Scala analysis: diamond9keemic
Keemic (875/864) tempering of 9-limit diamond, POTE tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 176.722 cents 176.721850 2: 203.747 cents 203.746530 3: 235.785 cents 235.785360 4: 262.341 cents 262.341370 5: 321.405 cents 321.404880 6: 380.468 cents 380.468390 7: 439.532 cents 439.531890 8: 498.127 cents 498.126730 9: 583.746 cents 583.746250 10: 616.254 cents 616.253750 11: 701.873 cents 701.873270 12: 760.468 cents 760.468110 13: 819.532 cents 819.531610 14: 878.595 cents 878.595120 15: 937.659 cents 937.658630 16: 964.215 cents 964.214640 17: 996.253 cents 996.253470 18: 1023.278 cents 1023.278150 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 176.7219 cents 176.7219 1: 176.7218 cents 176.7218 2: 27.0247 cents 27.0247 3: 32.0388 cents 32.0388 4: 26.5560 cents 26.5560 5: 59.0635 cents 59.0635 6: 59.0635 cents 59.0635 7: 59.0635 cents 59.0635 8: 58.5948 cents 58.5948 9: 85.6195 cents 85.6195 10: 32.5075 cents 32.5075 11: 85.6195 cents 85.6195 12: 58.5948 cents 58.5948 13: 59.0635 cents 59.0635 14: 59.0635 cents 59.0635 15: 59.0635 cents 59.0635 16: 26.5560 cents 26.5560 17: 32.0388 cents 32.0388 18: 27.0247 cents 27.0247 19: 176.7219 cents 176.7219
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 26.55601 cents 1: 2 27.02468 cents 1: 2 32.03883 cents 1: 1 32.50750 cents 1: 2 58.59484 cents 1: 6 59.06351 cents 1: 2 85.61952 cents 1: 2 176.72185 cents 2: 2 58.59484 cents 2: 2 59.06351 cents 2: 2 85.61952 cents 2: 2 117.65834 cents 2: 6 118.12702 cents 2: 2 144.21436 cents 2: 2 203.74653 cents 2: 1 353.44370 cents 3: 2 85.61952 cents 3: 2 117.65835 cents 3: 2 144.68303 cents 3: 4 176.72185 cents 3: 2 177.19052 cents 3: 2 203.27786 cents 3: 1 203.74654 cents 3: 2 235.78536 cents 3: 2 380.46838 cents 4: 2 144.68303 cents 4: 2 176.72186 cents 4: 2 203.74653 cents 4: 4 235.78536 cents 4: 6 262.34137 cents 4: 1 407.49306 cents 4: 2 412.50721 cents 5: 2 203.74654 cents 5: 2 235.78536 cents 5: 2 262.34137 cents 5: 2 294.84887 cents 5: 1 320.93622 cents 5: 6 321.40488 cents 5: 2 439.06322 cents 5: 2 439.53189 cents 6: 2 262.81004 cents 6: 2 294.38020 cents 6: 2 347.96089 cents 6: 2 353.91238 cents 6: 2 379.99972 cents 6: 4 380.46839 cents 6: 2 466.08790 cents 6: 1 471.57072 cents 6: 2 498.12673 cents 7: 2 321.40488 cents 7: 2 379.99972 cents 7: 2 380.46839 cents 7: 3 439.06323 cents 7: 4 439.53189 cents 7: 2 498.12673 cents 7: 2 525.15141 cents 7: 2 557.19024 cents 8: 2 407.02440 cents 8: 2 412.50722 cents 8: 2 466.08791 cents 8: 6 498.12673 cents 8: 1 524.68274 cents 8: 2 557.19024 cents 8: 2 584.21492 cents 8: 2 616.25374 cents 9: 2 439.53190 cents 9: 2 498.12674 cents 9: 2 524.68275 cents 9: 3 557.19024 cents 9: 4 583.74625 cents 9: 2 616.25375 cents 9: 2 643.27842 cents 9: 2 674.84858 cents 10: 2 525.15142 cents 10: 2 556.72158 cents 10: 2 583.74625 cents 10: 4 616.25375 cents 10: 3 642.80976 cents 10: 2 675.31725 cents 10: 2 701.87326 cents 10: 2 760.46810 cents 11: 2 583.74626 cents 