Scala analysis: xen07-chalmers-fokker-l
Fokker-L
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 175/162 133.633331 3: 125/112 190.115235 classic augmented semitone 4: 144/125 244.968860 classic diminished third 5: 6/5 315.641287 minor third 6: 56/45 378.602191 septimal narrow major third 7: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 8: 75/56 505.756522 marvelous fourth 9: 25/18 568.717426 classic augmented fourth 10: 36/25 631.282574 classic diminished fifth 11: 112/75 694.243478 marvelous fifth 12: 54/35 750.725382 septimal semi-augmented fifth 13: 45/28 821.397809 septimale wide minor sixth 14: 5/3 884.358713 major sixth, BP sixth 15: 125/72 955.031140 classic augmented sixth 16: 224/125 1009.884765 17: 324/175 1066.366669 18: 27/14 1137.039096 septimal major seventh 19: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 405/392 56.4819 greenwoodma 4: 16128/15625 54.8536 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 28/27 62.9609 Archytas' 1/3-tone 7: 25/24 70.6724 classic chromatic semitone, minor chroma 8: 405/392 56.4819 greenwoodma 9: 28/27 62.9609 Archytas' 1/3-tone 10: 648/625 62.5651 major diesis 11: 28/27 62.9609 Archytas' 1/3-tone 12: 405/392 56.4819 greenwoodma 13: 25/24 70.6724 classic chromatic semitone, minor chroma 14: 28/27 62.9609 Archytas' 1/3-tone 15: 25/24 70.6724 classic chromatic semitone, minor chroma 16: 16128/15625 54.8536 17: 405/392 56.4819 greenwoodma 18: 25/24 70.6724 classic chromatic semitone, minor chroma 19: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16128/15625 54.854 cents 1: 4 405/392 56.482 cents greenwoodma 1: 1 648/625 62.565 cents major diesis 1: 6 28/27 62.961 cents Archytas' 1/3-tone 1: 6 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 2 23328/21875 111.336 cents 2: 2 15/14 119.443 cents major diatonic semitone 2: 4 672/625 125.526 cents 2: 1 784/729 125.922 cents two (Archytas' 1/3-tone) 2: 4 3375/3136 127.154 cents 2: 6 175/162 133.633 cents 3: 6 972/875 182.008 cents 3: 3 6272/5625 188.487 cents 3: 6 125/112 190.115 cents classic augmented semitone 3: 2 2450/2187 196.594 cents 3: 2 4375/3888 204.306 cents 4: 6 144/125 244.969 cents classic diminished third 4: 4 81/70 252.680 cents Al-Hwarizmi's lute middle finger 4: 4 125/108 253.076 cents semi-augmented whole tone 4: 2 784/675 259.159 cents 4: 2 3125/2688 260.788 cents 4: 1 30625/26244 267.267 cents 5: 1 1458/1225 301.451 cents 5: 2 448/375 307.930 cents 5: 12 6/5 315.641 cents minor third 5: 4 3125/2592 323.749 cents 6: 4 243/196 372.123 cents 6: 10 56/45 378.602 cents septimal narrow major third 6: 1 15625/12544 380.230 cents two (classic augmented semitone) 6: 4 5/4 386.314 cents major third 7: 6 9/7 435.084 cents septimal major third, BP third 7: 2 4032/3125 441.167 cents 7: 2 1568/1215 441.563 cents 7: 3 2025/1568 442.796 cents 7: 6 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 8: 1 20736/15625 489.938 cents two (classic diminished third) 8: 2 5832/4375 497.649 cents 8: 2 12544/9375 504.128 cents 8: 10 75/56 505.757 cents marvelous fourth 8: 4 980/729 512.236 cents 9: 6 864/625 560.610 cents 9: 2 243/175 568.322 cents 9: 7 25/18 568.717 cents classic augmented fourth 9: 2 625/448 576.429 cents 9: 2 6125/4374 582.908 