Scala analysis: schis24
24 tone schismic temperament in its 94-et incarnation
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25.532 cents 25.531915 2: 89.362 cents 89.361702 3: 114.894 cents 114.893617 4: 178.723 cents 178.723404 5: 204.255 cents 204.255319 6: 293.617 cents 293.617021 7: 319.149 cents 319.148936 8: 382.979 cents 382.978723 9: 408.511 cents 408.510638 10: 497.872 cents 497.872340 11: 523.404 cents 523.404255 12: 587.234 cents 587.234043 13: 612.766 cents 612.765957 14: 676.596 cents 676.595745 15: 702.128 cents 702.127660 16: 791.489 cents 791.489362 17: 817.021 cents 817.021277 18: 880.851 cents 880.851064 19: 906.383 cents 906.382979 20: 995.745 cents 995.744681 21: 1021.277 cents 1021.276596 22: 1085.106 cents 1085.106383 23: 1110.638 cents 1110.638298 24: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 89.3617 cents 89.3617 1: 25.5319 cents 25.5319 2: 63.8298 cents 63.8298 3: 25.5319 cents 25.5319 4: 63.8298 cents 63.8298 5: 25.5319 cents 25.5319 6: 89.3617 cents 89.3617 7: 25.5319 cents 25.5319 8: 63.8298 cents 63.8298 9: 25.5319 cents 25.5319 10: 89.3617 cents 89.3617 11: 25.5319 cents 25.5319 12: 63.8298 cents 63.8298 13: 25.5319 cents 25.5319 14: 63.8298 cents 63.8298 15: 25.5319 cents 25.5319 16: 89.3617 cents 89.3617 17: 25.5319 cents 25.5319 18: 63.8298 cents 63.8298 19: 25.5319 cents 25.5319 20: 89.3617 cents 89.3617 21: 25.5319 cents 25.5319 22: 63.8298 cents 63.8298 23: 25.5319 cents 25.5319 24: 89.3617 cents 89.3617
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 25.53191 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: 2 523.40426 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: 2 676.59574 cents 14: 22 702.12766 cents 15: 1 702.12766 cents 15: 11 727.65957 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 : 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 25.5 : 63.8 89.4 153.2 178.7 268.1 293.6 357.4 383.0 472.3 497.9 561.7 587.2 651.1 676.6 766.0 791.5 855.3 880.9 970.2 995.7 1059.6 1085.1 1174.5 1200.0 89.4 : 25.5 89.4 114.9 204.3 229.8 293.6 319.1 408.5 434.0 497.9 523.4 587.2 612.8 702.1 727.7 791.5 817.0 906.4 931.9 995.7 1021.3 1110.6 1136.2 1200.0 114.9 : 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 1200.0 178.7 : 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 1200.0 204.3 : 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 1200.0 293.6 : 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 1200.0 319.1 : 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 1200.0 383.0 : 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 1200.0 408.5 : 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 1200.0 497.9 : 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 1200.0 523.4 : 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 1200.0 587.2 : 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 1200.0 612.8 : 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 1200.0 676.6 : 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 1200.0 702.1 : 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 1200.0 791.5 : 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 1085.1 1110.6 1200.0 817.0 : 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 