Scala analysis: indiang
Shruti/Mathieu's Magic Mode scale in 94-et (garibaldi) temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 89.362 cents 89.361702 2: 114.894 cents 114.893617 3: 178.723 cents 178.723404 4: 204.255 cents 204.255319 5: 293.617 cents 293.617021 6: 319.149 cents 319.148936 7: 382.979 cents 382.978723 8: 408.511 cents 408.510638 9: 497.872 cents 497.872340 10: 523.404 cents 523.404255 11: 587.234 cents 587.234043 12: 612.766 cents 612.765957 13: 702.128 cents 702.127660 14: 791.489 cents 791.489362 15: 817.021 cents 817.021277 16: 880.851 cents 880.851064 17: 906.383 cents 906.382979 18: 995.745 cents 995.744681 19: 1021.277 cents 1021.276596 20: 1085.106 cents 1085.106383 21: 1110.638 cents 1110.638298 22: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 89.3617 cents 89.3617 1: 89.3617 cents 89.3617 2: 25.5319 cents 25.5319 3: 63.8298 cents 63.8298 4: 25.5319 cents 25.5319 5: 89.3617 cents 89.3617 6: 25.5319 cents 25.5319 7: 63.8298 cents 63.8298 8: 25.5319 cents 25.5319 9: 89.3617 cents 89.3617 10: 25.5319 cents 25.5319 11: 63.8298 cents 63.8298 12: 25.5319 cents 25.5319 13: 89.3617 cents 89.3617 14: 89.3617 cents 89.3617 15: 25.5319 cents 25.5319 16: 63.8298 cents 63.8298 17: 25.5319 cents 25.5319 18: 89.3617 cents 89.3617 19: 25.5319 cents 25.5319 20: 63.8298 cents 63.8298 21: 25.5319 cents 25.5319 22: 89.3617 cents 89.3617
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 25.53191 cents 1: 5 63.82979 cents 1: 7 89.36170 cents 2: 10 89.36170 cents 2: 10 114.89362 cents 2: 2 178.72340 cents 3: 5 114.89362 cents 3: 3 140.42553 cents 3: 10 178.72340 cents 3: 4 204.25532 cents 4: 16 204.25532 cents 4: 2 229.78723 cents 4: 4 268.08511 cents 5: 6 229.78723 cents 5: 3 268.08511 cents 5: 13 293.61702 cents 6: 6 293.61702 cents 6: 10 319.14894 cents 6: 2 357.44681 cents 6: 4 382.97872 cents 7: 3 319.14894 cents 7: 1 344.68085 cents 7: 10 382.97872 cents 7: 8 408.51064 cents 8: 10 408.51064 cents 8: 4 434.04255 cents 8: 8 472.34043 cents 9: 2 434.04255 cents 9: 1 472.34043 cents 9: 19 497.87234 cents 10: 2 497.87234 cents 10: 10 523.40426 cents 10: 4 561.70213 cents 10: 6 587.23404 cents 11: 1 523.40425 cents 11: 10 587.23404 cents 11: 10 612.76596 cents 11: 1 676.59574 cents 12: 6 612.76596 cents 12: 4 638.29787 cents 12: 10 676.59575 cents 12: 2 702.12766 cents 13: 19 702.12766 cents 13: 1 727.65957 cents 13: 2 765.95745 cents 14: 8 727.65958 cents 14: 4 765.95745 cents 14: 10 791.48936 cents 15: 8 791.48936 cents 15: 10 817.02128 cents 15: 1 855.31915 cents 15: 3 880.85106 cents 16: 4 817.02128 cents 16: 2 842.55319 cents 16: 