Scala analysis: garibaldi24
Garibaldi[24] in 94-et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 63.830 cents 63.829787 2: 89.362 cents 89.361702 3: 178.723 cents 178.723404 4: 204.255 cents 204.255319 5: 268.085 cents 268.085106 6: 293.617 cents 293.617021 7: 382.979 cents 382.978723 8: 408.511 cents 408.510638 9: 472.340 cents 472.340426 10: 497.872 cents 497.872340 11: 561.702 cents 561.702128 12: 587.234 cents 587.234043 13: 676.596 cents 676.595745 14: 702.128 cents 702.127660 15: 765.957 cents 765.957447 16: 791.489 cents 791.489362 17: 880.851 cents 880.851064 18: 906.383 cents 906.382979 19: 970.213 cents 970.212766 20: 995.745 cents 995.744681 21: 1085.106 cents 1085.106383 22: 1110.638 cents 1110.638298 23: 1174.468 cents 1174.468085 24: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 25.5319 cents 25.5319 1: 63.8298 cents 63.8298 2: 25.5319 cents 25.5319 3: 89.3617 cents 89.3617 4: 25.5319 cents 25.5319 5: 63.8298 cents 63.8298 6: 25.5319 cents 25.5319 7: 89.3617 cents 89.3617 8: 25.5319 cents 25.5319 9: 63.8298 cents 63.8298 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: 25.5319 cents 25.5319 15: 63.8298 cents 63.8298 16: 25.5319 cents 25.5319 17: 89.3617 cents 89.3617 18: 25.5319 cents 25.5319 19: 63.8298 cents 63.8298 20: 25.5319 cents 25.5319 21: 89.3617 cents 89.3617 22: 25.5319 cents 25.5319 23: 63.8298 cents 63.8298 24: 25.5319 cents 25.5319
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 25.53192 cents 1: 7 63.82979 cents 1: 5 89.36170 cents 2: 14 89.36170 cents 2: 10 114.89362 cents 3: 7 114.89362 cents 3: 5 140.42553 cents 3: 2 153.19149 cents 3: 10 178.72340 cents 4: 4 178.72340 cents 4: 20 204.25532 cents 5: 2 204.25532 cents 5: 10 229.78723 cents 5: 9 268.08511 cents 5: 3 293.61702 cents 6: 18 293.61702 cents 6: 6 319.14894 cents 7: 9 319.14894 cents 7: 3 344.68085 cents 7: 4 357.44681 cents 7: 8 382.97872 cents 8: 8 382.97872 cents 8: 16 408.51064 cents 9: 4 408.51064 cents 9: 8 434.04255 cents 9: 11 472.34043 cents 9: 1 497.87234 cents 10: 22 497.87234 cents 10: 2 523.40425 cents 11: 11 523.40426 cents 11: 1 548.93617 cents 11: 6 561.70213 cents 11: 6 587.23404 cents 12: 12 587.23404 cents 12: 12 612.76596 cents 13: 6 612.76596 cents 13: 6 638.29787 cents 13: 1 651.06383 cents 13: 11 676.59574 cents 14: 2 676.59575 cents 14: 22 702.12766 cents 15: 1 702.12766 cents 15: 11 727.65958 cents 15: 8 765.95745 cents 15: 4 791.48936 cents 16: 16 791.48936 cents 16: 8 817.02128 cents 17: 8 817.02128 cents 17: 4 842.55319 cents 17: 3 855.31915 cents 17: 9 880.85106 cents 18: 6 880.85106 cents 18: 18 906.38298 cents 19: 3 906.38298 cents 19: 9 931.91489 cents 19: 10 970.21277 cents 19: 2 995.74468 cents 20: 20 995.74468 cents 20: 4 1021.27660 cents 21: 10 1021.27660 cents 21: 2 1046.80851 cents 21: 5 1059.57447 cents 21: 7 1085.10638 cents 22: 10 1085.10638 cents 22: 14 1110.63830 cents 23: 5 1110.63830 cents 23: 7 1136.17021 cents 23: 12 1174.46809 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 2.95652 = 68/23
