Scala analysis: 192_C10
Chromatic tetrachord 69/67 * 67/63 * 28/23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 69/67 50.922320 2: 23/21 157.493440 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 28/23 340.5516 1: 69/67 50.9223 2: 67/63 106.5711 3: 28/23 340.5516
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 69/67 50.922 cents 1: 1 67/63 106.571 cents 1: 1 28/23 340.552 cents 2: 1 23/21 157.493 cents 2: 1 84/67 391.474 cents 2: 1 268/207 447.123 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 : 50.9 157.5 498.0 50.9 : 106.6 447.1 498.0 157.5: 340.6 391.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.9223 .. 340.5516 cents 1876/1587, 289.6292 cents 69/67, 50.9223 cents 2: 157.4934 .. 447.1227 cents 1876/1587, 289.6292 cents 529/588,-183.0581 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 69/67, 50.9223 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 28/23, 340.5516 cents Average / Smallest step : 3.260162 Largest / Average step : 2.051330 Largest / Smallest step : 6.687668 Median interval of one step : 67/63, 106.5711 cents, amount: 1 Least squares average step : 132.86030 cents, oct.: 398.58090 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2103-tone equal temperament with octave 4/3 degrees: 215 665 2103 Least number of segments generator : 1052 of 249.141 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1790 of 423.918 cents and inv. generated superset size: 42 = 39 more = 1400.000% 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 50.92232 cents Scale diversity : 0.780054 Lumma stability : 0.204489 Lumma impropriety factor : 0.367553 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 : 69/67, 50.9223 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% -- Rational properties -- Prime limit : 67 Odd number limit : 207 (O: 69 U: 207) Highest odd numerator or denominator: 69 Scale harmonicity : 0.016749 Fundamental : 1/1407, -10.4584 octaves, 0.1859 Hz. Guide tone : 276, 8.1085 octaves, 72208.656 Hz. Exponens Consonantiae : 3.883320E+05, 18.56693 octaves Euler's gradus suavitatis : 101 Sum of Mann's harmonic distance : 93.5, average 31.16667 Mersenne's string divisions : 10472 Sum of van Prooijen's expressibility: 3.67770, average 1.22590 Sum of Tenney's harmonic distance : 7.42805, average 2.47602 Vogel's harmonic complexity : 67.33333 Wille's k value : 770 Wilson's harmonic complexity : 103 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.06789, average 2.17798 Lattice compactness (without 2's) : 10.03261, average 1.67210 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 1 -0.33333 3 1 7: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 1 67: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 18 31 43| Scale is weakly epimorphic with val: <6 10 19 32 44| Scale is weakly epimorphic with val: <6 10 19 36 43| Scale is weakly epimorphic with val: <6 10 20 33 45| Scale is weakly epimorphic with val: <6 10 21 34 43| Scale is weakly epimorphic with val: <6 10 22 35 44| Scale is weakly epimorphic with val: <6 10 22 36 43| Scale is weakly epimorphic with val: <6 11 18 32 44| Scale is weakly epimorphic with val: <6 11 19 33 45| Scale is weakly epimorphic with val: <6 11 19 35 43| Scale is weakly epimorphic with val: <6 11 20 34 43| Scale is weakly epimorphic with val: <6 11 20 36 44| Scale is weakly epimorphic with val: <6 11 21 35 44| Scale is weakly epimorphic with val: <6 11 22 35 43| Scale is weakly epimorphic with val: <6 11 22 36 45| Scale is weakly epimorphic with val: <7 10 18 31 45| Scale is weakly epimorphic with val: <7 10 18 36 43| Scale is weakly epimorphic with val: <7 10 19 32 43| Scale is weakly epimorphic with val: <7 10 20 33 44| Scale is weakly epimorphic with val: <7 10 21 34 45| Scale is weakly epimorphic with val: <7 10 21 36 43| Scale is weakly epimorphic with val: <7 10 22 35 43| Scale is weakly epimorphic with val: <7 11 18 30 45| Scale is weakly epimorphic with val: <7 11 18 31 44| Scale is weakly epimorphic with val: <7 11 18 33 45| Scale is weakly epimorphic with val: <7 11 18 34 44| Scale is weakly epimorphic with val: <7 11 18 36 45| Scale is weakly epimorphic with val: <7 11 19 31 43| Scale is weakly epimorphic with val: <7 11 19 32 45| Scale is weakly epimorphic with val: <7 11 19 34 43| Scale is weakly epimorphic with val: <7 11 19 35 45| Scale is weakly epimorphic with val: <7 11 20 30 43| Scale is weakly epimorphic with val: <7 11 