Scala analysis: madagascar19
Madagascar[19] (19&53&58) hobbit in 313et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 65.176 cents 65.175720 2: 138.019 cents 138.019170 3: 184.026 cents 184.025560 4: 249.201 cents 249.201280 5: 314.377 cents 314.377000 6: 387.220 cents 387.220450 7: 452.396 cents 452.396170 8: 498.403 cents 498.402560 9: 563.578 cents 563.578270 10: 636.422 cents 636.421730 11: 701.597 cents 701.597440 12: 747.604 cents 747.603830 13: 812.780 cents 812.779550 14: 885.623 cents 885.623000 15: 950.799 cents 950.798720 16: 1015.974 cents 1015.974440 17: 1061.981 cents 1061.980830 18: 1134.824 cents 1134.824280 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 65.1757 cents 65.1757 1: 65.1757 cents 65.1757 2: 72.8434 cents 72.8434 3: 46.0064 cents 46.0064 4: 65.1757 cents 65.1757 5: 65.1757 cents 65.1757 6: 72.8434 cents 72.8434 7: 65.1757 cents 65.1757 8: 46.0064 cents 46.0064 9: 65.1757 cents 65.1757 10: 72.8435 cents 72.8435 11: 65.1757 cents 65.1757 12: 46.0064 cents 46.0064 13: 65.1757 cents 65.1757 14: 72.8434 cents 72.8434 15: 65.1757 cents 65.1757 16: 65.1757 cents 65.1757 17: 46.0064 cents 46.0064 18: 72.8434 cents 72.8434 19: 65.1757 cents 65.1757
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 46.00639 cents 1: 10 65.17572 cents 1: 5 72.84345 cents 2: 6 111.18211 cents 2: 2 118.84984 cents 2: 3 130.35144 cents 2: 8 138.01917 cents 3: 4 176.35783 cents 3: 8 184.02556 cents 3: 7 203.19489 cents 4: 16 249.20128 cents 4: 2 268.37061 cents 4: 1 276.03834 cents 5: 1 295.20766 cents 5: 12 314.37700 cents 5: 6 322.04473 cents 6: 4 360.38339 cents 6: 1 368.05112 cents 6: 4 379.55271 cents 6: 10 387.22045 cents 7: 3 425.55910 cents 7: 6 433.22684 cents 7: 10 452.39617 cents 8: 13 498.40256 cents 8: 4 517.57188 cents 8: 2 525.23962 cents 9: 12 563.57827 cents 9: 5 571.24601 cents 9: 2 590.41534 cents 10: 2 609.58466 cents 10: 5 628.75399 cents 10: 12 636.42173 cents 11: 2 674.76038 cents 11: 4 682.42811 cents 11: 13 701.59744 cents 12: 10 747.60383 cents 12: 6 766.77316 cents 12: 3 774.44090 cents 13: 10 812.77955 cents 13: 4 820.44728 cents 13: 1 831.94888 cents 13: 4 839.61661 cents 14: 6 877.95527 cents 14: 12 885.62300 cents 14: 1 904.79234 cents 15: 1 923.96166 cents 15: 2 931.62939 cents 15: 16 950.79872 cents 16: 7 996.80511 cents 16: 8 1015.97444 cents 16: 4 1023.64217 cents 17: 8 1061.98083 cents 17: 3 1069.64856 cents 17: 2 1081.15016 cents 17: 6 1088.81789 cents 18: 5 1127.15655 cents 18: 10 1134.82428 cents 18: 4 1153.99361 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.22222 = 29/9
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 : 65.2 138.0 184.0 249.2 314.4 387.2 452.4 498.4 563.6 636.4 701.6 747.6 812.8 885.6 950.8 1016.0 1062.0 1134.8 1200.0 65.2 : 72.8 118.8 184.0 249.2 322.0 387.2 433.2 498.4 571.2 636.4 682.4 747.6 820.4 885.6 950.8 996.8 1069.6 1134.8 1200.0 138.0 : 46.0 111.2 176.4 249.2 314.4 360.4 425.6 498.4 563.6 609.6 674.8 747.6 812.8 878.0 924.0 996.8 1062.0 1127.2 1200.0 184.0 : 65.2 130.4 203.2 268.4 314.4 379.6 452.4 517.6 563.6 628.8 701.6 766.8 831.9 878.0 950.8 1016.0 1081.2 1154.0 1200.0 249.2 : 65.2 138.0 203.2 249.2 314.4 387.2 452.4 498.4 563.6 636.4 701.6 766.8 812.8 885.6 950.8 1016.0 1088.8 1134.8 1200.0 314.4 : 72.8 138.0 184.0 249.2 322.0 387.2 433.2 498.4 571.2 636.4 701.6 747.6 820.4 885.6 950.8 1023.6 1069.6 1134.8 1200.0 387.2 : 65.2 111.2 176.4 249.2 314.4 360.4 425.6 498.4 563.6 628.8 674.8 747.6 812.8 878.0 