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 23 24 0.0 : 63.8 89.4 178.7 204.3 268.1 293.6 383.0 408.5 472.3 497.9 561.7 587.2 676.6 702.1 766.0 791.5 880.9 906.4 970.2 995.7 1085.1 1110.6 1174.5 1200.0 63.8 : 25.5 114.9 140.4 204.3 229.8 319.1 344.7 408.5 434.0 497.9 523.4 612.8 638.3 702.1 727.7 817.0 842.6 906.4 931.9 1021.3 1046.8 1110.6 1136.2 1200.0 89.4 : 89.4 114.9 178.7 204.3 293.6 319.1 383.0 408.5 472.3 497.9 587.2 612.8 676.6 702.1 791.5 817.0 880.9 906.4 995.7 1021.3 1085.1 1110.6 1174.5 1200.0 178.7 : 25.5 89.4 114.9 204.3 229.8 293.6 319.1 383.0 408.5 497.9 523.4 587.2 612.8 702.1 727.7 791.5 817.0 906.4 931.9 995.7 1021.3 1085.1 1110.6 1200.0 204.3 : 63.8 89.4 178.7 204.3 268.1 293.6 357.4 383.0 472.3 497.9 561.7 587.2 676.6 702.1 766.0 791.5 880.9 906.4 970.2 995.7 1059.6 1085.1 1174.5 1200.0 268.1 : 25.5 114.9 140.4 204.3 229.8 293.6 319.1 408.5 434.0 497.9 523.4 612.8 638.3 702.1 727.7 817.0 842.6 906.4 931.9 995.7 1021.3 1110.6 1136.2 1200.0 293.6 : 89.4 114.9 178.7 204.3 268.1 293.6 383.0 408.5 472.3 497.9 587.2 612.8 676.6 702.1 791.5 817.0 880.9 906.4 970.2 995.7 1085.1 1110.6 1174.5 1200.0 383.0 : 25.5 89.4 114.9 178.7 204.3 293.6 319.1 383.0 408.5 497.9 523.4 587.2 612.8 702.1 727.7 791.5 817.0 880.9 906.4 995.7 1021.3 1085.1 1110.6 1200.0 408.5 : 63.8 89.4 153.2 178.7 268.1 293.6 357.4 383.0 472.3 497.9 561.7 587.2 676.6 702.1 766.0 791.5 855.3 880.9 970.2 995.7 1059.6 1085.1 1174.5 1200.0 472.3 : 25.5 89.4 114.9 204.3 229.8 293.6 319.1 408.5 434.0 497.9 523.4 612.8 638.3 702.1 727.7 791.5 817.0 906.4 931.9 995.7 1021.3 1110.6 1136.2 1200.0 497.9 : 63.8 89.4 178.7 204.3 268.1 293.6 383.0 408.5 472.3 497.9 587.2 612.8 676.6 702.1 766.0 791.5 880.9 906.4 970.2 995.7 1085.1 1110.6 1174.5 1200.0 561.7 : 25.5 114.9 140.4 204.3 229.8 319.1 344.7 408.5 434.0 523.4 548.9 612.8 638.3 702.1 727.7 817.0 842.6 906.4 931.9 1021.3 1046.8 1110.6 1136.2 1200.0 587.2 : 89.4 114.9 178.7 204.3 293.6 319.1 383.0 408.5 497.9 523.4 587.2 612.8 676.6 702.1 791.5 817.0 880.9 906.4 995.7 1021.3 1085.1 1110.6 1174.5 1200.0 676.6 : 25.5 89.4 114.9 204.3 229.8 293.6 319.1 408.5 434.0 497.9 523.4 587.2 612.8 702.1 727.7 791.5 817.0 906.4 931.9 995.7 1021.3 1085.1 1110.6 1200.0 702.1 : 63.8 89.4 178.7 204.3 268.1 293.6 383.0 408.5 472.3 497.9 561.7 587.2 676.6 702.1 766.0 791.5 880.9 906.4 970.2 995.7 1059.6 1085.1 1174.5 1200.0 766.0 : 25.5 114.9 140.4 204.3 229.8 319.1 344.7 408.5 434.0 497.9 523.4 612.8 638.3 702.1 727.7 817.0 842.6 906.4 931.9 995.7 1021.3 1110.6 1136.2 1200.0 791.5 : 89.4 114.9 178.7 204.3 293.6 319.1 383.0 408.5 472.3 497.9 587.2 612.8 676.6 702.1 791.5 817.0 880.9 906.4 970.2 995.7 1085.1 1110.6 1174.5 1200.0 880.9 : 25.5 89.4 114.9 204.3 229.8 293.6 319.1 383.0 408.5 497.9 523.4 587.2 612.8 