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