Scala analysis: xen18-ayers-table-71
7 Weighted Mediants between 1/1 and 2/1
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6/5 315.641287 minor third 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 7/4 968.825906 harmonic seventh 7: 9/5 1017.596288 just minor seventh, BP seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 6/5 315.6413 minor third 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 21/20 84.4672 minor semitone 7: 36/35 48.7704 septimal diesis, 1/4-tone 8: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 1: 1 6/5 315.641 cents minor third 2: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 1 10/9 182.404 cents minor whole tone 2: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 4/3 498.045 cents perfect fourth 3: 2 6/5 315.641 cents minor third 3: 1 5/4 386.314 cents major third 3: 1 21/16 470.781 cents narrow fourth 3: 2 4/3 498.045 cents perfect fourth 3: 1 48/35 546.815 cents septimal semi-augmented fourth 3: 1 25/18 568.717 cents classic augmented fourth 4: 1 4/3 498.045 cents perfect fourth 4: 1 27/20 519.551 cents acute fourth 4: 1 25/18 568.717 cents classic augmented fourth 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 10/7 617.488 cents Euler's tritone 4: 1 36/25 631.283 cents classic diminished fifth 4: 1 40/27 680.449 cents grave fifth 4: 1 3/2 701.955 cents perfect fifth 5: 1 36/25 631.283 cents classic diminished fifth 5: 1 35/24 653.185 cents septimal semi-diminished fifth 5: 2 3/2 701.955 cents perfect fifth 5: 1 32/21 729.219 cents wide fifth 5: 1 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 3/2 701.955 cents perfect fifth 6: 2 8/5 813.686 cents minor sixth 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 12/7 933.129 cents septimal major sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 50/27 1066.762 cents grave major seventh 7: 1 5/3 884.359 cents major sixth, BP sixth 7: 1 16/9 996.090 cents Pythagorean minor seventh 7: 2 9/5 1017.596 cents just minor seventh, BP seventh 7: 1 15/8 1088.269 cents classic major seventh 7: 1 40/21 1115.533 cents acute major seventh 7: 1 48/25 1129.328 cents classic diminished octave 7: 1 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.85714 = 48/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 315.6 386.3 498.0 702.0 884.4 968.8 1017.6 1200.0 315.6 : 70.7 182.4 386.3 568.7 653.2 702.0 884.4 1200.0 386.3 : 111.7 315.6 498.0 582.5 631.3 813.7 1129.3 1200.0 498.0 : 203.9 386.3 470.8 519.6 702.0 1017.6 1088.3 1200.0 702.0 : 182.4 266.9 315.6 498.0 813.7 884.4 996.1 1200.0 884.4 : 84.5 133.2 315.6 631.3 702.0 813.7 1017.6 1200.0 968.8 : 48.8 231.2 546.8 617.5 729.2 933.1 1115.5 1200.0 1017.6: 182.4 498.0 568.7 680.4 884.4 1066.8 1151.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 315.6413 cents 7/6, 266.8709 cents 36/35, 48.7704 cents 2: 133.2376 .. 498.0450 cents 100/81, 364.8074 cents 9/10,-182.4037 cents 3: 315.6413 .. 568.7174 cents 125/108, 253.0761 cents 9/10,-182.4037 cents 4: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 24/25,-70.6724 cents 5: 631.2826 .. 884.3587 cents 125/108, 253.0761 cents 24/25,-70.6724 cents 6: 701.9550 .. 1066.7624 cents 100/81, 364.8074 cents 9/10,-182.4037 cents 7: 884.3587 .. 1151.2296 cents 7/6, 266.8709 cents 9/10,-182.4037 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 3.075637 Largest / Average step : 2.104275 Largest / Smallest step : 6.471987 Median interval of one step : 147.06750 cents, amount: 0 Most common interval of one step : 10/9, 182.4037 cents, amount: 2 Least squares average step : 158.56935 cents, oct.: 1268.55477 cents Scale is not proper Step pattern alph. order: ABCDEFGE Step pattern size order : GBDFECAE Scale is not a Constant Structure Scale diversity : 1.580943 Lumma stability : 0.081284 Lumma impropriety factor : 0.725800 Rothenberg efficiency : 0.359821 redundancy: 0.640179 Efficiency x scale size : 2.878571 Number of different interval sizes : 34 = 4.85714 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 6.85714 = 48/7 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 