702.1 727.7 791.5 817.0 880.9 906.4 995.7 1021.3 1085.1 1110.6 1200.0 906.4 : 63.8 89.4 178.7 204.3 268.1 293.6 357.4 383.0 472.3 497.9 561.7 587.2 676.6 702.1 766.0 791.5 855.3 880.9 970.2 995.7 1059.6 1085.1 1174.5 1200.0 970.2 : 25.5 114.9 140.4 204.3 229.8 293.6 319.1 408.5 434.0 497.9 523.4 612.8 638.3 702.1 727.7 791.5 817.0 906.4 931.9 995.7 1021.3 1110.6 1136.2 1200.0 995.7 : 89.4 114.9 178.7 204.3 268.1 293.6 383.0 408.5 472.3 497.9 587.2 612.8 676.6 702.1 766.0 791.5 880.9 906.4 970.2 995.7 1085.1 1110.6 1174.5 1200.0 1085.1: 25.5 89.4 114.9 178.7 204.3 293.6 319.1 383.0 408.5 497.9 523.4 587.2 612.8 676.6 702.1 791.5 817.0 880.9 906.4 995.7 1021.3 1085.1 1110.6 1200.0 1110.6: 63.8 89.4 153.2 178.7 268.1 293.6 357.4 383.0 472.3 497.9 561.7 587.2 651.1 676.6 766.0 791.5 855.3 880.9 970.2 995.7 1059.6 1085.1 1174.5 1200.0 1174.5: 25.5 89.4 114.9 204.3 229.8 293.6 319.1 408.5 434.0 497.9 523.4 587.2 612.8 702.1 727.7 791.5 817.0 906.4 931.9 995.7 1021.3 1110.6 1136.2 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 25.53192 cents 2: 89.3617 .. 114.8936 cents 25.53191 cents 1/1, 0.0000 cents 3: 114.8936 .. 178.7234 cents 63.82979 cents 1/1, 0.0000 cents 4: 178.7234 .. 204.2553 cents 25.53191 cents 0.00000 cents 5: 204.2553 .. 293.6170 cents 89.36170 cents 0.00000 cents 6: 293.6170 .. 319.1489 cents 25.53192 cents 1/1, 0.0000 cents 7: 319.1489 .. 382.9787 cents 63.82979 cents 1/1, 0.0000 cents 8: 382.9787 .. 408.5106 cents 25.53191 cents 0.00000 cents 9: 408.5106 .. 497.8723 cents 89.36170 cents 0.00000 cents 10: 497.8723 .. 523.4043 cents 25.53191 cents 1/1, 0.0000 cents 11: 523.4043 .. 587.2340 cents 63.82979 cents 0.00000 cents 12: 587.2340 .. 612.7660 cents 25.53192 cents 1/1, 0.0000 cents 13: 612.7660 .. 676.5957 cents 63.82979 cents 1/1, 0.0000 cents 14: 676.5957 .. 702.1277 cents 25.53191 cents 1/1, 0.0000 cents 15: 702.1277 .. 791.4894 cents 89.36170 cents 1/1, 0.0000 cents 16: 791.4894 .. 817.0213 cents 25.53192 cents 1/1, 0.0000 cents 17: 817.0213 .. 880.8511 cents 63.82979 cents 1/1, 0.0000 cents 18: 880.8511 .. 906.3830 cents 25.53192 cents 1/1, 0.0000 cents 19: 906.3830 .. 995.7447 cents 89.36170 cents 1/1, 0.0000 cents 20: 995.7447 .. 1021.2766 cents 25.53191 cents 1/1, 0.0000 cents 21: 1021.2766 .. 1085.1064 cents 63.82979 cents 1/1, 0.0000 cents 22: 1085.1064 .. 1110.6383 cents 25.53191 cents 1/1, 0.0000 cents 23: 1110.6383 .. 1174.4681 cents 63.82979 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 25.53191 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 89.36170 cents Average / Smallest step : 1.958333 Largest / Average step : 1.787234 Largest / Smallest step : 3.500000 Median interval of one step : 44.68085 cents, amount: 0 Most common interval of one step : 25.53192 cents, amount: 12 Least squares average step : 50.72514 cents, oct.: 1217.40339 cents Scale is proper Scale is a mode of a 94-tone equal