Scala analysis: catakleismic34semitransversal
17 note 2.3.7 semitransversal of Catakleismic[34]
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: 243/224 140.949098 Archytas' 2/3-tone 3: 9/8 203.910002 major whole tone 4: 7/6 266.870906 septimal minor third 5: 243/196 372.123191 6: 9/7 435.084095 septimal major third, BP third 7: 4/3 498.044999 perfect fourth 8: 112/81 561.005903 9: 81/56 638.994097 10: 3/2 701.955001 perfect fifth 11: 14/9 764.915905 septimal minor sixth 12: 392/243 827.876809 13: 12/7 933.129094 septimal major sixth 14: 16/9 996.089998 Pythagorean minor seventh 15: 448/243 1059.050902 16: 27/14 1137.039096 septimal major seventh 17: 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: 6561/6272 77.9882 3: 28/27 62.9609 Archytas' 1/3-tone 4: 28/27 62.9609 Archytas' 1/3-tone 5: 729/686 105.2523 6: 28/27 62.9609 Archytas' 1/3-tone 7: 28/27 62.9609 Archytas' 1/3-tone 8: 28/27 62.9609 Archytas' 1/3-tone 9: 6561/6272 77.9882 10: 28/27 62.9609 Archytas' 1/3-tone 11: 28/27 62.9609 Archytas' 1/3-tone 12: 28/27 62.9609 Archytas' 1/3-tone 13: 729/686 105.2523 14: 28/27 62.9609 Archytas' 1/3-tone 15: 28/27 62.9609 Archytas' 1/3-tone 16: 6561/6272 77.9882 17: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 28/27 62.961 cents Archytas' 1/3-tone 1: 3 6561/6272 77.988 cents 1: 2 729/686 105.252 cents 2: 7 784/729 125.922 cents two (Archytas' 1/3-tone) 2: 6 243/224 140.949 cents Archytas' 2/3-tone 2: 4 54/49 168.213 cents Zalzal's mujannab 3: 2 21952/19683 188.883 cents 3: 9 9/8 203.910 cents major whole tone 3: 6 8/7 231.174 cents septimal whole tone 4: 8 7/6 266.871 cents septimal minor third 4: 1 59049/50176 281.898 cents two (Archytas' 2/3-tone) 4: 6 32/27 294.135 cents Pythagorean minor third 4: 2 6561/5488 309.162 cents 5: 5 98/81 329.832 cents 5: 2 2187/1792 344.859 cents 5: 4 896/729 357.096 cents 5: 6 243/196 372.123 cents 6: 2 2744/2187 392.793 cents 6: 3 81/64 407.820 cents Pythagorean major third 6: 2 25088/19683 420.057 cents 6: 10 9/7 435.084 cents septimal major third, BP third 7: 1 76832/59049 455.754 cents 7: 2 21/16 470.781 cents narrow fourth 7: 12 4/3 498.045 cents perfect fourth 7: 2 59049/43904 513.072 cents 8: 1 49/36 533.742 cents Arabic lute acute fourth 8: 10 112/81 561.006 cents 8: 6 2187/1568 576.033 cents 9: 6 3136/2187 623.967 cents 9: 10 81/56 638.994 cents 9: 1 72/49 666.258 cents Arabic lute grave fifth 10: 2 87808/59049 686.928 cents 10: 12 3/2 701.955 cents perfect fifth 10: 2 32/21 729.219 cents wide fifth 10: 1 59049/38416 744.246 cents 11: 10 14/9 764.916 cents septimal minor sixth 11: 2 19683/12544 779.943 cents 11: 3 128/81 792.180 cents Pythagorean minor sixth 11: 2 2187/1372 807.207 cents 12: 6 392/243 827.877 cents 12: 4 729/448 842.904 cents 12: 2 3584/2187 855.141 cents 12: 5 81/49 870.168 cents two (septimal major third, BP third) 13: 2 10976/6561 890.838 cents 13: 6 27/16 905.865 cents Pythagorean major sixth 13: 1 100352/59049 918.102 cents 13: 8 12/7 933.129 cents septimal major sixth 14: 6 7/4 968.826 cents harmonic seventh 14: 9 16/9 996.090 cents Pythagorean minor seventh 14: 2 19683/10976 1011.117 cents 15: 4 49/27 1031.787 cents 