Scala analysis: mandelbaum7keemun
Keemun Fokkerization of mandelbaum7
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: 15/14 119.442808 major diatonic semitone 3: 9/8 203.910002 major whole tone 4: 7/6 266.870906 septimal minor third 5: 6/5 315.641287 minor third 6: 5/4 386.313714 major third 7: 9/7 435.084095 septimal major third, BP third 8: 4/3 498.044999 perfect fourth 9: 7/5 582.512193 septimal or Huygens' tritone, BP 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: 7/4 968.825906 harmonic seventh 16: 9/5 1017.596288 just minor seventh, BP seventh 17: 15/8 1088.268715 classic 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: 36/35 48.7704 septimal diesis, 1/4-tone 3: 21/20 84.4672 minor semitone 4: 28/27 62.9609 Archytas' 1/3-tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 36/35 48.7704 septimal diesis, 1/4-tone 8: 28/27 62.9609 Archytas' 1/3-tone 9: 21/20 84.4672 minor semitone 10: 36/35 48.7704 septimal diesis, 1/4-tone 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: 21/20 84.4672 minor semitone 16: 36/35 48.7704 septimal diesis, 1/4-tone 17: 25/24 70.6724 classic chromatic semitone, minor chroma 18: 128/125 41.0589 minor diesis, diesis 19: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 128/125 41.059 cents minor diesis, diesis 1: 5 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 7 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 21/20 84.467 cents minor semitone 2: 6 16/15 111.731 cents minor diatonic semitone 2: 5 15/14 119.443 cents major diatonic semitone 2: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 2 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 2: 2 49/45 147.428 cents BP minor semitone 2: 1 35/32 155.140 cents septimal neutral second 3: 1 192/175 160.502 cents septimal 4/5-tone 3: 1 54/49 168.213 cents Zalzal's mujannab 3: 6 10/9 182.404 cents minor whole tone 3: 2 125/112 190.115 cents classic augmented semitone 3: 5 28/25 196.198 cents middle second 3: 4 9/8 203.910 cents major whole tone 4: 5 8/7 231.174 cents septimal whole tone 4: 4 144/125 244.969 cents classic diminished third 4: 2 125/108 253.076 cents semi-augmented whole tone 4: 5 7/6 266.871 cents septimal minor third 4: 3 75/64 274.582 cents classic augmented second 5: 1 32/27 294.135 cents Pythagorean minor third 5: 3 25/21 301.847 cents BP second, quasi-equal minor third 5: 12 6/5 315.641 cents minor third 5: 3 175/144 337.543 cents 6: 1 60/49 350.617 cents smaller approximation to neutral third 6: 1 768/625 356.700 cents 6: 2 216/175 364.412 cents 6: 4 56/45 378.602 cents septimal narrow major third 6: 11 5/4 386.314 cents major third 7: 6 32/25 427.373 cents classic diminished fourth 7: 5 9/7 435.084 cents septimal major third, BP third 7: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 7: 4 125/96 456.986 cents classic augmented third 7: 1 98/75 463.069 cents 7: 1 21/16 470.781 cents narrow fourth 8: 10 4/3 498.045 cents perfect fourth 8: 4 75/56 505.757 cents marvelous fourth 8: 2 168/125 511.840 cents 8: 2 27/20 519.551 cents acute fourth 8: 1 49/36 533.742 cents Arabic lute acute fourth 9: 