temperament with octave 1200.000 cents degrees: 5 7 14 16 21 23 30 32 37 39 44 46 53 55 60 62 69 71 76 78 85 87 92 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: 24 = 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: ABCBABCBABABCBABCBABCBAB Step pattern size order : MSLSMSLSMSMSLSMSLSMSLSMS Interval vector is [ 0 12 0 0 7 0 19 0 17 0 5 2 0 14 0 22 0 10 0 0 9 0 21 0 15 0 3 4 0 16 0 20 0 8 0 0 11 0 23 0 13 0 1 6 0 18 0 ] Scale is not a Constant Structure Scale diversity : 1.192010 Rothenberg stability : 0.282609 = 13/46 Lumma stability : 0.042553 Rothenberg efficiency : 0.694444 redundancy: 0.305556 Efficiency x scale size : 16.666667 Number of different interval sizes : 46 = 2.00000 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 2.95652 = 68/23 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 12.76596 cents Most common intervals : 497.87234 cents & inv., amount: 23 Scale has Generated (pseudo-Myhill) property, generator: 702.128 cents and inv. Scale is a chain of 12 triads 0.0 25.532 702.128 cents Most common triad is 0.0 497.872 702.128 cents, amount: 22 Number of recognisable fifths : 23, average 702.1277 cents Scale contains two identical disjunct "tetrachords" of 11 notes Formal octave complements present : 11 = 45.8333% Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 16-17 -- Rational properties --
FIT/MODE
24: 1 1 1 1 1 1 1 1 1 1 1 0 2 1 1 1 1 1 1 1 1 1 1 1 N T3 SD: 19.4773 c. M: 37.2340 c. 25: 1 1 1 1 1 1 2 0 2 0 1 1 2 0 2 0 2 1 1 0 2 1 1 1 N SD: 19.6756 c. M: 35.7447 c. 26: 1 1 2 0 2 0 2 1 1 1 1 1 2 0 2 0 2 1 1 1 2 0 1 1 N SD: 13.1275 c. M:-22.5859 c. 28: 1 1 2 1 1 1 2 0 2 0 2 0 3 0 2 0 2 1 1 1 2 1 1 1 N SD: 15.3544 c. M: 30.0912 c. 29: 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 P D3 SD: 12.5401 c. M: 23.7711 c. 30: 2 0 2 1 2 0 3 0 2 0 2 1 2 1 1 1 2 1 1 1 2 1 1 1 N SD: 11.2209 c. M: 18.7234 c. 32: 2 0 3 0 2 1 2 1 2 0 2 1 2 1 1 1 2 1 2 1 2 1 1 1 N SD: 10.7207 c. M: 18.3511 c. 35: 2 1 2 1 2 1 2 1 2 1 1 1 3 0 2 1 3 0 2 1 3 0 2 1 N SD: 10.0563 c. M: 16.4134 c. 36: 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 3 0 2 1 N SD: 8.5020 c. M: 16.3121 c. 37: 2 1 3 0 2 1 3 1 2 0 2 1 3 1 2 0 3 1 2 1 2 1 2 1 N SD: 9.3168 c. M:-15.8712 c. 38: 2 1 3 0 2 1 3 1 2 1 2 1 2 1 2 1 3 1 2 1 2 1 2 1 N SD: 8.8278 c. M: 15.4535 c. 39: 2 1 3 1 2 1 2 1 2 1 2 1 3 1 2 1 3 0 3 0 3 1 2 1 N SD: 8.6707 c. M:-14.4026 c. 40: 2 1 3 1 2 1 3 1 2 1 2 1 3 0 3 0 3 1 2 1 3 1 2 1 N SD: 8.4439 c. M:-14.0426 c. 41: 2 1 3 1 2 1 3 1 2 1 2 1 3 1 2 1 3 1 2 1 3 1 2 1 P SD: 2.9566 c. M: 5.6046 c. 53: 3 1 4 1 3 1 4 1 3 1 3 1 4 1 3 1 4 1 3 1 4 1 3 1 P G SD: 2.2872 c. M:-4.3356 c. 94: 5 2 7 2 5 2 7 2 5 2 5 2 7 2 5 2 7 2 5 2 7 2 5 2 P 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: 0.9040 cents 5 .. 10 match: 5 H SD: 7.6878 cents 6 .. 12 match: 6 H SD: 5.9894 cents 7 .. 14 match: 7 H SD: 8.2339 cents 8 .. 16 match: 8 H SD: 5.2396 cents 9 .. 