Scala analysis: xen11-chalmers-tetrachordal-04-02a
Malaka, a Lyra tuning: Soft or Intense Chromatic and Tonic Diatonic
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: 10/9 182.403712 minor whole tone 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: 28/27 62.9609 Archytas' 1/3-tone 2: 15/14 119.4428 major diatonic semitone 3: 6/5 315.6413 minor third 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: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 15/14 119.443 cents major diatonic semitone 1: 2 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 1 27/20 519.551 cents acute fourth 3: 1 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 81/56 638.994 cents 4: 1 112/81 561.006 cents 4: 1 10/7 617.488 cents Euler's tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 8/5 813.686 cents minor sixth 5: 1 40/27 680.449 cents grave fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 28/15 1080.557 cents grave major seventh 6: 2 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 63.0 182.4 498.0 702.0 764.9 996.1 1200.0 63.0 : 119.4 435.1 639.0 702.0 933.1 1137.0 1200.0 182.4 : 315.6 519.6 582.5 813.7 1017.6 1080.6 1200.0 498.0 : 203.9 266.9 498.0 702.0 764.9 884.4 1200.0 702.0 : 63.0 294.1 498.0 561.0 680.4 996.1 1200.0 764.9 : 231.2 435.1 498.0 617.5 933.1 1137.0 1200.0 996.1 : 203.9 266.9 386.3 702.0 905.9 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 315.6413 cents 81/70, 252.6804 cents 28/27, 62.9609 cents 2: 182.4037 .. 519.5513 cents 243/200, 337.1476 cents 25/27,-133.2376 cents 3: 386.3137 .. 638.9941 cents 81/70, 252.6804 cents 25/27,-133.2376 cents 4: 561.0059 .. 813.6863 cents 81/70, 252.6804 cents 6272/6561,-77.9882 cents 5: 680.4487 .. 1017.5963 cents 243/200, 337.1476 cents 25/27,-133.2376 cents 6: 884.3587 .. 1137.0391 cents 81/70, 252.6804 cents 25/27,-133.2376 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 : 6/5, 315.6413 cents Average / Smallest step : 2.722778 Largest / Average step : 1.841241 Largest / Smallest step : 5.013290 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 163.79173 cents, oct.: 1146.54214 cents Scale is not proper Step pattern alph. order: ABCDAED Step pattern size order : ABECADC Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.643636 Lumma stability : 0.104935 Lumma impropriety factor : 0.509115 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 81/80, 21.5063 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 5 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval class 4 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.030910 Average absolute harmonicity : 0.254593 Specific harmonicity : 0.190346 Fundamental : 1/54, -5.7549 octaves, 4.8449 Hz. Guide tone : 1680, 10.7142 octaves, 439530.950 Hz. Exponens Consonantiae : 9.072000E+04, 16.46913 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 68.5, average 9.78571 Mersenne's string divisions : 2523675 Sum of van Prooijen's expressibility: 5.24833, average 0.74976 Sum of Tenney's harmonic distance : 11.24986, average 1.60712 Vogel's harmonic complexity : 10.28571 Wille's k value : 40 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 76.36520, average 2.72733 Lattice compactness (without 2's) : 52.34146, average 1.86934 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.42857 12 1 3: -3 .. 1 -1.28571 11 3 5: 0 .. 1 0.14286 1 1 7: 0 .. 1 0.28571 2 2 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 10 18 22| Scale is JI-epimorphic with val: <7 11 17 20| Scale is weakly epimorphic with val: <7 12 16 18|
