Scala analysis: breed-46-17-41-parapyth17
Graham Breed 17-note parapyth (key 14 like pipedum_17c.scl)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57.423 cents 57.422500 2: 126.063 cents 126.062520 3: 207.446 cents 207.446430 4: 264.869 cents 264.868930 5: 346.253 cents 346.252840 6: 414.893 cents 414.892870 7: 472.315 cents 472.315370 8: 553.699 cents 553.699280 9: 622.339 cents 622.339310 10: 703.723 cents 703.723220 11: 761.146 cents 761.145710 12: 842.530 cents 842.529630 13: 911.170 cents 911.169650 14: 968.592 cents 968.592150 15: 1049.976 cents 1049.976060 16: 1118.616 cents 1118.616090 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 81.3839 cents 81.3839 1: 57.4225 cents 57.4225 2: 68.6400 cents 68.6400 3: 81.3839 cents 81.3839 4: 57.4225 cents 57.4225 5: 81.3839 cents 81.3839 6: 68.6400 cents 68.6400 7: 57.4225 cents 57.4225 8: 81.3839 cents 81.3839 9: 68.6400 cents 68.6400 10: 81.3839 cents 81.3839 11: 57.4225 cents 57.4225 12: 81.3839 cents 81.3839 13: 68.6400 cents 68.6400 14: 57.4225 cents 57.4225 15: 81.3839 cents 81.3839 16: 68.6400 cents 68.6400 17: 81.3839 cents 81.3839
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 57.42250 cents 1: 5 68.64002 cents 1: 7 81.38391 cents 2: 3 126.06252 cents 2: 7 138.80641 cents 2: 7 150.02393 cents 3: 13 207.44643 cents 3: 2 220.19032 cents 3: 2 231.40785 cents 4: 3 264.86893 cents 4: 3 276.08647 cents 4: 11 288.83034 cents 5: 8 346.25284 cents 5: 8 357.47037 cents 5: 1 370.21426 cents 6: 9 414.89287 cents 6: 4 427.63676 cents 6: 4 438.85429 cents 7: 1 472.31537 cents 7: 1 483.53289 cents 7: 15 496.27678 cents 8: 6 553.69928 cents 8: 6 564.91681 cents 8: 5 577.66070 cents 9: 5 622.33931 cents 9: 6 635.08319 cents 9: 6 646.30072 cents 10: 15 703.72322 cents 10: 1 716.46711 cents 10: 1 727.68463 cents 11: 4 761.14571 cents 11: 4 772.36325 cents 11: 9 785.10713 cents 12: 1 829.78574 cents 12: 8 842.52963 cents 12: 8 853.74715 cents 13: 11 911.16965 cents 13: 3 923.91354 cents 13: 3 935.13107 cents 14: 2 968.59215 cents 14: 2 979.80968 cents 14: 13 992.55356 cents 15: 7 1049.97606 cents 15: 7 1061.19359 cents 15: 3 1073.93748 cents 16: 7 1118.61609 cents 16: 5 1131.35998 cents 16: 5 1142.57750 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 57.4 126.1 207.4 264.9 346.3 414.9 472.3 553.7 622.3 703.7 761.1 842.5 911.2 968.6 1050.0 1118.6 1200.0 57.4 : 68.6 150.0 207.4 288.8 357.5 414.9 496.3 564.9 646.3 703.7 785.1 853.7 911.2 992.6 1061.2 1142.6 1200.0 126.1 : 81.4 138.8 220.2 288.8 346.3 427.6 496.3 577.7 635.1 716.5 785.1 842.5 923.9 992.6 1073.9 1131.4 1200.0 207.4 : 57.4 138.8 207.4 264.9 346.3 414.9 496.3 553.7 635.1 703.7 761.1 842.5 911.2 