11: 2 615.78508 cents 11: 2 642.80976 cents 11: 1 675.31726 cents 11: 6 701.87327 cents 11: 2 733.91209 cents 11: 2 787.49278 cents 11: 2 792.97560 cents 12: 2 642.80976 cents 12: 2 674.84859 cents 12: 2 701.87327 cents 12: 4 760.46811 cents 12: 3 760.93677 cents 12: 2 819.53161 cents 12: 2 820.00028 cents 12: 2 878.59512 cents 13: 2 701.87327 cents 13: 1 728.42928 cents 13: 2 733.91210 cents 13: 4 819.53161 cents 13: 2 820.00028 cents 13: 2 846.08762 cents 13: 2 852.03911 cents 13: 2 905.61980 cents 13: 2 937.18996 cents 14: 2 760.46811 cents 14: 2 760.93678 cents 14: 6 878.59512 cents 14: 1 879.06378 cents 14: 2 905.15113 cents 14: 2 937.65863 cents 14: 2 964.21464 cents 14: 2 996.25346 cents 15: 2 787.49279 cents 15: 1 792.50694 cents 15: 6 937.65863 cents 15: 4 964.21464 cents 15: 2 996.25347 cents 15: 2 1023.27814 cents 15: 2 1055.31697 cents 16: 2 819.53162 cents 16: 2 964.21464 cents 16: 1 996.25346 cents 16: 2 996.72214 cents 16: 2 1022.80948 cents 16: 4 1023.27815 cents 16: 2 1055.31697 cents 16: 2 1082.34165 cents 16: 2 1114.38048 cents 17: 1 846.55630 cents 17: 2 996.25347 cents 17: 2 1055.78564 cents 17: 6 1081.87298 cents 17: 2 1082.34166 cents 17: 2 1114.38048 cents 17: 2 1140.93649 cents 17: 2 1141.40516 cents 18: 2 1023.27815 cents 18: 2 1114.38048 cents 18: 6 1140.93649 cents 18: 2 1141.40516 cents 18: 1 1167.49250 cents 18: 2 1167.96117 cents 18: 2 1172.97532 cents 18: 2 1173.44399 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 8.11111 = 73/9
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 : 176.7 203.7 235.8 262.3 321.4 380.5 439.5 498.1 583.7 616.3 701.9 760.5 819.5 878.6 937.7 964.2 996.3 1023.3 1200.0 176.7 : 27.0 59.1 85.6 144.7 203.7 262.8 321.4 407.0 439.5 525.2 583.7 642.8 701.9 760.9 787.5 819.5 846.6 1023.3 1200.0 203.7 : 32.0 58.6 117.7 176.7 235.8 294.4 380.0 412.5 498.1 556.7 615.8 674.8 733.9 760.5 792.5 819.5 996.3 1173.0 1200.0 235.8 : 26.6 85.6 144.7 203.7 262.3 348.0 380.5 466.1 524.7 583.7 642.8 701.9 728.4 760.5 787.5 964.2 1140.9 1168.0 1200.0 262.3 : 59.1 118.1 177.2 235.8 321.4 353.9 439.5 498.1 557.2 616.3 675.3 701.9 733.9 760.9 937.7 1114.4 1141.4 1173.4 1200.0 321.4 : 59.1 118.1 176.7 262.3 294.8 380.5 439.1 498.1 557.2 616.3 642.8 674.8 701.9 878.6 1055.3 1082.3 1114.4 1140.9 1200.0 380.5 : 59.1 117.7 203.3 235.8 321.4 380.0 439.1 498.1 557.2 583.7 615.8 642.8 819.5 996.3 1023.3 1055.3 1081.9 1140.9 1200.0 439.5 : 58.6 144.2 176.7 262.3 320.9 380.0 439.1 498.1 524.7 556.7 583.7 760.5 937.2 964.2 996.3 1022.8 1081.9 1140.9 1200.0 498.1 : 85.6 118.1 203.7 262.3 321.4 380.5 439.5 466.1 498.1 525.2 701.9 878.6 905.6 937.7 964.2 1023.3 1082.3 1141.4 1200.0 583.7 : 32.5 118.1 176.7 235.8 294.8 353.9 380.5 412.5 439.5 616.3 793.0 820.0 852.0 878.6 937.7 996.7 1055.8 1114.4 1200.0 616.3 : 85.6 144.2 203.3 262.3 321.4 348.0 380.0 407.0 583.7 760.5 787.5 819.5 846.1 905.2 964.2 1023.3 1081.9 1167.5 1200.0 701.9 : 58.6 117.7 176.7 235.8 262.3 294.4 321.4 498.1 674.8 701.9 733.9 