10 880.85106 cents 16: 6 906.38298 cents 17: 13 906.38298 cents 17: 3 931.91489 cents 17: 6 970.21277 cents 18: 4 931.91489 cents 18: 2 970.21277 cents 18: 16 995.74468 cents 19: 4 995.74468 cents 19: 10 1021.27660 cents 19: 3 1059.57447 cents 19: 5 1085.10638 cents 20: 2 1021.27660 cents 20: 10 1085.10638 cents 20: 10 1110.63830 cents 21: 7 1110.63830 cents 21: 5 1136.17021 cents 21: 10 1174.46809 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 : 89.4 114.9 178.7 204.3 293.6 319.1 383.0 408.5 497.9 523.4 587.2 612.8 702.1 791.5 817.0 880.9 906.4 995.7 1021.3 1085.1 1110.6 1200.0 89.4 : 25.5 89.4 114.9 204.3 229.8 293.6 319.1 408.5 434.0 497.9 523.4 612.8 702.1 727.7 791.5 817.0 906.4 931.9 995.7 1021.3 1110.6 1200.0 114.9 : 63.8 89.4 178.7 204.3 268.1 293.6 383.0 408.5 472.3 497.9 587.2 676.6 702.1 766.0 791.5 880.9 906.4 970.2 995.7 1085.1 1174.5 1200.0 178.7 : 25.5 114.9 140.4 204.3 229.8 319.1 344.7 408.5 434.0 523.4 612.8 638.3 702.1 727.7 817.0 842.6 906.4 931.9 1021.3 1110.6 1136.2 1200.0 204.3 : 89.4 114.9 178.7 204.3 293.6 319.1 383.0 408.5 497.9 587.2 612.8 676.6 702.1 791.5 817.0 880.9 906.4 995.7 1085.1 1110.6 1174.5 1200.0 293.6 : 25.5 89.4 114.9 204.3 229.8 293.6 319.1 408.5 497.9 523.4 587.2 612.8 702.1 727.7 791.5 817.0 906.4 995.7 1021.3 1085.1 1110.6 1200.0 319.1 : 63.8 89.4 178.7 204.3 268.1 293.6 383.0 472.3 497.9 561.7 587.2 676.6 702.1 766.0 791.5 880.9 970.2 995.7 1059.6 1085.1 1174.5 1200.0 383.0 : 25.5 114.9 140.4 204.3 229.8 319.1 408.5 434.0 497.9 523.4 612.8 638.3 702.1 727.7 817.0 906.4 931.9 995.7 1021.3 1110.6 1136.2 1200.0 408.5 : 89.4 114.9 178.7 204.3 293.6 383.0 408.5 472.3 497.9 587.2 612.8 676.6 702.1 791.5 880.9 906.4 970.2 995.7 1085.1 1110.6 1174.5 1200.0 497.9 : 25.5 89.4 114.9 204.3 293.6 319.1 383.0 408.5 497.9 523.4 587.2 612.8 702.1 791.5 817.0 880.9 906.4 995.7 1021.3 1085.1 1110.6 1200.0 523.4 : 63.8 89.4 178.7 268.1 293.6 357.4 383.0 472.3 497.9 561.7 587.2 676.6 766.0 791.5 855.3 880.9 970.2 995.7 1059.6 1085.1 1174.5 1200.0 587.2 : 25.5 114.9 204.3 229.8 293.6 319.1 408.5 434.0 497.9 523.4 612.8 702.1 727.7 791.5 817.0 906.4 931.9 995.7 1021.3 1110.6 1136.2 1200.0 612.8 : 89.4 178.7 204.3 268.1 293.6 383.0 408.5 472.3 497.9 587.2 676.6 702.1 766.0 791.5 880.9 906.4 970.2 995.7 1085.1 1110.6 1174.5 1200.0 702.1 : 89.4 114.9 178.7 204.3 293.6 319.1 383.0 408.5 497.9 587.2 612.8 676.6 702.1 791.5 817.0 880.9 906.4 995.7 1021.3 1085.1 1110.6 1200.0 791.5 : 25.5 89.4 114.9 204.3 229.8 293.6 319.1 408.5 497.9 523.4 587.2 612.8 702.1 727.7 791.5 817.0 906.4 931.9 995.7 1021.3 1110.6 1200.0 817.0 : 63.8 89.4 