Scala analysis: xen11-chalmers-tetrachordal-04-02b
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: 22/21 80.537035 undecimal minor semitone 2: 8/7 231.174094 septimal 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: 22/21 80.5370 undecimal minor semitone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 7/6 266.8709 septimal 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: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 33/28 284.447 cents undecimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 21/16 470.781 cents narrow fourth 3: 1 9/7 435.084 cents septimal major third, BP third 3: 3 4/3 498.045 cents perfect fourth 3: 1 66/49 515.621 cents 3: 1 49/36 533.742 cents Arabic lute acute fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 1 72/49 666.258 cents Arabic lute grave fifth 4: 1 49/33 684.379 cents 4: 3 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 1 32/21 729.219 cents wide fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 11/7 782.492 cents undecimal augmented fifth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 56/33 915.553 cents 5: 1 12/7 933.129 cents septimal major sixth 5: 1 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 21/11 1119.463 cents undecimal major seventh 6: 1 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 80.5 231.2 498.0 702.0 764.9 996.1 1200.0 80.5 : 150.6 417.5 621.4 684.4 915.6 1119.5 1200.0 231.2 : 266.9 470.8 533.7 764.9 968.8 1049.4 1200.0 498.0 : 203.9 266.9 498.0 702.0 782.5 933.1 1200.0 702.0 : 63.0 294.1 498.0 578.6 729.2 996.1 1200.0 764.9 : 231.2 435.1 515.6 666.3 933.1 1137.0 1200.0 996.1 : 203.9 284.4 435.1 702.0 905.9 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 266.8709 cents 9/8, 203.9100 cents 28/27, 62.9609 cents 2: 231.1741 .. 470.7809 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 6: 933.1291 .. 1137.0391 cents 9/8, 203.9100 cents 48/49,-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 : 7/6, 266.8709 cents Average / Smallest step : 2.722778 Largest / Average step : 1.556747 Largest / Smallest step : 4.238677 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 164.61400 cents, oct.: 1152.29799 cents Scale is not proper Step pattern alph. order: ABCDEFD Step pattern size order : BCFDAED Scale is not a Constant Structure Scale diversity : 1.545848 Lumma stability : 0.104935 Lumma impropriety factor : 0.154686 Rothenberg efficiency : 0.368707 redundancy: 0.631293 Efficiency x scale size : 2.580952 Number of different interval sizes : 30 = 5.00000 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 6.00000 = 6 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 896/891, 9.6880 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 3 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 3, 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 -- Rational properties -- Prime limit : 11 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.019322 Average absolute harmonicity : 0.251530 Specific harmonicity : 0.136450 Fundamental : 1/126, -6.9773 octaves, 2.0764 Hz. Guide tone : 3696, 11.8517 octaves, 966968.089 Hz. Exponens Consonantiae : 4.656960E+05, 18.82903 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 60.5, average 8.64286 Mersenne's string divisions : 519225 Sum of van Prooijen's expressibility: 5.03004, average 0.71858 Sum of Tenney's harmonic distance : 10.82993, average 1.54713 Vogel's harmonic complexity : 14.00000 Wille's k value : 94 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 75.64845, average 2.70173 Lattice compactness (without 2's) : 46.86511, average 1.67375 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.57143 13 1 3: -2 .. 