 8:9:10:11:12:14 S SD: 18.7835 cents 8 x 9 x 11:12:14:16 SD: 18.7247 cents 9 x 11:12 x 14:16:18 SD: 16.1074 cents 10 x 12:13:14:16:18:20 S SD: 14.5328 cents 11:12:13 x 15:17:20:22 SD: 17.0013 cents 12:13:14:16:17:19:21:24 SD: 13.6748 cents 13:14:15:17:18:20:23:26 SD: 11.2542 cents 14:15:16:19 x 22:25:28 SD: 12.6621 cents 15:16:18:20:21:23:27:30 SD: 11.3413 cents 16:17:19:21:22:25:28:32 SD: 9.4139 cents 18:19:21:24:25:28:32:36 SD: 4.5139 cents 23:24:27:31:32:36:41:46 SD: 4.1207 cents 24:25:28:32:33:37:43:48 SD: 3.4283 cents 29:30:34:39:40:45:52:58 SD: 3.4068 cents 31:32:36:41:43:48:55:62 SD: 2.9642 cents 36:37:42:48:50:56:64:72 SD: 2.4766 cents 47:49:55:63:65:73:84:94 SD: 2.4231 cents 48:50:56:64:66:75:85:96 SD: 2.2978 cents 49:51:57:65:68:76:87:98 SD: 2.0885 cents 54:56:63:72:75:84:96:108 SD: 1.1016 cents 78:81:91:104:108:121:139:156 SD: 1.0228 cents 84:87:98:112:116:131:149:168 SD: 0.9496 cents 102:106:119:136:141:159:181:204 SD: 0.8661 cents 108:112:126:144:149:168:192:216 SD: 0.5527 cents 162:168:189:216:224:252:288:324 S SD: 0.0000 cents