Scala analysis: beatles17
17-note MOS of beatles temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 93.309 cents 93.309000 2: 131.187 cents 131.187000 3: 224.496 cents 224.496000 4: 262.374 cents 262.374000 5: 355.683 cents 355.683000 6: 448.992 cents 448.992000 7: 486.870 cents 486.870000 8: 580.179 cents 580.179000 9: 618.057 cents 618.057000 10: 711.366 cents 711.366000 11: 749.244 cents 749.244000 12: 842.553 cents 842.553000 13: 935.862 cents 935.862000 14: 973.740 cents 973.740000 15: 1067.049 cents 1067.049000 16: 1104.927 cents 1104.927000 17: 1198.236 cents 1198.236000
SHOW/INTERVAL
0: 93.3090 cents 93.3090 1: 93.3090 cents 93.3090 2: 37.8780 cents 37.8780 3: 93.3090 cents 93.3090 4: 37.8780 cents 37.8780 5: 93.3090 cents 93.3090 6: 93.3090 cents 93.3090 7: 37.8780 cents 37.8780 8: 93.3090 cents 93.3090 9: 37.8780 cents 37.8780 10: 93.3090 cents 93.3090 11: 37.8780 cents 37.8780 12: 93.3090 cents 93.3090 13: 93.3090 cents 93.3090 14: 37.8780 cents 37.8780 15: 93.3090 cents 93.3090 16: 37.8780 cents 37.8780 17: 93.3090 cents 93.3090
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 37.87800 cents 1: 10 93.30900 cents 2: 14 131.18700 cents 2: 3 186.61800 cents 3: 4 169.06500 cents 3: 13 224.49600 cents 4: 11 262.37400 cents 4: 6 317.80500 cents 5: 1 300.25200 cents 5: 16 355.68300 cents 6: 8 393.56100 cents 6: 9 448.99200 cents 7: 15 486.87000 cents 7: 2 542.30100 cents 8: 5 524.74800 cents 8: 12 580.17900 cents 9: 12 618.05700 cents 9: 5 673.48800 cents 10: 2 655.93500 cents 10: 15 711.36600 cents 11: 9 749.24400 cents 11: 8 804.67500 cents 12: 16 842.55300 cents 12: 1 897.98400 cents 13: 6 880.43100 cents 13: 11 935.86200 cents 14: 13 973.74000 cents 14: 4 1029.17100 cents 15: 3 1011.61800 cents 15: 14 1067.04900 cents 16: 10 1104.92700 cents 16: 7 1160.35800 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 93.3 131.2 224.5 262.4 355.7 449.0 486.9 580.2 618.1 711.4 749.2 842.6 935.9 973.7 1067.0 1104.9 1198.2 93.3 : 37.9 131.2 169.1 262.4 355.7 393.6 486.9 524.7 618.1 655.9 749.2 842.6 880.4 973.7 1011.6 1104.9 1198.2 131.2 : 93.3 131.2 224.5 317.8 355.7 449.0 486.9 580.2 618.1 711.4 804.7 842.6 935.9 973.7 1067.0 1160.4 1198.2 224.5 : 37.9 131.2 224.5 262.4 355.7 393.6 486.9 524.7 618.1 711.4 749.2 842.6 880.4 973.7 1067.0 1104.9 1198.2 262.4 : 93.3 186.6 224.5 317.8 355.7 449.0 486.9 580.2 673.5 711.4 804.7 842.6 935.9 1029.2 1067.0 1160.4 1198.2 355.7 : 93.3 131.2 224.5 262.4 355.7 393.6 486.9 580.2 618.1 711.4 749.2 842.6 935.9 973.7 1067.0 1104.9 1198.2 449.0 : 37.9 131.2 169.1 262.4 300.3 393.6 486.9 524.7 618.1 655.9 749.2 842.6 880.4 973.7 1011.6 1104.9 1198.2 486.9 : 93.3 131.2 224.5 262.4 355.7 449.0 486.9 580.2 618.1 711.4 804.7 842.6 935.9 973.7 1067.0 1160.4 1198.2 580.2 : 37.9 131.2 169.1 262.4 355.7 393.6 486.9 524.7 618.1 711.4 749.2 842.6 880.4 973.7 1067.0 1104.9 1198.2 618.1 : 93.3 131.2 224.5 317.8 355.7 449.0 486.9 580.2 673.5 711.4 804.7 842.6 935.9 1029.2 1067.0 1160.4 1198.2 711.4 : 37.9 131.2 224.5 262.4 355.7 393.6 486.9 580.2 618.1 711.4 749.2 842.6 935.9 973.7 1067.0 1104.9 1198.2 749.2 : 93.3 186.6 224.5 317.8 355.7 449.0 542.3 580.2 673.5 711.4 804.7 898.0 935.9 1029.2 1067.0 1160.4 1198.2 842.6 : 93.3 131.2 224.5 262.4 355.7 449.0 486.9 580.2 618.1 711.4 804.7 842.6 935.9 973.7 1067.0 1104.9 1198.2 935.9 : 37.9 131.2 169.1 262.4 355.7 393.6 486.9 524.7 618.1 711.4 749.2 842.6 880.4 973.7 1011.6 1104.9 1198.2 973.7 : 93.3 131.2 224.5 317.8 355.7 449.0 486.9 580.2 673.5 711.4 804.7 842.6 935.9 973.7 1067.0 1160.4 1198.2 1067.0: 37.9 131.2 224.5 262.4 355.7 393.6 486.9 580.2 618.1 711.4 749.2 842.6 880.4 973.7 1067.0 1104.9 1198.2 1104.9: 93.3 186.6 224.5 317.8 355.7 449.0 542.3 580.2 673.5 711.4 804.7 842.6 935.9 1029.2 1067.0 1160.4 1198.2 1198.