5 48/35 546.815 cents septimal semi-augmented fourth 9: 1 864/625 560.610 cents 9: 6 25/18 568.717 cents classic augmented fourth 9: 5 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 9: 2 45/32 590.224 cents diatonic tritone 10: 2 64/45 609.776 cents 2nd tritone 10: 5 10/7 617.488 cents Euler's tritone 10: 6 36/25 631.283 cents classic diminished fifth 10: 1 625/432 639.390 cents 10: 5 35/24 653.185 cents septimal semi-diminished fifth 11: 1 72/49 666.258 cents Arabic lute grave fifth 11: 2 40/27 680.449 cents grave fifth 11: 2 125/84 688.160 cents 11: 4 112/75 694.243 cents marvelous fifth 11: 10 3/2 701.955 cents perfect fifth 12: 1 32/21 729.219 cents wide fifth 12: 1 75/49 736.931 cents BP fifth 12: 4 192/125 743.014 cents classic diminished sixth 12: 2 54/35 750.725 cents septimal semi-augmented fifth 12: 5 14/9 764.916 cents septimal minor sixth 12: 6 25/16 772.627 cents classic augmented fifth 13: 11 8/5 813.686 cents minor sixth 13: 4 45/28 821.398 cents septimale wide minor sixth 13: 2 175/108 835.588 cents 13: 1 625/384 843.300 cents 13: 1 49/30 849.383 cents larger approximation to neutral sixth 14: 3 288/175 862.457 cents 14: 12 5/3 884.359 cents major sixth, BP sixth 14: 3 42/25 898.153 cents quasi-equal major sixth 14: 1 27/16 905.865 cents Pythagorean major sixth 15: 3 128/75 925.418 cents diminished seventh 15: 5 12/7 933.129 cents septimal major sixth 15: 2 216/125 946.924 cents semi-augmented sixth 15: 4 125/72 955.031 cents classic augmented sixth 15: 5 7/4 968.826 cents harmonic seventh 16: 4 16/9 996.090 cents Pythagorean minor seventh 16: 5 25/14 1003.802 cents middle minor seventh 16: 2 224/125 1009.885 cents 16: 6 9/5 1017.596 cents just minor seventh, BP seventh 16: 1 49/27 1031.787 cents 16: 1 175/96 1039.498 cents 17: 1 64/35 1044.860 cents septimal neutral seventh 17: 2 90/49 1052.572 cents 17: 2 1152/625 1058.655 cents 17: 3 50/27 1066.762 cents grave major seventh 17: 5 28/15 1080.557 cents grave major seventh 17: 6 15/8 1088.269 cents classic major seventh 18: 3 40/21 1115.533 cents acute major seventh 18: 7 48/25 1129.328 cents classic diminished octave 18: 2 27/14 1137.039 cents septimal major seventh 18: 5 35/18 1151.230 cents septimal semi-diminished octave 18: 2 125/64 1158.941 cents classic augmented seventh, octave - minor diesis Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.22222 = 47/9
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 : 70.7 119.4 203.9 266.9 315.6 386.3 435.1 498.0 582.5 631.3 702.0 772.6 813.7 884.4 968.8 1017.6 1088.3 1129.3 1200.0 70.7 : 48.8 133.2 196.2 245.0 315.6 364.4 427.4 511.8 560.6 631.3 702.0 743.0 813.7 898.2 946.9 1017.6 1058.7 1129.3 1200.0 119.4 : 84.5 147.4 196.2 266.9 315.6 378.6 463.1 511.8 582.5 653.2 694.2 764.9 849.4 898.2 968.8 1009.9 1080.6 1151.2 1200.0 203.9 : 63.0 111.7 182.4 231.2 294.1 378.6 427.4 498.0 568.7 609.8 680.4 764.9 813.7 884.4 925.4 996.1 1066.8 1115.5 1200.0 266.9 : 48.8 119.4 168.2 231.2 315.6 364.4 435.1 505.8 546.8 617.5 702.0 750.7 821.4 862.5 933.1 1003.8 1052.6 1137.0 1200.0 315.6 : 70.7 119.4 182.4 266.9 315.6 386.3 457.0 