Scala analysis: didymus19sync
Didymus[19] hobbit (81/80) in synchronized tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 41.376 cents 41.376460 2: 119.285 cents 119.284780 3: 192.286 cents 192.286090 4: 233.663 cents 233.662540 5: 311.571 cents 311.570870 6: 384.572 cents 384.572170 7: 462.481 cents 462.480500 8: 503.857 cents 503.856960 9: 545.233 cents 545.233410 10: 654.767 cents 654.766590 11: 696.143 cents 696.143040 12: 737.519 cents 737.519500 13: 815.428 cents 815.427830 14: 888.429 cents 888.429130 15: 966.337 cents 966.337460 16: 1007.714 cents 1007.713910 17: 1080.715 cents 1080.715220 18: 1158.624 cents 1158.623540 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 41.3765 cents 41.3765 1: 41.3765 cents 41.3765 2: 77.9083 cents 77.9083 3: 73.0013 cents 73.0013 4: 41.3765 cents 41.3765 5: 77.9083 cents 77.9083 6: 73.0013 cents 73.0013 7: 77.9083 cents 77.9083 8: 41.3765 cents 41.3765 9: 41.3765 cents 41.3765 10: 109.5332 cents 109.5332 11: 41.3765 cents 41.3765 12: 41.3765 cents 41.3765 13: 77.9083 cents 77.9083 14: 73.0013 cents 73.0013 15: 77.9083 cents 77.9083 16: 41.3765 cents 41.3765 17: 73.0013 cents 73.0013 18: 77.9083 cents 77.9083 19: 41.3765 cents 41.3765
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 41.37646 cents 1: 4 73.00131 cents 1: 6 77.90832 cents 1: 1 109.53318 cents 2: 3 82.75291 cents 2: 2 114.37776 cents 2: 6 119.28478 cents 2: 8 150.90963 cents 3: 4 160.66124 cents 3: 13 192.28609 cents 3: 2 228.81796 cents 4: 8 233.66254 cents 4: 1 238.56956 cents 4: 2 265.28739 cents 4: 8 270.19441 cents 5: 3 275.03900 cents 5: 10 311.57087 cents 5: 6 343.19571 cents 6: 8 352.94732 cents 6: 7 384.57217 cents 6: 4 421.10404 cents 7: 8 425.94863 cents 7: 3 430.85566 cents 7: 8 462.48050 cents 8: 1 467.32508 cents 8: 16 503.85696 cents 8: 2 535.48181 cents 9: 8 545.23341 cents 9: 5 576.85826 cents 9: 4 581.76529 cents 9: 2 613.39013 cents 10: 2 586.60987 cents 10: 4 618.23472 cents 10: 5 623.14174 cents 10: 8 654.76659 cents 11: 2 664.51819 cents 11: 16 696.14304 cents 11: 1 732.67492 cents 12: 8 737.51950 cents 12: 3 769.14435 cents 12: 8 774.05137 cents 13: 4 778.89596 cents 13: 7 815.42783 cents 13: 8 847.05267 cents 14: 6 856.80429 cents 14: 10 888.42913 cents 14: 3 924.96100 cents 15: 8 929.80559 cents 15: 2 934.71261 cents 15: 1 961.43044 cents 15: 8 966.33746 cents 16: 2 971.18204 cents 16: 13 1007.71391 cents 16: 4 1039.33876 cents 17: 8 1049.09037 cents 17: 6 1080.71522 cents 17: 2 1085.62224 cents 17: 3 1117.24708 cents 18: 1 1090.46682 cents 18: 6 1122.09168 cents 18: 4 1126.99869 cents 18: 8 1158.62354 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.44444 = 31/9