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 37.8780 .. 93.3090 cents 55.43100 cents 37.87800 cents 2: 131.1870 .. 186.6180 cents 55.43100 cents 37.87800 cents 3: 169.0650 .. 224.4960 cents 55.43100 cents -17.55300 cents 4: 262.3740 .. 317.8050 cents 55.43100 cents 37.87800 cents 5: 300.2520 .. 355.6830 cents 55.43100 cents -17.55300 cents 6: 393.5610 .. 448.9920 cents 55.43100 cents 37.87800 cents 7: 486.8700 .. 542.3010 cents 55.43100 cents 37.87800 cents 8: 524.7480 .. 580.1790 cents 55.43100 cents -17.55300 cents 9: 618.0570 .. 673.4880 cents 55.43100 cents 37.87800 cents 10: 655.9350 .. 711.3660 cents 55.43100 cents -17.55300 cents 11: 749.2440 .. 804.6750 cents 55.43100 cents 37.87800 cents 12: 842.5530 .. 897.9840 cents 55.43100 cents 37.87800 cents 13: 880.4310 .. 935.8620 cents 55.43100 cents -17.55300 cents 14: 973.7400 .. 1029.1710 cents 55.43100 cents 37.87800 cents 15: 1011.6180 .. 1067.0490 cents 55.43100 cents -17.55300 cents 16: 1104.9270 .. 1160.3580 cents 55.43100 cents 37.87800 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 37.87800 cents, class 1 Average step (divided formal octave): 70.4845 cents Largest one step interval : 93.30900 cents Average / Smallest step : 1.860829 Largest / Average step : 1.323824 Largest / Smallest step : 2.463409 Median interval of one step : 93.30900 cents, amount: 10 Most common interval of one step : 93.30900 cents, amount: 10 Least squares average step : 70.29815 cents, oct.: 1195.06851 cents Scale is not proper Scale has Myhill's property chromas: 55.43100 cents and 17.55300 cents, ratio: 3.157922 generators: 5 of 355.68300 cents and 12 of 842.55300 cents ET pair of linear temperament : 10&27 Scale is distributional even Scale is a mode of a 1297-tone equal temperament with octave 1198.236 cents degrees: 101 142 243 284 385 486 527 628 669 770 811 912 1013 1054 1155 1196 1297 generators: 385 and 912 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABABABAABABA Step pattern size order : LSLSLLSLSLSLLSLSL Scale is a Constant Structure, by a margin of 17.55300 cents Scale diversity : 1.206807 Lumma stability : 0.347726 Lumma impropriety factor : 0.087894 Rothenberg efficiency : 0.705882 redundancy: 0.294118 Efficiency x scale size : 12.000000 Number of different interval sizes : 32 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 17.55300 cents Most common intervals : 355.68300 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 448.992 842.553 cents Most common triad is 0.0 355.683 842.553 cents, amount: 15 Number of recognisable fifths : 15, average 711.3660 cents Number of recognisable fourths : 15, average 486.8700 cents Scale contains two identical conjunct "tetrachords" of 8 notes Best fifths form a closed circle Formal octave complements present : 17 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 8-9 -- 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: 15.9738 c. M:-26.0852 c. 23: 2 1 1 1 2 2 0 2 1 2 0 2 2 1 1 1 2 N D3 I SD: 14.8022 c. M:-25.1047 c. 24: 2 1 1 1 2 2 1 2 0 2 1 2 2 1 1 1 2 N D3 I SD: 14.2095 c. M:-24.7900 c. 26: 2 1 2 1 2 2 1 2 0 2 1 2 2 1 2 1 2 N T3 