498.0 568.7 653.2 702.0 772.6 813.7 884.4 955.0 1003.8 1088.3 1151.2 1200.0 386.3 : 48.8 111.7 196.2 245.0 315.6 386.3 427.4 498.0 582.5 631.3 702.0 743.0 813.7 884.4 933.1 1017.6 1080.6 1129.3 1200.0 435.1 : 63.0 147.4 196.2 266.9 337.5 378.6 449.3 533.7 582.5 653.2 694.2 764.9 835.6 884.4 968.8 1031.8 1080.6 1151.2 1200.0 498.0 : 84.5 133.2 203.9 274.6 315.6 386.3 470.8 519.6 590.2 631.3 702.0 772.6 821.4 905.9 968.8 1017.6 1088.3 1137.0 1200.0 582.5 : 48.8 119.4 190.1 231.2 301.8 386.3 435.1 505.8 546.8 617.5 688.2 736.9 821.4 884.4 933.1 1003.8 1052.6 1115.5 1200.0 631.3 : 70.7 141.3 182.4 253.1 337.5 386.3 457.0 498.0 568.7 639.4 688.2 772.6 835.6 884.4 955.0 1003.8 1066.8 1151.2 1200.0 702.0 : 70.7 111.7 182.4 266.9 315.6 386.3 427.4 498.0 568.7 617.5 702.0 764.9 813.7 884.4 933.1 996.1 1080.6 1129.3 1200.0 772.6 : 41.1 111.7 196.2 245.0 315.6 356.7 427.4 498.0 546.8 631.3 694.2 743.0 813.7 862.5 925.4 1009.9 1058.7 1129.3 1200.0 813.7 : 70.7 155.1 203.9 274.6 315.6 386.3 457.0 505.8 590.2 653.2 702.0 772.6 821.4 884.4 968.8 1017.6 1088.3 1158.9 1200.0 884.4 : 84.5 133.2 203.9 245.0 315.6 386.3 435.1 519.6 582.5 631.3 702.0 750.7 813.7 898.2 946.9 1017.6 1088.3 1129.3 1200.0 968.8 : 48.8 119.4 160.5 231.2 301.8 350.6 435.1 498.0 546.8 617.5 666.3 729.2 813.7 862.5 933.1 1003.8 1044.9 1115.5 1200.0 1017.6: 70.7 111.7 182.4 253.1 301.8 386.3 449.3 498.0 568.7 617.5 680.4 764.9 813.7 884.4 955.0 996.1 1066.8 1151.2 1200.0 1088.3: 41.1 111.7 182.4 231.2 315.6 378.6 427.4 498.0 546.8 609.8 694.2 743.0 813.7 884.4 925.4 996.1 1080.6 1129.3 1200.0 1129.3: 70.7 141.3 190.1 274.6 337.5 386.3 457.0 505.8 568.7 653.2 702.0 772.6 843.3 884.4 955.0 1039.5 1088.3 1158.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 84.4672 cents 525/512, 43.4083 cents 128/125, 41.0589 cents 2: 111.7313 .. 155.1396 cents 525/512, 43.4083 cents 64/63, 27.2641 cents 3: 160.5017 .. 203.9100 cents 525/512, 43.4083 cents 6144/6125, 5.3620 cents 4: 231.1741 .. 274.5824 cents 525/512, 43.4083 cents 64/63, 27.2641 cents 5: 294.1350 .. 337.5433 cents 525/512, 43.4083 cents 2048/2025, 19.5526 cents 6: 350.6169 .. 386.3137 cents 49/48, 35.6968 cents 1728/1715, 13.0736 cents 7: 427.3726 .. 470.7809 cents 525/512, 43.4083 cents 128/125, 41.0589 cents 8: 498.0450 .. 533.7418 cents 49/48, 35.6968 cents 64/63, 27.2641 cents 9: 546.8154 .. 590.2237 cents 525/512, 43.4083 cents 1728/1715, 13.0736 cents 10: 609.7763 .. 653.1846 cents 525/512, 43.4083 cents 2048/2025, 19.5526 cents 11: 666.2582 .. 701.9550 cents 49/48, 35.6968 cents 1728/1715, 13.0736 cents 12: 729.2191 .. 772.6274 cents 525/512, 43.4083 cents 64/63, 27.2641 cents 13: 813.6863 .. 849.3831 cents 49/48, 35.6968 cents 128/125, 41.0589 cents 14: 862.4567 .. 905.8650 cents 525/512, 43.4083 cents 1728/1715, 13.0736 cents 15: 925.4176 .. 968.8259 cents 525/512, 43.4083 cents 2048/2025, 19.5526 cents 16: 996.0900 .. 1039.4983 cents 525/512, 43.4083 cents 64/63, 27.2641 cents 17: 1044.8604 .. 1088.2687 cents 525/512, 43.4083 cents 6144/6125, 5.3620 cents 18: 1115.5328 .. 