Scala analysis: parapyth17
A triple Fokker block of the 2.3.7.11.13 temperament called "parapyth" (TOP tuning)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58.236 cents 58.236040 2: 124.602 cents 124.602380 3: 206.959 cents 206.958660 4: 265.195 cents 265.194710 5: 347.551 cents 347.550990 6: 413.917 cents 413.917330 7: 472.153 cents 472.153370 8: 554.510 cents 554.509650 9: 620.876 cents 620.875990 10: 703.232 cents 703.232270 11: 761.468 cents 761.468320 12: 843.825 cents 843.824600 13: 910.191 cents 910.190940 14: 968.427 cents 968.426980 15: 1050.783 cents 1050.783260 16: 1117.150 cents 1117.149600 17: 1199.506 cents 1199.505880
SHOW/INTERVAL
0: 82.3563 cents 82.3563 1: 58.2360 cents 58.2360 2: 66.3663 cents 66.3663 3: 82.3563 cents 82.3563 4: 58.2361 cents 58.2361 5: 82.3563 cents 82.3563 6: 66.3663 cents 66.3663 7: 58.2360 cents 58.2360 8: 82.3563 cents 82.3563 9: 66.3663 cents 66.3663 10: 82.3563 cents 82.3563 11: 58.2361 cents 58.2361 12: 82.3563 cents 82.3563 13: 66.3663 cents 66.3663 14: 58.2360 cents 58.2360 15: 82.3563 cents 82.3563 16: 66.3663 cents 66.3663 17: 82.3563 cents 82.3563
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 58.23604 cents 1: 5 66.36634 cents 1: 7 82.35628 cents 2: 3 124.60238 cents 2: 7 140.59233 cents 2: 7 148.72262 cents 3: 13 206.95866 cents 3: 2 222.94861 cents 3: 2 231.07890 cents 4: 3 265.19471 cents 4: 3 273.32500 cents 4: 11 289.31495 cents 5: 8 347.55099 cents 5: 8 355.68129 cents 5: 1 371.67123 cents 6: 9 413.91733 cents 6: 4 429.90727 cents 6: 4 438.03756 cents 7: 1 472.15337 cents 7: 1 480.28366 cents 7: 15 496.27361 cents 8: 6 554.50965 cents 8: 6 562.63995 cents 8: 5 578.62989 cents 9: 5 620.87599 cents 9: 6 636.86594 cents 9: 6 644.99623 cents 10: 15 703.23227 cents 10: 1 719.22222 cents 10: 1 727.35251 cents 11: 4 761.46832 cents 11: 4 769.59861 cents 11: 9 785.58856 cents 12: 1 827.83465 cents 12: 8 843.82460 cents 12: 8 851.95490 cents 13: 11 910.19094 cents 13: 3 926.18088 cents 13: 3 934.31117 cents 14: 2 968.42698 cents 14: 2 976.55727 cents 14: 13 992.54722 cents 15: 7 1050.78326 cents 15: 7 1058.91356 cents 15: 3 1074.90350 cents 16: 7 1117.14960 cents 16: 5 1133.13954 cents 16: 5 1141.26984 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 : 58.2 124.6 207.0 265.2 347.6 413.9 472.2 554.5 620.9 703.2 761.5 843.8 910.2 968.4 1050.8 1117.1 1199.5 58.2 : 66.4 148.7 207.0 289.3 355.7 413.9 496.3 562.6 645.0 703.2 785.6 852.0 910.2 992.5 1058.9 1141.3 1199.5 124.6 : 82.4 140.6 222.9 289.3 347.6 429.9 496.3 578.6 636.9 719.2 785.6 843.8 926.2 992.5 1074.9 1133.1 1199.5 207.0 : 58.2 140.6 207.0 