Scala analysis: zorro
zarlino union inverted zarlino
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 9/8 203.910002 major whole tone 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 3/2 701.955001 perfect fifth 7: 8/5 813.686286 minor sixth 8: 5/3 884.358713 major sixth, BP sixth 9: 16/9 996.089998 Pythagorean minor seventh 10: 15/8 1088.268715 classic major seventh 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 16/15 111.7313 minor diatonic semitone 2: 135/128 92.1787 major chroma, major limma 3: 16/15 111.7313 minor diatonic semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 16/15 111.7313 minor diatonic semitone 6: 9/8 203.9100 major whole tone 7: 16/15 111.7313 minor diatonic semitone 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 16/15 111.7313 minor diatonic semitone 10: 135/128 92.1787 major chroma, major limma 11: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 135/128 92.179 cents major chroma, major limma 1: 6 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 2: 4 10/9 182.404 cents minor whole tone 2: 4 9/8 203.910 cents major whole tone 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 2 6/5 315.641 cents minor third 3: 2 75/64 274.582 cents classic augmented second 3: 2 32/27 294.135 cents Pythagorean minor third 3: 4 6/5 315.641 cents minor third 3: 2 5/4 386.314 cents major third 3: 1 32/25 427.373 cents classic diminished fourth 4: 4 5/4 386.314 cents major third 4: 1 81/64 407.820 cents Pythagorean major third 4: 2 32/25 427.373 cents classic diminished fourth 4: 4 4/3 498.045 cents perfect fourth 5: 4 4/3 498.045 cents perfect fourth 5: 2 27/20 519.551 cents acute fourth 5: 1 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 6: 2 45/32 590.224 cents diatonic tritone 6: 2 64/45 609.776 cents 2nd tritone 6: 1 36/25 631.283 cents classic diminished fifth 6: 2 40/27 680.449 cents grave fifth 6: 4 3/2 701.955 cents perfect fifth 7: 4 3/2 701.955 cents perfect fifth 7: 2 25/16 772.627 cents classic augmented fifth 7: 1 128/81 792.180 cents Pythagorean minor sixth 7: 4 8/5 813.686 cents minor sixth 8: 1 25/16 772.627 cents classic augmented fifth 8: 2 8/5 813.686 cents minor sixth 8: 4 5/3 884.359 cents major sixth, BP sixth 8: 2 27/16 905.865 cents Pythagorean major sixth 8: 2 128/75 925.418 cents diminished seventh 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 1 225/128 976.537 cents augmented sixth 9: 4 16/9 996.090 cents Pythagorean minor seventh 9: 4 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 6 15/8 1088.269 cents classic major seventh 10: 2 256/135 1107.821 cents octave - major chroma 10: 2 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.40000 = 22/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 111.7 203.9 315.6 386.3 498.0 702.0 813.7 884.4 996.1 1088.3 1200.0 111.7 : 92.2 203.9 274.6 386.3 590.2 702.0 772.6 884.4 976.5 1088.3 1200.0 203.9 : 111.7 182.4 294.1 498.0 609.8 680.4 792.2 884.4 996.1 1107.8 1200.0 315.6 : 70.7 182.4 386.3 498.0 568.7 680.4 772.6 884.4 996.1 1088.3 1200.0 386.3 : 111.7 315.6 427.4 498.0 609.8 702.0 813.7 925.4 1017.6 1129.3 