Scala analysis: 194_C11
Chromatic tetrachord 112/107 * 107/102 * 17/14
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 112/107 79.065523 2: 56/51 161.915496 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/14 336.1295 supraminor third 1: 112/107 79.0655 2: 107/102 82.8500 3: 17/14 336.1295 supraminor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 112/107 79.066 cents 1: 1 107/102 82.850 cents 1: 1 17/14 336.130 cents supraminor third 2: 1 56/51 161.915 cents 2: 1 136/107 415.195 cents 2: 1 107/84 418.979 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 79.1 161.9 498.0 79.1 : 82.8 419.0 498.0 161.9: 336.1 415.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 79.0655 .. 336.1295 cents 1819/1568, 257.0640 cents 112/107, 79.0655 cents 2: 161.9155 .. 418.9795 cents 1819/1568, 257.0640 cents 784/867,-174.2140 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 112/107, 79.0655 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 2.099714 Largest / Average step : 2.024694 Largest / Smallest step : 4.251278 Median interval of one step : 107/102, 82.8500 cents, amount: 1 Least squares average step : 135.50225 cents, oct.: 406.50675 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1052-tone equal temperament with octave 4/3 degrees: 167 342 1052 Least number of segments generator : 527 of 249.496 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 877 of 415.195 cents and inv. generated superset size: 27 = 24 more = 900.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 79.06552 cents Scale diversity : 0.881369 Lumma stability : 0.317504 Lumma impropriety factor : 0.349796 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 11449/11424, 3.7845 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 253.2795 cents: 2 -- Rational properties -- Prime limit : 107 Odd number limit : 107 (O: 107 U: 107) Highest odd numerator or denominator: 107 Scale harmonicity : 0.021245 Fundamental : 1/5457, -12.4139 octaves, 0.0479 Hz. Guide tone : 112, 6.8074 octaves, 29302.063 Hz. Exponens Consonantiae : 6.111840E+05, 19.22125 octaves Euler's gradus suavitatis : 135 Sum of Mann's harmonic distance : 166.5, average 55.50000 Mersenne's string divisions : 164031 Sum of van Prooijen's expressibility: 4.21408, average 1.40469 Sum of Tenney's harmonic distance : 8.61354, average 2.87118 Vogel's harmonic complexity : 91.33333 Wille's k value : 909 Wilson's harmonic complexity : 134 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 15.73687, average 2.62281 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 .. 0 -0.66667 2 1 7: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 107: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 22 27 48| Scale is weakly epimorphic with val: <7 10 19 27 48| Scale is weakly epimorphic with val: <7 10 20 28 49| Scale is weakly epimorphic with val: <7 10 21 29 50| Scale is weakly epimorphic with val: <7 10 22 30 48| Scale is weakly epimorphic with val: <7 11 18 27 50| Scale is weakly epimorphic with val: <7 11 18 29 48| Scale is weakly epimorphic with val: <7 11 18 30 50| Scale is weakly epimorphic with val: <7 11 18 32 48| Scale is weakly epimorphic with val: <7 11 18 33 50| Scale is weakly epimorphic with val: <7 11 19 27 49| Scale is weakly epimorphic with val: <7 11 19 28 48| Scale is weakly epimorphic with val: <7 11 19 30 49| Scale is weakly epimorphic with val: <7 11 19 31 48| Scale is weakly epimorphic with val: <7 11 19 33 49| Scale is weakly epimorphic with val: <7 11 20 28 50| Scale is weakly epimorphic with val: <7 11 20 29 49| Scale is weakly epimorphic with val: <7 11 20 31 50| Scale is weakly epimorphic with val: <7 11 20 32 49| Scale is weakly epimorphic with val: <7 11 21 27 50| Scale is JI-epimorphic with val: <7 11 21 29 48| Scale is weakly epimorphic with val: <7 11 21 30 50| Scale is weakly epimorphic with val: <7 11 21 32 48| Scale is weakly epimorphic with val: <7 11 21 33 50| Scale is weakly