178.7 204.3 268.1 293.6 383.0 472.3 497.9 561.7 587.2 676.6 702.1 766.0 791.5 880.9 906.4 970.2 995.7 1085.1 1174.5 1200.0 880.9 : 25.5 114.9 140.4 204.3 229.8 319.1 408.5 434.0 497.9 523.4 612.8 638.3 702.1 727.7 817.0 842.6 906.4 931.9 1021.3 1110.6 1136.2 1200.0 906.4 : 89.4 114.9 178.7 204.3 293.6 383.0 408.5 472.3 497.9 587.2 612.8 676.6 702.1 791.5 817.0 880.9 906.4 995.7 1085.1 1110.6 1174.5 1200.0 995.7 : 25.5 89.4 114.9 204.3 293.6 319.1 383.0 408.5 497.9 523.4 587.2 612.8 702.1 727.7 791.5 817.0 906.4 995.7 1021.3 1085.1 1110.6 1200.0 1021.3: 63.8 89.4 178.7 268.1 293.6 357.4 383.0 472.3 497.9 561.7 587.2 676.6 702.1 766.0 791.5 880.9 970.2 995.7 1059.6 1085.1 1174.5 1200.0 1085.1: 25.5 114.9 204.3 229.8 293.6 319.1 408.5 434.0 497.9 523.4 612.8 638.3 702.1 727.7 817.0 906.4 931.9 995.7 1021.3 1110.6 1136.2 1200.0 1110.6: 89.4 178.7 204.3 268.1 293.6 383.0 408.5 472.3 497.9 587.2 612.8 676.6 702.1 791.5 880.9 906.4 970.2 995.7 1085.1 1110.6 1174.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.5319 .. 89.3617 cents 63.82979 cents 25.53191 cents 2: 89.3617 .. 178.7234 cents 89.36170 cents 1/1, 0.0000 cents 3: 114.8936 .. 204.2553 cents 89.36170 cents -63.82979 cents 4: 204.2553 .. 268.0851 cents 63.82979 cents 1/1, 0.0000 cents 5: 229.7872 .. 293.6170 cents 63.82979 cents -38.29787 cents 6: 293.6170 .. 382.9787 cents 89.36170 cents 1/1, 0.0000 cents 7: 319.1489 .. 408.5106 cents 89.36170 cents -63.82979 cents 8: 408.5106 .. 472.3404 cents 63.82979 cents -0.00000 cents 9: 434.0426 .. 497.8723 cents 63.82979 cents -38.29787 cents 10: 497.8723 .. 587.2340 cents 89.36170 cents 0.00000 cents 11: 523.4043 .. 676.5957 cents 153.19149 cents -63.82979 cents 12: 612.7660 .. 702.1277 cents 89.36170 cents -63.82979 cents 13: 702.1277 .. 765.9574 cents 63.82979 cents 0.00000 cents 14: 727.6596 .. 791.4894 cents 63.82979 cents -38.29787 cents 15: 791.4894 .. 880.8511 cents 89.36170 cents 1/1, 0.0000 cents 16: 817.0213 .. 906.3830 cents 89.36170 cents -63.82979 cents 17: 906.3830 .. 970.2128 cents 63.82979 cents 1/1, 0.0000 cents 18: 931.9149 .. 995.7447 cents 63.82979 cents -38.29787 cents 19: 995.7447 .. 1085.1064 cents 89.36170 cents 1/1, 0.0000 cents 20: 1021.2766 .. 1110.6383 cents 89.36170 cents -63.82979 cents 21: 1110.6383 .. 