I SD: 12.6408 c. M:-20.0760 c. 27: 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 P M ME I SD: 3.1849 c. M:-5.2009 c. 37: 3 1 3 1 3 3 1 3 1 3 1 3 3 1 3 1 3 N M DE I SD: 2.6911 c. M:-4.3946 c. 64: 5 2 5 2 5 5 2 5 2 5 2 5 5 2 5 2 5 N M DE I SD: 0.2122 c. M:-0.3465 c. 219: 17 7 17 7 17 17 7 17 7 17 7 17 17 7 17 7 17 N M DE I SD: 0.2066 c. M:-0.3374 c. 283: 22 9 22 9 22 22 9 22 9 22 9 22 22 9 22 9 22 N M DE I SD: 0.1119 c. M:-0.1828 c. 347: 27 11 27 11 27 27 11 27 11 27 11 27 27 11 27 11 27 N M DE I SD: 0.0521 c. M:-0.0851 c. 411: 32 13 32 13 32 32 13 32 13 32 13 32 32 13 32 13 32 N M DE I SD: 0.0110 c. M:-0.0179 c. 886: 69 28 69 28 69 69 28 69 28 69 28 69 69 28 69 28 69 N M DE I SD: 0.0051 c. M:-0.0084 c. 1297: 101 41 101 41 101 101 41 101 41 101 41 101 101 41 101 41 101 N M DE I SD: 0.0000 c. M:-0.0001 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 1.7640 cents 2 .. 4 match: 2 H SD: 4.7874 cents 3 .. 6 match: 3 H SD: 14.4365 cents 4 .. 8 match: 4 H SD: 8.1166 cents 5 .. 10 match: 5 H SD: 13.2190 cents 6 .. 12 match: 6 H SD: 7.9884 cents 7 .. 14 match: 7 H SD: 5.2992 cents 8 .. 16 match: 8 H SD: 6.3645 cents 9 .. 18 match: 9 H SD: 7.7145 cents 10 .. 20 match: 10 H SD: 7.7226 cents 11 .. 22 match: 11 H SD: 7.2528 cents 12 .. 24 match: 12 H SD: 6.5317 cents 13 .. 26 match: 13 H SD: 4.8855 cents 14 .. 28 match: 14 H SD: 5.5115 cents 15 .. 30 match: 11 SD: 6.4839 cents 16 .. 32 match: 14 S SD: 5.4270 cents 17 .. 34 match: 14 S SD: 4.9595 cents 18 .. 36 match: 16 SD: 4.2137 cents 19 .. 38 match: 12 SD: 4.8984 cents 20 .. 40 match: 15 SD: 4.3586 cents 21 .. 42 match: 15 SD: 3.3022 cents 22 .. 44 match: 15 SD: 3.3879 cents 23 .. 46 match: 15 SD: 3.8520 cents 24 .. 48 match: 16 SD: 3.4071 cents 26 .. 52 match: 15 SD: 3.2160 cents 27 .. 54 match: 16 SD: 3.2196 cents 28 .. 56 match: 16 SD: 2.6374 cents 29 .. 58 match: 14 SD: 3.1239 cents 30 .. 60 match: 16 SD: 2.4257 cents 31 .. 62 match: 16 SD: 2.5621 cents 33 .. 66 match: 16 SD: 2.7538 cents 34 .. 68 match: 17 SD: 2.6925 cents 35 .. 70 match: 17 SD: 1.8381 cents 37 .. 74 match: 17 SD: 1.6786 cents 49 .. 98 match: 17 SD: 1.5881 cents 50 .. 100 match: 17 SD: 1.5502 cents 53 .. 106 match: 17 SD: 1.2497 cents 61 .. 122 match: 17 SD: 1.2001 cents 65 .. 130 match: 17 SD: 1.0790 cents 67 .. 134 match: 17 SD: 1.0677 cents 73 .. 146 match: 17 SD: 1.0133 cents 74 .. 148 match: 17 SD: 0.8591 cents 87 .. 174 match: 17 SD: 0.8473 cents 88 .. 176 match: 17 SD: 0.8297 cents 91 .. 182 match: 17 SD: 0.8209 cents 92 .. 184 match: 17 SD: 0.8203 cents 93 .. 186 match: 17 SD: 0.8044 cents 102 .. 204 match: 17 SD: 0.6600 cents 110 .. 220 match: 17 SD: 0.6455 cents 114 .. 228 match: 17 SD: 0.6295 cents 123 .. 246 match: 17 SD: 0.5801 cents 128 .. 256 match: 17 SD: 0.4953 cents 142 .. 284 match: 17 SD: 0.4907 cents 163 .. 326 match: 17 SD: 0.4245 cents 166 .. 332 match: 17 SD: 0.3480 cents 179 .. 358 match: 17 SD: 0.3435 cents 203 .. 406 match: 17 SD: 0.3118 cents 216 .. 432 match: 17 SD: 0.2816 cents 268 .. 535 match: 17 SD: 0.2355 cents 311 .. 621 match: 17 SD: 0.2338 cents 317 .. 633 match: 17 SD: 0.2219 cents 342 .. 683 match: 17 SD: 0.2012 cents 354 .. 707 match: 17 SD: 0.1758 cents 392 .. 783 match: 17 SD: 0.1732 cents 421 .. 841 match: 17 SD: 0.1683 cents 434 .. 867 match: 17 SD: 0.1517 cents 447 .. 893 match: 17 SD: 0.1497 cents 469 .. 937 match: 17 SD: 0.1194 cents 543 .. 1085 match: 17 SD: 0.1122 cents 600 .. 1199 match: 17 SD: 0.1058 cents