Scala analysis: xen11-chalmers-tetrachordal-06-02
Transposition by B
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: 16/15 111.731285 minor diatonic semitone 3: 448/405 174.692189 4: 256/225 223.462571 Neapolitan diminished third 5: 4/3 498.044999 perfect fourth 6: 64/45 609.776284 2nd tritone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 45/32 590.2237 diatonic tritone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 75/64 274.5824 classic augmented second 6: 16/15 111.7313 minor diatonic semitone 7: 45/32 590.2237 diatonic tritone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 75/64 274.582 cents classic augmented second 1: 1 45/32 590.224 cents diatonic tritone 2: 3 16/15 111.731 cents minor diatonic semitone 2: 1 135/112 323.353 cents septimal wide minor third 2: 1 5/4 386.314 cents major third 2: 1 35/24 653.185 cents septimal semi-diminished fifth 2: 1 3/2 701.955 cents perfect fifth 3: 1 192/175 160.502 cents septimal 4/5-tone 3: 1 448/405 174.692 cents 3: 1 5/4 386.314 cents major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 1 3/2 701.955 cents perfect fifth 3: 1 14/9 764.916 cents septimal minor sixth 3: 1 225/128 976.537 cents augmented sixth 4: 1 256/225 223.463 cents Neapolitan diminished third 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 4/3 498.045 cents perfect fourth 4: 1 14/9 764.916 cents septimal minor sixth 4: 1 8/5 813.686 cents minor sixth 4: 1 405/224 1025.308 cents 4: 1 175/96 1039.498 cents 5: 1 4/3 498.045 cents perfect fourth 5: 1 48/35 546.815 cents septimal semi-augmented fourth 5: 1 8/5 813.686 cents minor sixth 5: 1 224/135 876.647 cents narrow septimal major sixth 5: 3 15/8 1088.269 cents classic major seventh 6: 1 64/45 609.776 cents 2nd tritone 6: 1 128/75 925.418 cents diminished seventh 6: 1 15/8 1088.269 cents classic major seventh 6: 2 27/14 1137.039 cents septimal major seventh 6: 2 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.66667 = 17/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 63.0 111.7 174.7 223.5 498.0 609.8 1200.0 63.0 : 48.8 111.7 160.5 435.1 546.8 1137.0 1200.0 111.7 : 63.0 111.7 386.3 498.0 1088.3 1151.2 1200.0 174.7 : 48.8 323.4 435.1 1025.3 1088.3 1137.0 1200.0 223.5 : 274.6 386.3 976.5 1039.5 1088.3 1151.2 1200.0 498.0 : 111.7 702.0 764.9 813.7 876.6 925.4 1200.0 609.8 : 590.2 653.2 702.0 764.9 813.7 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 590.2237 cents 175/128, 541.4533 cents 36/35, 48.7704 cents 2: 111.7313 .. 701.9550 cents 45/32, 590.2237 cents 512/675,-478.4924 cents 3: 160.5017 .. 976.5374 cents 13125/8192, 816.0358 cents 128/175,-541.4533 cents 4: 223.4626 .. 1039.4983 cents 13125/8192, 816.0358 cents 32768/50625,-753.0749 cents 5: 498.0450 .. 1088.2687 cents 45/32, 590.2237 cents 128/175,-541.4533 cents 6: 609.7763 .. 