1174.4681 cents 63.82979 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 25.53191 cents, class 1 Average step (divided formal octave): 54.5455 cents Largest one step interval : 89.36170 cents Average / Smallest step : 2.136364 Largest / Average step : 1.638298 Largest / Smallest step : 3.500000 Median interval of one step : 63.82979 cents, amount: 5 Most common interval of one step : 25.53191 cents, amount: 10 Least squares average step : 54.08460 cents, oct.: 1189.86124 cents Scale is not proper Scale is a mode of a 94-tone equal temperament with octave 1200.000 cents degrees: 7 9 14 16 23 25 30 32 39 41 46 48 55 62 64 69 71 78 80 85 87 94 Least number of segments generator : 55 of 702.128 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 55 of 702.128 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 94-tone equal temperament Step pattern alph. order: ABCBABCBABCBAABCBABCBA Step pattern size order : LSMSLSMSLSMSLLSMSLSMSL Interval vector is [ 0 10 0 0 5 0 17 0 15 0 3 0 0 12 0 20 0 8 0 0 7 0 19 0 13 0 1 2 0 14 0 18 0 6 0 0 9 0 21 0 11 0 0 4 0 16 0 ] Scale is not a Constant Structure Scale diversity : 1.200667 Lumma stability : 0.042553 Lumma impropriety factor : 0.446809 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 : 12.76596 cents Most common intervals : 497.87234 cents & inv., amount: 21 Scale has Generated (pseudo-Myhill) property, generator: 702.128 cents and inv. Scale is a chain of 11 triads 0.0 178.723 702.128 cents Most common triad is 0.0 497.872 702.128 cents, amount: 20 Number of recognisable fifths : 21, average 702.1277 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 1 1 1 1 0 2 2 0 1 1 1 1 1 0 2 N SD: 15.2163 c. M:-27.8530 c. 23: 2 0 1 1 2 0 1 1 2 0 1 1 1 2 1 1 0 2 1 1 0 2 N SD: 14.7891 c. M: 23.8668 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: 13.5403 c. M: 23.4043 c. 26: 2 0 2 0 2 1 1 1 2 0 2 0 2 2 1 1 1 2 0 1 1 2 N SD: 13.0562 c. M: 23.5679 c. 27: 2 1 1 1 2 0 2 0 2 1 1 1 2 2 0 2 0 2 1 1 1 2 N SD: 12.1213 c. M:-18.4397 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: 8.4044 c. M:-14.5268 c. 39: 3 1 2 1 3 0 2 1 3 1 2 1 3 3 1 2 0 3 1 2 1 3 N SD: 8.8570 c. M:-14.0753 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: 1.9815 c. M:-3.4250 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: 1.5329 c. M: 2.6495 c. 94: 7 2 5 2 7 2 5 2 7 2 5 2 7 7 2 5 2 7 2 5 2 7 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: 0.0863 cents 3 .. 6 match: 3 H SD: 1.1706 cents 4 .. 8 match: 4 H SD: 6.7813 cents 5 .. 10 match: 5 H SD: 1.5397 cents 6 .. 12 match: 6 H SD: 6.4905 cents 7 .. 14 match: 7 H SD: 7.0408 cents 8 .. 16 match: 8 H SD: 5.6976 cents 9 .. 18 match: 9 H SD: 5.2017 cents 10 .. 20 match: 10 H SD: 4.8002 cents 11 .. 22 match: 11 H SD: 7.2983 cents 12 .. 24 match: 12 H SD: 4.6925 cents 13 .. 26 match: 13 H SD: 7.4785 cents 14 .. 28 match: 14 H SD: 4.5096 cents 15 .. 30 match: 12 SD: 3.4279 cents 16 .. 32 match: 15 S SD: 3.9950 cents 17 .. 