Scala analysis: indians
Shruti/Mathieu's Magic Mode scale in 289-equal (schismic) temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 91.349 cents 91.349481 2: 112.111 cents 112.110727 3: 182.699 cents 182.698962 4: 203.460 cents 203.460208 5: 294.810 cents 294.809689 6: 315.571 cents 315.570934 7: 386.159 cents 386.159170 8: 406.920 cents 406.920415 9: 498.270 cents 498.269896 10: 519.031 cents 519.031142 11: 589.619 cents 589.619377 12: 610.381 cents 610.380623 13: 701.730 cents 701.730104 14: 793.080 cents 793.079585 15: 813.841 cents 813.840830 16: 884.429 cents 884.429066 17: 905.190 cents 905.190311 18: 996.540 cents 996.539792 19: 1017.301 cents 1017.301038 20: 1087.889 cents 1087.889273 21: 1108.651 cents 1108.650519 22: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 91.3495 cents 91.3495 1: 91.3495 cents 91.3495 2: 20.7612 cents 20.7612 3: 70.5882 cents 70.5882 4: 20.7612 cents 20.7612 5: 91.3495 cents 91.3495 6: 20.7612 cents 20.7612 7: 70.5882 cents 70.5882 8: 20.7612 cents 20.7612 9: 91.3495 cents 91.3495 10: 20.7612 cents 20.7612 11: 70.5882 cents 70.5882 12: 20.7612 cents 20.7612 13: 91.3495 cents 91.3495 14: 91.3495 cents 91.3495 15: 20.7612 cents 20.7612 16: 70.5882 cents 70.5882 17: 20.7612 cents 20.7612 18: 91.3495 cents 91.3495 19: 20.7612 cents 20.7612 20: 70.5882 cents 70.5882 21: 20.7612 cents 20.7612 22: 91.3495 cents 91.3495
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 20.76125 cents 1: 5 70.58824 cents 1: 7 91.34948 cents 2: 10 91.34948 cents 2: 10 112.11073 cents 2: 2 182.69896 cents 3: 5 112.11073 cents 3: 3 132.87197 cents 3: 10 182.69896 cents 3: 4 203.46021 cents 4: 16 203.46021 cents 4: 2 224.22145 cents 4: 4 274.04844 cents 5: 6 224.22145 cents 5: 3 274.04844 cents 5: 13 294.80969 cents 6: 6 294.80969 cents 6: 10 315.57093 cents 6: 2 365.39792 cents 6: 4 386.15917 cents 7: 3 315.57093 cents 7: 1 336.33218 cents 7: 10 386.15917 cents 7: 8 406.92041 cents 8: 10 406.92042 cents 8: 4 427.68166 cents 8: 8 477.50865 cents 9: 2 427.68166 cents 9: 1 477.50865 cents 9: 19 498.26990 cents 10: 2 498.26990 cents 10: 10 519.03114 cents 10: 4 568.85813 cents 10: 6 589.61938 cents 11: 1 519.03114 cents 11: 10 589.61938 cents 11: 10 610.38062 cents 11: 1 680.96886 cents 12: 6 610.38062 cents 12: 4 631.14187 cents 12: 10 680.96886 cents 12: 2 701.73010 cents 13: 19 701.73010 cents 13: 1 722.49135 cents 13: 2 772.31834 cents 14: 8 722.49135 cents 14: 4 772.31834 cents 14: 10 793.07958 cents 15: 8 793.07958 cents 15: 10 813.84083 cents 15: 1 863.66782 cents 15: 3 884.42907 cents 16: 4 813.84083 cents 16: 2 834.60208 cents 16: 10 884.42907 cents 16: 6 905.19031 cents 17: 13 905.19031 cents 17: 3 925.95156 cents 17: 6 975.77855 cents 18: 4 925.95156 cents 18: 2 975.77855 cents 18: 16 996.53979 cents 19: 4 996.53979 cents 19: 10 1017.30104 cents 19: 3 1067.12803 cents 19: 5 