Scala analysis: xen09-wilson-marwa-07-05
Marwa permutation 5 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: 28/27 62.960904 Archytas' 1/3-tone 2: 7/6 266.870906 septimal minor third 3: 21/16 470.780907 narrow fourth 4: 3/2 701.955001 perfect fifth 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: 9/8 203.9100 major whole tone 4: 8/7 231.1741 septimal whole tone 5: 28/27 62.9609 Archytas' 1/3-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 : 63.0 266.9 470.8 702.0 764.9 968.8 1200.0 63.0 : 203.9 407.8 639.0 702.0 905.9 1137.0 1200.0 266.9 : 203.9 435.1 498.0 702.0 933.1 996.1 1200.0 470.8 : 231.2 294.1 498.0 729.2 792.2 996.1 1200.0 702.0 : 63.0 266.9 498.0 561.0 764.9 968.8 1200.0 764.9 : 203.9 435.1 498.0 702.0 905.9 1137.0 1200.0 968.8 : 231.2 294.1 498.0 702.0 933.1 996.1 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 : 163.24572 cents, oct.: 1142.72002 cents Scale is not proper Step pattern alph. order: ABBCABC Step pattern size order : SMMLSML 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 Hypolydian octave species of abstract tetrachord Scale is Hypophrygian 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 2 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: 5 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.037102 Average absolute harmonicity : 0.227750 Specific harmonicity : 0.187709 Fundamental : 1/432, -8.7549 octaves, 0.6056 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 3.628800E+04, 15.14720 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 73.5, average 10.50000 Mersenne's string divisions : 1825395 Sum of van Prooijen's expressibility: 5.87514, average 0.83931 Sum of Tenney's harmonic distance : 11.65482, average 1.66497 Vogel's harmonic complexity : 15.71429 Wille's k value : 283 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 87.54315, average 3.12654 Lattice compactness (without 2's) : 52.38921, average 1.87104 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.57143 12 1 3: -3 .. 1 -0.57143 8 1 7: 0 .. 1 0.71429 5 5 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 13 / 7 = 1.85714 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 1 1 2 0 1 2 N T3 SD: 83.1930 c. M: 127.9238 c. 8: 0 2 1 2 0 1 2 N T3 SD: 42.6971 c. M: 68.8259 c. 10: 1 1 2 2 0 2 2 P D3 S SD: 30.4290 c. M:-57.0391 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 28.1062 c. M:-37.0391 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 13: 1 2 2 3 0 2 3 N SD: 27.1852 c. M: 45.7490 c. 14: 1 2 2 3 1 2 3 P T3 SD: 21.9563 c. M: 42.2095 c. 15: 1 2 3 3 1 2 3 N SD: 19.7549 c. M:-35.0841 c. 17: 1 3 3 3 1 3 3 N M DE S SD: 13.9803 c. M:-23.3367 c. 21: 1 4 3 4 1 4 4 N T3 S SD: 13.7946 c. M: 22.0588 c. 22: 1 4 4 4 1 4 4 N M DE S SD: 10.2234 c. M:-20.1282 c. Raga Bilashkhani Todi 26: 1 5 4 5 2 4 5 N SD: 11.6512 c. M:-19.6995 c. 27: 1 5 5 5 1 5 5 N M DE S SD: 11.4791 c. M: 18.5165 c. 31: 2 5 5 6 2 5 6 N SD: 7.3598 c. M:-14.4585 c. 33: 2 5 6 6 2 6 6 N SD: 8.8118 c. M:-12.9923 c. 36: 2 6 6 7 2 6 7 N SD: 2.4568 c. M: 4.1142 c. 77: 4 13 13 15 4 13 15 N SD: 1.8313 c. M: 3.2484 c. 94: 5 16 16 18 5 16 18 N SD: 1.0488 c. M:-1.5595 c. 130: 7 22 22 25 7 22 25 N SD: 0.8687 c. M:-1.6545 c. 135: 7 23 23 26 7 23 26 N SD: 0.3768 c. M: 0.7387 c. 171: 9 29 29 33 9 29 33 N SD: 0.3050 c. M: 0.6055 c. 265: 14 45 45 51 14 45 51 N SD: 0.2667 c. M:-0.4353 c. 306: 16 52 52 59 16 52 59 N SD: 0.1728 c. M: 0.2158 c. 400: 21 68 68 77 21 68 77 N SD: 0.1228 c. M:-0.2191 c. 571: 30 97 97 110 30 97 110 N SD: 0.0435 c. M:-0.0864 c. 706: 37 120 120 136 37 120 136 N SD: 0.0374 c. M: 0.0714 c. 1277: 67 217 217 246 67 217 246 N SD: 0.0052 c. M:-0.0100 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: 29.5861 cents 4 x x 5:6 x 7:8 S SD: 21.1168 cents 5 x 6:7 x 8:9:10 S SD: 28.0139 cents 6 x 7:8:9 x 11:12 SD: 17.0053 cents 7 x 8:9 x 11:12:14 SD: 12.8557 cents 8 x 9:11:12 x 14:16 SD: 20.4453 cents 9 x 11:12 x 14:16:18 SD: 17.8582 cents 10 x 12:13:15:16:18:20 SD: 14.3470 cents 11:12:13:14 x 17:19:22 SD: 17.9996 cents 12:13:14:16:18:19:21:24 SD: 12.2885 cents 13:14:15:17 x 20:23:26 SD: 12.2466 cents 14:15:16:18:21:22:25:28 SD: 12.1814 cents 15:16:18:20 x 23:26:30 SD: 13.3286 cents 16:17:19:21:24:25:28:32 SD: 7.5077 cents 17:18:20:22 x 26:30:34 SD: 9.3877 cents 18:19:21:24:27:28:32:36 SD: 7.0358 cents 20:21:23:26:30:31:35:40 SD: 5.3373 cents 22:23:26:29:33:34:39:44 SD: 5.3012 cents 23:24:27:30:35:36:40:46 SD: 4.9445 cents 24:25:28:32:36:37:42:48 SD: 4.6156 cents 25:26:29:33:38:39:44:50 SD: 4.2080 cents 28:29:33:37:42:44:49:56 SD: 3.9396 cents 29:30:34:38:44:45:51:58 SD: 3.4428 cents 32:33:37:42:48:50:56:64 SD: 2.8371 cents 36:37:42:47:54:56:63:72 SD: 2.5771 cents 48:50:56:63:72:75:84:96 SD: 1.5580 cents 54:56:63:71:81:84:95:108 SD: 1.3760 cents 76:79:89:100:114:118:133:152 SD: 1.3409 cents 80:83:93:105:120:124:140:160 SD: 1.2562 cents 83:86:97:109:125:129:145:166 SD: 1.2066 cents 84:87:98:110:126:131:147:168 SD: 0.9011 cents 108:112:126:142:162:168:189:216 SD: 0.4358 cents 192:199:224:252:288:299:336:384 SD: 0.3085 cents 240:249:280:315:360:373:420:480 SD: 0.2470 cents 324:336:378:425:486:504:567:648 SD: 0.1454 cents 432:448:504:567:648:672:756:864 S SD: 0.0000 cents