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 : 41.4 119.3 192.3 233.7 311.6 384.6 462.5 503.9 545.2 654.8 696.1 737.5 815.4 888.4 966.3 1007.7 1080.7 1158.6 1200.0 41.4 : 77.9 150.9 192.3 270.2 343.2 421.1 462.5 503.9 613.4 654.8 696.1 774.1 847.1 925.0 966.3 1039.3 1117.2 1158.6 1200.0 119.3 : 73.0 114.4 192.3 265.3 343.2 384.6 425.9 535.5 576.9 618.2 696.1 769.1 847.1 888.4 961.4 1039.3 1080.7 1122.1 1200.0 192.3 : 41.4 119.3 192.3 270.2 311.6 352.9 462.5 503.9 545.2 623.1 696.1 774.1 815.4 888.4 966.3 1007.7 1049.1 1127.0 1200.0 233.7 : 77.9 150.9 228.8 270.2 311.6 421.1 462.5 503.9 581.8 654.8 732.7 774.1 847.1 925.0 966.3 1007.7 1085.6 1158.6 1200.0 311.6 : 73.0 150.9 192.3 233.7 343.2 384.6 425.9 503.9 576.9 654.8 696.1 769.1 847.1 888.4 929.8 1007.7 1080.7 1122.1 1200.0 384.6 : 77.9 119.3 160.7 270.2 311.6 352.9 430.9 503.9 581.8 623.1 696.1 774.1 815.4 856.8 934.7 1007.7 1049.1 1127.0 1200.0 462.5 : 41.4 82.8 192.3 233.7 275.0 352.9 425.9 503.9 545.2 618.2 696.1 737.5 778.9 856.8 929.8 971.2 1049.1 1122.1 1200.0 503.9 : 41.4 150.9 192.3 233.7 311.6 384.6 462.5 503.9 576.9 654.8 696.1 737.5 815.4 888.4 929.8 1007.7 1080.7 1158.6 1200.0 545.2 : 109.5 150.9 192.3 270.2 343.2 421.1 462.5 535.5 613.4 654.8 696.1 774.1 847.1 888.4 966.3 1039.3 1117.2 1158.6 1200.0 654.8 : 41.4 82.8 160.7 233.7 311.6 352.9 425.9 503.9 545.2 586.6 664.5 737.5 778.9 856.8 929.8 1007.7 1049.1 1090.5 1200.0 696.1 : 41.4 119.3 192.3 270.2 311.6 384.6 462.5 503.9 545.2 623.1 696.1 737.5 815.4 888.4 966.3 1007.7 1049.1 1158.6 1200.0 737.5 : 77.9 150.9 228.8 270.2 343.2 421.1 462.5 503.9 581.8 654.8 696.1 774.1 847.1 925.0 966.3 1007.7 1117.2 1158.6 1200.0 815.4 : 73.0 150.9 192.3 265.3 343.2 384.6 425.9 503.9 576.9 618.2 696.1 769.1 847.1 888.4 929.8 1039.3 1080.7 1122.1 1200.0 888.4 : 77.9 119.3 192.3 270.2 311.6 352.9 430.9 503.9 545.2 623.1 696.1 774.1 815.4 856.8 966.3 1007.7 1049.1 1127.0 1200.0 966.3 : 41.4 114.4 192.3 233.7 275.0 352.9 425.9 467.3 545.2 618.2 696.1 737.5 778.9 888.4 929.8 971.2 1049.1 1122.1 1200.0 1007.7: 73.0 150.9 192.3 233.7 311.6 384.6 425.9 503.9 576.9 654.8 696.1 737.5 847.1 888.4 929.8 1007.7 1080.7 1158.6 1200.0 1080.7: 77.9 119.3 160.7 238.6 311.6 352.9 430.9 503.9 581.8 623.1 664.5 774.1 815.4 856.8 934.7 1007.7 1085.6 1127.0 1200.0 1158.6: 41.4 82.8 160.7 233.7 275.0 352.9 425.9 503.9 545.2 586.6 696.1 737.5 778.9 856.8 929.8 1007.7 1049.1 1122.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.3765 .. 109.5332 cents 68.15672 cents 41.37646 cents 2: 82.7529 .. 150.9096 cents 68.15672 cents -26.78027 cents 3: 160.6612 .. 228.8180 cents 68.15672 cents 9.75161 cents 4: 233.6625 .. 270.1944 cents 36.53187 cents 4.84458 cents 5: 275.0390 .. 343.1957 cents 68.15671 cents 4.84459 cents 6: 352.9473 .. 421.1040 cents 68.15672 cents 9.75161 cents 7: 425.9486 .. 462.4805 cents 36.53187 cents 4.84459 cents 8: 467.3251 .. 535.4818 cents 68.15673 cents 4.84458 cents 9: 545.2334 .. 613.3901 cents 68.15672 cents 9.75160 cents 10: 586.6099 .. 654.7666 cents 68.15672 cents -26.78026 cents 11: 664.5182 .. 732.6749 cents 68.15673 cents 9.75160 cents 12: 737.5195 .. 