Scala analysis: xen12-hanson-02-ten
Ten tones, Figure 2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 6/5 315.641287 minor third 3: 5/4 386.313714 major third 4: 4/3 498.044999 perfect fourth 5: 3/2 701.955001 perfect fifth 6: 8/5 813.686286 minor sixth 7: 5/3 884.358713 major sixth, BP sixth 8: 9/5 1017.596288 just minor seventh, BP seventh 9: 15/8 1088.268715 classic major seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 9/8 203.9100 major whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 16/15 111.7313 minor diatonic semitone 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 25/24 70.6724 classic chromatic semitone, minor chroma 8: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 4 16/15 111.731 cents minor diatonic semitone 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 2 9/8 203.910 cents major whole tone 2: 4 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 4 6/5 315.641 cents minor third 3: 1 75/64 274.582 cents classic augmented second 3: 1 32/27 294.135 cents Pythagorean minor third 3: 2 6/5 315.641 cents minor third 3: 4 5/4 386.314 cents major third 3: 2 32/25 427.373 cents classic diminished fourth 4: 2 5/4 386.314 cents major third 4: 6 4/3 498.045 cents perfect fourth 4: 2 27/20 519.551 cents acute fourth 5: 1 4/3 498.045 cents perfect fourth 5: 2 25/18 568.717 cents classic augmented fourth 5: 2 45/32 590.224 cents diatonic tritone 5: 2 64/45 609.776 cents 2nd tritone 5: 2 36/25 631.283 cents classic diminished fifth 5: 1 3/2 701.955 cents perfect fifth 6: 2 40/27 680.449 cents grave fifth 6: 6 3/2 701.955 cents perfect fifth 6: 2 8/5 813.686 cents minor sixth 7: 2 25/16 772.627 cents classic augmented fifth 7: 4 8/5 813.686 cents minor sixth 7: 2 5/3 884.359 cents major sixth, BP sixth 7: 1 27/16 905.865 cents Pythagorean major sixth 7: 1 128/75 925.418 cents diminished seventh 8: 4 5/3 884.359 cents major sixth, BP sixth 8: 2 16/9 996.090 cents Pythagorean minor seventh 8: 4 9/5 1017.596 cents just minor seventh, BP seventh 9: 2 16/9 996.090 cents Pythagorean minor seventh 9: 1 50/27 1066.762 cents grave major seventh 9: 4 15/8 1088.269 cents classic major seventh 9: 3 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 203.9 315.6 386.3 498.0 702.0 813.7 884.4 1017.6 1088.3 1200.0 203.9 : 111.7 182.4 294.1 498.0 609.8 680.4 813.7 884.4 996.1 1200.0 315.6 : 70.7 182.4 386.3 498.0 568.7 702.0 772.6 884.4 1088.3 1200.0 386.3 : 111.7 315.6 427.4 498.0 631.3 702.0 813.7 1017.6 1129.3 1200.0 498.0 : 203.9 315.6 386.3 519.6 590.2 702.0 905.9 1017.6 1088.3 1200.0 702.0 : 111.7 182.4 315.6 386.3 498.0 702.0 813.7 884.4 996.1 1200.0 813.7 : 70.7 203.9 274.6 386.3 590.2 702.0 772.6 884.4 1088.3 1200.0 884.4 : 133.2 203.9 315.6 519.6 631.3 702.0 813.7 1017.6 1129.3 1200.0 1017.6: 70.7 182.4 386.3 498.0 568.7 680.4 884.4 996.1 1066.8 1200.0 1088.3: 111.7 315.6 427.4 498.0 609.8 813.7 925.4 996.1 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 203.9100 cents 27/25, 133.2376 cents 25/24, 70.6724 cents 2: 182.4037 .. 315.6413 cents 27/25, 133.2376 cents 80/81,-21.5063 cents 3: 274.5824 .. 427.3726 cents 2048/1875, 152.7901 cents 125/128,-41.0589 cents 4: 386.3137 .. 519.5513 cents 27/25, 133.2376 cents 125/128,-41.0589 cents 5: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 80/81,-21.5063 cents 6: 680.4487 .. 813.6863 cents 27/25, 133.2376 cents 80/81,-21.5063 cents 7: 772.6274 .. 925.4176 cents 2048/1875, 152.7901 cents 125/128,-41.0589 cents 8: 884.3587 .. 1017.5963 cents 27/25, 133.2376 cents 125/128,-41.0589 cents 9: 996.0900 .. 