Scala analysis: xen09-wilson-marwa-08-02
Marwa permutation 2 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: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal 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: 9/8 203.9100 major whole tone 7: 8/7 231.1741 septimal 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: 2 7/6 266.871 cents septimal minor third 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 81/64 407.820 cents Pythagorean major third 2: 2 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: 2 14/9 764.916 cents septimal minor sixth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 5: 2 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: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 63.0 266.9 498.0 561.0 764.9 968.8 1200.0 63.0 : 203.9 435.1 498.0 702.0 905.9 1137.0 1200.0 266.9 : 231.2 294.1 498.0 702.0 933.1 996.1 1200.0 498.0 : 63.0 266.9 470.8 702.0 764.9 968.8 1200.0 561.0 : 203.9 407.8 639.0 702.0 905.9 1137.0 1200.0 764.9 : 203.9 435.1 498.0 702.0 933.1 996.1 1200.0 968.8 : 231.2 294.1 498.0 729.2 792.2 996.1 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 : 159.80283 cents, oct.: 1118.61981 cents Scale is not proper Step pattern alph. order: ABCABBC Step pattern size order : SMLSMML Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.378117 Lumma stability : 0.223924 Lumma impropriety factor : 0.064990 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 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: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord Scale is Phrygian octave species of abstract tetrachord All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 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 : 0.037102 Average absolute harmonicity : 0.216699 Specific harmonicity : 0.183933 Fundamental : 1/324, -8.3399 octaves, 0.8075 Hz. Guide tone : 112, 6.8074 octaves, 29302.063 Hz. Exponens Consonantiae : 3.628800E+04, 15.14720 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 152.5, average 21.78571 Mersenne's string divisions : 66651585 Sum of van Prooijen's expressibility: 6.46141, average 0.92306 Sum of Tenney's harmonic distance : 13.38721, average 1.91246 Vogel's harmonic complexity : 15.28571 Wille's k value : 283 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 88.09156, average 3.14613 Lattice compactness (without 2's) : 55.09810, average 1.96779 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.00000 13 1 3: -4 .. 0 -1.57143 11 1 7: 0 .. 1 0.71429 5 5 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 16 / 7 = 2.28571 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: 56.0955 c. M: 79.2016 c. 8: 0 2 1 1 1 1 2 P D3 S SD: 44.4811 c. M: 68.8259 c. 9: 0 2 2 0 2 1 2 N T3 S SD: 34.7764 c. M: 62.9609 c. 11: 1 2 2 0 2 2 2 N T3 SD: 34.7158 c. M:-60.4018 c. 13: 0 3 2 1 2 2 3 N SD: 34.3135 c. M: 62.9609 c. 14: 1 2 3 1 2 2 3 P T3 SD: 21.0898 c. M:-38.9941 c. 15: 1 2 3 1 3 2 3 N T3 SD: 19.4488 c. M:-35.0841 c. 16: 1 3 3 1 2 3 3 P SD: 23.1461 c. M:-38.9941 c. 17: 1 3 3 1 3 3 3 N M DE S SD: 10.9363 c. M:-19.4094 c. Safi al-Din's maqam Abu Salik 19: 1 3 4 1 3 3 4 N SD: 10.8206 c. M: 21.4575 c. 22: 1 4 4 1 4 4 4 N M DE S SD: 9.0105 c. M: 15.5514 c. 31: 2 5 6 2 5 5 6 N SD: 10.1814 c. M:-19.6393 c. 32: 2 5 6 2 5 6 6 N SD: 8.7675 c. M: 14.9159 c. 36: 2 6 7 2 6 6 7 N SD: 2.8628 c. M:-5.6608 c. 41: 2 7 8 2 7 7 8 N SD: 3.3850 c. M: 4.9083 c. 58: 3 10 11 3 10 10 11 N SD: 1.9397 c. M:-3.5879 c. 77: 4 13 15 4 13 13 15 N SD: 1.3588 c. M: 2.5921 c. 94: 5 16 18 5 16 16 18 N SD: 0.9065 c. M:-1.3869 c. 135: 7 23 26 7 23 23 26 N SD: 0.5206 c. M: 1.0059 c. 171: 9 29 33 9 29 29 33 N SD: 0.2515 c. M: 0.4049 c. 306: 16 52 59 16 52 52 59 N SD: 0.1776 c. M: 0.2216 c. 400: 21 68 77 21 68 68 77 N SD: 0.0907 c. M:-0.1741 c. 571: 30 97 110 30 97 97 110 N SD: 0.0606 c. M:-0.1149 c. 706: 37 120 136 37 120 120 136 N SD: 0.0508 c. M: 0.0994 c. 877: 46 149 169 46 149 149 169 N SD: 0.0366 c. M: 0.0688 c. 1277: 67 217 246 67 217 217 246 N SD: 0.0038 c. M:-0.0073 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: 28.1557 cents 4 x x 5 x 6:7:8 S SD: 32.0624 cents 5 x 6 x 7:8:9:10 S SD: 17.4335 cents 6 x 7:8 x 9:11:12 SD: 20.4453 cents 7 x 8:9:10:11:12:14 S SD: 16.6764 cents 8 x 9 x 11:12:14:16 SD: 17.9131 cents 9 x 11:12 x 14:16:18 SD: 17.0053 cents 10 x 12:13:14:16:18:20 S SD: 16.2612 cents 11:12:13 x 15:17:19:22 SD: 16.1625 cents 12:13:14:16:17:19:21:24 SD: 13.1084 cents 13:14:15:17:18:20:23:26 SD: 11.5128 cents 14:15:16:19 x 22:25:28 SD: 13.8801 cents 15:16:18:20:21:23:26:30 SD: 11.1708 cents 16:17:19:21:22:25:28:32 SD: 8.5704 cents 18:19:21:24:25:28:32:36 SD: 5.9620 cents 23:24:27:31:32:36:40:46 SD: 4.3479 cents 24:25:28:32:33:37:42:48 SD: 2.8371 cents 36:37:42:48:50:56:63:72 SD: 2.4766 cents 47:49:55:63:65:73:82:94 SD: 2.1718 cents 48:50:56:64:66:75:84:96 SD: 2.0839 cents 52:54:61:69:72:81:91:104 SD: 1.8981 cents 54:56:63:72:75:84:95:108 SD: 1.7079 cents 60:62:70:80:83:93:105:120 SD: 1.2562 cents 78:81:91:104:108:121:137:156 SD: 1.2293 cents 79:82:92:105:109:123:138:158 SD: 1.1823 cents 83:86:97:111:115:129:145:166 SD: 1.1231 cents 84:87:98:112:116:131:147:168 SD: 0.7722 cents 108:112:126:144:149:168:189:216 SD: 0.5527 cents 162:168:189:216:224:252:284:324 SD: 0.4358 cents 216:224:252:288:299:336:378:432 SD: 0.2759 cents 240:249:280:320:332:373:420:480 SD: 0.2705 cents 300:311:350:400:415:467:525:600 SD: 0.2262 cents 324:336:378:432:448:504:567:648 S SD: 0.0000 cents