Scala analysis: xen07-chalmers-wurschmidt-2
Wurschmidt-2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 3: 9/8 203.910002 major whole tone 4: 75/64 274.582429 classic augmented second 5: 6/5 315.641287 minor third 6: 5/4 386.313714 major third 7: 32/25 427.372572 classic diminished fourth 8: 4/3 498.044999 perfect fourth 9: 25/18 568.717426 classic augmented fourth 10: 36/25 631.282574 classic diminished fifth 11: 3/2 701.955001 perfect fifth 12: 25/16 772.627428 classic augmented fifth 13: 8/5 813.686286 minor sixth 14: 5/3 884.358713 major sixth, BP sixth 15: 128/75 925.417571 diminished seventh 16: 16/9 996.089998 Pythagorean minor seventh 17: 50/27 1066.762425 grave major seventh 18: 48/25 1129.327573 classic diminished octave 19: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 648/625 62.5651 major diesis 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 128/125 41.0589 minor diesis, diesis 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 128/125 41.0589 minor diesis, diesis 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 648/625 62.5651 major diesis 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 25/24 70.6724 classic chromatic semitone, minor chroma 13: 128/125 41.0589 minor diesis, diesis 14: 25/24 70.6724 classic chromatic semitone, minor chroma 15: 128/125 41.0589 minor diesis, diesis 16: 25/24 70.6724 classic chromatic semitone, minor chroma 17: 25/24 70.6724 classic chromatic semitone, minor chroma 18: 648/625 62.5651 major diesis 19: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 128/125 41.059 cents minor diesis, diesis 1: 3 648/625 62.565 cents major diesis 1: 12 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 8 16/15 111.731 cents minor diatonic semitone 2: 6 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 5 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 3: 2 2048/1875 152.790 cents double diminished third 3: 8 10/9 182.404 cents minor whole tone 3: 9 9/8 203.910 cents major whole tone 4: 4 256/225 223.463 cents Neapolitan diminished third 4: 4 144/125 244.969 cents classic diminished third 4: 4 125/108 253.076 cents semi-augmented whole tone 4: 1 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 4: 6 75/64 274.582 cents classic augmented second 5: 6 32/27 294.135 cents Pythagorean minor third 5: 8 6/5 315.641 cents minor third 5: 2 243/200 337.148 cents acute minor third 5: 3 625/512 345.255 cents classic neutral third 6: 4 768/625 356.700 cents 6: 4 100/81 364.807 cents grave major third 6: 8 5/4 386.314 cents major third 6: 3 81/64 407.820 cents Pythagorean major third 7: 9 32/25 427.373 cents classic diminished fourth 7: 2 625/486 435.480 cents 7: 2 162/125 448.879 cents 7: 4 125/96 456.986 cents classic augmented third 7: 2 675/512 478.492 cents wide augmented third 8: 14 4/3 498.045 cents perfect fourth 8: 4 27/20 519.551 cents acute fourth 8: 1 5625/4096 549.165 cents double augmented third 9: 2 512/375 539.104 cents double diminished fifth 9: 4 864/625 560.610 cents 9: 9 25/18 568.717 cents classic augmented fourth 9: 4 45/32 590.224 cents