126/125, 13.7948 cents 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 3 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 62.5000% 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 classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 7 Odd number limit : 35 (O: 35 U: 35) Highest odd numerator or denominator: 9 Scale harmonicity : 0.028502 Average absolute harmonicity : 0.247789 Specific harmonicity : 0.190072 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 1260, 10.2992 octaves, 329648.212 Hz. Exponens Consonantiae : 7.560000E+04, 16.20610 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 34.0, average 4.25000 Mersenne's string divisions : 27720 Sum of van Prooijen's expressibility: 4.85049, average 0.60631 Sum of Tenney's harmonic distance : 9.21298, average 1.15162 Vogel's harmonic complexity : 11.50000 Wille's k value : 52 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 88.62303, average 2.46175 Lattice compactness (without 2's) : 57.66075, average 1.60169 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.12500 9 1 3: -1 .. 2 0.25000 6 2 5: -1 .. 1 0.00000 4 4 7: 0 .. 1 0.12500 1 1 Average exponent except 2's : 3 / 8 = 0.37500 Average absolute exponent except 2's: 11 / 8 = 1.37500
FIT/MODE
8: 2 1 0 2 1 0 1 1 N T3 SD: 43.2274 c. M: 68.8259 c. 9: 2 1 1 1 2 0 1 1 N D3 SD: 37.3204 c. M:-49.0704 c. 10: 2 1 1 2 1 1 0 2 N SD: 39.4148 c. M: 75.6413 c. 11: 3 1 1 1 2 1 0 2 N SD: 33.0147 c. M:-50.0499 c. 12: 3 1 1 2 2 1 0 2 N SD: 15.6753 c. M:-31.1741 c. 15: 4 1 1 3 2 1 1 2 N SD: 13.4925 c. M:-22.4037 c. 19: 5 1 2 3 3 1 1 3 N SD: 9.1441 c. M: 21.4575 c. 22: 6 1 2 4 3 2 1 3 N SD: 10.6867 c. M:-18.7673 c. 26: 7 1 3 4 4 2 1 4 N SD: 8.6139 c. M: 17.0829 c. 27: 7 2 2 5 4 2 1 4 N SD: 7.8864 c. M:-13.6863 c. 31: 8 2 3 5 5 2 1 5 N SD: 5.5992 c. M: 11.1447 c. 38: 10 2 4 6 6 3 1 6 N SD: 6.2344 c. M:-10.1215 c. 41: 11 2 4 7 6 3 2 6 N SD: 4.5966 c. M:-6.7940 c. 46: 12 3 4 8 7 3 2 7 N SD: 2.8044 c. M:-4.9906 c. 53: 14 3 5 9 8 4 2 8 N SD: 1.9316 c. M:-4.7590 c. 72: 19 4 7 12 11 5 3 11 N SD: 1.7377 c. M: 2.9804 c. 99: 26 6 9 17 15 7 4 15 N SD: 0.8905 c. M:-1.5651 c. 171: 45 10 16 29 26 12 7 26 N SD: 0.2271 c. M: 0.4049 c. 270: 71 16 25 46 41 19 11 41 N SD: 0.1997 c. M:-0.3530 c. 441: 116 26 41 75 67 31 18 67 N SD: 0.0738 c. M: 0.1184 c. 1053: 277 62 98 179 160 74 43 160 N SD: 0.0676 c. M: 0.1649 c. 1277: 336 75 119 217 194 90 52 194 N SD: 0.0699 c. M:-0.1014 c. 1407: 370 83 131 239 214 99 57 214 N SD: 0.0616 c. M: 0.1123 c. 1547: 407 91 144 263 235 109 63 235 N SD: 0.0587 c. M:-0.1154 c. 1578: 415 93 147 268 240 111 64 240 N SD: 0.0529 c. M: 0.1058 c. 1677: 441 99 156 285 255 118 68 255 N SD: 0.0582 c. M:-0.0906 c. 1718: 452 101 160 292 261 121 70 261 N SD: 0.0562 c. M:-0.0987 c. 1749: 460 103 163 297 266 123 71 266 N SD: 0.0556 c. M: 0.1006 c. 1848: 486 109 172 314 281 130 75 281 N SD: 0.0406 c. M: 0.0638 c. 2019: 531 119 188 343 307 142 82 307 N SD: 0.0341 c. M: 0.0629 c. 2190: 576 129 204 372 333 154 89 333 N SD: 0.0378 c. M: 0.0620 c. 2243: 590 132 209 381 341 158 91 341 N SD: 0.0335 c. M:-0.0551 c. 2289: 602 135 213 389 348 161 93 348 N SD: 0.0334 c. M:-0.0559 c. 2342: 616 138 218 398 356 165 95 356 N SD: 0.0337 c. M:-0.0896 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x x 6 S SD: 0.0000 cents 4 x 5 x 6 x 7 x 8 S SD: 0.0000 cents 5:6 x 7 x 8 x 9:10 S SD: 22.0266 cents 6:7 x 8:9:10 x 11:12 S SD: 9.7006 cents 7:8:9 x 11 x 12:13:14 SD: 23.6884 cents 8 x 10:11:12:13:14 x 16 S SD: 11.4978 cents 9:11 x 12:14:15 x 16:18 SD: 12.2879 cents 10:12 x 13:15:17 x 18:20 SD: 9.2743 cents 12:14:15:16:18:20:21:22:24 S SD: 7.2755 cents 13 x 16:17:20:22:23 x 26 SD: 11.5811 cents 14:17:18:19:21:23 x 25:28 SD: 9.6342 cents 15:18:19:20:23:25:26:27:30 SD: 5.9268 cents 16:19:20:21:24:27:28:29:32 SD: 5.1205 cents 18:22:23:24:27:30 x 32:36 SD: 7.7189 cents 19:23:24:25:29:32:33:34:38 SD: 6.3641 cents 20:24:25:27:30:33:35:36:40 SD: 3.4579 cents 24:29:30:32:36:40:42:43:48 SD: 1.8031 cents 36:43:45:48:54:60:63:65:72 SD: 1.2055 cents 60:72:75:80:90:100:105:108:120 S SD: 0.0000 cents