1059.6 1085.1 1174.5 1200.0 880.9 : 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 1200.0 906.4 : 89.4 114.9 178.7 204.3 293.6 319.1 383.0 408.5 472.3 497.9 587.2 612.8 676.6 702.1 791.5 817.0 880.9 906.4 970.2 995.7 1085.1 1110.6 1174.5 1200.0 995.7 : 25.5 89.4 114.9 204.3 229.8 293.6 319.1 383.0 408.5 497.9 523.4 587.2 612.8 702.1 727.7 791.5 817.0 880.9 906.4 995.7 1021.3 1085.1 1110.6 1200.0 1021.3: 63.8 89.4 178.7 204.3 268.1 293.6 357.4 383.0 472.3 497.9 561.7 587.2 676.6 702.1 766.0 791.5 855.3 880.9 970.2 995.7 1059.6 1085.1 1174.5 1200.0 1085.1: 25.5 114.9 140.4 204.3 229.8 293.6 319.1 408.5 434.0 497.9 523.4 612.8 638.3 702.1 727.7 791.5 817.0 906.4 931.9 995.7 1021.3 1110.6 1136.2 1200.0 1110.6: 89.4 114.9 178.7 204.3 268.1 293.6 383.0 408.5 472.3 497.9 587.2 612.8 676.6 702.1 766.0 791.5 880.9 906.4 970.2 995.7 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 .. 114.8936 cents 25.53191 cents -0.00000 cents 3: 114.8936 .. 178.7234 cents 63.82979 cents 1/1, 0.0000 cents 4: 178.7234 .. 204.2553 cents 25.53191 cents 1/1, 0.0000 cents 5: 204.2553 .. 293.6170 cents 89.36170 cents -0.00000 cents 6: 293.6170 .. 319.1489 cents 25.53191 cents 1/1, 0.0000 cents 7: 319.1489 .. 382.9787 cents 63.82979 cents 0.00000 cents 8: 382.9787 .. 408.5106 cents 25.53191 cents 1/1, 0.0000 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 1/1, 0.0000 cents 12: 587.2340 .. 612.7660 cents 25.53191 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 0.00000 cents 16: 791.4894 .. 817.0213 cents 25.53191 cents -0.00000 cents 17: 817.0213 .. 880.8511 cents 63.82979 cents 1/1, 0.0000 cents 18: 880.8511 .. 906.3830 cents 25.53191 cents -0.00000 cents 19: 906.3830 .. 995.7447 cents 89.36170 cents -0.00000 cents 20: 995.7447 .. 1021.2766 cents 25.53191 cents 1/1, 0.0000 cents 21: 1021.2766 .. 1085.1064 cents 63.82979 cents 0.00000 cents 22: 1085.1064 .. 1110.6383 cents 25.53191 cents 1/1, 0.0000 cents 23: 1110.6383 .. 1174.4681 cents 63.82979 cents 0.00000 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 : 25.53191 cents, amount: 12 Least squares average step : 48.56795 cents, oct.: 1165.63092 cents Scale is proper Scale is a mode of a 94-tone equal temperament with octave 2/1 degrees: 2 7 9 14 16 23 25 30 32 39 41 46 48 53 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: 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: ABABACABACABABACABACABAC Step pattern size order : SMSMSLSMSLSMSMSLSMSLSMSL 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 conjunct "tetrachords" of 11 notes Formal octave complements present : 23 = 95.8333% Limited inverse transpositions : 15 Inversional symmetry on intervals : 7-8 19-20 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