15: 6 448/243 1059.051 cents 15: 7 729/392 1074.078 cents 16: 2 1372/729 1094.748 cents 16: 3 12544/6561 1122.012 cents 16: 12 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.50000 = 7/2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 63.0 140.9 203.9 266.9 372.1 435.1 498.0 561.0 639.0 702.0 764.9 827.9 933.1 996.1 1059.1 1137.0 1200.0 63.0 : 78.0 140.9 203.9 309.2 372.1 435.1 498.0 576.0 639.0 702.0 764.9 870.2 933.1 996.1 1074.1 1137.0 1200.0 140.9 : 63.0 125.9 231.2 294.1 357.1 420.1 498.0 561.0 624.0 686.9 792.2 855.1 918.1 996.1 1059.1 1122.0 1200.0 203.9 : 63.0 168.2 231.2 294.1 357.1 435.1 498.0 561.0 624.0 729.2 792.2 855.1 933.1 996.1 1059.1 1137.0 1200.0 266.9 : 105.3 168.2 231.2 294.1 372.1 435.1 498.0 561.0 666.3 729.2 792.2 870.2 933.1 996.1 1074.1 1137.0 1200.0 372.1 : 63.0 125.9 188.9 266.9 329.8 392.8 455.8 561.0 624.0 686.9 764.9 827.9 890.8 968.8 1031.8 1094.7 1200.0 435.1 : 63.0 125.9 203.9 266.9 329.8 392.8 498.0 561.0 624.0 702.0 764.9 827.9 905.9 968.8 1031.8 1137.0 1200.0 498.0 : 63.0 140.9 203.9 266.9 329.8 435.1 498.0 561.0 639.0 702.0 764.9 842.9 905.9 968.8 1074.1 1137.0 1200.0 561.0 : 78.0 140.9 203.9 266.9 372.1 435.1 498.0 576.0 639.0 702.0 779.9 842.9 905.9 1011.1 1074.1 1137.0 1200.0 639.0 : 63.0 125.9 188.9 294.1 357.1 420.1 498.0 561.0 624.0 702.0 764.9 827.9 933.1 996.1 1059.1 1122.0 1200.0 702.0 : 63.0 125.9 231.2 294.1 357.1 435.1 498.0 561.0 639.0 702.0 764.9 870.2 933.1 996.1 1059.1 1137.0 1200.0 764.9 : 63.0 168.2 231.2 294.1 372.1 435.1 498.0 576.0 639.0 702.0 807.2 870.2 933.1 996.1 1074.1 1137.0 1200.0 827.9 : 105.3 168.2 231.2 309.2 372.1 435.1 513.1 576.0 639.0 744.2 807.2 870.2 933.1 1011.1 1074.1 1137.0 1200.0 933.1 : 63.0 125.9 203.9 266.9 329.8 407.8 470.8 533.7 639.0 702.0 764.9 827.9 905.9 968.8 1031.8 1094.7 1200.0 996.1 : 63.0 140.9 203.9 266.9 344.9 407.8 470.8 576.0 639.0 702.0 764.9 842.9 905.9 968.8 1031.8 1137.0 1200.0 1059.1: 78.0 140.9 203.9 281.9 344.9 407.8 513.1 576.0 639.0 702.0 779.9 842.9 905.9 968.8 1074.1 1137.0 1200.0 1137.0: 63.0 125.9 203.9 266.9 329.8 435.1 498.0 561.0 624.0 702.0 764.9 827.9 890.8 996.1 1059.1 1122.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 105.2523 cents 19683/19208, 42.2914 cents 28/27, 62.9609 cents 2: 125.9218 .. 168.2132 cents 19683/19208, 42.2914 cents 537824/531441, 20.6695 cents 3: 188.8827 .. 231.1741 cents 19683/19208, 42.2914 cents 537824/531441, 20.6695 cents 4: 266.8709 .. 309.1623 cents 19683/19208, 42.2914 cents 49/48, 35.6968 cents 5: 329.8318 .. 372.1232 cents 19683/19208, 42.2914 cents 537824/531441, 20.6695 cents 6: 392.7927 .. 435.0841 cents 19683/19208, 42.2914 cents 537824/531441, 20.6695 cents 7: 455.7536 .. 513.0723 cents 57.31867 cents 537824/531441, 20.6695 cents 8: 533.7418 .. 576.0332 cents 19683/19208, 42.2914 cents 537824/531441, 20.6695 cents 9: 623.9668 .. 666.2582 cents 19683/19208, 42.2914 cents 4917248/4782969, 47.9336 cents 10: 686.9277 .. 744.2464 cents 57.31867 cents 537824/531441, 20.6695 cents 11: 764.9159 .. 807.2073 cents 19683/19208, 42.2914 cents 537824/531441, 20.6695 cents 12: 827.8768 .. 870.1682 cents 19683/19208, 42.2914 cents 537824/531441, 20.6695 cents 13: 890.8377 .. 