cents 10: 2 8748/6125 617.092 cents 10: 2 896/625 623.571 cents 10: 7 36/25 631.283 cents classic diminished fifth 10: 2 350/243 631.678 cents 10: 6 625/432 639.390 cents 11: 4 729/490 687.764 cents 11: 10 112/75 694.243 cents marvelous fifth 11: 2 9375/6272 695.872 cents 11: 2 4375/2916 702.351 cents 11: 1 15625/10368 710.062 cents 12: 6 54/35 750.725 cents septimal semi-augmented fifth 12: 3 3136/2025 757.204 cents two (septimal narrow major third) 12: 2 1215/784 758.437 cents 12: 2 3125/2016 758.833 cents 12: 6 14/9 764.916 cents septimal minor sixth 13: 4 8/5 813.686 cents minor sixth 13: 1 25088/15625 819.770 cents 13: 10 45/28 821.398 cents septimale wide minor sixth 13: 4 392/243 827.877 cents 14: 4 5184/3125 876.251 cents 14: 12 5/3 884.359 cents major sixth, BP sixth 14: 2 375/224 892.070 cents 14: 1 1225/729 898.549 cents two (septimal semi-diminished fourth, 9/4-tone) 15: 1 52488/30625 932.733 cents 15: 2 5376/3125 939.212 cents 15: 2 675/392 940.841 cents 15: 4 216/125 946.924 cents semi-augmented sixth 15: 4 140/81 947.320 cents 15: 6 125/72 955.031 cents classic augmented sixth 16: 2 7776/4375 995.694 cents 16: 2 2187/1225 1003.406 cents 16: 6 224/125 1009.885 cents 16: 3 5625/3136 1011.513 cents two (marvelous fourth) 16: 6 875/486 1017.992 cents 17: 6 324/175 1066.367 cents 17: 4 6272/3375 1072.846 cents 17: 1 729/392 1074.078 cents 17: 4 625/336 1074.474 cents 17: 2 28/15 1080.557 cents grave major seventh 17: 2 21875/11664 1088.664 cents 18: 6 48/25 1129.328 cents classic diminished octave 18: 6 27/14 1137.039 cents septimal major seventh 18: 1 625/324 1137.435 cents octave - major diesis 18: 4 784/405 1143.518 cents 18: 2 15625/8064 1145.146 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.00000 = 5
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 : 63.0 133.6 190.1 245.0 315.6 378.6 449.3 505.8 568.7 631.3 694.2 750.7 821.4 884.4 955.0 1009.9 1066.4 1137.0 1200.0 63.0 : 70.7 127.2 182.0 252.7 315.6 386.3 442.8 505.8 568.3 631.3 687.8 758.4 821.4 892.1 946.9 1003.4 1074.1 1137.0 1200.0 133.6 : 56.5 111.3 182.0 245.0 315.6 372.1 435.1 497.6 560.6 617.1 687.8 750.7 821.4 876.3 932.7 1003.4 1066.4 1129.3 1200.0 190.1 : 54.9 125.5 188.5 259.2 315.6 378.6 441.2 504.1 560.6 631.3 694.2 764.9 819.8 876.3 946.9 1009.9 1072.8 1143.5 1200.0 245.0 : 70.7 133.6 204.3 260.8 323.7 386.3 449.3 505.8 576.4 639.4 710.1 764.9 821.4 892.1 955.0 1018.0 1088.7 1145.1 1200.0 315.6 : 63.0 133.6 190.1 253.1 315.6 378.6 435.1 505.8 568.7 639.4 694.2 750.7 821.4 884.4 947.3 1018.0 1074.5 1129.3 1200.0 378.6 : 70.7 127.2 190.1 252.7 315.6 372.1 442.8 505.8 576.4 631.3 687.8 758.4 821.4 884.4 955.0 1011.5 1066.4 1137.0 1200.0 449.3 : 56.5 119.4 182.0 245.0 301.5 372.1 435.1 505.8 560.6 617.1 687.8 750.7 813.7 884.4 940.8 995.7 1066.4 1129.3 1200.0 505.8 : 63.0 125.5 188.5 245.0 315.6 378.6 449.3 504.1 560.6 631.3 694.2 757.2 827.9 884.4 939.2 1009.9 1072.8 1143.5 1200.0 568.7 : 62.6 125.5 182.0 252.7 315.6 386.3 441.2 497.6 568.3 631.3 694.2 764.9 821.4 876.3 946.9 1009.9 1080.6 1137.0 1200.0 631.3 : 63.0 119.4 190.1 253.1 323.7 378.6 435.1 505.8 568.7 631.7 702.4 758.8 813.7 884.4 947.3 1018.0 1074.5 1137.4 1200.0 694.2 : 56.5 127.2 190.1 260.8 315.6 372.1 442.8 