24: 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 N T3 SD: 27.9065 c. M: 47.8723 c. 25: 1 1 0 2 0 2 1 1 1 1 1 1 1 1 1 2 0 1 1 2 0 2 0 2 N SD: 13.9626 c. M:-24.5106 c. 27: 1 1 1 1 1 2 0 2 0 2 1 1 1 1 1 2 0 2 0 2 1 1 1 2 N SD: 12.3973 c. M:-18.9125 c. 29: 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1 1 2 1 1 1 2 P D3 SD: 9.1654 c. M:-15.8474 c. 39: 1 2 1 2 1 3 0 2 1 3 1 2 1 2 1 3 1 2 0 3 1 2 1 3 N SD: 8.5473 c. M: 14.0753 c. 40: 1 2 1 2 1 3 1 2 1 3 0 3 0 3 0 3 1 2 1 3 1 2 1 3 N SD: 8.6632 c. M: 13.4043 c. 41: 1 2 1 2 1 3 1 2 1 3 1 2 1 2 1 3 1 2 1 3 1 2 1 3 P SD: 2.1609 c. M:-3.7364 c. 53: 1 3 1 3 1 4 1 3 1 4 1 3 1 3 1 4 1 3 1 4 1 3 1 4 P G SD: 1.6717 c. M: 2.8904 c. 94: 2 5 2 5 2 7 2 5 2 7 2 5 2 5 2 7 2 5 2 7 2 5 2 7 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: 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: 7.0031 cents 12 .. 24 match: 12 H SD: 4.6925 cents 13 .. 26 match: 13 H SD: 6.8289 cents 14 .. 28 match: 14 H SD: 4.5096 cents 15 .. 30 match: 13 SD: 3.3314 cents 16 .. 32 match: 15 S SD: 3.9950 cents 17 .. 34 match: 16 S SD: 4.2922 cents 18 .. 36 match: 15 S SD: 3.9967 cents 19 .. 38 match: 14 SD: 3.3488 cents 20 .. 40 match: 15 SD: 3.3104 cents 21 .. 42 match: 19 SD: 3.5789 cents 22 .. 44 match: 17 SD: 3.3721 cents 23 .. 46 match: 19 SD: 3.1831 cents 24 .. 48 match: 17 SD: 3.3293 cents 25 .. 50 match: 19 SD: 3.1215 cents 26 .. 52 match: 18 SD: 2.8004 cents 27 .. 54 match: 17 SD: 2.9080 cents 28 .. 56 match: 21 SD: 2.7964 cents 29 .. 58 match: 18 SD: 2.5231 cents 30 .. 60 match: 22 SD: 2.4382 cents 31 .. 62 match: 19 SD: 2.6115 cents 32 .. 64 match: 20 SD: 2.5862 cents 33 .. 66 match: 22 SD: 2.2510 cents 34 .. 68 match: 20 SD: 2.5423 cents 35 .. 70 match: 19 SD: 2.4107 cents 36 .. 72 match: 21 SD: 2.0926 cents 37 .. 74 match: 22 SD: 2.1905 cents 38 .. 76 match: 23 SD: 1.8502 cents 39 .. 78 match: 23 SD: 1.9248 cents 40 .. 80 match: 24 SD: 1.6255 cents 41 .. 82 match: 21 SD: 1.9184 cents 42 .. 84 match: 23 SD: 1.6312 cents 43 .. 86 match: 22 SD: 1.9683 cents 44 .. 88 match: 24 SD: 1.7493 cents 45 .. 90 match: 24 SD: 1.4332 cents 46 .. 92 match: 23 SD: 1.7058 cents 48 .. 96 match: 23 SD: 1.1913 cents 49 .. 98 match: 23 SD: 1.5267 cents 50 .. 100 match: 23 SD: 1.4386 cents 51 .. 102 match: 23 SD: 1.7521 cents 52 .. 104 match: 24 SD: 1.5550 cents 53 .. 106 match: 24 SD: 1.4466 cents 54 .. 108 match: 24 SD: 1.0669 cents 64 .. 128 match: 24 SD: 1.0404 cents 70 .. 140 match: 24 SD: 1.0214 cents 71 .. 142 match: 24 SD: 0.8294 cents 80 .. 160 match: 24 SD: 0.8187 cents 90 .. 180 match: 24 SD: 0.6923 cents 102 .. 204 match: 24 SD: 0.6595 cents 112 .. 224 match: 24 SD: 0.6427 cents 113 .. 226 match: 24 SD: 0.5577 cents 118 .. 236 match: 24 SD: 0.5388 cents 128 .. 256 match: 24 SD: 0.4524 cents 134 .. 268 match: 24 SD: 0.4471 cents 148 .. 296 match: 24 SD: 0.4217 cents 158 .. 316 match: 24 SD: 0.3991 cents 173 .. 346 match: 24 SD: 0.3989 cents 174 .. 348 match: 24 SD: 0.3611 cents 184 .. 368 match: 24 SD: 0.3391 cents 190 .. 380 match: 24 SD: 0.3374 cents 193 .. 386 match: 24 SD: 0.3089 cents 202 .. 404 match: 24 SD: 0.2939 cents 222 .. 444 match: 24 SD: 0.2796 cents 247 .. 494 match: 24 SD: 0.2271 cents 264 .. 528 match: 24 SD: 0.2238 cents 266 .. 532 match: 24 SD: 0.2113 cents 318 .. 636 match: 24 SD: 0.2063 cents 320 .. 640 match: 24 SD: 0.1560 cents 396 .. 792 match: 24 SD: 0.1508 cents 416 .. 832 match: 24 SD: 0.1453 cents 448 .. 896 match: 24 SD: 0.1379 cents 454 .. 908 match: 24 SD: 0.1280 cents 478 .. 956 match: 24 SD: 0.1261 cents 525 .. 1050 match: 24 SD: 0.1037 cents 552 .. 1104 match: 24 SD: 0.0897 cents