1 -0.71429 7 3 7: -1 .. 1 -0.14286 3 2 11: 0 .. 1 0.14286 1 1 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 10 22 23| Scale is weakly epimorphic with val: <7 11 20 26| Scale is weakly epimorphic with val: <7 12 18 22| Scale is weakly epimorphic with val: <7 12 20 24|
FIT/MODE
7: 0 1 2 1 0 2 1 N T3 SD: 50.5840 c. M: 80.5370 c. 10: 1 1 2 2 0 2 2 P D3 S SD: 28.3004 c. M: 44.9159 c. 12: 1 1 3 2 1 2 2 N SD: 19.2890 c. M:-35.0841 c. Mela Ratnangi, Raga Phenadyuti 14: 1 2 3 2 1 3 2 P T3 SD: 18.2293 c. M:-32.4814 c. 17: 1 2 4 3 1 3 3 N SD: 10.0126 c. M: 19.4094 c. 25: 2 3 5 5 1 5 4 N SD: 12.6469 c. M:-18.0450 c. 26: 2 3 6 4 2 5 4 N SD: 12.4511 c. M:-19.6995 c. 27: 2 3 6 5 1 5 5 N SD: 10.2853 c. M: 18.3122 c. 29: 2 4 6 5 1 6 5 N SD: 10.1018 c. M: 20.0883 c. 31: 2 4 7 5 2 6 5 N SD: 6.0712 c. M:-10.3616 c. 36: 2 5 8 6 2 7 6 N SD: 5.6448 c. M: 13.8704 c. 41: 3 5 9 7 2 8 7 N SD: 3.3506 c. M:-7.2678 c. 57: 4 7 13 9 3 11 10 N SD: 5.4894 c. M:-7.2182 c. 58: 4 7 13 10 3 11 10 N SD: 2.1230 c. M: 3.5879 c. 72: 5 9 16 12 4 14 12 N SD: 2.3446 c. M:-3.9100 c. 77: 5 10 17 13 4 15 13 N SD: 1.5937 c. M: 2.6150 c. 94: 6 12 21 16 5 18 16 N SD: 1.6354 c. M: 3.9413 c. 118: 8 15 26 20 6 23 20 N SD: 1.3813 c. M:-2.7242 c. 130: 9 16 29 22 7 25 22 N SD: 1.1457 c. M:-2.5399 c. 135: 9 17 30 23 7 26 23 N SD: 0.3671 c. M: 0.5370 c. 342: 23 43 76 58 18 66 58 N SD: 0.2486 c. M:-0.4049 c. 400: 27 50 89 68 21 77 68 N SD: 0.1942 c. M:-0.4630 c. 477: 32 60 106 81 25 92 81 N SD: 0.1319 c. M:-0.2724 c. 535: 36 67 119 91 28 103 91 N SD: 0.1363 c. M:-0.2106 c. 612: 41 77 136 104 32 118 104 N SD: 0.1223 c. M: 0.2100 c. 742: 50 93 165 126 39 143 126 N SD: 0.1436 c. M:-0.3255 c. 836: 56 105 186 142 44 161 142 N SD: 0.0954 c. M:-0.1559 c. 877: 59 110 195 149 46 169 149 N SD: 0.0800 c. M:-0.1927 c. 1012: 68 127 225 172 53 195 172 N SD: 0.0576 c. M:-0.0954 c. 1371: 92 172 305 233 72 264 233 N SD: 0.0494 c. M: 0.1019 c. 1506: 101 189 335 256 79 290 256 N SD: 0.0560 c. M: 0.0984 c. 1713: 115 215 381 291 90 330 291 N SD: 0.0354 c. M:-0.0578 c. 1848: 124 232 411 314 97 356 314 N SD: 0.0119 c. M:-0.0192 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: 26.1614 cents 6 x 7:8:9 x 11:12 SD: 12.8254 cents 7 x 8:9 x 11:12:14 SD: 18.1517 cents 8 x 9:11:12 x 14:16 SD: 13.1524 cents 9 x 10:12 x 14:16:18 S SD: 9.7541 cents 10 x 11:13:15:16:18:20 SD: 15.9345 cents 11:12:13:15 x 17:20:22 SD: 17.8237 cents 12:13:14:16:18:19:21:24 SD: 11.3611 cents 13:14:15:17 x 20:23:26 SD: 10.6995 cents 14:15:16:19:21:22:25:28 SD: 7.5876 cents 15:16:17:20 x 23:27:30 SD: 7.9338 cents 16:17:18:21:24:25:28:32 SD: 7.6741 cents 17:18:19:23 x 26:30:34 SD: 9.8510 cents 18:19:21:24:27:28:32:36 SD: 5.4304 cents 20:21:23:27:30:31:36:40 SD: 4.7277 cents 22:23:25:29:33:34:39:44 SD: 3.6507 cents 36:38:41:48:54:56:64:72 SD: 2.0553 cents 42:44:48:56:63:65:75:84 SD: 1.6775 cents 63:66:72:84:95:98:112:126 SD: 1.3051 cents 84:88:96:112:126:131:149:168 SD: 0.8381 cents 90:94:103:120:135:140:160:180 SD: 0.8254 cents 104:109:119:139:156:162:185:208 SD: 0.7680 cents 126:132:144:168:189:196:224:252 S SD: 0.0000 cents