992.6 1050.0 1118.6 1200.0 264.9 : 81.4 150.0 207.4 288.8 357.5 438.9 496.3 577.7 646.3 703.7 785.1 853.7 935.1 992.6 1061.2 1142.6 1200.0 346.3 : 68.6 126.1 207.4 276.1 357.5 414.9 496.3 564.9 622.3 703.7 772.4 853.7 911.2 979.8 1061.2 1118.6 1200.0 414.9 : 57.4 138.8 207.4 288.8 346.3 427.6 496.3 553.7 635.1 703.7 785.1 842.5 911.2 992.6 1050.0 1131.4 1200.0 472.3 : 81.4 150.0 231.4 288.8 370.2 438.9 496.3 577.7 646.3 727.7 785.1 853.7 935.1 992.6 1073.9 1142.6 1200.0 553.7 : 68.6 150.0 207.4 288.8 357.5 414.9 496.3 564.9 646.3 703.7 772.4 853.7 911.2 992.6 1061.2 1118.6 1200.0 622.3 : 81.4 138.8 220.2 288.8 346.3 427.6 496.3 577.7 635.1 703.7 785.1 842.5 923.9 992.6 1050.0 1131.4 1200.0 703.7 : 57.4 138.8 207.4 264.9 346.3 414.9 496.3 553.7 622.3 703.7 761.1 842.5 911.2 968.6 1050.0 1118.6 1200.0 761.1 : 81.4 150.0 207.4 288.8 357.5 438.9 496.3 564.9 646.3 703.7 785.1 853.7 911.2 992.6 1061.2 1142.6 1200.0 842.5 : 68.6 126.1 207.4 276.1 357.5 414.9 483.5 564.9 622.3 703.7 772.4 829.8 911.2 979.8 1061.2 1118.6 1200.0 911.2 : 57.4 138.8 207.4 288.8 346.3 414.9 496.3 553.7 635.1 703.7 761.1 842.5 911.2 992.6 1050.0 1131.4 1200.0 968.6 : 81.4 150.0 231.4 288.8 357.5 438.9 496.3 577.7 646.3 703.7 785.1 853.7 935.1 992.6 1073.9 1142.6 1200.0 1050.0: 68.6 150.0 207.4 276.1 357.5 414.9 496.3 564.9 622.3 703.7 772.4 853.7 911.2 992.6 1061.2 1118.6 1200.0 1118.6: 81.4 138.8 207.4 288.8 346.3 427.6 496.3 553.7 635.1 703.7 785.1 842.5 923.9 992.6 1050.0 1131.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.4225 .. 81.3839 cents 23.96141 cents 57.42250 cents 2: 126.0625 .. 150.0239 cents 23.96141 cents 44.67861 cents 3: 207.4464 .. 231.4078 cents 23.96142 cents 57.42250 cents 4: 264.8689 .. 288.8303 cents 23.96141 cents 33.46108 cents 5: 346.2528 .. 370.2143 cents 23.96142 cents 57.42250 cents 6: 414.8929 .. 438.8543 cents 23.96142 cents 44.67861 cents 7: 472.3154 .. 496.2768 cents 23.96141 cents 33.46108 cents 8: 553.6993 .. 577.6607 cents 23.96142 cents 57.42250 cents 9: 622.3393 .. 646.3007 cents 23.96141 cents 44.67861 cents 10: 703.7232 .. 727.6846 cents 23.96141 cents 57.42250 cents 11: 761.1457 .. 785.1071 cents 23.96142 cents 33.46108 cents 12: 829.7857 .. 853.7471 cents 23.96141 cents 44.67861 cents 13: 911.1697 .. 935.1311 cents 23.96142 cents 57.42250 cents 14: 968.5921 .. 992.5536 cents 23.96141 cents 33.46108 cents 15: 1049.9761 .. 1073.9375 cents 23.96142 cents 57.42250 cents 16: 1118.6161 .. 