18 match: 9 H SD: 6.0682 cents 10 .. 20 match: 10 H SD: 4.6314 cents 11 .. 22 match: 11 H SD: 6.6970 cents 12 .. 24 match: 12 H SD: 4.8788 cents 13 .. 26 match: 13 H SD: 5.9319 cents 14 .. 28 match: 14 H SD: 6.4696 cents 15 .. 30 match: 14 S SD: 4.1314 cents 16 .. 32 match: 12 SD: 1.7412 cents 17 .. 34 match: 15 S SD: 4.2463 cents 18 .. 36 match: 14 SD: 3.3840 cents 19 .. 38 match: 17 S SD: 3.7952 cents 20 .. 40 match: 19 S SD: 3.4584 cents 21 .. 42 match: 17 SD: 3.5373 cents 22 .. 44 match: 18 SD: 3.3021 cents 23 .. 46 match: 18 SD: 2.6658 cents 24 .. 48 match: 19 SD: 2.5048 cents 25 .. 50 match: 16 SD: 2.8478 cents 26 .. 52 match: 20 SD: 2.8741 cents 27 .. 54 match: 19 SD: 2.4108 cents 28 .. 56 match: 17 SD: 2.5225 cents 29 .. 58 match: 23 SD: 2.3144 cents 30 .. 60 match: 21 SD: 2.4947 cents 31 .. 62 match: 21 SD: 2.3391 cents 32 .. 64 match: 24 SD: 2.0719 cents 33 .. 66 match: 21 SD: 1.9802 cents 34 .. 68 match: 19 SD: 2.2421 cents 35 .. 70 match: 20 SD: 2.1783 cents 36 .. 72 match: 24 SD: 1.8269 cents 37 .. 74 match: 21 SD: 1.9578 cents 38 .. 76 match: 23 SD: 1.7346 cents 39 .. 78 match: 22 SD: 1.7869 cents 40 .. 80 match: 21 SD: 1.6210 cents 41 .. 82 match: 23 SD: 1.7263 cents 42 .. 84 match: 22 SD: 1.4254 cents 43 .. 86 match: 21 SD: 2.1002 cents 44 .. 88 match: 23 SD: 1.6920 cents 45 .. 90 match: 22 SD: 1.4432 cents 46 .. 92 match: 23 SD: 1.7990 cents 47 .. 94 match: 23 SD: 1.5542 cents 48 .. 96 match: 24 SD: 1.1873 cents 51 .. 102 match: 22 SD: 1.7264 cents 52 .. 104 match: 24 SD: 1.3445 cents 54 .. 108 match: 24 SD: 0.9908 cents 71 .. 142 match: 24 SD: 0.9324 cents 72 .. 144 match: 24 SD: 0.8268 cents 76 .. 152 match: 24 SD: 0.8227 cents 80 .. 160 match: 24 SD: 0.7959 cents 86 .. 172 match: 24 SD: 0.7727 cents 90 .. 180 match: 24 SD: 0.7330 cents 96 .. 192 match: 24 SD: 0.6997 cents 101 .. 202 match: 24 SD: 0.6957 cents 102 .. 204 match: 24 SD: 0.5087 cents 109 .. 218 match: 24 SD: 0.5018 cents 112 .. 224 match: 24 SD: 0.5002 cents 128 .. 256 match: 24 SD: 0.4806 cents 131 .. 262 match: 24 SD: 0.4703 cents 136 .. 272 match: 24 SD: 0.4176 cents 157 .. 314 match: 24 SD: 0.3890 cents 166 .. 332 match: 24 SD: 0.3456 cents 185 .. 370 match: 24 SD: 0.3189 cents 210 .. 420 match: 24 SD: 0.2667 cents 238 .. 476 match: 24 SD: 0.2383 cents 240 .. 480 match: 24 SD: 0.2363 cents 264 .. 528 match: 24 SD: 0.2125 cents 286 .. 572 match: 24 SD: 0.2091 cents 297 .. 594 match: 24 SD: 0.1937 cents 318 .. 636 match: 24 SD: 0.1829 cents 341 .. 682 match: 24 SD: 0.1825 cents 342 .. 684 match: 24 SD: 0.1571 cents 376 .. 752 match: 24 SD: 0.1433 cents 399 .. 798 match: 24 SD: 0.1423 cents 448 .. 896 match: 24 SD: 0.1368 cents 454 .. 908 match: 24 SD: 0.1297 cents 478 .. 956 match: 24 SD: 0.1138 cents 514 .. 1028 match: 24 SD: 0.1137 cents 525 .. 1050 match: 24 SD: 0.1103 cents 552 .. 1104 match: 24 SD: 0.1021 cents 590 .. 1180 match: 24 SD: 0.0886 cents