34 match: 15 S SD: 4.5395 cents 18 .. 36 match: 15 S SD: 3.9967 cents 19 .. 38 match: 13 SD: 3.5835 cents 20 .. 40 match: 15 SD: 3.3104 cents 21 .. 42 match: 18 SD: 3.7755 cents 22 .. 44 match: 17 SD: 3.3721 cents 23 .. 46 match: 18 SD: 3.3599 cents 24 .. 48 match: 16 SD: 3.2206 cents 25 .. 50 match: 18 SD: 3.2928 cents 26 .. 52 match: 17 SD: 2.7315 cents 27 .. 54 match: 16 SD: 3.0803 cents 28 .. 56 match: 20 SD: 2.8200 cents 29 .. 58 match: 17 SD: 2.6530 cents 30 .. 60 match: 20 SD: 2.0725 cents 31 .. 62 match: 17 SD: 2.3171 cents 32 .. 64 match: 18 SD: 2.3457 cents 33 .. 66 match: 20 SD: 2.0664 cents 34 .. 68 match: 18 SD: 2.4203 cents 35 .. 70 match: 17 SD: 2.2634 cents 36 .. 72 match: 19 SD: 1.9710 cents 37 .. 74 match: 20 SD: 2.1228 cents 38 .. 76 match: 21 SD: 1.7851 cents 39 .. 78 match: 21 SD: 1.8534 cents 40 .. 80 match: 22 SD: 1.5821 cents 41 .. 82 match: 19 SD: 1.8495 cents 42 .. 84 match: 21 SD: 1.6295 cents 43 .. 86 match: 20 SD: 1.9559 cents 44 .. 88 match: 22 SD: 1.8083 cents 45 .. 90 match: 22 SD: 1.3411 cents 46 .. 92 match: 21 SD: 1.7832 cents 48 .. 96 match: 21 SD: 1.2105 cents 49 .. 98 match: 21 SD: 1.5334 cents 50 .. 100 match: 21 SD: 1.5162 cents 51 .. 102 match: 21 SD: 1.8313 cents 52 .. 104 match: 22 SD: 1.6565 cents 53 .. 106 match: 22 SD: 1.5081 cents 54 .. 108 match: 22 SD: 1.1152 cents 64 .. 128 match: 22 SD: 1.0847 cents 70 .. 140 match: 22 SD: 1.0533 cents 71 .. 142 match: 22 SD: 0.9020 cents 76 .. 152 match: 22 SD: 0.9018 cents 80 .. 160 match: 22 SD: 0.8575 cents 86 .. 172 match: 22 SD: 0.8562 cents 90 .. 180 match: 22 SD: 0.6966 cents 102 .. 204 match: 22 SD: 0.6073 cents 113 .. 226 match: 22 SD: 0.5670 cents 118 .. 236 match: 22 SD: 0.5312 cents 128 .. 256 match: 22 SD: 0.4822 cents 146 .. 292 match: 22 SD: 0.4790 cents 148 .. 296 match: 22 SD: 0.4405 cents 157 .. 314 match: 22 SD: 0.4396 cents 158 .. 316 match: 22 SD: 0.3713 cents 174 .. 348 match: 22 SD: 0.3423 cents 193 .. 386 match: 22 SD: 0.3230 cents 202 .. 404 match: 22 SD: 0.3022 cents 222 .. 444 match: 22 SD: 0.2841 cents 238 .. 476 match: 22 SD: 0.2634 cents 247 .. 494 match: 22 SD: 0.2237 cents 297 .. 594 match: 22 SD: 0.2144 cents 302 .. 604 match: 22 SD: 0.2040 cents 320 .. 640 match: 22 SD: 0.1594 cents 396 .. 792 match: 22 SD: 0.1555 cents 416 .. 832 match: 22 SD: 0.1546 cents 433 .. 866 match: 22 SD: 0.1398 cents 448 .. 896 match: 22 SD: 0.1355 cents 454 .. 908 match: 22 SD: 0.1321 cents 478 .. 956 match: 22 SD: 0.1281 cents 504 .. 1008 match: 22 SD: 0.1184 cents 525 .. 1050 match: 22 SD: 0.1091 cents 552 .. 1104 match: 22 SD: 0.0936 cents