265.2 347.6 413.9 496.3 554.5 636.9 703.2 761.5 843.8 910.2 992.5 1050.8 1117.1 1199.5 265.2 : 82.4 148.7 207.0 289.3 355.7 438.0 496.3 578.6 645.0 703.2 785.6 852.0 934.3 992.5 1058.9 1141.3 1199.5 347.6 : 66.4 124.6 207.0 273.3 355.7 413.9 496.3 562.6 620.9 703.2 769.6 852.0 910.2 976.6 1058.9 1117.1 1199.5 413.9 : 58.2 140.6 207.0 289.3 347.6 429.9 496.3 554.5 636.9 703.2 785.6 843.8 910.2 992.5 1050.8 1133.1 1199.5 472.2 : 82.4 148.7 231.1 289.3 371.7 438.0 496.3 578.6 645.0 727.4 785.6 852.0 934.3 992.5 1074.9 1141.3 1199.5 554.5 : 66.4 148.7 207.0 289.3 355.7 413.9 496.3 562.6 645.0 703.2 769.6 852.0 910.2 992.5 1058.9 1117.1 1199.5 620.9 : 82.4 140.6 222.9 289.3 347.6 429.9 496.3 578.6 636.9 703.2 785.6 843.8 926.2 992.5 1050.8 1133.1 1199.5 703.2 : 58.2 140.6 207.0 265.2 347.6 413.9 496.3 554.5 620.9 703.2 761.5 843.8 910.2 968.4 1050.8 1117.1 1199.5 761.5 : 82.4 148.7 207.0 289.3 355.7 438.0 496.3 562.6 645.0 703.2 785.6 852.0 910.2 992.5 1058.9 1141.3 1199.5 843.8 : 66.4 124.6 207.0 273.3 355.7 413.9 480.3 562.6 620.9 703.2 769.6 827.8 910.2 976.6 1058.9 1117.1 1199.5 910.2 : 58.2 140.6 207.0 289.3 347.6 413.9 496.3 554.5 636.9 703.2 761.5 843.8 910.2 992.5 1050.8 1133.1 1199.5 968.4 : 82.4 148.7 231.1 289.3 355.7 438.0 496.3 578.6 645.0 703.2 785.6 852.0 934.3 992.5 1074.9 1141.3 1199.5 1050.8: 66.4 148.7 207.0 273.3 355.7 413.9 496.3 562.6 620.9 703.2 769.6 852.0 910.2 992.5 1058.9 1117.1 1199.5 1117.1: 82.4 140.6 207.0 289.3 347.6 429.9 496.3 554.5 636.9 703.2 785.6 843.8 926.2 992.5 1050.8 1133.1 1199.5 1199.5
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.2360 .. 82.3563 cents 24.12024 cents 58.23604 cents 2: 124.6024 .. 148.7226 cents 24.12024 cents 42.24610 cents 3: 206.9587 .. 231.0789 cents 24.12024 cents 58.23604 cents 4: 265.1947 .. 289.3150 cents 24.12024 cents 34.11581 cents 5: 347.5510 .. 371.6712 cents 24.12024 cents 58.23604 cents 6: 413.9173 .. 438.0376 cents 24.12023 cents 42.24610 cents 7: 472.1534 .. 496.2736 cents 24.12024 cents 34.11581 cents 8: 554.5096 .. 578.6299 cents 24.12024 cents 58.23604 cents 9: 620.8760 .. 644.9962 cents 24.12024 cents 42.24610 cents 10: 703.2323 .. 727.3525 cents 24.12024 cents 58.23604 cents 11: 761.4683 .. 785.5886 cents 24.12024 cents 34.11581 cents 12: 827.8346 .. 851.9549 cents 24.12025 cents 42.24609 cents 13: 910.1909 .. 934.3112 cents 24.12023 cents 58.23604 cents 14: 968.4270 .. 992.5472 cents 24.12024 cents 34.11581 cents 15: 1050.7833 .. 1074.9035 cents 24.12024 cents 58.23604 cents 16: 1117.1496 .. 