1129.3276 cents 27/25, 133.2376 cents 80/81,-21.5063 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.697975 Largest / Average step : 1.699250 Largest / Smallest step : 2.885284 Median interval of one step : 16/15, 111.7313 cents, amount: 4 Most common interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 125.98417 cents, oct.: 1259.84172 cents Scale is not proper Step pattern alph. order: ABCBABCDCB Step pattern size order : DBABDBACAB Scale is not a Constant Structure Scale diversity : 1.364981 Lumma stability : 0.117787 Lumma impropriety factor : 0.208550 Rothenberg efficiency : 0.447857 redundancy: 0.552143 Efficiency x scale size : 4.478571 Number of different interval sizes : 28 = 3.11111 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.00000 = 4 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Number of recognisable fifths : 7, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 5 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 70.0000% Scale is n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 6 and 7 combined Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 7-8 -- Rational properties -- Prime limit : 5 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 15 Scale harmonicity : 0.037313 Average absolute harmonicity : 0.221017 Specific harmonicity : 0.198621 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 4.320000E+04, 15.39874 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 55.0, average 5.50000 Mersenne's string divisions : 140900760 Sum of van Prooijen's expressibility: 6.83470, average 0.68347 Sum of Tenney's harmonic distance : 13.30439, average 1.33044 Vogel's harmonic complexity : 12.30000 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 165.98973, average 3.01800 Lattice compactness (without 2's) : 92.56848, average 1.68306 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 -0.20000 16 1 3: -1 .. 2 0.50000 9 3 5: -1 .. 1 0.00000 6 6 Average exponent except 2's : 5 / 10 = 0.50000 Average absolute exponent except 2's: 15 / 10 = 1.50000
FIT/MODE
10: 2 1 0 1 2 1 0 1 1 1 N T3 SD: 32.6491 c. M: 57.5963 c. 11: 2 1 0 1 2 1 1 1 1 1 N D3 SD: 37.1543 c. M: 61.6814 c. 12: 2 1 1 1 2 1 1 1 1 1 P D3 SD: 11.5504 c. M: 17.5963 c. Major/Minor mixed, Supermode 19: 3 2 1 2 3 2 1 2 1 2 N G SD: 8.2697 c. M: 14.5845 c. 31: 5 3 2 3 5 3 2 3 2 3 N G SD: 6.1396 c. M: 11.1447 c. Major/Minor mixed, Supermode 34: 6 3 2 3 6 3 2 4 2 3 N SD: 4.2117 c. M:-7.8547 c. 41: 7 4 2 4 7 4 2 5 2 4 N SD: 4.7288 c. M:-6.7940 c. 46: 8 4 3 4 8 4 3 5 3 4 N SD: 3.9016 c. M:-7.3835 c. 53: 9 5 3 5 9 5 3 6 3 5 N SD: 1.0668 c. M: 1.4763 c. 118: 20 11 7 11 20 11 7 13 7 11 N SD: 0.3427 c. M: 0.6471 c. 171: 29 16 10 16 29 16 10 19 10 16 N SD: 0.2887 c. M: 0.5494 c. 289: 49 27 17 27 49 27 17 32 17 27 N SD: 0.2434 c. M: 0.4498 c. 323: 55 30 19 30 55 30 19 36 19 30 N SD: 0.2299 c. M:-0.4244 c. 388: 66 36 23 36 66 36 23 43 23 36 N SD: 0.2123 c. M:-0.3911 c. 441: 75 41 26 41 75 41 26 49 26 41 N SD: 0.0966 c. M:-0.1716 c. 559: 95 52 33 52 95 52 33 62 33 52 N SD: 0.0666 c. M:-0.1034 c. 612: 104 57 36 57 104 57 36 68 36 57 N SD: 0.0332 c. M:-0.0508 c. 1171: 199 109 69 109 199 109 69 130 69 109 N SD: 0.0172 c. M:-0.0319 c. 1783: 303 166 105 166 303 166 105 198 105 166 N SD: 0.0088 c. M:-0.0160 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x 4 x x 5 x x 6 S SD: 0.0000 cents 4 x x 5 x 6 x x 7 x 8 S SD: 12.1926 cents 5 x 6 x 7 x 8 x 9 x 10 S SD: 16.8934 cents 6 x 7 x 8:9 x 10:11 x 12 S SD: 9.7006 cents 7:8 x 9 x x 11:12 x 13:14 SD: 13.6910 cents 8:9 x 10:11:12:13 x 14:15:16 S SD: 9.6315 cents 9:10:11 x 12 x 14:15:16:17:18 S SD: 8.3628 cents 10:11:12 x 13:15:16:17:18:19:20 SD: 7.9628 cents 11:12:13:14:15:17 x 18:20:21:22 SD: 11.6425 cents 12 x 14:15:16:18:19:20:22:23:24 S SD: 7.9847 cents 13:15 x 16:17:20:21:22:23:24:26 SD: 10.1089 cents 14:16:17:18:19:21:22:23:25:26:28 SD: 8.0864 cents 15:17:18:19:20:23:24:25:27:28:30 SD: 4.6865 cents 24:27:29:30:32:36:38:40:43:45:48 SD: 2.3167 cents 39:44:47:49:52:59:62:65:70:73:78 SD: 2.3052 cents 40:45:48:50:53:60:64:67:72:75:80 SD: 1.3870 cents 64:72:77:80:85:96:102:107:115:120:128 SD: 1.2261 cents 72:81:86:90:96:108:115:120:130:135:144 SD: 1.0102 cents 80:90:96:100:107:120:128:133:144:150:160 SD: 0.6925 cents 96:108:115:120:128:144:154:160:173:180:192 SD: 0.5773 cents 120:135:144:150:160:180:192:200:216:225:240 SD: 0.0000 cents