1151.2296 cents 175/128, 541.4533 cents 512/675,-478.4924 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 45/32, 590.2237 cents Average / Smallest step : 3.515014 Largest / Average step : 3.442972 Largest / Smallest step : 12.102093 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 116.09452 cents, oct.: 812.66165 cents Scale is not proper Step pattern alph. order: ABABCDE Step pattern size order : BABADCE Scale is not a Constant Structure Scale diversity : 1.638891 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 7 Mean interval variety : 5.66667 = 17/3 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 245/243, 14.1905 cents Most common intervals : 16/15, 111.7313 cents & inv., amount: 4 Most common triad is 0.0 1088.269 1151.230 cents, amount: 2 Number of recognisable fifths : 2, average 701.9550 cents Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 7 Odd number limit : 405 (O: 405 U: 405) Highest odd numerator or denominator: 405 Scale harmonicity : 0.023951 Average absolute harmonicity : 0.209250 Specific harmonicity : 0.130356 Fundamental : 1/2025, -10.9837 octaves, 0.1292 Hz. Guide tone : 1792, 10.8074 octaves, 468833.013 Hz. Exponens Consonantiae : 3.628800E+06, 21.79106 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 769.5, average 109.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.69743, average 1.38535 Sum of Tenney's harmonic distance : 20.11749, average 2.87393 Vogel's harmonic complexity : 19.00000 Wille's k value : 1012 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 117.50259, average 4.19652 Lattice compactness (without 2's) : 59.27752, average 2.11705 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 8 4.14286 29 1 3: -4 .. 0 -1.85714 13 1 5: -2 .. 0 -0.71429 5 3 7: 0 .. 1 0.28571 2 2 Average exponent except 2's :-16 / 7 =-2.28571 Average absolute exponent except 2's: 20 / 7 = 2.85714 Scale is weakly epimorphic with val: <7 11 15 18| Scale is weakly epimorphic with val: <7 12 17 19|
FIT/MODE
7: 0 1 0 0 2 1 3 N SD: 48.2203 c. M:-75.9380 c. 10: 0 1 0 1 2 1 5 N SD: 33.2058 c. M: 62.9609 c. 12: 1 0 1 0 3 1 6 N SD: 19.9996 c. M:-37.0391 c. 14: 1 0 1 1 3 1 7 N SD: 19.6358 c. M:-33.6803 c. 15: 1 0 1 1 3 2 7 N SD: 20.7903 c. M: 31.7313 c. 16: 1 0 1 1 4 1 8 N SD: 20.4532 c. M: 36.7313 c. 17: 1 1 1 0 4 2 8 N SD: 21.0543 c. M:-37.0725 c. 18: 1 1 1 0 4 2 9 N SD: 19.8262 c. M: 31.3783 c. 19: 1 1 1 1 4 2 9 N SD: 16.0781 c. M:-29.1690 c. 20: 1 1 1 1 4 2 10 N SD: 10.6904 c. M: 18.0450 c. 21: 1 1 1 1 5 2 10 N SD: 9.9581 c. M:-18.7951 c. 22: 1 1 1 1 5 2 11 N SD: 7.3135 c. M: 11.0558 c. 33: 2 1 2 1 8 3 16 N SD: 7.3064 c. M:-11.0459 c. 34: 2 1 2 1 8 3 17 N SD: 7.0040 c. M: 11.6979 c. 41: 2 2 2 2 9 4 20 N SD: 5.1676 c. M:-10.6838 c. 43: 2 2 2 2 10 4 21 N SD: 4.4637 c. M: 7.2503 c. 53: 3 2 3 2 12 5 26 N SD: 3.3678 c. M:-6.4399 c. 55: 3 