774.0514 cents 36.53187 cents 4.84458 cents 13: 778.8960 .. 847.0527 cents 68.15671 cents 4.84459 cents 14: 856.8043 .. 924.9610 cents 68.15671 cents 9.75162 cents 15: 929.8056 .. 966.3375 cents 36.53187 cents 4.84459 cents 16: 971.1820 .. 1039.3388 cents 68.15672 cents 4.84458 cents 17: 1049.0904 .. 1117.2471 cents 68.15671 cents 9.75161 cents 18: 1090.4668 .. 1158.6235 cents 68.15672 cents -26.78026 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 41.37645 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 109.53318 cents Average / Smallest step : 1.526421 Largest / Average step : 1.734275 Largest / Smallest step : 2.647235 Median interval of one step : 73.00131 cents, amount: 4 Most common interval of one step : 41.37646 cents, amount: 8 Least squares average step : 63.38946 cents, oct.: 1204.39978 cents Scale is not proper Step pattern alph. order: ABCABCBAADAABCBACBA Step pattern size order : ACBACBCAADAACBCABCA Scale is a Constant Structure, by a margin of 4.84458 cents Scale diversity : 1.263660 Lumma stability : 0.150016 Lumma impropriety factor : 0.066951 Number of different interval sizes : 62 = 3.44444 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.44444 = 31/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 4.84458 cents Most common intervals : 503.85696 cents & inv., amount: 16 Most common triad is 0.0 503.857 696.143 cents, amount: 13 Number of recognisable fifths : 16, average 696.1430 cents Best major thirds form a closed circle Formal octave complements present : 19 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties --
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: 14.1266 c. M:-23.1876 c. 24: 1 1 2 1 1 2 1 1 1 2 1 1 1 2 1 1 2 1 1 P D3 I SD: 11.8675 c. M: 19.2848 c. 26: 1 2 1 1 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1 P M ME I SD: 9.8157 c. M: 19.1768 c. 27: 1 2 1 1 2 2 1 1 1 3 1 1 1 2 2 1 1 2 1 N D3 I SD: 12.4703 c. M: 18.0361 c. 28: 1 2 1 1 2 2 2 1 1 2 1 1 2 2 2 1 1 2 1 N D3 I SD: 11.9859 c. M: 20.8575 c. 29: 1 2 2 1 2 1 2 1 1 3 1 1 2 1 2 1 2 2 1 N D3 I SD: 10.9416 c. M:-19.4636 c. 30: 1 2 2 1 2 2 2 1 1 2 1 1 2 2 2 1 2 2 1 N I SD: 11.2237 c. M: 17.5195 c. 31: 1 2 2 1 2 2 2 1 1 3 1 1 2 2 2 1 2 2 1 N D3 I SD: 2.2008 c. M:-3.2979 c. 81: 3 5 5 3 5 5 5 3 3 7 3 3 5 5 5 3 5 5 3 N D3 I SD: 2.0765 c. M:-3.3745 c. 88: 3 6 5 3 6 5 6 3 3 8 3 3 6 5 6 3 5 6 3 N I SD: 1.8087 c. M: 3.4425 c. 112: 4 7 7 4 7 7 7 4 4 10 4 4 7 7 7 4 7 7 4 N D3 I SD: 1.2746 c. M: 2.0517 c. 119: 4 8 7 4 8 7 8 4 4 11 4 4 8 7 8 4 7 8 4 N I SD: 1.1704 c. M: 1.7298 c. 143: 5 9 9 5 9 9 9 5 5 13 5 5 9 9 9 5 9 9 5 N D3 I SD: 1.0320 c. M: 1.8023 c. 150: 5 10 9 5 10 9 10 5 5 14 5 5 10 9 10 5 9 10 5 N I SD: 1.0060 c. M:-1.6625 c. 169: 6 11 10 6 11 10 11 6 6 15 6 6 11 10 11 6 10 11 6 N I SD: 1.0042 c. M:-1.5122 c. 200: 7 13 12 7 13 12 13 7 7 18 7 7 13 12 13 7 12 13 7 N I SD: 0.5075 c. M:-0.7666 c. 231: 8 15 14 8 15 14 15 8 8 21 8 8 15 14 15 8 14 15 8 N I SD: 0.1442 c. M:-0.2211 c. 262: 9 17 16 9 17 16 17 9 9 24 9 9 17 16 17 9 16 17 9 N I SD: 0.1336 c. M: 0.2008 c. 493: 17 32 30 17 32 30 32 17 17 45 17 17 32 30 32 17 30 32 17 N I SD: 0.0081 c. M: 0.0150 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 2.9060 cents 3 .. 