diatonic tritone 10: 4 64/45 609.776 cents 2nd tritone 10: 9 36/25 631.283 cents classic diminished fifth 10: 4 625/432 639.390 cents 10: 2 375/256 660.896 cents double augmented fourth 11: 1 8192/5625 650.835 cents double diminished sixth 11: 4 40/27 680.449 cents grave fifth 11: 14 3/2 701.955 cents perfect fifth 12: 2 1024/675 721.508 cents narrow diminished sixth 12: 4 192/125 743.014 cents classic diminished sixth 12: 2 125/81 751.121 cents 12: 2 972/625 764.520 cents 12: 9 25/16 772.627 cents classic augmented fifth 13: 3 128/81 792.180 cents Pythagorean minor sixth 13: 8 8/5 813.686 cents minor sixth 13: 4 81/50 835.193 cents acute minor sixth 13: 4 625/384 843.300 cents 14: 3 1024/625 854.745 cents two (classic diminished fourth) 14: 2 400/243 862.852 cents grave major sixth 14: 8 5/3 884.359 cents major sixth, BP sixth 14: 6 27/16 905.865 cents Pythagorean major sixth 15: 6 128/75 925.418 cents diminished seventh 15: 1 1250/729 933.525 cents 15: 4 216/125 946.924 cents semi-augmented sixth 15: 4 125/72 955.031 cents classic augmented sixth 15: 4 225/128 976.537 cents augmented sixth 16: 9 16/9 996.090 cents Pythagorean minor seventh 16: 8 9/5 1017.596 cents just minor seventh, BP seventh 16: 2 1875/1024 1047.210 cents double augmented sixth 17: 5 1152/625 1058.655 cents 17: 6 50/27 1066.762 cents grave major seventh 17: 8 15/8 1088.269 cents classic major seventh 18: 12 48/25 1129.328 cents classic diminished octave 18: 3 625/324 1137.435 cents octave - major diesis 18: 4 125/64 1158.941 cents classic augmented seventh, octave - minor diesis Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.77778 = 34/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 70.7 133.2 203.9 274.6 315.6 386.3 427.4 498.0 568.7 631.3 702.0 772.6 813.7 884.4 925.4 996.1 1066.8 1129.3 1200.0 70.7 : 62.6 133.2 203.9 245.0 315.6 356.7 427.4 498.0 560.6 631.3 702.0 743.0 813.7 854.7 925.4 996.1 1058.7 1129.3 1200.0 133.2 : 70.7 141.3 182.4 253.1 294.1 364.8 435.5 498.0 568.7 639.4 680.4 751.1 792.2 862.9 933.5 996.1 1066.8 1137.4 1200.0 203.9 : 70.7 111.7 182.4 223.5 294.1 364.8 427.4 498.0 568.7 609.8 680.4 721.5 792.2 862.9 925.4 996.1 1066.8 1129.3 1200.0 274.6 : 41.1 111.7 152.8 223.5 294.1 356.7 427.4 498.0 539.1 609.8 650.8 721.5 792.2 854.7 925.4 996.1 1058.7 1129.3 1200.0 315.6 : 70.7 111.7 182.4 253.1 315.6 386.3 457.0 498.0 568.7 609.8 680.4 751.1 813.7 884.4 955.0 1017.6 1088.3 1158.9 1200.0 386.3 : 41.1 111.7 182.4 245.0 315.6 386.3 427.4 498.0 539.1 609.8 680.4 743.0 813.7 884.4 946.9 1017.6 1088.3 1129.3 1200.0 427.4 : 70.7 141.3 203.9 274.6 345.3 386.3 457.0 498.0 568.7 639.4 702.0 772.6 843.3 905.9 976.5 1047.2 1088.3 1158.9 1200.0 498.0 : 70.7 133.2 203.9 274.6 315.6 386.3 427.4 498.0 568.7 631.3 702.0 772.6 835.2 905.9 976.5 1017.6 1088.3 1129.3 1200.0 568.7 : 62.6 133.2 203.9 245.0 315.6 356.7 427.4 498.0 560.6 631.3 702.0 764.5 835.2 905.9 946.9 1017.6 1058.7 1129.3 1200.0 631.3 : 70.7 141.3 182.4 253.1 294.1 364.8 435.5 498.0 568.7 639.4 702.0 772.6 843.3 884.4 955.0 996.1 1066.8 1137.4 1200.0 702.0 : 70.7 111.7 182.4 