1142.5775 cents 23.96141 cents 44.67861 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 57.42249 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 81.38391 cents Average / Smallest step : 1.229279 Largest / Average step : 1.152939 Largest / Smallest step : 1.417283 Median interval of one step : 68.64002 cents, amount: 5 Most common interval of one step : 81.38391 cents, amount: 7 Least squares average step : 69.76024 cents, oct.: 1185.92404 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCACBACBCACBACBC Step pattern size order : SMLSLMSLMLSLMSLML Scale is a Constant Structure, by a margin of 33.46108 cents Scale diversity : 1.219740 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.680514 Number of different interval sizes : 48 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 11.21752 cents Most common intervals : 496.27678 cents & inv., amount: 15 Scale is a chain of 8 triads 0.0 357.470 703.723 cents Most common triad is 0.0 496.277 703.723 cents, amount: 13 Number of recognisable fifths : 16, average 704.5197 cents Number of appreciable fifths : 15, average 703.7232 cents Best fifths form a closed circle Formal octave complements present : 1 = 5.8824% Limited inverse transpositions with margin 23.9614 cents: 2 -- Rational properties -- Prime limit : 2 (not all pitches rational)
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: 12.1083 c. M:-21.8023 c. 28: 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 P M ME S SD: 12.1211 c. M:-21.4525 c. 29: 1 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 2 P M ME S SD: 11.7112 c. M: 17.1430 c. 30: 1 2 2 2 2 1 2 2 2 2 1 2 2 1 2 2 2 P D3 SD: 10.7704 c. M:-17.6607 c. 31: 1 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 P M ME S SD: 10.2505 c. M: 20.8471 c. 36: 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 3 2 SP M ME S SD: 9.8745 c. M: 16.6427 c. 37: 2 2 2 2 3 2 2 2 2 3 1 3 2 2 2 2 3 SP D3 S SD: 9.1370 c. M: 15.9134 c. 38: 2 2 3 1 3 2 2 3 2 2 2 3 2 2 2 2 3 P D3 SD: 8.5897 c. M:-14.7218 c. 41: 2 2 3 2 3 2 2 3 2 3 2 3 2 2 3 2 3 SP M ME S SD: 4.4787 c. M: 8.9893 c. 46: 2 3 3 2 3 3 2 3 3 3 2 3 3 2 3 3 3 SP M ME S SD: 4.3788 c. M: 7.7470 c. 58: 3 3 4 3 4 3 3 4 3 4 3 4 3 3 4 3 4 SP M ME S SD: 3.5099 c. M:-5.7462 c. 83: 4 5 5 4 6 5 4 5 5 6 4 5 5 4 6 4 6 SP SD: 3.8181 c. M:-5.4456 c. 87: 4 5 6 4 6 5 4 6 5 6 4 6 5 4 6 5 6 SP T3 SD: 1.8894 c. M: 3.3499 c. 104: 5 6 7 5 7 6 5 7 6 7 5 7 6 5 7 6 7 SP T3 SD: 0.4651 c. M:-0.8606 c. 249: 12 14 17 12 17 14 12 17 14 17 12 17 14 12 17 14 17 SP T3 SD: 0.4771 c. M:-0.8439 c. 295: 14 17 20 14 20 17 14 20 17 20 14 20 17 14 20 17 20 SP T3 SD: 0.3449 c. M: 0.4957 c. 353: 17 20 24 17 24 20 17 24 20 24 17 24 20 17 24 20 24 SP T3 SD: 0.3016 c. M:-0.5299 c. 399: 19 23 27 19 27 23 19 27 23 27 19 27 23 19 27 23 27 SP T3 SD: 0.2383 c. M: 0.4244 c. 457: 22 26 31 22 31 26 22 31 26 31 22 31 26 22 31 26 31 SP T3 SD: 0.2517 