6 match: 3 H SD: 2.3652 cents 4 .. 8 match: 4 H SD: 1.6394 cents 5 .. 10 match: 5 H SD: 7.7639 cents 6 .. 12 match: 6 H SD: 7.7637 cents 7 .. 14 match: 7 H SD: 9.4925 cents 8 .. 16 match: 8 H SD: 3.7546 cents 9 .. 18 match: 9 H SD: 6.1470 cents 10 .. 20 match: 10 H SD: 6.4772 cents 11 .. 22 match: 11 H SD: 7.5344 cents 12 .. 24 match: 11 S SD: 5.7420 cents 13 .. 26 match: 13 H SD: 4.5573 cents 14 .. 28 match: 14 H SD: 5.8235 cents 15 .. 30 match: 15 H SD: 3.7023 cents 16 .. 32 match: 16 H SD: 4.0865 cents 17 .. 34 match: 14 SD: 4.4608 cents 18 .. 36 match: 16 S SD: 4.9226 cents 19 .. 38 match: 16 SD: 4.1468 cents 20 .. 40 match: 17 SD: 3.6238 cents 21 .. 42 match: 16 SD: 3.9338 cents 22 .. 44 match: 17 SD: 4.3271 cents 23 .. 46 match: 17 SD: 4.2083 cents 24 .. 48 match: 18 SD: 2.9148 cents 25 .. 50 match: 18 SD: 3.3649 cents 26 .. 52 match: 19 SD: 3.1262 cents 27 .. 54 match: 19 SD: 2.7274 cents 28 .. 56 match: 18 SD: 2.6771 cents 30 .. 60 match: 18 SD: 2.3290 cents 31 .. 62 match: 18 SD: 3.1600 cents 32 .. 64 match: 19 SD: 2.3063 cents 35 .. 70 match: 19 SD: 2.1720 cents 36 .. 72 match: 19 SD: 1.9537 cents 40 .. 80 match: 19 SD: 1.6787 cents 41 .. 82 match: 19 SD: 1.6641 cents 42 .. 84 match: 19 SD: 1.6555 cents 43 .. 86 match: 19 SD: 1.5365 cents 51 .. 102 match: 19 SD: 1.5157 cents 52 .. 104 match: 19 SD: 1.4774 cents 55 .. 110 match: 19 SD: 1.4541 cents 56 .. 112 match: 19 SD: 1.3086 cents 60 .. 120 match: 19 SD: 1.3008 cents 67 .. 134 match: 19 SD: 1.1853 cents 68 .. 136 match: 19 SD: 0.9639 cents 75 .. 150 match: 19 SD: 0.9598 cents 76 .. 152 match: 19 SD: 0.8632 cents 83 .. 166 match: 19 SD: 0.7756 cents 85 .. 170 match: 19 SD: 0.6849 cents 111 .. 222 match: 19 SD: 0.5842 cents 124 .. 248 match: 19 SD: 0.5672 cents 127 .. 254 match: 19 SD: 0.5063 cents 137 .. 274 match: 19 SD: 0.4826 cents 151 .. 302 match: 19 SD: 0.4797 cents 152 .. 304 match: 19 SD: 0.4663 cents 153 .. 306 match: 19 SD: 0.4369 cents 166 .. 332 match: 19 SD: 0.4180 cents 168 .. 336 match: 19 SD: 0.4057 cents 172 .. 344 match: 19 SD: 0.4002 cents 194 .. 388 match: 19 SD: 0.3488 cents 198 .. 396 match: 19 SD: 0.3407 cents 209 .. 418 match: 19 SD: 0.3235 cents 213 .. 426 match: 19 SD: 0.2405 cents 248 .. 496 match: 19 SD: 0.2384 cents 249 .. 498 match: 19 SD: 0.2326 cents 254 .. 508 match: 19 SD: 0.2213 cents 324 .. 648 match: 19 SD: 0.1918 cents 346 .. 692 match: 19 SD: 0.1918 cents 365 .. 730 match: 19 SD: 0.1705 cents 376 .. 752 match: 19 SD: 0.1586 cents 422 .. 844 match: 19 SD: 0.1543 cents 450 .. 900 match: 19 SD: 0.1295 cents 491 .. 982 match: 19 SD: 0.1265 cents 503 .. 1006 match: 19 SD: 0.1054 cents