1158.9411 cents 525/512, 43.4083 cents 64/63, 27.2641 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 : 21/20, 84.4672 cents Average / Smallest step : 1.538228 Largest / Average step : 1.337397 Largest / Smallest step : 2.057222 Median interval of one step : 25/24, 70.6724 cents, amount: 7 Most common interval of one step : 25/24, 70.6724 cents, amount: 7 Least squares average step : 63.50794 cents, oct.: 1206.65089 cents Scale is strictly proper Step pattern alph. order: ABCDBABDCBAAEACBAEA Step pattern size order : DBECBDBCEBDDADEBDAD Scale is a Constant Structure, by a margin of 5.36205 cents Scale diversity : 1.427657 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.374580 Number of different interval sizes : 94 = 5.22222 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.22222 = 47/9 Median interval variety : 4.5 Lowest interval variety : 4 Smallest interval difference : 6144/6125, 5.3620 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 12 Number of recognisable fifths : 16, average 698.3028 cents Number of appreciable fifths : 14, average 699.7517 cents Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 3 5 15 25 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 9 = 47.3684% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 7 Odd number limit : 625 (O: 625 U: 625) Highest odd numerator or denominator: 25 Scale harmonicity : 0.016085 Average absolute harmonicity : 0.144792 Specific harmonicity : 0.114116 Fundamental : 1/8400, -13.0362 octaves, 0.0311 Hz. Guide tone : 25200, 14.6211 octaves, 6592964.246 Hz. Exponens Consonantiae : 2.116800E+08, 27.65731 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 207.5, average 10.92105 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 17.09209, average 0.89958 Sum of Tenney's harmonic distance : 33.45406, average 1.76074 Vogel's harmonic complexity : 25.42105 Wille's k value : 6562 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 9 Triangular lattice diameter : 4 Lattice compactness : 655.20778, average 3.44846 Lattice compactness (without 2's) : 401.78825, average 2.11468 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 -0.36842 33 1 3: -1 .. 2 0.47368 17 3 5: -2 .. 2 0.00000 16 10 7: -1 .. 1 0.05263 5 5 Average exponent except 2's : 10 / 19 = 0.52632 Average absolute exponent except 2's: 38 / 19 = 2.00000 Scale is JI-epimorphic with val: <19 30 44 53| = 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: 10.1883 c. M: 21.4575 c. 29: 2 1 2 1 2 1 2 1 2 1 2 2 1 1 2 2 1 1 2 P D3 S SD: 12.5145 c. M:-20.0883 c. 31: 2 1 2 2 1 2 1 2 2 1 2 2 1 2 2 1 2 1 2 P M ME S SD: 6.2036 c. M: 11.9277 c. 46: 3 2 3 2 2 3 2 2 3 2 3 3 1 3 3 2 3 1 3 P D3 SD: 6.1056 c. M:-10.9920 c. 50: 3 2 3 3 2 3 2 3 3 2 3 3 2 3 3 2 3 2 3 SP M ME S SD: 5.7436 c. M: 11.9100 c. 53: 3 2 4 3 2 3 2 3 4 2 3 3 2 3 4 2 3 2 3 P T3 SD: 3.1491 c. M: 6.2353 c. 72: 4 3 5 4 3 4 3 4 5 3 4 4 3 4 5 3 4 3 4 SP T3 SD: 2.8654 c. M: 5.9608 c. 87: 5 4 6 4 4 5 4 4 6 4 5 5 3 5 6 4 5 3 5 SP SD: 2.8290 c. M:-6.2952 c. 90: 5 4 6 5 4 5 4 4 7 3 6 5 3 5 7 3 6 3 5 P SD: 3.6832 c. M:-5.0646 c. 99: 6 4 7 5 4 6 4 5 7 4 6 6 3 6 7 4 6 3 6 P SD: 1.5370 c. M:-3.1301 c. 118: 7 5 8 6 5 7 