1200.0 498.0 : 203.9 315.6 386.3 498.0 590.2 702.0 813.7 905.9 1017.6 1088.3 1200.0 702.0 : 111.7 182.4 294.1 386.3 498.0 609.8 702.0 813.7 884.4 996.1 1200.0 813.7 : 70.7 182.4 274.6 386.3 498.0 590.2 702.0 772.6 884.4 1088.3 1200.0 884.4 : 111.7 203.9 315.6 427.4 519.6 631.3 702.0 813.7 1017.6 1129.3 1200.0 996.1 : 92.2 203.9 315.6 407.8 519.6 590.2 702.0 905.9 1017.6 1088.3 1200.0 1088.3: 111.7 223.5 315.6 427.4 498.0 609.8 813.7 925.4 996.1 1107.8 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 .. 498.0450 cents 16/15, 111.7313 cents 125/128,-41.0589 cents 5: 498.0450 .. 609.7763 cents 16/15, 111.7313 cents 1/1, 0.0000 cents 6: 590.2237 .. 701.9550 cents 16/15, 111.7313 cents 2025/2048,-19.5526 cents 7: 701.9550 .. 813.6863 cents 16/15, 111.7313 cents 1/1, 0.0000 cents 8: 772.6274 .. 925.4176 cents 2048/1875, 152.7901 cents 125/128,-41.0589 cents 9: 884.3587 .. 1017.5963 cents 27/25, 133.2376 cents 125/128,-41.0589 cents 10: 996.0900 .. 1129.3276 cents 27/25, 133.2376 cents 80/81,-21.5063 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.543613 Largest / Average step : 1.869175 Largest / Smallest step : 2.885284 Median interval of one step : 16/15, 111.7313 cents, amount: 6 Most common interval of one step : 16/15, 111.7313 cents, amount: 6 Least squares average step : 109.74675 cents, oct.: 1207.21426 cents Scale is not proper Step pattern alph. order: ABACADACABA Step pattern size order : CBCACDCACBC Scale is not a Constant Structure Scale diversity : 1.332298 Lumma stability : 0.117787 Lumma impropriety factor : 0.189000 Rothenberg efficiency : 0.428571 redundancy: 0.571429 Efficiency x scale size : 4.714286 Number of different interval sizes : 32 = 3.20000 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.40000 = 22/5 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 8 Most common triad is 0.0 498.045 701.955 cents, amount: 5 Number of recognisable fifths : 8, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 5 15 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 11 = 100.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 7 and 8 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 5-6 -- Rational properties -- Prime limit : 5 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 15 Scale harmonicity : 0.032823 Average absolute harmonicity : 0.209874 Specific harmonicity : 0.187272 Fundamental : 1/360, -8.4919 octaves, 0.7267 Hz. Guide tone : 720, 9.4919 octaves, 188370.407 Hz. Exponens Consonantiae : 2.592000E+05, 17.98371 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 76.0, average 6.90909 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.01079, average 0.72825 Sum of Tenney's harmonic distance : 16.18975, average 1.47180 Vogel's harmonic complexity : 14.54545 Wille's k value : 337 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 233.99215, average 3.54534 Lattice compactness (without 2's) : 115.76620, average 1.75403 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.54545 24 1 3: -2 .. 2 0.00000 10 4 5: -1 .. 1 0.00000 6 6 Average exponent except 2's : 0 / 11 = 0.00000 Average absolute exponent except 2's: 16 / 11 = 1.45455 Scale is weakly epimorphic with val: <11 15 27| Scale is weakly epimorphic with val: <11 15 28| Scale is weakly epimorphic with val: <11 16 24| Scale is weakly epimorphic with val: <11 17 24| Scale is weakly epimorphic with val: <11 18 27| Scale is weakly epimorphic with val: <11 18 28|