950.8 996.8 1062.0 1127.2 1200.0 452.4 : 46.0 111.2 184.0 249.2 295.2 360.4 433.2 498.4 563.6 609.6 682.4 747.6 812.8 885.6 931.6 996.8 1062.0 1134.8 1200.0 498.4 : 65.2 138.0 203.2 249.2 314.4 387.2 452.4 517.6 563.6 636.4 701.6 766.8 839.6 885.6 950.8 1016.0 1088.8 1154.0 1200.0 563.6 : 72.8 138.0 184.0 249.2 322.0 387.2 452.4 498.4 571.2 636.4 701.6 774.4 820.4 885.6 950.8 1023.6 1088.8 1134.8 1200.0 636.4 : 65.2 111.2 176.4 249.2 314.4 379.6 425.6 498.4 563.6 628.8 701.6 747.6 812.8 878.0 950.8 1016.0 1062.0 1127.2 1200.0 701.6 : 46.0 111.2 184.0 249.2 314.4 360.4 433.2 498.4 563.6 636.4 682.4 747.6 812.8 885.6 950.8 996.8 1062.0 1134.8 1200.0 747.6 : 65.2 138.0 203.2 268.4 314.4 387.2 452.4 517.6 590.4 636.4 701.6 766.8 839.6 904.8 950.8 1016.0 1088.8 1154.0 1200.0 812.8 : 72.8 138.0 203.2 249.2 322.0 387.2 452.4 525.2 571.2 636.4 701.6 774.4 839.6 885.6 950.8 1023.6 1088.8 1134.8 1200.0 885.6 : 65.2 130.4 176.4 249.2 314.4 379.6 452.4 498.4 563.6 628.8 701.6 766.8 812.8 878.0 950.8 1016.0 1062.0 1127.2 1200.0 950.8 : 65.2 111.2 184.0 249.2 314.4 387.2 433.2 498.4 563.6 636.4 701.6 747.6 812.8 885.6 950.8 996.8 1062.0 1134.8 1200.0 1016.0: 46.0 118.8 184.0 249.2 322.0 368.1 433.2 498.4 571.2 636.4 682.4 747.6 820.4 885.6 931.6 996.8 1069.6 1134.8 1200.0 1062.0: 72.8 138.0 203.2 276.0 322.0 387.2 452.4 525.2 590.4 636.4 701.6 774.4 839.6 885.6 950.8 1023.6 1088.8 1154.0 1200.0 1134.8: 65.2 130.4 203.2 249.2 314.4 379.6 452.4 517.6 563.6 628.8 701.6 766.8 812.8 878.0 950.8 1016.0 1081.2 1127.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 46.0064 .. 72.8434 cents 26.83706 cents 46.00639 cents 2: 111.1821 .. 138.0192 cents 26.83706 cents 38.33866 cents 3: 176.3578 .. 203.1949 cents 26.83706 cents 38.33866 cents 4: 249.2013 .. 276.0383 cents 26.83706 cents 46.00639 cents 5: 295.2077 .. 322.0447 cents 26.83707 cents 19.16932 cents 6: 360.3834 .. 387.2204 cents 26.83706 cents 38.33866 cents 7: 425.5591 .. 452.3962 cents 26.83707 cents 38.33865 cents 8: 498.4026 .. 525.2396 cents 26.83706 cents 46.00639 cents 9: 563.5783 .. 590.4153 cents 26.83707 cents 38.33865 cents 10: 609.5847 .. 636.4217 cents 26.83707 cents 19.16932 cents 11: 674.7604 .. 701.5974 cents 26.83706 cents 38.33865 cents 12: 747.6038 .. 774.4409 cents 26.83707 cents 46.00639 cents 13: 812.7795 .. 839.6166 cents 26.83706 cents 38.33865 cents 14: 877.9553 .. 904.7923 cents 26.83707 cents 38.33866 cents 15: 923.9617 .. 950.7987 cents 26.83706 cents 19.16932 cents 16: 996.8051 .. 1023.6422 cents 26.83706 cents 46.00639 cents 17: 1061.9808 .. 1088.8179 cents 26.83706 cents 38.33866 cents 18: 1127.1566 .. 1153.9936 cents 26.83706 cents 38.33866 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 46.00639 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 72.84345 cents Average / Smallest step : 1.372807 Largest / Average step : 1.153355 Largest / Smallest step : 1.583333 Median interval of one step : 65.17572 cents, amount: 10 Most common interval of one step : 65.17572 cents, amount: 10 Least squares average step : 63.08805 cents, oct.: 1198.67289 cents Scale is strictly proper Scale is a mode of a 313-tone equal temperament with octave 1200.000 cents degrees: 17 36 48 65 82 101 118 130 147 166 183 195 212 231 248 265 277 296 313 Least number of segments generator : 157 of 601.917 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 248 of 950.799 cents and inv. generated superset size: 41 = 22 more = 