epimorphic with val: <7 11 22 27 49| Scale is weakly epimorphic with val: <7 11 22 28 48| Scale is JI-epimorphic with val: <7 11 22 30 49| Scale is weakly epimorphic with val: <7 11 22 31 48| Scale is weakly epimorphic with val: <7 11 22 33 49| Scale is weakly epimorphic with val: <7 12 21 27 48| Scale is weakly epimorphic with val: <7 12 22 28 49| Scale is weakly epimorphic with val: <8 11 18 28 49| Scale is weakly epimorphic with val: <8 11 19 28 48| Scale is weakly epimorphic with val: <8 11 19 29 50| Scale is weakly epimorphic with val: <8 11 19 31 48| Scale is weakly epimorphic with val: <8 11 20 29 49| Scale is weakly epimorphic with val: <8 11 20 30 48| Scale is weakly epimorphic with val: <8 11 20 32 49| Scale is weakly epimorphic with val: <8 11 21 27 50| Scale is weakly epimorphic with val: <8 11 21 30 50| Scale is weakly epimorphic with val: <8 11 21 31 49| Scale is weakly epimorphic with val: <8 11 21 33 50| Scale is weakly epimorphic with val: <8 11 22 32 50| Scale is weakly epimorphic with val: <8 12 18 27 48| Scale is weakly epimorphic with val: <8 12 19 28 49| Scale is weakly epimorphic with val: <8 12 19 29 48| Scale is weakly epimorphic with val: <8 12 19 32 48| Scale is weakly epimorphic with val: <8 12 20 27 49| Scale is weakly epimorphic with val: <8 12 20 29 50| Scale is weakly epimorphic with val: <8 12 20 30 49| Scale is weakly epimorphic with val: <8 12 20 33 49| Scale is weakly epimorphic with val: <8 12 21 28 50| Scale is weakly epimorphic with val: <8 12 21 30 48| Scale is weakly epimorphic with val: <8 12 21 31 50| Scale is weakly epimorphic with val: <8 12 22 31 49|
FIT/MODE
3: 0 1 2 N G T3 SD: 45.7098 c. M: 79.0655 c. 4: 0 1 3 N G T3 SD: 50.4990 c. M: 79.0655 c. 5: 1 1 3 N M DE S SD: 24.5867 c. M:-37.3025 c. 6: 1 1 4 N M DE S SD: 3.2836 c. M:-4.0995 c. 19: 3 3 13 N M DE S SD: 2.6891 c. M: 4.6381 c. 25: 4 4 17 N M DE S SD: 1.5104 c. M: 2.5411 c. 31: 5 5 21 N M DE S SD: 1.0288 c. M:-1.2643 c. 37: 6 6 25 N M DE S SD: 1.0058 c. M:-1.6985 c. 43: 7 7 29 N M DE S SD: 1.1695 c. M:-2.0116 c. 64: 10 11 43 N T3 SD: 1.1283 c. M:-1.5055 c. 68: 11 11 46 N M DE S SD: 0.9773 c. M:-1.5006 c. 71: 11 12 48 N T3 SD: 1.1484 c. M: 1.9036 c. 76: 12 13 51 N T3 SD: 1.1328 c. M:-1.9151 c. 77: 12 13 52 N T3 SD: 0.8450 c. M: 1.4481 c. 83: 13 14 56 N T3 SD: 0.6138 c. M: 1.0585 c. 89: 14 15 60 N T3 SD: 0.4678 c. M: 0.7214 c. 95: 15 16 64 N T3 SD: 0.4272 c. M:-0.6045 c. 108: 17 18 73 N T3 SD: 0.4866 c. M: 0.6696 c. 114: 18 19 77 N T3 SD: 0.2914 c. M: 0.4268 c. 120: 19 20 81 N T3 SD: 0.1239 c. M: 0.2084 c. 126: 20 21 85 N T3 SD: 0.0850 c. M:-0.1468 c. 246: 39 41 166 N T3 SD: 0.0684 c. M: 0.1072 c. 277: 44 46 187 N T3 SD: 0.0614 c. M: 0.0958 c. 372: 59 62 251 N T3 SD: 0.0644 c. M:-0.0830 c. 397: 63 66 268 N T3 SD: 0.0507 c. M: 0.0822 c. 403: 64 67 272 N T3 SD: 0.0201 c. M:-0.0285 c. 523: 83 87 353 N T3 SD: 0.0216 c. M: 0.0271 c. 529: 84 88 357 N T3 SD: 0.0159 c. M:-0.0197 c. 649: 103 108 438 N T3 SD: 0.0138 c. M: 0.0229 c. 932: 148 155 629 N T3 SD: 0.0135 c. M:-0.0232 c. 1052: 167 175 710 N T3 SD: 0.0028 c. M: 0.0035 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 87.7017 cents 6 x 7:8 S SD: 52.4777 cents 7 x 8:9 S SD: 46.7996 cents 8 x 9:11 SD: 33.9173 cents 9 x 10:12 S SD: 10.2441 cents 10 x 11:13 SD: 21.9699 cents 11 x 12:15 S SD: 20.2538 cents 12 x 13:16 SD: 11.6714 cents 13 x 14:17 SD: 23.7710 cents 14:15 x 19 SD: 25.3440 cents 15:16 x 20 S SD: 16.3329 cents 17:18:19:23 SD: 14.8072 cents 18:19:20:24 S SD: 8.3739 cents 20:21:22:27 SD: 7.4628 cents 21:22:23:28 SD: 1.5535 cents 81:85:89:108 SD: 1.5102 cents 102:107:112:136 SD: 1.2615 cents 111:116:122:148 SD: 1.0832 cents 132:138:145:176 SD: 0.7410 cents 153:160:168:204 SD: 0.5391 cents 174:182:191:232 SD: 0.4512 cents 195:204:214:260 SD: 0.4485 cents 213:223:234:284 SD: 0.3144 cents 234:245:257:312 SD: 0.2030 cents 255:267:280:340 SD: 0.1818 cents 387:405:425:516 SD: 0.1440 cents 408:427:448:544 SD: 0.0884 cents