1087.88927 cents 20: 2 1017.30104 cents 20: 10 1087.88927 cents 20: 10 1108.65052 cents 21: 7 1108.65052 cents 21: 5 1129.41177 cents 21: 10 1179.23875 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.42857 = 24/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0.0 : 91.3 112.1 182.7 203.5 294.8 315.6 386.2 406.9 498.3 519.0 589.6 610.4 701.7 793.1 813.8 884.4 905.2 996.5 1017.3 1087.9 1108.7 1200.0 91.3 : 20.8 91.3 112.1 203.5 224.2 294.8 315.6 406.9 427.7 498.3 519.0 610.4 701.7 722.5 793.1 813.8 905.2 926.0 996.5 1017.3 1108.7 1200.0 112.1 : 70.6 91.3 182.7 203.5 274.0 294.8 386.2 406.9 477.5 498.3 589.6 681.0 701.7 772.3 793.1 884.4 905.2 975.8 996.5 1087.9 1179.2 1200.0 182.7 : 20.8 112.1 132.9 203.5 224.2 315.6 336.3 406.9 427.7 519.0 610.4 631.1 701.7 722.5 813.8 834.6 905.2 926.0 1017.3 1108.7 1129.4 1200.0 203.5 : 91.3 112.1 182.7 203.5 294.8 315.6 386.2 406.9 498.3 589.6 610.4 681.0 701.7 793.1 813.8 884.4 905.2 996.5 1087.9 1108.7 1179.2 1200.0 294.8 : 20.8 91.3 112.1 203.5 224.2 294.8 315.6 406.9 498.3 519.0 589.6 610.4 701.7 722.5 793.1 813.8 905.2 996.5 1017.3 1087.9 1108.7 1200.0 315.6 : 70.6 91.3 182.7 203.5 274.0 294.8 386.2 477.5 498.3 568.9 589.6 681.0 701.7 772.3 793.1 884.4 975.8 996.5 1067.1 1087.9 1179.2 1200.0 386.2 : 20.8 112.1 132.9 203.5 224.2 315.6 406.9 427.7 498.3 519.0 610.4 631.1 701.7 722.5 813.8 905.2 926.0 996.5 1017.3 1108.7 1129.4 1200.0 406.9 : 91.3 112.1 182.7 203.5 294.8 386.2 406.9 477.5 498.3 589.6 610.4 681.0 701.7 793.1 884.4 905.2 975.8 996.5 1087.9 1108.7 1179.2 1200.0 498.3 : 20.8 91.3 112.1 203.5 294.8 315.6 386.2 406.9 498.3 519.0 589.6 610.4 701.7 793.1 813.8 884.4 905.2 996.5 1017.3 1087.9 1108.7 1200.0 519.0 : 70.6 91.3 182.7 274.0 294.8 365.4 386.2 477.5 498.3 568.9 589.6 681.0 772.3 793.1 863.7 884.4 975.8 996.5 1067.1 1087.9 1179.2 1200.0 589.6 : 20.8 112.1 203.5 224.2 294.8 315.6 406.9 427.7 498.3 519.0 610.4 701.7 722.5 793.1 813.8 905.2 926.0 996.5 1017.3 1108.7 1129.4 1200.0 610.4 : 91.3 182.7 203.5 274.0 294.8 386.2 406.9 477.5 498.3 589.6 681.0 701.7 772.3 793.1 884.4 905.2 975.8 996.5 1087.9 1108.7 1179.2 1200.0 701.7 : 91.3 112.1 182.7 203.5 294.8 315.6 386.2 406.9 498.3 589.6 610.4 681.0 701.7 793.1 813.8 884.4 905.2 996.5 1017.3 1087.9 1108.7 1200.0 793.1 : 20.8 91.3 112.1 203.5 224.2 294.8 315.6 406.9 498.3 519.0 589.6 610.4 701.7 722.5 793.1 813.8 905.2 926.0 996.5 1017.3 1108.7 1200.0 813.8 : 70.6 91.3 182.7 203.5 274.0 294.8 386.2 477.5 498.3 568.9 589.6 681.0 701.7 772.3 793.1 884.4 905.2 975.8 996.5 1087.9 1179.2 1200.0 884.4 : 20.8 112.1 132.9 203.5 224.2 315.6 406.9 427.7 498.3 519.0 610.4 631.1 701.7 722.5 813.8 834.6 905.2 926.0 1017.3 1108.7 1129.4 1200.0 905.2 : 91.3 112.1 182.7 203.5 294.8 386.2 406.9 477.5 498.3 589.6 610.4 681.0 701.7 793.1 813.8 884.4 905.2 996.5 1087.9 1108.7 1179.2 1200.0 996.5 : 20.8 91.3 112.1 203.5 294.8 