215.789% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCAABACABACABAACBA Step pattern size order : MLSMMLMSMLMSMLMMSLM Scale is a Constant Structure, by a margin of 19.16932 cents Scale diversity : 1.257890 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.597444 Number of different interval sizes : 58 = 3.22222 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.22222 = 29/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 7.66773 cents Most common intervals : 249.20128 cents & inv., amount: 16 Most common triad is 0.0 249.201 950.799 cents, amount: 13 Number of recognisable fifths : 13, average 701.5974 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor 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: 6.7227 c. M: 11.7034 c. 34: 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 P M ME I SD: 4.2747 c. M: 7.5550 c. 53: 3 3 2 3 3 3 3 2 3 3 3 2 3 3 3 3 2 3 3 SP M ME I SD: 2.0292 c. M: 2.8935 c. 96: 5 6 4 5 5 6 5 4 5 6 5 4 5 6 5 5 4 6 5 SP T3 I SD: 1.8693 c. M: 3.4744 c. 111: 6 7 4 6 6 7 6 4 6 7 6 4 6 7 6 6 4 7 6 SP I SD: 1.3539 c. M: 2.5214 c. 130: 7 8 5 7 7 8 7 5 7 8 7 5 7 8 7 7 5 8 7 SP I SD: 0.4137 c. M:-0.5898 c. 183: 10 11 7 10 10 11 10 7 10 11 10 7 10 11 10 10 7 11 10 SP I SD: 0.2939 c. M: 0.4190 c. 313: 17 19 12 17 17 19 17 12 17 19 17 12 17 19 17 17 12 19 17 SP I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.1788 cents 3 .. 6 match: 3 H SD: 0.4380 cents 4 .. 8 match: 4 H SD: 4.5134 cents 5 .. 10 match: 5 H SD: 3.8134 cents 6 .. 12 match: 6 H SD: 3.6258 cents 7 .. 14 match: 7 H SD: 6.8619 cents 8 .. 16 match: 8 H SD: 6.0372 cents 9 .. 18 match: 9 H SD: 6.0160 cents 10 .. 20 match: 10 H SD: 4.8177 cents 11 .. 22 match: 11 H SD: 5.9722 cents 12 .. 24 match: 12 H SD: 3.9837 cents 13 .. 26 match: 13 H SD: 4.3384 cents 14 .. 28 match: 14 H SD: 4.9903 cents 15 .. 30 match: 15 H SD: 4.0850 cents 16 .. 32 match: 16 H SD: 4.6097 cents 17 .. 34 match: 15 SD: 5.7974 cents 18 .. 36 match: 17 SD: 3.9069 cents 19 .. 38 match: 17 SD: 4.3197 cents 20 .. 40 match: 18 SD: 2.9970 cents 21 .. 42 match: 18 S SD: 3.7364 cents 22 .. 44 match: 17 SD: 4.1940 cents 23 .. 46 match: 19 SD: 3.8736 cents 24 .. 48 match: 19 SD: 2.5415 cents 26 .. 52 match: 19 SD: 2.5319 cents 31 .. 62 match: 18 SD: 2.6601 cents 33 .. 66 match: 19 SD: 2.3622 cents 34 .. 68 match: 19 SD: 2.2320 cents 36 .. 72 match: 19 SD: 2.0532 cents 40 .. 80 match: 19 SD: 2.0508 cents 44 .. 88 match: 19 SD: 1.6250 cents 45 .. 90 match: 19 SD: 1.4753 cents 50 .. 100 match: 19 SD: 1.4386 cents 52 .. 104 match: 19 SD: 1.2667 cents 60 .. 120 match: 19 SD: 0.9775 cents 70 .. 140 match: 19 SD: 0.8905 cents 72 .. 144 match: 19 SD: 0.8884 cents 80 .. 160 match: 19 SD: 0.8829 cents 84 .. 168 match: 19 SD: 0.8037 cents 96 .. 192 match: 19 SD: 0.6602 cents 104 .. 208 match: 19 SD: 0.6260 cents 120 .. 240 match: 19 SD: 0.6078 cents 124 .. 248 match: 19 SD: 0.4830 cents 135 .. 270 match: 19 SD: 0.3969 cents 180 .. 360 match: 19 SD: 0.2885 cents 231 .. 462 match: 19 SD: 0.2718 cents 232 .. 464 match: 19 SD: 0.2542 cents 252 .. 504 match: 19 SD: 0.2401 cents 291 .. 582 match: 19 SD: 0.2281 cents 302 .. 604 match: 19 SD: 0.2086 cents 311 .. 622 match: 19 SD: 0.1944 cents 312 .. 624 match: 19 SD: 0.1904 cents 362 .. 724 match: 19 SD: 0.1785 cents 387 .. 774 match: 19 SD: 0.1723 cents 392 .. 784 match: 19 SD: 0.1529 cents 446 .. 892 match: 19 SD: 0.1190 cents 491 .. 982 match: 19 SD: 0.1177 cents 518 .. 1036 match: 19 SD: 0.1174 cents 542 .. 1084 match: 19 SD: 0.1056 cents