20 32 44| Scale is JI-epimorphic with val: <7 11 20 33 43| Scale is weakly epimorphic with val: <7 11 20 35 44| Scale is weakly epimorphic with val: <7 11 20 36 43| Scale is weakly epimorphic with val: <7 11 21 30 45| Scale is weakly epimorphic with val: <7 11 21 31 44| Scale is weakly epimorphic with val: <7 11 21 33 45| Scale is JI-epimorphic with val: <7 11 21 34 44| Scale is weakly epimorphic with val: <7 11 21 36 45| Scale is weakly epimorphic with val: <7 11 22 31 43| Scale is weakly epimorphic with val: <7 11 22 32 45| Scale is weakly epimorphic with val: <7 11 22 34 43| Scale is JI-epimorphic with val: <7 11 22 35 45| Scale is weakly epimorphic with val: <7 12 18 33 44| Scale is weakly epimorphic with val: <7 12 18 34 43| Scale is weakly epimorphic with val: <7 12 19 34 45| Scale is weakly epimorphic with val: <7 12 19 35 44| Scale is weakly epimorphic with val: <7 12 20 35 43| Scale is weakly epimorphic with val: <7 12 20 36 45| Scale is weakly epimorphic with val: <7 12 21 34 43| Scale is weakly epimorphic with val: <7 12 21 36 44| Scale is weakly epimorphic with val: <7 12 22 35 44| Scale is weakly epimorphic with val: <8 11 18 32 45| Scale is weakly epimorphic with val: <8 11 18 36 44| Scale is weakly epimorphic with val: <8 11 19 33 43| Scale is weakly epimorphic with val: <8 11 20 34 44| Scale is weakly epimorphic with val: <8 11 20 35 43| Scale is weakly epimorphic with val: <8 11 21 35 45| Scale is weakly epimorphic with val: <8 11 21 36 44| Scale is weakly epimorphic with val: <8 11 22 36 43| Scale is weakly epimorphic with val: <8 12 18 33 43| Scale is weakly epimorphic with val: <8 12 18 35 44| Scale is weakly epimorphic with val: <8 12 19 34 44| Scale is weakly epimorphic with val: <8 12 19 36 45| Scale is weakly epimorphic with val: <8 12 20 34 43| Scale is weakly epimorphic with val: <8 12 20 35 45| Scale is weakly epimorphic with val: <8 12 21 35 44| Scale is weakly epimorphic with val: <8 12 21 36 43| Scale is weakly epimorphic with val: <8 12 22 36 45|
FIT/MODE
3: 0 1 2 N G T3 SD: 29.8088 c. M: 50.9223 c. 4: 0 1 3 N G T3 SD: 35.0281 c. M: 50.9223 c. 6: 1 1 4 N M DE S SD: 19.1666 c. M:-32.0852 c. 7: 1 1 5 N M DE S SD: 14.6061 c. M:-20.2270 c. 9: 1 2 6 N T3 SD: 5.5413 c. M:-8.5216 c. 10: 1 2 7 N T3 SD: 4.7094 c. M: 8.0799 c. 19: 2 4 13 N T3 SD: 0.8769 c. M:-1.5035 c. 60: 6 13 41 N T3 SD: 0.6578 c. M: 1.1178 c. 79: 8 17 54 N T3 SD: 0.2892 c. M: 0.4874 c. 98: 10 21 67 N T3 SD: 0.0656 c. M: 0.1014 c. 215: 22 46 147 N T3 SD: 0.0283 c. M:-0.0404 c. 313: 32 67 214 N T3 SD: 0.0204 c. M:-0.0352 c. 528: 54 113 361 N T3 SD: 0.0203 c. M:-0.0322 c. 743: 76 159 508 N T3 SD: 0.0218 c. M:-0.0309 c. 841: 86 180 575 N T3 SD: 0.0197 c. M:-0.0333 c. 958: 98 205 655 N T3 SD: 0.0230 c. M:-0.0302 c. 1037: 106 222 709 N T3 SD: 0.0225 c. M:-0.0367 c. 1154: 118 247 789 N T3 SD: 0.0197 c. M:-0.0338 c. 1173: 120 251 802 N T3 SD: 0.0238 c. M:-0.0297 c. 1262: 129 270 863 N T3 SD: 0.0184 c. M: 0.0291 c. 1360: 139 291 930 N T3 SD: 0.0174 c. M: 0.0233 c. 1379: 141 295 943 N T3 SD: 0.0150 c. M: 0.0260 c. 1477: 151 316 1010 N T3 SD: 0.0124 c. M: 0.0209 c. 1575: 161 337 1077 N T3 SD: 0.0114 c. M: 0.0164 c. 1673: 171 358 1144 N T3 SD: 0.0118 c. M: 0.0163 c. 1692: 173 362 1157 N T3 SD: 0.0085 c. M: 0.0147 c. 1790: 183 383 1224 N T3 SD: 0.0070 c. M: 0.0111 c. 1888: 193 404 1291 N T3 SD: 0.0073 c. M: 0.0099 c. 1907: 195 408 1304 N T3 SD: 0.0064 c. M: 0.0099 c. 2005: 205 429 1371 N T3 SD: 0.0040 c. M: 0.0069 c. 2103: 215 450 1438 N T3 SD: 0.0036 c. M: 0.0047 c. 2220: 227 475 1518 N T3 SD: 0.0030 c. M:-0.0039 c. 2318: 237 496 1585 N T3 SD: 0.0008 c. M: 0.0012 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: 89.6458 cents 6 x 7:8 S SD: 54.6887 cents 7 x 8:9 S SD: 48.4585 cents 8 x 9:11 SD: 35.3288 cents 9 x 10:12 S SD: 12.4551 cents 10 x 11:13 SD: 22.2350 cents 11 x 12:15 S SD: 19.7527 cents 12 x 13:16 SD: 9.4604 cents 13 x 14:17 SD: 22.2625 cents 14 x 15:19 SD: 24.4274 cents 15 x 16:20 S SD: 22.8811 cents 16 x 18:21 S SD: 26.9157 cents 17:18:19:23 SD: 21.5390 cents 18:19:20:24 S SD: 16.4727 cents 19:20:21:25 SD: 15.6681 cents 20:21:22:27 SD: 13.5162 cents 21:22:23:28 SD: 9.8716 cents 24:25:26:32 SD: 9.1169 cents 28:29:31:37 SD: 8.7432 cents 29:30:32:39 SD: 7.0582 cents 30:31:33:40 SD: 3.1723 cents 33:34:36:44 SD: 2.2995 cents 63:65:69:84 SD: 1.0610 cents 105:108:115:140 SD: 0.7173 cents 135:139:148:180 SD: 0.5709 cents 168:173:184:224 SD: 0.0498 cents