5 6 8 5 7 7 4 7 8 5 7 4 7 SP SD: 1.3681 c. M: 2.8512 c. 152: 9 6 11 8 6 9 6 8 11 6 9 9 5 9 11 6 9 5 9 P SD: 1.0007 c. M:-2.2267 c. 171: 10 7 12 9 7 10 7 9 12 7 10 10 6 10 12 7 10 6 10 SP SD: 0.3349 c. M: 0.6976 c. 441: 26 18 31 23 18 26 18 23 31 18 26 26 15 26 31 18 26 15 26 SP SD: 0.1436 c. M:-0.2901 c. 612: 36 25 43 32 25 36 25 32 43 25 36 36 21 36 43 25 36 21 36 SP SD: 0.1069 c. M:-0.2100 c. 935: 55 38 66 49 38 55 38 49 66 38 55 55 32 55 66 38 55 32 55 SP SD: 0.0984 c. M:-0.1616 c. 1106: 65 45 78 58 45 65 45 58 78 45 65 65 38 65 78 45 65 38 65 SP SD: 0.0940 c. M:-0.1822 c. 1376: 81 56 97 72 56 81 56 72 97 56 81 81 47 81 97 56 81 47 81 SP SD: 0.0756 c. M:-0.1598 c. 1407: 83 57 99 74 57 83 57 74 99 57 83 83 48 83 99 57 83 48 83 SP SD: 0.0780 c. M: 0.1525 c. 1547: 91 63 109 81 63 91 63 81 109 63 91 91 53 91 109 63 91 53 91 SP SD: 0.0651 c. M:-0.1331 c. 1578: 93 64 111 83 64 93 64 83 111 64 93 93 54 93 111 64 93 54 93 SP SD: 0.0601 c. M: 0.1077 c. 1749: 103 71 123 92 71 103 71 92 123 71 103 103 60 103 123 71 103 60 103 SP SD: 0.0639 c. M: 0.1364 c. 1848: 109 75 130 97 75 109 75 97 130 75 109 109 63 109 130 75 109 63 109 SP SD: 0.0595 c. M: 0.1137 c. 2019: 119 82 142 106 82 119 82 106 142 82 119 119 69 119 142 82 119 69 119 SP SD: 0.0385 c. M: 0.0790 c. 2190: 129 89 154 115 89 129 89 115 154 89 129 129 75 129 154 89 129 75 129 SP SD: 0.0370 c. M: 0.0744 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: 0.0000 cents 5 .. 10 match: 5 H SD: 0.0000 cents 6 .. 12 match: 6 H SD: 5.2944 cents 7 .. 14 match: 7 H SD: 7.2558 cents 8 .. 16 match: 8 H SD: 5.1441 cents 9 .. 18 match: 9 H SD: 5.1942 cents 10 .. 20 match: 10 H SD: 5.8168 cents 11 .. 22 match: 11 H SD: 6.9706 cents 12 .. 24 match: 12 H SD: 3.8483 cents 13 .. 26 match: 13 H SD: 5.8745 cents 14 .. 28 match: 13 SD: 4.5731 cents 15 .. 30 match: 15 H SD: 3.8293 cents 16 .. 32 match: 16 H SD: 3.8716 cents 17 .. 34 match: 15 S SD: 4.7090 cents 18 .. 36 match: 16 S SD: 3.7706 cents 19 .. 38 match: 14 SD: 5.1574 cents 20 .. 40 match: 16 SD: 3.1915 cents 21 .. 42 match: 18 SD: 4.1022 cents 22 .. 44 match: 17 SD: 4.0139 cents 23 .. 46 match: 19 SD: 3.4092 cents 24 .. 48 match: 18 SD: 2.4057 cents 25 .. 50 match: 19 SD: 2.2041 cents 26 .. 52 match: 18 SD: 3.3244 cents 27 .. 54 match: 18 SD: 2.7955 cents 30 .. 60 match: 19 SD: 2.2735 cents 32 .. 64 match: 19 SD: 2.2519 cents 39 .. 78 match: 19 SD: 2.0251 cents 40 .. 80 match: 19 SD: 1.7706 cents 45 .. 90 match: 19 SD: 1.6612 cents 48 .. 96 match: 19 SD: 1.2308 cents 55 .. 110 match: 19 SD: 1.1799 cents 66 .. 132 match: 19 SD: 1.1224 cents 70 .. 140 match: 19 SD: 1.0235 cents 71 .. 142 match: 19 SD: 1.0005 cents 72 .. 144 match: 19 SD: 0.8878 cents 80 .. 160 match: 19 SD: 0.7494 cents 95 .. 190 match: 19 SD: 0.6822 cents 96 .. 192 match: 19 SD: 0.5768 cents 120 .. 240 match: 19 SD: 0.4642 cents 144 .. 288 match: 19 SD: 0.3967 cents 168 .. 336 match: 19 SD: 0.3227 cents 192 .. 384 match: 19 SD: 0.3099 cents 210 .. 420 match: 19 SD: 0.2944 cents 240 .. 480 match: 19 SD: 0.1767 cents 336 .. 672 match: 19 SD: 0.1214 cents 480 .. 960 match: 19 SD: 0.0726 cents