1141.2698 cents 24.12024 cents 42.24610 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 58.23604 cents, class 1 Average step (divided formal octave): 70.5592 cents Largest one step interval : 82.35628 cents Average / Smallest step : 1.211607 Largest / Average step : 1.167195 Largest / Smallest step : 1.414181 Median interval of one step : 66.36634 cents, amount: 5 Most common interval of one step : 82.35628 cents, amount: 7 Least squares average step : 69.74340 cents, oct.: 1185.63772 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 34.11581 cents Scale diversity : 1.216728 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.678264 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 : 8.13029 cents Most common intervals : 496.27361 cents & inv., amount: 15 Scale is a chain of 8 triads 0.0 355.681 703.232 cents Most common triad is 0.0 496.274 703.232 cents, amount: 13 Number of recognisable fifths : 16, average 704.2316 cents Number of appreciable fifths : 15, average 703.2323 cents Number of recognisable fourths : 16, average 495.2742 cents Number of appreciable fourths : 15, average 496.2736 cents Best fifths form a closed circle Formal octave complements present : 1 = 5.8824% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 24.1202 cents: 2 -- Rational properties --
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: 12.0784 c. M:-21.7608 c. 27: 1 2 2 1 2 1 2 1 2 2 1 2 1 2 2 1 2 P M ME S SD: 11.9240 c. M: 21.6681 c. 29: 1 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 2 P M ME S SD: 12.2801 c. M: 17.1684 c. 30: 1 2 2 2 2 1 2 2 2 2 1 2 2 1 2 2 2 P D3 SD: 10.8511 c. M:-18.8605 c. 31: 2 1 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 P D3 S SD: 9.9329 c. M:-19.1514 c. 33: 2 1 3 1 3 1 2 2 2 2 2 2 2 2 2 2 2 P D3 S SD: 10.1066 c. M:-15.9356 c. 37: 2 2 2 2 3 2 2 2 2 3 1 3 2 2 2 2 3 SP D3 S SD: 9.0998 c. M: 15.8295 c. 38: 2 2 3 1 3 2 2 3 2 2 2 3 2 2 2 2 3 P D3 SD: 8.4802 c. M:-14.0029 c. 40: 2 2 3 2 3 2 2 2 3 2 2 3 2 2 3 2 3 P D3 SD: 8.3430 c. M: 14.7320 c. 41: 2 2 3 2 3 2 2 3 2 3 2 3 2 2 3 2 3 SP M ME S SD: 3.7183 c. M: 7.5774 c. 58: 3 3 4 3 4 3 3 4 3 4 3 4 3 3 4 3 4 SP M ME S SD: 2.7818 c. M:-4.1020 c. 87: 4 5 6 4 6 5 4 6 5 6 4 6 5 4 6 5 6 SP T3 SD: 2.2598 c. M: 3.3810 c. 104: 5 6 7 5 7 6 5 7 6 7 5 7 6 5 7 6 7 SP T3 SD: 1.1857 c. M:-2.2684 c. 145: 7 8 10 7 10 8 7 10 8 10 7 10 8 7 10 8 10 SP T3 SD: 0.3480 c. M: 0.6235 c. 307: 15 17 21 15 21 17 15 21 17 21 15 21 17 15 21 17 21 SP T3 SD: 0.3421 c. M:-0.6160 c. 394: 19 22 27 19 27 22 19 27 22 27 19 27 22 19 27 22 27 SP T3 SD: 0.3047 c. M: 0.5172 c. 452: 22 25 31 22 31 25 22 31 25 31 22 31 25 22 31 25 31 SP T3 SD: 0.1232 c. M:-0.2184 c. 597: 29 33 41 29 41 33 29 41 33 41 29 41 33 29 41 33 41 SP T3 SD: 0.0273 c. M:-0.0489 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.4941 cents 2 .. 