223.5 294.1 364.8 427.4 498.0 568.7 631.3 702.0 772.6 813.7 884.4 925.4 996.1 1066.8 1129.3 1200.0 772.6 : 41.1 111.7 152.8 223.5 294.1 356.7 427.4 498.0 560.6 631.3 702.0 743.0 813.7 854.7 925.4 996.1 1058.7 1129.3 1200.0 813.7 : 70.7 111.7 182.4 253.1 315.6 386.3 457.0 519.6 590.2 660.9 702.0 772.6 813.7 884.4 955.0 1017.6 1088.3 1158.9 1200.0 884.4 : 41.1 111.7 182.4 245.0 315.6 386.3 448.9 519.6 590.2 631.3 702.0 743.0 813.7 884.4 946.9 1017.6 1088.3 1129.3 1200.0 925.4 : 70.7 141.3 203.9 274.6 345.3 407.8 478.5 549.2 590.2 660.9 702.0 772.6 843.3 905.9 976.5 1047.2 1088.3 1158.9 1200.0 996.1 : 70.7 133.2 203.9 274.6 337.1 407.8 478.5 519.6 590.2 631.3 702.0 772.6 835.2 905.9 976.5 1017.6 1088.3 1129.3 1200.0 1066.8: 62.6 133.2 203.9 266.5 337.1 407.8 448.9 519.6 560.6 631.3 702.0 764.5 835.2 905.9 946.9 1017.6 1058.7 1129.3 1200.0 1129.3: 70.7 141.3 203.9 274.6 345.3 386.3 457.0 498.0 568.7 639.4 702.0 772.6 843.3 884.4 955.0 996.1 1066.8 1137.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 70.6724 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 2: 111.7313 .. 141.3449 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 3: 152.7901 .. 203.9100 cents 16875/16384, 51.1199 cents 393216/390625, 11.4453 cents 4: 223.4626 .. 274.5824 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 5: 294.1350 .. 345.2549 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 6: 356.7001 .. 407.8200 cents 16875/16384, 51.1199 cents 393216/390625, 11.4453 cents 7: 427.3726 .. 478.4924 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 8: 498.0450 .. 549.1649 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 9: 539.1039 .. 590.2237 cents 16875/16384, 51.1199 cents 2097152/2109375,-10.0610 cents 10: 609.7763 .. 660.8961 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 11: 650.8351 .. 701.9550 cents 16875/16384, 51.1199 cents 2097152/2109375,-10.0610 cents 12: 721.5076 .. 772.6274 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 13: 792.1800 .. 843.2999 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 14: 854.7451 .. 905.8650 cents 16875/16384, 51.1199 cents 393216/390625, 11.4453 cents 15: 925.4176 .. 976.5374 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 16: 996.0900 .. 1047.2099 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 17: 1058.6551 .. 1088.2687 cents 3125/3072, 29.6136 cents 393216/390625, 11.4453 cents 18: 1129.3276 .. 1158.9411 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 128/125, 41.0589 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 25/24, 70.6724 cents Average / Smallest step : 1.538228 Largest / Average step : 1.118980 Largest / Smallest step : 1.721247 Median interval of one step : 25/24, 70.6724 cents, amount: 12 Most common interval of one step : 25/24, 70.6724 cents, amount: 12 Least squares average step : 62.90854 cents, oct.: 1195.26220 cents Scale is not proper Step pattern alph. order: ABAACACAABAACACAABA Step pattern size order : LMLLSLSLLMLLSLSLLML Scale is a Constant Structure, by a margin of 10.06100 cents Scale diversity : 1.366399 Lumma stability : 