505.8 568.7 639.4 695.9 750.7 821.4 884.4 955.0 1011.5 1074.5 1137.0 1200.0 750.7 : 70.7 133.6 204.3 259.2 315.6 386.3 449.3 512.2 582.9 639.4 694.2 764.9 827.9 898.5 955.0 1018.0 1080.6 1143.5 1200.0 821.4 : 63.0 133.6 188.5 245.0 315.6 378.6 441.6 512.2 568.7 623.6 694.2 757.2 827.9 884.4 947.3 1009.9 1072.8 1129.3 1200.0 884.4 : 70.7 125.5 182.0 252.7 315.6 378.6 449.3 505.8 560.6 631.3 694.2 764.9 821.4 884.4 946.9 1009.9 1066.4 1137.0 1200.0 955.0 : 54.9 111.3 182.0 245.0 307.9 378.6 435.1 489.9 560.6 623.6 694.2 750.7 813.7 876.3 939.2 995.7 1066.4 1129.3 1200.0 1009.9: 56.5 127.2 190.1 253.1 323.7 380.2 435.1 505.8 568.7 639.4 695.9 758.8 821.4 884.4 940.8 1011.5 1074.5 1145.1 1200.0 1066.4: 70.7 133.6 196.6 267.3 323.7 378.6 449.3 512.2 582.9 639.4 702.4 764.9 827.9 884.4 955.0 1018.0 1088.7 1143.5 1200.0 1137.0: 63.0 125.9 196.6 253.1 307.9 378.6 441.6 512.2 568.7 631.7 694.2 757.2 813.7 884.4 947.3 1018.0 1072.8 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.8536 .. 70.6724 cents 390625/387072, 15.8188 cents 16128/15625, 54.8536 cents 2: 111.3355 .. 133.6333 cents 3828125/3779136, 22.2978 cents 559872/546875, 40.6631 cents 3: 182.0080 .. 204.3058 cents 3828125/3779136, 22.2978 cents 157464/153125, 48.3746 cents 4: 244.9689 .. 267.2667 cents 3828125/3779136, 22.2978 cents 559872/546875, 40.6631 cents 5: 301.4508 .. 323.7486 cents 3828125/3779136, 22.2978 cents 38263752/37515625, 34.1841 cents 6: 372.1232 .. 386.3137 cents 245/243, 14.1905 cents 157464/153125, 48.3746 cents 7: 435.0841 .. 449.2746 cents 245/243, 14.1905 cents 36/35, 48.7704 cents 8: 489.9377 .. 512.2355 cents 3828125/3779136, 22.2978 cents 559872/546875, 40.6631 cents 9: 560.6101 .. 582.9079 cents 3828125/3779136, 22.2978 cents 157464/153125, 48.3746 cents 10: 617.0921 .. 639.3899 cents 3828125/3779136, 22.2978 cents 38263752/37515625, 34.1841 cents 11: 687.7645 .. 710.0623 cents 3828125/3779136, 22.2978 cents 157464/153125, 48.3746 cents 12: 750.7254 .. 764.9159 cents 245/243, 14.1905 cents 559872/546875, 40.6631 cents 13: 813.6863 .. 827.8768 cents 245/243, 14.1905 cents 36/35, 48.7704 cents 14: 876.2514 .. 898.5492 cents 3828125/3779136, 22.2978 cents 157464/153125, 48.3746 cents 15: 932.7333 .. 955.0311 cents 3828125/3779136, 22.2978 cents 38263752/37515625, 34.1841 cents 16: 995.6942 .. 1017.9920 cents 3828125/3779136, 22.2978 cents 559872/546875, 40.6631 cents 17: 1066.3667 .. 1088.6645 cents 3828125/3779136, 22.2978 cents 157464/153125, 48.3746 cents 18: 1129.3276 .. 1145.1464 cents 390625/387072, 15.8188 cents 559872/546875, 40.6631 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 16128/15625, 54.8536 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 25/24, 70.6724 cents Average / Smallest step : 1.151390 Largest / Average step : 1.118980 Largest / Smallest step : 1.288382 Median interval of one step : 28/27, 62.9609 cents, amount: 6 Least squares average step : 63.13185 cents, oct.: 1199.50509 cents Scale is strictly proper Step pattern alph. order: ABCDBABCAEACBABDCBA Step pattern size order : DEBAEDEBDCDBEDEABED Scale is a Constant Structure, by a margin of 34.18410 cents Scale diversity : 1.212146 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.703356 Number