933.1291 cents 19683/19208, 42.2914 cents 537824/531441, 20.6695 cents 14: 968.8259 .. 1011.1173 cents 19683/19208, 42.2914 cents 49/48, 35.6968 cents 15: 1031.7868 .. 1074.0782 cents 19683/19208, 42.2914 cents 537824/531441, 20.6695 cents 16: 1094.7477 .. 1137.0391 cents 19683/19208, 42.2914 cents 537824/531441, 20.6695 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 729/686, 105.2523 cents Average / Smallest step : 1.121144 Largest / Average step : 1.491074 Largest / Smallest step : 1.671709 Median interval of one step : 28/27, 62.9609 cents, amount: 12 Most common interval of one step : 28/27, 62.9609 cents, amount: 12 Least squares average step : 70.66833 cents, oct.: 1201.36168 cents Scale is strictly proper Step pattern alph. order: ABAACAAABAAACAABA Step pattern size order : SMSSLSSSMSSSLSSMS Scale is a Constant Structure, by a margin of 20.66952 cents Scale diversity : 1.347439 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.411069 Number of different interval sizes : 56 = 3.50000 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.50000 = 7/2 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 1605632/1594323, 12.2368 cents Number of recognisable fifths : 14, average 699.8082 cents Number of appreciable fifths : 12, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 3 7 9 27 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 17 = 100.0000% Scale is n-1 differentially coherent in interval classes 3 and 4 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 8-9 -- Rational properties -- Prime limit : 7 Odd number limit : 59049 (O: 59049 U: 59049) Highest odd numerator or denominator: 243 Scale harmonicity : 0.012689 Average absolute harmonicity : 0.134325 Specific harmonicity : 0.084028 Fundamental : 1/381024, -18.5395 octaves, 0.0007 Hz. Guide tone : 762048, 19.5395 octaves, 199371238.786 Hz. Exponens Consonantiae : 2.903586E+11, 38.07904 octaves Euler's gradus suavitatis : 56 Sum of Mann's harmonic distance : 1393.0, average 81.94118 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 22.68353, average 1.33433 Sum of Tenney's harmonic distance : 46.12118, average 2.71301 Vogel's harmonic complexity : 34.52941 Wille's k value : 206671 Wilson's harmonic complexity : 58 Rectangular lattice diameter : 14 Triangular lattice diameter : 10 Lattice compactness : 823.55692, average 5.38272 Lattice compactness (without 2's) : 609.19938, average 3.98170 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 6 0.52941 41 1 3: -5 .. 5 0.00000 46 4 7: -2 .. 2 0.00000 14 12 Average exponent except 2's : 0 / 17 = 0.00000 Average absolute exponent except 2's: 60 / 17 = 3.52941 Scale is weakly epimorphic with val: <17 26 50| Scale is JI-epimorphic with val: <17 27 48| = patent Scale is weakly epimorphic with val: <17 28 46|