760.5 819.5 878.6 937.7 996.3 1081.9 1114.4 1200.0 760.5 : 59.1 118.1 177.2 203.7 235.8 262.8 439.5 616.3 643.3 675.3 701.9 760.9 820.0 879.1 937.7 1023.3 1055.8 1141.4 1200.0 819.5 : 59.1 118.1 144.7 176.7 203.7 380.5 557.2 584.2 616.3 642.8 701.9 760.9 820.0 878.6 964.2 996.7 1082.3 1140.9 1200.0 878.6 : 59.1 85.6 117.7 144.7 321.4 498.1 525.2 557.2 583.7 642.8 701.9 760.9 819.5 905.2 937.7 1023.3 1081.9 1140.9 1200.0 937.7 : 26.6 58.6 85.6 262.3 439.1 466.1 498.1 524.7 583.7 642.8 701.9 760.5 846.1 878.6 964.2 1022.8 1081.9 1140.9 1200.0 964.2 : 32.0 59.1 235.8 412.5 439.5 471.6 498.1 557.2 616.3 675.3 733.9 819.5 852.0 937.7 996.3 1055.3 1114.4 1173.4 1200.0 996.3 : 27.0 203.7 380.5 407.5 439.5 466.1 525.2 584.2 643.3 701.9 787.5 820.0 905.6 964.2 1023.3 1082.3 1141.4 1168.0 1200.0 1023.3: 176.7 353.4 380.5 412.5 439.1 498.1 557.2 616.3 674.8 760.5 793.0 878.6 937.2 996.3 1055.3 1114.4 1140.9 1173.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.5560 .. 176.7218 cents 150.16584 cents 26.55601 cents 2: 58.5948 .. 353.4437 cents 294.84886 cents -118.12701 cents 3: 85.6195 .. 380.4684 cents 294.84886 cents -267.82418 cents 4: 144.6830 .. 412.5072 cents 267.82418 cents -235.78535 cents 5: 203.7465 .. 439.5319 cents 235.78535 cents -208.76067 cents 6: 262.8100 .. 498.1267 cents 235.31669 cents -176.72185 cents 7: 321.4049 .. 557.1902 cents 235.78536 cents -176.72185 cents 8: 407.0244 .. 616.2537 cents 209.22934 cents -150.16584 cents 9: 439.5319 .. 674.8486 cents 235.31668 cents -176.72184 cents 10: 525.1514 .. 760.4681 cents 235.31668 cents -149.69716 cents 11: 583.7463 .. 792.9756 cents 209.22934 cents -176.72184 cents 12: 642.8098 .. 878.5951 cents 235.78536 cents -150.16584 cents 13: 701.8733 .. 937.1900 cents 235.31669 cents -176.72185 cents 14: 760.4681 .. 996.2535 cents 235.78535 cents -176.72185 cents 15: 787.4928 .. 1055.3170 cents 267.82418 cents -208.76067 cents 16: 819.5316 .. 1114.3805 cents 294.84886 cents -235.78535 cents 17: 846.5563 .. 1141.4052 cents 294.84886 cents -267.82418 cents 18: 1023.2781 .. 1173.4440 cents 150.16584 cents -118.12701 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 26.55601 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 176.72185 cents Average / Smallest step : 2.378290 Largest / Average step : 2.798096 Largest / Smallest step : 6.654684 Median interval of one step : 59.06351 cents, amount: 6 Most common interval of one step : 59.06351 cents, amount: 6 Least squares average step : 61.60197 cents, oct.: 1170.43736 cents Scale is not proper Step pattern alph. order: ABCDEEEFGHGFEEEDCBA Step pattern size order : HBCAFFFEGDGEFFFACBH Scale is not a Constant Structure Scale diversity : 1.289867 Lumma stability : 0.044260 Lumma impropriety factor : 0.902342 Number of different interval sizes : 82 = 4.55556 / class Number of one step interval sizes : 8 Highest interval variety : 9 Mean interval variety : 8.11111 = 73/9 Median interval variety : 7.5 Lowest interval variety : 7 Smallest interval difference : 0.46866 cents Most common intervals : 498.12673 cents & inv., amount: 12 Most common triad is 0.0 498.127 701.873 cents, amount: 7 Number of recognisable fifths : 12, average 701.8733 cents Formal octave complements present : 19 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties --
FIT/MODE
19: 3 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 3 N I SD: 10.6161 c. M: 16.8462 c. 29: 4 1 1 0 2 1 2 1 2 1 2 1 2 1 2 0 1 1 4 N I SD: 9.8071 c. M:-15.6405 c. 31: 5 0 1 1 1 2 1 2 2 1 2 2 1 2 1 1 1 0 5 N I SD: 9.6216 c. M:-16.8265 c. 35: 5 1 1 1 1 2 2 2 2 1 2 2 2 2 1 1 1 1 5 N I SD: 8.3867 c. M: 16.1590 c. 37: 5 1 1 1 2 2 2 1 3 1 3 1 2 2 2 1 1 1 5 N I SD: 9.2436 c. M:-14.5597 c. 41: 6 1 1 1 2 2 2 2 3 1 3 2 2 2 2 1 1 1 6 N I SD: 1.0185 c. M: 1.6390 c. 142: 21 3 4 3 7 7 7 7 10 4 10 7 7 7 7 3 4 3 21 N I SD: 0.5625 c. M:-0.9296 c. 183: 27 4 5 4 9 9 9 9 13 5 13 9 9 9 9 4 5 4 27 N I SD: 0.2394 c. M:-0.4678 c. 224: 33 5 6 5 11 11 11 11 16 6 16 11 11 11 11 5 6 5 33 N I SD: 0.1374 c. M: 0.2462 c. 855: 126 19 23 19 42 42 42 42 61 23 61 42 42 42 42 19 23 19 126 N I SD: 0.1375 c. M:-0.2378 c. 1079: 159 24 29 24 53 53 53 53 77 29 77 53 53 53 53 24 29 24 159 N I SD: 0.1361 c. M: 0.2362 c. 1303: 192 29 35 29 64 64 64 64 93 35 93 64 64 64 64 29 35 29 192 N I SD: 0.1356 c. M: 0.2380 c. 1318: 194 30 35 29 65 65 65 64 94 36 94 64 65 65 65 29 35 30 194 N I SD: 0.1277 c. M:-0.2253 c. 1359: 200 31 36 30 67 67 67 66 97 37 97 66 67 67 67 30 36 31 200 N I SD: 0.1244 c. M:-0.2270 c. 1460: 215 33 39 32 72 72 72 71 104 40 104 71 72 72 72 32 39 33 215 N I SD: 0.1137 c. M:-0.1941 c. 1501: 221 34 40 33 74 74 74 73 107 41 107 73 74 74 74 33 40 34 221 N I SD: 0.0979 c. M:-0.1750 c. 1542: 227 35 41 34 76 76 76 75 110 42 110 75 76 76 76 34 41 35 227 N I SD: 0.0897 c. M: 0.1568 c. 1583: 233 36 42 35 78 78 78 77 113 43 113 77 78 78 78 35 42 36 233 N I SD: 0.0896 c. M:-0.1701 c. 1684: 248 38 45 37 83 83 83 82 120 46 120 82 83 83 83 37 45 38 248 N I SD: 0.0812 c. M:-0.1358 c. 1725: 254 39 46 38 85 85 85 84 123 47 123 84 85 85 85 38 46 39 254 N I SD: 0.0673 c. M:-0.1203 c. 1766: 260 40 47 39 87 87 87 86 126 48 126 86 87 87 87 39 47 40 260 N I SD: 0.0615 c. M:-0.1057 c. 1908: 281 43 51 42 94 94 94 93 136 52 136 93 94 94 94 42 51 43 281 N I SD: 0.0567 c. M:-0.0985 c. 1949: 287 44 52 43 96 96 96 95 139 53 139 95 96 96 96 43 52 44 287 N I SD: 0.0438 c. M:-0.0782 c. 1990: 293 45 53 44 98 98 98 97 142 54 142 97 98 98 98 44 53 45 293 N I SD: 0.0401 c. M:-0.0726 c. 2132: 314 48 57 47 105 105 105 104 152 58 152 104 105 105 105 47 57 48 314 N I SD: 0.0382 c. M:-0.0690 c. 2173: 320 49 58 48 107 107 107 106 155 59 155 106 107 107 107 48 58 49 320 N I SD: 0.0252 c. M:-0.0447 c. 2214: 326 50 59 49 109 109 109 108 158 60 158 108 109 109 109 49 59 50 326 N I SD: 0.0241 c. M:-0.0475 c. 2397: 353 54 64 53 118 118 118 117 171 65 171 117 118 118 118 53 64 54 353 N I SD: 0.0103 c. M:-0.0175 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.0409 cents 3 .. 