0.321658 Lumma impropriety factor : 0.016768 Number of different interval sizes : 68 = 3.77778 / class Number of one step interval sizes : 3 Highest interval variety : 5 Mean interval variety : 3.77778 = 34/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 15625/15552, 8.1073 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 14 Most common triad is 0.0 498.045 701.955 cents, amount: 9 Number of recognisable fifths : 14, average 701.9550 cents Scale contains two identical conjunct "tetrachords" of 9 notes Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 9 25 75 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 19 = 100.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties -- Prime limit : 5 Odd number limit : 5625 (O: 5625 U: 5625) Highest odd numerator or denominator: 75 Scale harmonicity : 0.018315 Average absolute harmonicity : 0.139864 Specific harmonicity : 0.108358 Fundamental : 1/43200, -15.3987 octaves, 0.0061 Hz. Guide tone : 86400, 16.3987 octaves, 22604448.842 Hz. Exponens Consonantiae : 3.732480E+09, 31.79749 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 446.5, average 23.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 20.65910, average 1.08732 Sum of Tenney's harmonic distance : 42.32345, average 2.22755 Vogel's harmonic complexity : 25.52632 Wille's k value : 25312 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 928.30616, average 4.88582 Lattice compactness (without 2's) : 514.19786, average 2.70630 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 7 0.52632 50 1 3: -3 .. 3 0.00000 22 4 5: -2 .. 2 0.00000 24 14 Average exponent except 2's : 0 / 19 = 0.00000 Average absolute exponent except 2's: 46 / 19 = 2.42105 Scale is weakly epimorphic with val: <19 29 46| Scale is weakly epimorphic with val: <19 30 43| Scale is JI-epimorphic with val: <19 30 44| = patent
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.8490 c. M: 21.9508 c. 27: 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 2 N D3 I SD: 12.1181 c. M:-18.3122 c. 28: 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 P D3 I SD: 11.7159 c. M: 17.4396 c. 29: 2 1 2 2 1 1 1 2 2 1 2 2 1 1 1 2 2 1 2 N D3 I SD: 11.2108 c. M:-15.3932 c. 30: 2 1 2 2 1 2 1 1 2 2 2 1 1 2 1 2 2 1 2 N D3 I SD: 10.6339 c. M:-18.0450 c. 31: 2 1 2 2 1 2 1 2 2 1 2 2 1 2 1 2 2 1 2 P M ME I SD: 8.3754 c. M: 17.1085 c. 34: 2 2 2 2 1 2 1 2 2 2 2 2 1 2 1 2 2 2 2 N D3 I SD: 5.0169 c. M: 7.9389 c. 53: 3 3 3 3 2 3 2 3 3 3 3 3 2 3 2 3 3 3 3 P D3 I SD: 2.0927 c. M: 2.8843 c. 99: 6 5 6 6 3 6 3 6 6 5 6 6 3 6 3 6 6 5 6 N I SD: 2.0811 c. M: 4.2055 c. 118: 7 6 7 7 4 7 4 7 7 6 7 7 4 7 4 7 7 6 7 N I SD: 0.5132 c. M: 1.0342 c. 171: 10 9 10 10 6 10 6 10 10 9 10 10 6 10 6 10 10 9 10 N I SD: 0.4568 c. M: 0.8982 c. 289: 17 15 17 17 10 17 10 17 17 15 17 17 10 17 10 17 17 15 17 N I SD: 0.2943 c. M: 0.5340 c. 323: 19 17 19 19 11 19 11 19 19 17 19 19 11 19 11 19 19 17 19 N I SD: 0.2785 c. M: 0.5086 c. 441: 26 23 26 26 15 26 15 26 26 23 26 26 15 26 15 26 26 23 26 N I SD: 0.1239 c. M: 0.2475 c. 559: 33 29 33 33 19 33 19 33 33 29 33 33 19 33 19 33 33 29 33 N I