of different interval sizes : 90 = 5.00000 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 4375/4374, 0.3958 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 12 Most common triad is 0.0 315.641 884.359 cents, amount: 7 Number of recognisable fifths : 19, average 694.7368 cents Number of appreciable fifths : 15, average 696.5961 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 7 27 45 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% Limited transpositions with margin 22.2978 cents: 1 6 13 18 Limited inverse transpositions with margin 22.2978 cents: 1 6 13 18 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties -- Prime limit : 7 Odd number limit : 30625 (O: 30625 U: 30625) Highest odd numerator or denominator: 175 Scale harmonicity : 0.011198 Average absolute harmonicity : 0.096269 Specific harmonicity : 0.063888 Fundamental : 1/1134000, -20.1130 octaves, 0.0002 Hz. Guide tone : 2268000, 21.1130 octaves, 593366782.103 Hz. Exponens Consonantiae : 2.571912E+12, 41.22598 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 1376.5, average 72.44737 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 30.07495, average 1.58289 Sum of Tenney's harmonic distance : 60.32784, average 3.17515 Vogel's harmonic complexity : 38.52632 Wille's k value : 632812 Wilson's harmonic complexity : 68 Rectangular lattice diameter : 16 Triangular lattice diameter : 8 Lattice compactness : 965.68479, average 5.08255 Lattice compactness (without 2's) : 742.20852, average 3.90636 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.52632 40 1 3: -4 .. 4 0.00000 36 5: -3 .. 3 0.00000 30 6 7: -1 .. 1 0.00000 12 12 Average exponent except 2's : 0 / 19 = 0.00000 Average absolute exponent except 2's: 78 / 19 = 4.10526 Scale is weakly epimorphic with val: <19 29 44 50| 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: 4.1623 c. M:-7.6627 c. 64: 3 4 3 3 4 3 4 3 3 4 3 3 4 3 4 3 3 4 3 SP M ME I SD: 3.5705 c. M:-6.7109 c. 69: 4 4 3 3 4 4 4 3 4 3 4 3 4 4 4 3 3 4 4 SP D3 I SD: 3.8066 c. M: 6.6043 c. 80: 4 5 4 3 5 4 5 4 4 4 4 4 5 4 5 3 4 5 4 SP D3 I SD: 3.1246 c. M:-4.9689 c. 83: 4 5 4 4 5 4 5 4 4 5 4 4 5 4 5 4 4 5 4 SP M ME I SD: 2.9392 c. M:-5.1296 c. 88: 5 5 4 4 5 5 5 4 5 4 5 4 5 5 5 4 4 5 5 SP D3 I SD: 2.6757 c. M:-5.2209 c. 99: 5 6 5 4 6 5 6 5 5 5 5 5 6 5 6 4 5 6 5 SP D3 I SD: 2.2424 c. M:-3.8242 c. 107: 6 6 5 5 6 6 6 5 6 5 6 5 6 6 6 5 5 6 6 SP D3 I SD: 2.1799 c. M: 4.3288 c. 114: 6 7 5 5 7 6 7 5 6 6 6 5 7 6 7 5 5 7 6 SP I SD: 1.7973 c. M: 3.3570 c. 118: 6 7 6 5 7 6 7 6 6 6 6 6 7 6 7 5 6 7 6 SP D3 I SD: 1.8680 c. M: 3.1051 c. 133: 7 8 6 6 8 7 8 6 7 7 7 6 8 7 8 6 6 8 7 SP I SD: 0.9794 c. M: 1.8532 c. 152: 8 9 7 7 9 8 9 7 8 8 8 7 9 8 9 7 7 9 8 SP I SD: 0.4396 c. M: 0.7254 c. 171: 9 10 8 8 10 9 10 8 9 9 9 8 10 9 10 8 8 10 9 SP I SD: 0.3910 c. M:-0.6452 c. 323: 17 19 15 15 19 17 19 15 17 17 17 15 19 17 19 15 15 19 17 SP I SD: 0.3337 c. M:-0.6416 c. 422: 22 25 20 19 25 22 25 20 22 22 22 20 25 22 25 19 20 25 22 SP I SD: 0.2953 c. M:-0.4191 c. 441: 23 26 21 20 26 23 26 21 23 23 23 21 26 23 26 20 21 26 23 SP I SD: 0.2763 c. M: 0.3759 c. 574: 30 34 27 26 34 30 34 27 30 30 30 27 34 30 34 26 27 34 30 SP I SD: 0.1940 c. M:-0.3696 c. 593: 31 35 28 27 35 31 35 28 31 31 31 28 35 31 