FIT/MODE
7: 0 1 2 1 0 2 1 N T3 SD: 41.3003 c. M: 79.2016 c. 9: 0 1 3 1 1 1 2 N SD: 44.7721 c. M: 62.9609 c. 11: 0 1 3 2 1 2 2 N SD: 47.2023 c. M: 73.3128 c. 12: 1 1 3 2 1 2 2 N SD: 20.4777 c. M:-37.0391 c. Mela Ratnangi, Raga Phenadyuti 13: 1 1 3 3 0 3 2 N SD: 25.6451 c. M:-36.5065 c. 14: 1 1 4 2 1 3 2 N SD: 17.9807 c. M:-32.4814 c. 17: 1 2 4 3 1 3 3 N SD: 12.7968 c. M:-29.3610 c. 19: 1 2 5 3 1 4 3 N SD: 7.6712 c. M:-14.4363 c. 31: 2 3 8 5 2 6 5 N SD: 9.1055 c. M:-14.4585 c. 33: 2 3 9 5 2 6 6 N SD: 8.8242 c. M: 14.2718 c. 34: 2 3 9 6 2 6 6 N SD: 6.7552 c. M:-11.5547 c. 36: 2 3 10 6 2 7 6 N SD: 6.4074 c. M: 15.7370 c. 39: 2 4 10 7 2 7 7 N SD: 5.6446 c. M: 11.4746 c. 41: 2 4 11 7 2 8 7 N SD: 3.4364 c. M: 6.7940 c. 53: 3 5 14 9 3 10 9 N SD: 2.6792 c. M:-4.9636 c. 58: 3 6 15 10 3 11 10 N SD: 2.0354 c. M:-3.8032 c. 72: 4 7 19 12 4 14 12 N SD: 2.4081 c. M:-3.9100 c. 77: 4 8 20 13 4 15 13 N SD: 1.9219 c. M:-4.6093 c. 94: 5 9 25 16 5 18 16 N SD: 1.4911 c. M: 3.6803 c. 99: 5 10 26 17 5 19 17 N SD: 1.4374 c. M: 2.3548 c. 113: 6 11 30 19 6 22 19 N SD: 1.2563 c. M:-2.1401 c. 118: 6 12 31 20 6 23 20 N SD: 1.1626 c. M: 2.2040 c. 130: 7 13 34 22 7 25 22 N SD: 1.2073 c. M:-2.2117 c. 152: 8 15 40 26 8 29 26 N SD: 0.7772 c. M: 1.3532 c. 171: 9 17 45 29 9 33 29 N SD: 0.2011 c. M:-0.4012 c. 441: 23 44 116 75 23 85 75 N SD: 0.1992 c. M: 0.3759 c. 494: 26 49 130 84 26 95 84 N SD: 0.1629 c. M:-0.2663 c. 571: 30 57 150 97 30 110 97 N SD: 0.1705 c. M:-0.4334 c. 612: 32 61 161 104 32 118 104 N SD: 0.1155 c. M: 0.2158 c. 665: 35 66 175 113 35 128 113 N SD: 0.1192 c. M:-0.1970 c. 783: 41 78 206 133 41 151 133 N SD: 0.0871 c. M: 0.1649 c. 935: 49 93 246 159 49 180 159 N SD: 0.0970 c. M: 0.1577 c. 954: 50 95 251 162 50 184 162 N SD: 0.0855 c. M:-0.1364 c. 1065: 56 106 280 181 56 205 181 N SD: 0.0940 c. M:-0.1545 c. 1106: 58 110 291 188 58 213 188 N SD: 0.0582 c. M: 0.1252 c. 1277: 67 127 336 217 67 246 217 N SD: 0.0384 c. M: 0.1014 c. 1448: 76 144 381 246 76 279 246 N SD: 0.0381 c. M: 0.0833 c. 1506: 79 150 396 256 79 290 256 N SD: 0.0437 c. M: 0.0741 c. 1677: 88 167 441 285 88 323 285 N SD: 0.0286 c. M:-0.0650 c. 1848: 97 184 486 314 97 356 314 N SD: 0.0278 c. M:-0.0638 c. 2019: 106 201 531 343 106 389 343 N SD: 0.0362 c. M:-0.0629 c. 2289: 120 228 602 389 120 441 389 N SD: 0.0296 c. M: 0.0513 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 x 5:6 x 7:8 S SD: 28.7524 cents 5 x 6:7 x 8:9:10 S SD: 33.3035 cents 6 x 7:8:9 x 11:12 SD: 19.9727 cents 7 x 8:9 x 11:12:14 SD: 20.6064 cents 8 x 9:11:12 x 14:16 SD: 12.7183 cents 9 x 10:12 x 14:16:18 S SD: 0.0000 cents 10 x 11:13:15:16:18:20 SD: 11.8614 cents 11 x 12:15 x 17:20:22 SD: 12.9053 cents 12 x 13:16:18:19:21:24 SD: 10.0048 cents 13 x 14:17 x 20:23:26 SD: 13.4061 cents 14:15:16:19:21:22:25:28 SD: 11.8460 cents 15:16:17:20 x 23:27:30 SD: 11.3491 cents 16:17:18:21:24:25:28:32 SD: 8.7740 cents 17:18:19:23 x 26:30:34 SD: 9.2221 cents 18:19:20:24:27:28:32:36 S SD: 4.3774 cents 26:27:29:35:39:40:46:52 SD: 3.9379 cents 27:28:30:36:41:42:48:54 SD: 3.0346 cents 36:37:40:48:54:56:64:72 SD: 2.2181 cents 52:54:58:69:78:81:92:104 SD: 1.9933 cents 54:56:60:72:81:84:96:108 S SD: 0.0000 cents