c. M:-0.3588 c. 503: 24 29 34 24 34 29 24 34 29 34 24 34 29 24 34 29 34 SP T3 SD: 0.2215 c. M: 0.3825 c. 544: 26 31 37 26 37 31 26 37 31 37 26 37 31 26 37 31 37 SP T3 SD: 0.1681 c. M: 0.3272 c. 648: 31 37 44 31 44 37 31 44 37 44 31 44 37 31 44 37 44 SP T3 SD: 0.0678 c. M: 0.1366 c. 752: 36 43 51 36 51 43 36 51 43 51 36 51 43 36 51 43 51 SP T3 SD: 0.0177 c. M:-0.0251 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.8841 cents 3 .. 6 match: 3 H SD: 12.3866 cents 4 .. 8 match: 4 H SD: 7.1587 cents 5 .. 10 match: 5 H SD: 12.0791 cents 6 .. 12 match: 6 H SD: 6.2101 cents 7 .. 14 match: 7 H SD: 7.0045 cents 8 .. 16 match: 8 H SD: 5.2487 cents 9 .. 18 match: 9 H SD: 6.3754 cents 10 .. 20 match: 10 H SD: 7.4871 cents 11 .. 22 match: 11 H SD: 5.0305 cents 12 .. 24 match: 12 H SD: 5.2568 cents 13 .. 26 match: 13 H SD: 4.1396 cents 14 .. 28 match: 14 H SD: 5.0732 cents 15 .. 30 match: 13 SD: 6.1857 cents 16 .. 32 match: 15 SD: 4.0359 cents 17 .. 34 match: 14 S SD: 5.5378 cents 18 .. 36 match: 16 SD: 4.3978 cents 19 .. 38 match: 15 SD: 4.3298 cents 20 .. 40 match: 16 SD: 5.2535 cents 21 .. 42 match: 16 SD: 4.8569 cents 22 .. 44 match: 17 S SD: 3.6581 cents 23 .. 46 match: 17 SD: 3.1154 cents 26 .. 52 match: 17 SD: 2.7762 cents 29 .. 58 match: 17 SD: 2.5981 cents 30 .. 60 match: 17 SD: 2.4903 cents 32 .. 64 match: 17 SD: 2.0130 cents 40 .. 80 match: 17 SD: 1.8598 cents 48 .. 96 match: 17 SD: 1.5990 cents 53 .. 106 match: 17 SD: 1.4076 cents 54 .. 108 match: 17 SD: 1.2405 cents 55 .. 110 match: 17 SD: 1.1981 cents 64 .. 128 match: 17 SD: 1.1051 cents 67 .. 134 match: 17 SD: 1.0383 cents 77 .. 154 match: 17 SD: 1.0305 cents 78 .. 156 match: 17 SD: 0.9656 cents 80 .. 160 match: 17 SD: 0.9113 cents 85 .. 170 match: 17 SD: 0.8019 cents 92 .. 184 match: 17 SD: 0.7534 cents 96 .. 192 match: 17 SD: 0.7149 cents 108 .. 216 match: 17 SD: 0.6392 cents 118 .. 236 match: 17 SD: 0.6080 cents 121 .. 242 match: 17 SD: 0.5739 cents 140 .. 280 match: 17 SD: 0.5165 cents 143 .. 286 match: 17 SD: 0.4867 cents 144 .. 288 match: 17 SD: 0.4691 cents 159 .. 318 match: 17 SD: 0.4495 cents 172 .. 344 match: 17 SD: 0.4258 cents 175 .. 350 match: 17 SD: 0.3906 cents 181 .. 362 match: 17 SD: 0.3701 cents 188 .. 376 match: 17 SD: 0.3531 cents 199 .. 398 match: 17 SD: 0.3149 cents 235 .. 470 match: 17 SD: 0.3105 cents 236 .. 472 match: 17 SD: 0.2364 cents 303 .. 606 match: 17 SD: 0.1927 cents 361 .. 722 match: 17 SD: 0.1740 cents 393 .. 786 match: 17 SD: 0.1721 cents 411 .. 822 match: 17 SD: 0.1401 cents 478 .. 956 match: 17 SD: 0.1341 cents 501 .. 1002 match: 17 SD: 0.1238 cents 568 .. 1136 match: 17 SD: 0.1140 cents 592 .. 1184 match: 17 SD: 0.1093 cents