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.2337 c. M: 19.1820 c. 19: 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 P M ME I SD: 9.8715 c. M: 14.6333 c. 34: 2 2 2 2 3 1 2 2 2 2 2 1 3 2 2 2 2 N T3 I SD: 9.5907 c. M: 16.1121 c. 35: 2 2 2 2 3 2 2 1 3 1 2 2 3 2 2 2 2 P D3 I SD: 8.8169 c. M:-16.2407 c. 36: 2 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 2 SP M ME I SD: 4.2808 c. M: 7.6158 c. 57: 3 4 3 3 5 3 3 3 3 3 3 3 5 3 3 4 3 P I SD: 6.2722 c. M:-7.4151 c. 58: 3 4 3 3 5 3 3 3 4 3 3 3 5 3 3 4 3 SP I SD: 2.1007 c. M: 3.8785 c. 77: 4 5 4 4 7 4 4 4 5 4 4 4 7 4 4 5 4 SP I SD: 1.1893 c. M:-1.9358 c. 94: 5 6 5 5 8 5 5 5 6 5 5 5 8 5 5 6 5 SP I SD: 0.9623 c. M: 1.9104 c. 135: 7 9 7 7 12 7 7 7 9 7 7 7 12 7 7 9 7 SP I SD: 0.7869 c. M: 1.2731 c. 171: 9 11 9 9 15 9 9 9 11 9 9 9 15 9 9 11 9 SP I SD: 0.3134 c. M: 0.5982 c. 229: 12 15 12 12 20 12 12 12 15 12 12 12 20 12 12 15 12 SP I SD: 0.3103 c. M: 0.5356 c. 306: 16 20 16 16 27 16 16 16 20 16 16 16 27 16 16 20 16 SP I SD: 0.2209 c. M: 0.4258 c. 400: 21 26 21 21 35 21 21 21 26 21 21 21 35 21 21 26 21 SP I SD: 0.0791 c. M: 0.1291 c. 706: 37 46 37 37 62 37 37 37 46 37 37 37 62 37 37 46 37 SP I SD: 0.0770 c. M:-0.1274 c. 877: 46 57 46 46 77 46 46 46 57 46 46 46 77 46 46 57 46 SP I SD: 0.0324 c. M: 0.0547 c. 1277: 67 83 67 67 112 67 67 67 83 67 67 67 112 67 67 83 67 SP I SD: 0.0037 c. M: 0.0063 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: 16.2568 cents 4 .. 8 match: 4 H SD: 7.6840 cents 5 .. 10 match: 5 H SD: 11.8405 cents 6 .. 12 match: 6 H SD: 8.2872 cents 7 .. 14 match: 7 H SD: 5.8464 cents 8 .. 16 match: 8 H SD: 5.6628 cents 9 .. 18 match: 9 H SD: 7.6603 cents 10 .. 20 match: 10 H SD: 7.2987 cents 11 .. 22 match: 11 H SD: 5.2779 cents 12 .. 24 match: 11 SD: 5.2959 cents 13 .. 26 match: 13 H SD: 4.1042 cents 14 .. 28 match: 14 H SD: 5.2625 cents 15 .. 30 match: 14 S SD: 6.0758 cents 16 .. 32 match: 15 S SD: 5.1690 cents 17 .. 34 match: 15 SD: 5.5253 cents 18 .. 36 match: 16 SD: 3.1600 cents 19 .. 38 match: 15 SD: 5.7310 cents 20 .. 40 match: 16 SD: 4.1862 cents 21 .. 42 match: 17 SD: 4.1455 cents 22 .. 44 match: 17 SD: 3.8719 cents 23 .. 46 match: 17 SD: 3.7446 cents 24 .. 48 match: 17 SD: 2.2425 cents 34 .. 68 match: 17 SD: 2.1827 cents 36 .. 72 match: 17 SD: 2.1669 cents 38 .. 76 match: 17 SD: 2.1661 cents 42 .. 84 match: 17 SD: 1.8597 cents 46 .. 92 match: 17 SD: 1.7595 cents 47 .. 94 match: 17 SD: 1.7326 cents 49 .. 98 match: 17 SD: 1.4157 cents 54 .. 108 match: 17 SD: 1.3400 cents 58 .. 116 match: 17 SD: 1.2761 cents 60 .. 120 match: 17 SD: 1.2611 cents 70 .. 140 match: 17 SD: 1.0326 cents 72 .. 144 match: 17 SD: 0.9780 cents 78 .. 156 match: 17 SD: 0.9229 cents 83 .. 166 match: 17 SD: 0.8658 cents 96 .. 192 match: 17 SD: 0.7597 cents 104 .. 208 match: 17 SD: 0.6882 cents 108 .. 216 match: 17 SD: 0.5732 cents 126 .. 252 match: 17 SD: 0.4933 cents 144 .. 288 match: 17 SD: 0.4871 cents 154 .. 308 match: 17 SD: 0.4596 cents 162 .. 324 match: 17 SD: 0.3840 cents 168 .. 336 match: 17 SD: 0.3327 cents 186 .. 372 match: 17 SD: 0.3239 cents 210 .. 420 match: 17 SD: 0.3142 cents 222 .. 444 match: 17 SD: 0.3083 cents 238 .. 476 match: 17 SD: 0.2467 cents 270 .. 540 match: 17 SD: 0.2363 cents 295 .. 590 match: 17 SD: 0.2345 cents 318 .. 636 match: 17 SD: 0.1836 cents 354 .. 708 match: 17 SD: 0.1710 cents 378 .. 756 match: 17 SD: 0.1337 cents 462 .. 924 match: 17 SD: 0.1204 cents 486 .. 972 match: 17 SD: 0.1090 cents 504 .. 1008 match: 17 SD: 0.0873 cents