2 3 2 13 5 27 N SD: 2.8440 c. M: 5.2808 c. 75: 4 3 4 3 17 7 37 N SD: 1.2241 c. M: 2.0450 c. 96: 5 4 5 4 22 9 47 N SD: 1.4394 c. M:-2.7237 c. 118: 6 5 6 5 27 11 58 N SD: 1.0260 c. M: 1.9440 c. 130: 7 5 7 5 30 12 64 N SD: 1.0899 c. M: 1.9241 c. 171: 9 7 9 7 39 16 84 N SD: 0.6220 c. M:-1.0988 c. 193: 10 8 10 8 44 18 95 N SD: 0.5005 c. M: 0.7847 c. 248: 13 10 13 10 57 23 122 N SD: 0.4393 c. M: 0.8819 c. 289: 15 12 15 12 66 27 142 N SD: 0.4903 c. M:-0.7589 c. 301: 16 12 16 12 69 28 148 N SD: 0.4443 c. M:-0.8265 c. 323: 17 13 17 13 74 30 159 N SD: 0.3185 c. M: 0.5524 c. 419: 22 17 22 17 96 39 206 N SD: 0.1469 c. M:-0.2844 c. 494: 26 20 26 20 113 46 243 N SD: 0.1136 c. M:-0.2066 c. 612: 32 25 32 25 140 57 301 N SD: 0.1110 c. M: 0.2158 c. 913: 48 37 48 37 209 85 449 N SD: 0.0809 c. M:-0.1278 c. 1031: 54 42 54 42 236 96 507 N SD: 0.0839 c. M:-0.1170 c. 1106: 58 45 58 45 253 103 544 N SD: 0.0266 c. M:-0.0456 c. 1525: 80 62 80 62 349 142 750 N SD: 0.0310 c. M:-0.0598 c. 2019: 106 82 106 82 462 188 993 N SD: 0.0285 c. M:-0.0478 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3:4 S SD: 46.0894 cents 3 x x x x 4 x 6 S SD: 0.0000 cents 4 x x x x 5:6:8 S SD: 48.2825 cents 5 x x x 6 x 7:10 SD: 32.0421 cents 6 x x x 7:8:9:12 S SD: 25.4720 cents 7 x x x 8:9:10:14 SD: 15.9746 cents 8 x x x 9:11 x 16 SD: 18.9159 cents 9 x x 10 x 12:13:18 SD: 6.9818 cents 10 x x 11 x 13:14:20 SD: 13.1300 cents 11 x x 12:13:15:16:22 SD: 17.8086 cents 12 x 13 x 14:16:17:24 SD: 10.2969 cents 13 x 14 x 15:17:18:26 SD: 12.8786 cents 14 x 15 x 16:19:20:28 SD: 6.6853 cents 15 x 16 x 17:20:21:30 SD: 5.6187 cents 16 x 17 x 18:21:23:32 SD: 7.7813 cents 17 x 18:19 x 23:24:34 SD: 7.1678 cents 18 x 19:20 x 24:26:36 SD: 6.6590 cents 19 x 20:21:22:25:27:38 SD: 7.4093 cents 20:21 x 22:23:27:28:40 SD: 7.6456 cents 21:22 x 23:24:28:30:42 SD: 4.4835 cents 22:23 x 24:25:29:31:44 SD: 6.2993 cents 23:24 x 25:26:31:33:46 SD: 6.9583 cents 24:25:26 x 27:32:34:48 SD: 5.7931 cents 25:26:27:28 x 33:36:50 SD: 6.9015 cents 26:27:28:29:30:35:37:52 SD: 5.2513 cents 27:28:29:30:31:36:38:54 SD: 3.9857 cents 28:29:30:31:32:37:40:56 SD: 2.9509 cents 29:30:31:32:33:39:41:58 SD: 2.7743 cents 30:31:32:33:34:40:43:60 SD: 2.7092 cents 45:47:48:50:51:60:64:90 SD: 2.2911 cents 56:58:60:62:64:75:80:112 SD: 2.2363 cents 57:59:61:63:65:76:81:114 SD: 1.1275 cents 102:106:109:113:116:136:145:204 SD: 0.8005 cents 132:137:141:146:150:176:188:264 SD: 0.6180 cents 161:167:172:178:183:215:229:322 SD: 0.6129 cents 168:174:179:186:191:224:239:336 SD: 0.5135 cents 210:218:224:232:239:280:299:420 SD: 0.4941 cents 225:233:240:249:256:300:320:450 SD: 0.3704 cents 270:280:288:299:307:360:384:540 SD: 0.3194 cents 327:339:349:362:372:436:465:654 SD: 0.2573 cents 348:361:371:385:396:464:495:696 SD: 0.1640 cents 405:420:432:448:461:540:576:810 SD: 0.1073 cents