315.6 386.2 406.9 498.3 519.0 589.6 610.4 701.7 722.5 793.1 813.8 905.2 996.5 1017.3 1087.9 1108.7 1200.0 1017.3: 70.6 91.3 182.7 274.0 294.8 365.4 386.2 477.5 498.3 568.9 589.6 681.0 701.7 772.3 793.1 884.4 975.8 996.5 1067.1 1087.9 1179.2 1200.0 1087.9: 20.8 112.1 203.5 224.2 294.8 315.6 406.9 427.7 498.3 519.0 610.4 631.1 701.7 722.5 813.8 905.2 926.0 996.5 1017.3 1108.7 1129.4 1200.0 1108.7: 91.3 182.7 203.5 274.0 294.8 386.2 406.9 477.5 498.3 589.6 610.4 681.0 701.7 793.1 884.4 905.2 975.8 996.5 1087.9 1108.7 1179.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.7612 .. 91.3495 cents 70.58824 cents 20.76125 cents 2: 91.3495 .. 182.6990 cents 91.34948 cents 1/1, 0.0000 cents 3: 112.1107 .. 203.4602 cents 91.34948 cents -70.58823 cents 4: 203.4602 .. 274.0484 cents 70.58824 cents 1/1, 0.0000 cents 5: 224.2215 .. 294.8097 cents 70.58824 cents -49.82699 cents 6: 294.8097 .. 386.1592 cents 91.34948 cents 1/1, 0.0000 cents 7: 315.5709 .. 406.9204 cents 91.34948 cents -70.58824 cents 8: 406.9204 .. 477.5087 cents 70.58824 cents 1/1, 0.0000 cents 9: 427.6817 .. 498.2699 cents 70.58824 cents -49.82699 cents 10: 498.2699 .. 589.6194 cents 91.34948 cents 1/1, 0.0000 cents 11: 519.0311 .. 680.9689 cents 161.93772 cents -70.58824 cents 12: 610.3806 .. 701.7301 cents 91.34948 cents -70.58824 cents 13: 701.7301 .. 772.3183 cents 70.58824 cents 1/1, 0.0000 cents 14: 722.4913 .. 793.0796 cents 70.58824 cents -49.82699 cents 15: 793.0796 .. 884.4291 cents 91.34948 cents 1/1, 0.0000 cents 16: 813.8408 .. 905.1903 cents 91.34948 cents -70.58824 cents 17: 905.1903 .. 975.7785 cents 70.58824 cents 1/1, 0.0000 cents 18: 925.9516 .. 996.5398 cents 70.58824 cents -49.82699 cents 19: 996.5398 .. 1087.8893 cents 91.34948 cents 1/1, 0.0000 cents 20: 1017.3010 .. 1108.6505 cents 91.34948 cents -70.58823 cents 21: 1108.6505 .. 1179.2388 cents 70.58824 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 20.76124 cents, class 1 Average step (divided formal octave): 54.5455 cents Largest one step interval : 91.34948 cents Average / Smallest step : 2.627273 Largest / Average step : 1.674740 Largest / Smallest step : 4.400000 Median interval of one step : 70.58824 cents, amount: 5 Most common interval of one step : 20.76125 cents, amount: 10 Least squares average step : 54.06239 cents, oct.: 1189.37265 cents Scale is not proper Scale is a mode of a 289-tone equal temperament with octave 1200.000 cents degrees: 22 27 44 49 71 76 93 98 120 125 142 147 169 191 196 213 218 240 245 262 267 289 Least number of segments generator : 147 of 610.381 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 169 of 701.730 cents and inv. generated superset size: 22 = 0 more = 100.000% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 289-tone equal temperament Step pattern alph. order: ABCBABCBABCBAABCBABCBA Step pattern size order : LSMSLSMSLSMSLLSMSLSMSL Scale is not a Constant Structure Scale diversity : 1.160305 Lumma stability : 0.034602 Lumma impropriety factor : 0.519031 Rothenberg efficiency : 0.696970 redundancy: 0.303030 Efficiency x scale size : 15.333333 Number of different interval sizes : 42 = 2.00000 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.42857 = 24/7 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 20.76124 cents Most common intervals : 498.26990 cents & inv., amount: 21 Scale has Generated (pseudo-Myhill) property, generator: 701.730 cents and inv. Scale is a chain of 11 triads 0.0 182.699 701.730 cents Most common triad is 0.0 498.270 701.730 cents, amount: 20 Number of recognisable fifths : 21, average 701.7301 cents Scale contains two identical disjunct "tetrachords" of 10 notes Formal octave complements present : 21 = 95.4545% Limited inverse transpositions : 13 Inversional symmetry on intervals : 6-7 17-18 -- Rational properties --
FIT/MODE
22: 2 0 1 1 1 1 1 0 2 1 1 0 2 2 0 1 1 1 1 1 0 2 N SD: 15.6337 c. M:-26.4234 c. 24: 2 0 2 0 2 0 2 0 2 0 2 0 2 2 0 2 0 2 0 2 0 2 N D3 SD: 11.0103 c. M: 19.0311 c. 29: 2 1 1 1 2 1 1 1 2 1 1 1 2 2 1 1 1 2 1 1 1 2 N SD: 10.9344 c. M:-18.8999 c. 30: 2 1 2 0 2 1 2 0 2 1 2 0 3 2 0 2 1 2 0 2 1 2 N SD: 11.3729 c. M:-18.2699 c. 31: 2 1 2 0 3 0 2 0 3 0 2 1 2 2 1 2 0 3 0 2 1 2 N SD: 10.8194 c. M: 19.8236 c. 32: 2 1 2 0 3 0 2 1 2 1 2 0 3 2 1 2 0 3 0 2 1 2 N SD: 10.4961 c. M: 16.3495 c. 34: 3 0 2 1 2 1 2 1 2 1 2 0 3 2 1 2 1 2 1 2 0 3 N SD: 9.4209 c. M:-16.6090 c. 35: 3 0 2 1 3 0 2 1 3 0 2 1 2 3 1 2 0 3 1 2 0 3 N SD: 9.5520 c. M:-16.0158 c. 37: 3 0 3 0 3 1 2 1 2 1 2 1 3 2 1 2 1 3 0 3 0 3 N SD: 9.3336 c. M:-14.8134 c. 38: 3 0 3 0 3 1 2 1 3 0 2 1 3 3 1 2 0 3 1 2 1 3 N SD: 10.9764 c. M: 21.1983 c. 39: 3 1 2 1 3 0 3 0 3 1 2 1 3 3 0 3 0 3 1 2 1 3 N SD: 8.5456 c. M:-13.8408 c. 41: 3 1 2 1 3 1 2 1 3 1 2 1 3 3 1 2 1 3 1 2 1 3 N SD: 4.5115 c. M:-7.7981 c. 53: 4 1 3 1 4 1 3 1 4 1 3 1 4 4 1 3 1 4 1 3 1 4 N G SD: 0.9972 c. M:-1.7236 c. 118: 9 2 7 2 9 2 7 2 9 2 7 2 9 9 2 7 2 9 2 7 2 9 N G SD: 0.2239 c. M: 0.3871 c. 171: 13 3 10 3 13 3 10 3 13 3 10 3 13 13 3 10 3 13 3 10 3 13 N G SD: 0.1545 c. M:-0.2671 c. 289: 22 5 17 5 22 5 17 5 22 5 17 5 22 22 5 17 5 22 5 17 5 22 N G 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: 0.1124 cents 3 .. 6 match: 3 H SD: 0.0785 cents 4 .. 8 match: 4 H SD: 6.9288 cents 5 .. 10 match: 5 H SD: 1.4231 cents 6 .. 12 match: 6 H SD: 7.0880 cents 7 .. 14 match: 7 H SD: 7.5139 cents 8 .. 16 match: 8 H SD: 6.2788 cents 9 .. 18 match: 9 H SD: 5.6145 cents 10 .. 20 match: 10 H SD: 4.9921 cents 11 .. 22 match: 11 H SD: 7.9462 cents 12 .. 24 match: 12 H SD: 5.0344 cents 13 .. 26 match: 12 S SD: 7.6093 cents 14 .. 28 match: 14 H SD: 4.9584 cents 15 .. 30 match: 12 SD: 3.4860 cents 16 .. 32 match: 15 S SD: 4.3343 cents 17 .. 34 match: 15 S SD: 4.7749 cents 18 .. 