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 30.4470 c. M: 50.0499 c. 12: 1 1 1 1 1 2 1 1 1 1 1 P M ME I SD: 10.3458 c. M: 15.6413 c. 19: 2 1 2 1 2 3 2 1 2 1 2 N I SD: 9.7933 c. M: 14.5845 c. 22: 2 2 2 1 2 4 2 1 2 2 2 N I SD: 8.7082 c. M:-14.2718 c. 31: 3 2 3 2 3 5 3 2 3 2 3 N G I SD: 5.8733 c. M:-10.3616 c. 34: 3 3 3 2 3 6 3 2 3 3 3 N I SD: 4.6524 c. M:-7.8547 c. 41: 4 3 4 2 4 7 4 2 4 3 4 N I SD: 4.3372 c. M:-6.3099 c. 53: 5 4 5 3 5 9 5 3 5 4 5 N I SD: 1.0428 c. M:-1.4763 c. 118: 11 9 11 7 11 20 11 7 11 9 11 N I SD: 0.3080 c. M:-0.5202 c. 289: 27 22 27 17 27 49 27 17 27 22 27 N I SD: 0.2782 c. M:-0.4498 c. 323: 30 25 30 19 30 55 30 19 30 25 30 N I SD: 0.2440 c. M:-0.4244 c. 376: 35 29 35 22 35 64 35 22 35 29 35 N I SD: 0.2218 c. M:-0.3453 c. 441: 41 34 41 26 41 75 41 26 41 34 41 N I SD: 0.1137 c. M:-0.1716 c. 494: 46 38 46 29 46 84 46 29 46 38 46 N I SD: 0.0975 c. M: 0.1482 c. 559: 52 43 52 33 52 95 52 33 52 43 52 N I SD: 0.0684 c. M:-0.1034 c. 612: 57 47 57 36 57 104 57 36 57 47 57 N I SD: 0.0297 c. M:-0.0450 c. 1171: 109 90 109 69 109 199 109 69 109 90 109 N I SD: 0.0197 c. M:-0.0319 c. 1783: 166 137 166 105 166 303 166 105 166 137 166 N I SD: 0.0091 c. M:-0.0160 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x 5 x x 6 S SD: 0.0000 cents 4 x x x 5 x 6 x x 7 x 8 S SD: 6.8160 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 17.4324 cents 6 x x 7 x 8:9 x 10 x 11:12 S SD: 10.3979 cents 7 x 8 x 9 x x 11:12 x 13:14 SD: 13.6910 cents 8 x 9 x 10:11:12:13 x 14:15:16 S SD: 8.1985 cents 9 x 10:11 x 12 x 14:15:16:17:18 S SD: 7.9190 cents 10 x 11:12 x 13:15:16:17:18:19:20 SD: 8.3137 cents 11:12 x 13:14:15:17 x 18:20:21:22 SD: 11.5822 cents 12:13 x 14:15:16:18:19:20:21:23:24 SD: 7.4959 cents 13:14:15 x 16:17:20:21:22:23:24:26 SD: 8.7923 cents 14:15:16:17:18:19:21:22:23:25:26:28 SD: 7.3110 cents 15:16:17:18:19:20:23:24:25:27:28:30 SD: 4.6877 cents 24:26:27:29:30:32:36:38:40:43:45:48 SD: 3.3700 cents 30:32:34:36:38:40:45:48:50:53:56:60 SD: 2.6758 cents 32:34:36:38:40:43:48:51:53:57:60:64 SD: 2.4582 cents 40:43:45:48:50:53:60:64:67:71:75:80 SD: 1.7750 cents 48:51:54:58:60:64:72:77:80:85:90:96 SD: 1.4535 cents 60:64:68:72:75:80:90:96:100:107:113:120 SD: 1.4413 cents 63:67:71:76:79:84:95:101:105:112:118:126 SD: 1.4319 cents 64:68:72:77:80:85:96:102:107:114:120:128 SD: 1.2811 cents 72:77:81:86:90:96:108:115:120:128:135:144 SD: 0.8807 cents 90:96:101:108:113:120:135:144:150:160:169:180 SD: 0.8323 cents 104:111:117:125:130:139:156:166:173:185:195:208 SD: 0.6778 cents 105:112:118:126:131:140:158:168:175:187:197:210 SD: 0.6749 cents 120:128:135:144:150:160:180:192:200:213:225:240 SD: 0.2461 cents 240:256:270:288:300:320:360:384:400:427:450:480 SD: 0.1229 cents 360:384:405:432:450:480:540:576:600:640:675:720 SD: 0.0000 cents