SD: 0.1291 c. M: 0.1940 c. 612: 36 32 36 36 21 36 21 36 36 32 36 36 21 36 21 36 36 32 36 N I SD: 0.0645 c. M: 0.0958 c. 730: 43 38 43 43 25 43 25 43 43 38 43 43 25 43 25 43 43 38 43 N I SD: 0.0485 c. M: 0.0869 c. 1171: 69 61 69 69 40 69 40 69 69 61 69 69 40 69 40 69 69 61 69 N I SD: 0.0300 c. M: 0.0546 c. 1783: 105 93 105 105 61 105 61 105 105 93 105 105 61 105 61 105 105 93 105 N I SD: 0.0109 c. M: 0.0210 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.0000 cents 3 .. 6 match: 3 H SD: 0.0000 cents 4 .. 8 match: 4 H SD: 6.8160 cents 5 .. 10 match: 5 H SD: 5.1101 cents 6 .. 12 match: 6 H SD: 3.1720 cents 7 .. 14 match: 7 H SD: 4.8954 cents 8 .. 16 match: 8 H SD: 5.9016 cents 9 .. 18 match: 9 H SD: 5.3971 cents 10 .. 20 match: 10 H SD: 5.2507 cents 11 .. 22 match: 11 H SD: 6.3205 cents 12 .. 24 match: 12 H SD: 3.9717 cents 13 .. 26 match: 13 H SD: 5.2167 cents 14 .. 28 match: 14 H SD: 4.2032 cents 15 .. 30 match: 15 H SD: 4.5873 cents 16 .. 32 match: 15 S SD: 4.5894 cents 17 .. 34 match: 15 SD: 5.2253 cents 18 .. 36 match: 17 SD: 3.3928 cents 19 .. 38 match: 15 SD: 5.2792 cents 20 .. 40 match: 18 S SD: 3.9739 cents 21 .. 42 match: 18 SD: 3.5214 cents 22 .. 44 match: 17 SD: 3.5552 cents 23 .. 46 match: 18 SD: 2.9712 cents 24 .. 48 match: 18 SD: 2.5370 cents 26 .. 52 match: 18 SD: 3.0831 cents 27 .. 54 match: 18 SD: 2.9423 cents 28 .. 56 match: 19 SD: 2.6712 cents 30 .. 60 match: 18 SD: 2.4726 cents 32 .. 64 match: 18 SD: 2.5724 cents 34 .. 68 match: 19 SD: 2.5487 cents 35 .. 70 match: 19 SD: 2.4354 cents 36 .. 72 match: 19 SD: 2.1108 cents 39 .. 78 match: 19 SD: 1.8239 cents 40 .. 80 match: 19 SD: 1.7575 cents 46 .. 92 match: 19 SD: 1.6411 cents 48 .. 96 match: 19 SD: 1.2373 cents 64 .. 128 match: 19 SD: 0.9385 cents 72 .. 144 match: 19 SD: 0.8942 cents 75 .. 150 match: 19 SD: 0.7217 cents 96 .. 192 match: 19 SD: 0.6971 cents 100 .. 200 match: 19 SD: 0.6087 cents 120 .. 240 match: 19 SD: 0.5988 cents 121 .. 242 match: 19 SD: 0.5985 cents 123 .. 246 match: 19 SD: 0.5983 cents 126 .. 252 match: 19 SD: 0.5743 cents 128 .. 256 match: 19 SD: 0.5608 cents 135 .. 270 match: 19 SD: 0.5463 cents 136 .. 272 match: 19 SD: 0.5034 cents 144 .. 288 match: 19 SD: 0.4788 cents 150 .. 300 match: 19 SD: 0.4148 cents 174 .. 348 match: 19 SD: 0.4142 cents 175 .. 350 match: 19 SD: 0.3579 cents 200 .. 400 match: 19 SD: 0.3458 cents 210 .. 420 match: 19 SD: 0.3297 cents 215 .. 430 match: 19 SD: 0.3053 cents 216 .. 432 match: 19 SD: 0.2918 cents 239 .. 478 match: 19 SD: 0.2778 cents 240 .. 480 match: 19 SD: 0.2394 cents 288 .. 576 match: 19 SD: 0.2322 cents 304 .. 608 match: 19 SD: 0.2306 cents 311 .. 622 match: 19 SD: 0.2204 cents 336 .. 672 match: 19 SD: 0.1586 cents 360 .. 720 match: 19 SD: 0.1493 cents 400 .. 800 match: 19 SD: 0.1466 cents 432 .. 864 match: 19 SD: 0.1370 cents 450 .. 900 match: 19 SD: 0.1267 cents 504 .. 1008 match: 19 SD: 0.1263 cents 512 .. 1024 match: 19 SD: 0.1247 cents 525 .. 1050 match: 19 SD: 0.1125 cents 528 .. 1056 match: 19 SD: 0.1111 cents 576 .. 1152 match: 19 SD: 0.0825 cents 600 .. 1200 match: 19 SD: 0.0696 cents