36 match: 15 S SD: 4.3308 cents 19 .. 38 match: 13 SD: 3.8330 cents 20 .. 40 match: 14 SD: 2.6979 cents 21 .. 42 match: 17 SD: 3.9970 cents 22 .. 44 match: 16 SD: 3.4935 cents 23 .. 46 match: 18 SD: 3.7251 cents 24 .. 48 match: 15 SD: 3.3245 cents 25 .. 50 match: 17 SD: 3.5067 cents 26 .. 52 match: 16 SD: 2.6884 cents 27 .. 54 match: 15 SD: 3.0484 cents 28 .. 56 match: 17 SD: 2.5266 cents 29 .. 58 match: 17 SD: 2.8186 cents 30 .. 60 match: 19 SD: 2.2715 cents 31 .. 62 match: 17 SD: 2.4555 cents 32 .. 64 match: 16 SD: 1.8015 cents 33 .. 66 match: 19 SD: 2.3129 cents 34 .. 68 match: 17 SD: 2.3949 cents 35 .. 70 match: 16 SD: 1.9275 cents 36 .. 72 match: 18 SD: 1.8394 cents 37 .. 74 match: 18 SD: 2.0331 cents 38 .. 76 match: 20 SD: 2.0624 cents 39 .. 78 match: 19 SD: 1.9221 cents 40 .. 80 match: 21 SD: 1.7028 cents 41 .. 82 match: 18 SD: 1.7713 cents 42 .. 84 match: 20 SD: 1.6632 cents 43 .. 86 match: 20 SD: 1.9425 cents 44 .. 88 match: 19 SD: 1.7294 cents 45 .. 90 match: 22 SD: 1.4568 cents 46 .. 92 match: 20 SD: 1.7594 cents 47 .. 94 match: 18 SD: 1.5777 cents 48 .. 96 match: 21 SD: 1.3223 cents 49 .. 98 match: 21 SD: 1.5126 cents 50 .. 100 match: 19 SD: 1.4064 cents 51 .. 102 match: 20 SD: 1.6909 cents 52 .. 104 match: 19 SD: 1.3517 cents 53 .. 106 match: 21 SD: 1.6652 cents 54 .. 108 match: 22 SD: 1.1942 cents 55 .. 110 match: 22 SD: 1.1921 cents 57 .. 114 match: 21 SD: 1.0805 cents 59 .. 118 match: 21 SD: 1.2629 cents 60 .. 120 match: 21 SD: 0.8823 cents 62 .. 124 match: 21 SD: 1.3153 cents 63 .. 126 match: 22 SD: 1.2318 cents 64 .. 128 match: 22 SD: 0.9969 cents 65 .. 130 match: 21 SD: 1.1476 cents 66 .. 132 match: 21 SD: 1.2124 cents 67 .. 134 match: 21 SD: 1.3644 cents 68 .. 136 match: 21 SD: 1.2844 cents 69 .. 138 match: 22 SD: 1.0604 cents 71 .. 142 match: 22 SD: 0.8750 cents 72 .. 144 match: 22 SD: 0.8340 cents 80 .. 160 match: 22 SD: 0.7704 cents 90 .. 180 match: 22 SD: 0.6822 cents 105 .. 210 match: 22 SD: 0.6518 cents 108 .. 216 match: 22 SD: 0.6128 cents 114 .. 228 match: 22 SD: 0.6018 cents 120 .. 240 match: 22 SD: 0.5357 cents 128 .. 256 match: 22 SD: 0.5093 cents 135 .. 270 match: 22 SD: 0.3930 cents 168 .. 336 match: 22 SD: 0.3866 cents 177 .. 354 match: 22 SD: 0.3842 cents 180 .. 360 match: 22 SD: 0.3511 cents 200 .. 400 match: 22 SD: 0.3037 cents 215 .. 430 match: 22 SD: 0.2927 cents 224 .. 448 match: 22 SD: 0.2693 cents 225 .. 450 match: 22 SD: 0.2554 cents 264 .. 528 match: 22 SD: 0.2553 cents 272 .. 544 match: 22 SD: 0.2509 cents 279 .. 558 match: 22 SD: 0.2292 cents 280 .. 560 match: 22 SD: 0.1988 cents 312 .. 624 match: 22 SD: 0.1857 cents 360 .. 720 match: 22 SD: 0.1460 cents 441 .. 882 match: 22 SD: 0.1460 cents 449 .. 898 match: 22 SD: 0.1448 cents 464 .. 928 match: 22 SD: 0.1275 cents 480 .. 960 match: 22 SD: 0.1061 cents 495 .. 990 match: 22 SD: 0.0999 cents 540 .. 1080 match: 22 SD: 0.0976 cents