6 match: 3 H SD: 1.9214 cents 4 .. 8 match: 4 H SD: 1.8614 cents 5 .. 10 match: 5 H SD: 2.0119 cents 6 .. 12 match: 6 H SD: 4.5159 cents 7 .. 14 match: 7 H SD: 7.6838 cents 8 .. 16 match: 7 S SD: 5.6205 cents 9 .. 18 match: 8 S SD: 4.2869 cents 10 .. 20 match: 9 S SD: 3.1734 cents 11 .. 22 match: 10 S SD: 7.3344 cents 12 .. 24 match: 11 S SD: 4.9754 cents 13 .. 26 match: 11 SD: 7.4673 cents 14 .. 28 match: 11 SD: 4.1882 cents 15 .. 30 match: 11 SD: 3.7390 cents 16 .. 32 match: 13 SD: 4.8298 cents 17 .. 34 match: 13 SD: 4.4598 cents 18 .. 36 match: 15 S SD: 3.2542 cents 19 .. 38 match: 12 SD: 5.0668 cents 20 .. 40 match: 16 S SD: 2.9556 cents 21 .. 42 match: 16 SD: 3.5857 cents 22 .. 44 match: 15 SD: 4.3471 cents 23 .. 46 match: 17 SD: 3.9562 cents 24 .. 48 match: 15 SD: 2.2980 cents 25 .. 50 match: 16 SD: 2.8931 cents 26 .. 52 match: 16 SD: 3.4036 cents 27 .. 54 match: 17 SD: 3.0367 cents 28 .. 56 match: 18 SD: 2.5413 cents 29 .. 58 match: 16 SD: 2.9632 cents 30 .. 60 match: 17 SD: 2.3325 cents 31 .. 62 match: 18 SD: 2.6427 cents 32 .. 64 match: 18 SD: 2.4501 cents 33 .. 66 match: 17 SD: 2.3077 cents 34 .. 68 match: 18 SD: 2.7164 cents 35 .. 70 match: 18 SD: 1.9550 cents 36 .. 72 match: 18 SD: 1.8807 cents 37 .. 74 match: 18 SD: 2.4227 cents 38 .. 76 match: 18 SD: 1.8012 cents 39 .. 78 match: 18 SD: 2.1633 cents 40 .. 80 match: 19 SD: 1.7822 cents 42 .. 84 match: 18 SD: 1.5840 cents 43 .. 86 match: 18 SD: 2.1414 cents 44 .. 88 match: 18 SD: 1.7812 cents 45 .. 90 match: 18 SD: 1.6384 cents 48 .. 96 match: 19 SD: 1.3864 cents 52 .. 104 match: 18 SD: 1.8511 cents 53 .. 106 match: 19 SD: 1.5566 cents 54 .. 108 match: 19 SD: 1.2048 cents 56 .. 112 match: 19 SD: 1.1622 cents 63 .. 126 match: 19 SD: 1.1361 cents 68 .. 136 match: 19 SD: 1.1120 cents 72 .. 144 match: 19 SD: 1.0361 cents 73 .. 146 match: 19 SD: 0.9643 cents 74 .. 148 match: 19 SD: 0.9025 cents 82 .. 164 match: 19 SD: 0.7914 cents 94 .. 188 match: 19 SD: 0.6959 cents 102 .. 204 match: 19 SD: 0.6860 cents 103 .. 206 match: 19 SD: 0.5890 cents 114 .. 228 match: 19 SD: 0.5666 cents 122 .. 244 match: 19 SD: 0.4510 cents 152 .. 304 match: 19 SD: 0.4323 cents 159 .. 318 match: 19 SD: 0.4200 cents 170 .. 340 match: 19 SD: 0.3906 cents 177 .. 354 match: 19 SD: 0.3732 cents 192 .. 384 match: 19 SD: 0.3439 cents 207 .. 414 match: 19 SD: 0.3150 cents 225 .. 450 match: 19 SD: 0.2662 cents 232 .. 464 match: 19 SD: 0.2534 cents 274 .. 548 match: 19 SD: 0.2288 cents 288 .. 576 match: 19 SD: 0.2028 cents 330 .. 660 match: 19 SD: 0.1994 cents 334 .. 668 match: 19 SD: 0.1988 cents 337 .. 674 match: 19 SD: 0.1975 cents 342 .. 684 match: 19 SD: 0.1530 cents 402 .. 804 match: 19 SD: 0.1508 cents 416 .. 832 match: 19 SD: 0.1500 cents 426 .. 852 match: 19 SD: 0.1478 cents 446 .. 892 match: 19 SD: 0.1409 cents 464 .. 928 match: 19 SD: 0.1276 cents 519 .. 1038 match: 19 SD: 0.1207 cents 558 .. 1116 match: 19 SD: 0.1205 cents 568 .. 1136 match: 19 SD: 0.1105 cents 594 .. 1188 match: 19 SD: 0.1042 cents