4 match: 2 H SD: 0.6848 cents 3 .. 6 match: 3 H SD: 12.1926 cents 4 .. 8 match: 4 H SD: 6.9101 cents 5 .. 10 match: 5 H SD: 12.3488 cents 6 .. 12 match: 6 H SD: 6.1110 cents 7 .. 14 match: 7 H SD: 7.0738 cents 8 .. 16 match: 8 H SD: 5.0443 cents 9 .. 18 match: 9 H SD: 6.3101 cents 10 .. 20 match: 10 H SD: 7.6648 cents 11 .. 22 match: 11 H SD: 5.1716 cents 12 .. 24 match: 12 H SD: 5.1824 cents 13 .. 26 match: 13 H SD: 4.2437 cents 14 .. 28 match: 13 S SD: 4.8144 cents 15 .. 30 match: 13 SD: 6.2127 cents 16 .. 32 match: 15 SD: 4.0288 cents 17 .. 34 match: 14 S SD: 5.4278 cents 18 .. 36 match: 16 SD: 4.3362 cents 19 .. 38 match: 16 SD: 4.3989 cents 20 .. 40 match: 15 SD: 4.9306 cents 21 .. 42 match: 16 SD: 4.8937 cents 22 .. 44 match: 17 SD: 3.6961 cents 23 .. 46 match: 17 SD: 3.1662 cents 26 .. 52 match: 17 SD: 2.7544 cents 29 .. 58 match: 17 SD: 2.6751 cents 30 .. 60 match: 17 SD: 2.4221 cents 32 .. 64 match: 17 SD: 2.0036 cents 40 .. 80 match: 17 SD: 1.8734 cents 48 .. 96 match: 17 SD: 1.6274 cents 53 .. 106 match: 17 SD: 1.4234 cents 54 .. 108 match: 17 SD: 1.2064 cents 64 .. 128 match: 17 SD: 1.1680 cents 67 .. 134 match: 17 SD: 1.0756 cents 77 .. 154 match: 17 SD: 1.0553 cents 78 .. 156 match: 17 SD: 1.0273 cents 79 .. 158 match: 17 SD: 1.0208 cents 80 .. 160 match: 17 SD: 0.9498 cents 84 .. 168 match: 17 SD: 0.8980 cents 85 .. 170 match: 17 SD: 0.8107 cents 95 .. 190 match: 17 SD: 0.7773 cents 96 .. 192 match: 17 SD: 0.7058 cents 108 .. 216 match: 17 SD: 0.6026 cents 116 .. 232 match: 17 SD: 0.5854 cents 121 .. 242 match: 17 SD: 0.5491 cents 140 .. 280 match: 17 SD: 0.5046 cents 148 .. 296 match: 17 SD: 0.4858 cents 156 .. 312 match: 17 SD: 0.4608 cents 170 .. 340 match: 17 SD: 0.4586 cents 172 .. 344 match: 17 SD: 0.4116 cents 174 .. 348 match: 17 SD: 0.4023 cents 175 .. 350 match: 17 SD: 0.3491 cents 188 .. 376 match: 17 SD: 0.3207 cents 204 .. 408 match: 17 SD: 0.2670 cents 259 .. 518 match: 17 SD: 0.2632 cents 266 .. 532 match: 17 SD: 0.2485 cents 292 .. 584 match: 17 SD: 0.2439 cents 296 .. 592 match: 17 SD: 0.2422 cents 297 .. 594 match: 17 SD: 0.2212 cents 315 .. 630 match: 17 SD: 0.2063 cents 347 .. 694 match: 17 SD: 0.1953 cents 363 .. 726 match: 17 SD: 0.1899 cents 373 .. 746 match: 17 SD: 0.1825 cents 387 .. 774 match: 17 SD: 0.1618 cents 411 .. 822 match: 17 SD: 0.1560 cents 440 .. 880 match: 17 SD: 0.1441 cents 441 .. 882 match: 17 SD: 0.1411 cents 471 .. 942 match: 17 SD: 0.1205 cents 575 .. 1150 match: 17 SD: 0.1111 cents