35 27 28 35 31 SP I SD: 0.1247 c. M: 0.2290 c. 745: 39 44 35 34 44 39 44 35 39 39 39 35 44 39 44 34 35 44 39 SP I SD: 0.0950 c. M: 0.1421 c. 764: 40 45 36 35 45 40 45 36 40 40 40 36 45 40 45 35 36 45 40 SP I SD: 0.0862 c. M:-0.1337 c. 1445: 76 85 68 66 85 76 85 68 76 75 76 68 85 76 85 66 68 85 76 SP I SD: 0.0818 c. M: 0.1533 c. 1509: 79 89 71 69 89 79 89 71 79 79 79 71 89 79 89 69 71 89 79 SP I SD: 0.0739 c. M:-0.1378 c. 1886: 99 111 89 86 111 99 111 89 99 98 99 89 111 99 111 86 89 111 99 SP I SD: 0.0672 c. M:-0.1287 c. 2019: 106 119 95 92 119 106 119 95 106 105 106 95 119 106 119 92 95 119 106 SP I SD: 0.0637 c. M:-0.0962 c. 2038: 107 120 96 93 120 107 120 96 107 106 107 96 120 107 120 93 96 120 107 SP I SD: 0.0416 c. M:-0.0755 c. 2190: 115 129 103 100 129 115 129 103 115 114 115 103 129 115 129 100 103 129 115 SP I SD: 0.0390 c. M:-0.0653 c. 2209: 116 130 104 101 130 116 130 104 116 115 116 104 130 116 130 101 104 130 116 SP I SD: 0.0294 c. M:-0.0540 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 3.8558 cents 3 .. 6 match: 3 H SD: 2.5705 cents 4 .. 8 match: 4 H SD: 4.3962 cents 5 .. 10 match: 5 H SD: 3.5170 cents 6 .. 12 match: 6 H SD: 4.9659 cents 7 .. 14 match: 7 H SD: 6.5454 cents 8 .. 16 match: 8 H SD: 5.0743 cents 9 .. 18 match: 9 H SD: 5.7893 cents 10 .. 20 match: 10 H SD: 5.3541 cents 11 .. 22 match: 11 H SD: 6.6007 cents 12 .. 24 match: 12 H SD: 4.3656 cents 13 .. 26 match: 13 H SD: 3.9682 cents 14 .. 28 match: 14 H SD: 4.4967 cents 15 .. 30 match: 15 H SD: 4.1143 cents 16 .. 32 match: 16 H SD: 4.2686 cents 17 .. 34 match: 15 SD: 5.5631 cents 18 .. 36 match: 17 SD: 3.8631 cents 19 .. 38 match: 17 SD: 4.5679 cents 20 .. 40 match: 18 SD: 2.9467 cents 21 .. 42 match: 18 SD: 3.5812 cents 22 .. 44 match: 17 SD: 4.3605 cents 23 .. 46 match: 19 SD: 3.6790 cents 24 .. 48 match: 19 SD: 2.8141 cents 26 .. 52 match: 19 SD: 2.3148 cents 33 .. 66 match: 19 SD: 2.0891 cents 41 .. 82 match: 19 SD: 1.7231 cents 46 .. 92 match: 19 SD: 1.6593 cents 48 .. 96 match: 19 SD: 1.6096 cents 50 .. 100 match: 19 SD: 1.4581 cents 51 .. 102 match: 19 SD: 1.4564 cents 52 .. 104 match: 19 SD: 1.4380 cents 53 .. 106 match: 19 SD: 1.1787 cents 54 .. 108 match: 19 SD: 1.1760 cents 59 .. 118 match: 19 SD: 1.1631 cents 61 .. 122 match: 19 SD: 0.9347 cents 77 .. 154 match: 19 SD: 0.8572 cents 85 .. 170 match: 19 SD: 0.7253 cents 105 .. 210 match: 19 SD: 0.6609 cents 110 .. 220 match: 19 SD: 0.6245 cents 111 .. 222 match: 19 SD: 0.5160 cents 136 .. 272 match: 19 SD: 0.4572 cents 159 .. 318 match: 19 SD: 0.4448 cents 162 .. 324 match: 19 SD: 0.4150 cents 164 .. 328 match: 19 SD: 0.3842 cents 186 .. 372 match: 19 SD: 0.3735 cents 188 .. 376 match: 19 SD: 0.3707 cents 189 .. 378 match: 19 SD: 0.3437 cents 209 .. 418 match: 19 SD: 0.3081 cents 216 .. 432 match: 19 SD: 0.2656 cents 249 .. 498 match: 19 SD: 0.2503 cents 250 .. 500 match: 19 SD: 0.1909 cents 348 .. 696 match: 19 SD: 0.1859 cents 375 .. 750 match: 19 SD: 0.1676 cents 389 .. 778 match: 19 SD: 0.1634 cents 409 .. 818 match: 19 SD: 0.1519 cents 450 .. 900 match: 19 SD: 0.1482 cents 466 .. 932 match: 19 SD: 0.1206 cents 486 .. 972 match: 19 SD: 0.1057 cents 560 .. 1120 match: 19 SD: 0.0979 cents 586 .. 1172 match: 19 SD: 0.0973 cents