Scala analysis: 178_C8
Chromatic tetrachord 36/35 * 35/33 * 11/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 12/11 150.637059 undecimal neutral second, 3/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 11/9 347.4079 undecimal neutral third 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 35/33 101.8667 3: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 35/33 101.867 cents 1: 1 11/9 347.408 cents undecimal neutral third 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 44/35 396.178 cents 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 : 48.8 150.6 498.0 48.8 : 101.9 449.3 498.0 150.6: 347.4 396.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 347.4079 cents 385/324, 298.6376 cents 36/35, 48.7704 cents 2: 150.6371 .. 449.2746 cents 385/324, 298.6376 cents 108/121,-196.7709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 3.404013 Largest / Average step : 2.092630 Largest / Smallest step : 7.123339 Median interval of one step : 35/33, 101.8667 cents, amount: 1 Least squares average step : 131.72711 cents, oct.: 395.18132 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1501-tone equal temperament with octave 4/3 degrees: 147 454 1501 Least number of segments generator : 751 of 249.188 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1131 of 375.276 cents and inv. generated superset size: 29 = 26 more = 966.667% 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 48.77038 cents Scale diversity : 0.737416 Lumma stability : 0.195847 Lumma impropriety factor : 0.395087 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 : 36/35, 48.7704 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 11 Odd number limit : 35 (O: 35 U: 35) Highest odd numerator or denominator: 35 Scale harmonicity : 0.022288 Average absolute harmonicity : 0.099895 Specific harmonicity : 0.116559 Fundamental : 1/1155, -10.1737 octaves, 0.2265 Hz. Guide tone : 36, 5.1699 octaves, 9418.520 Hz. Exponens Consonantiae : 4.158000E+04, 15.34360 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 50.5, average 16.83333 Mersenne's string divisions : 11431 Sum of van Prooijen's expressibility: 3.06258, average 1.02086 Sum of Tenney's harmonic distance : 6.30013, average 2.10004 Vogel's harmonic complexity : 22.33333 Wille's k value : 192 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.40053, average 2.56675 Lattice compactness (without 2's) : 12.41640, average 2.06940 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 2 0.66667 4 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 1 11: -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: <7 11 15 19 24| Scale is weakly epimorphic with val: <7 11 15 19 27| Scale is JI-epimorphic with val: <7 11 15 20 23| Scale is weakly epimorphic with val: <7 11 15 20 26| Scale is weakly epimorphic with val: <7 11 15 22 24| Scale is weakly epimorphic with val: <7 11 15 22 27| Scale is weakly epimorphic with val: <7 11 16 18 24| Scale is weakly epimorphic with val: <7 11 16 18 27| Scale is JI-epimorphic with val: <7 11 16 19 23| Scale is weakly epimorphic with val: <7 11 16 19 26| Scale is weakly epimorphic with val: <7 11 16 21 24| Scale is weakly epimorphic with val: <7 11 16 21 27| Scale is weakly epimorphic with val: <7 11 16 22 23| Scale is weakly epimorphic with val: <7 11 16 22 26| Scale is JI-epimorphic with val: <7 11 17 18 23| Scale is weakly epimorphic with val: <7 11 17 18 26| Scale is weakly epimorphic with val: <7 11 17 20 24| Scale is weakly epimorphic with val: <7 11 17 20 27| Scale is weakly epimorphic with val: <7 11 17 21 23| Scale is weakly epimorphic with val: <7 11 17 21 26| Scale is weakly epimorphic with val: <7 11 18 19 24| Scale is weakly epimorphic with val: <7 11 18 19 27| Scale is weakly epimorphic with val: <7 11 18 20 23| Scale is weakly epimorphic with val: <7 11 18 20 26| Scale is weakly epimorphic with val: <7 11 18 22 24| Scale is weakly epimorphic with val: <7 11 18 22 27| Scale is weakly epimorphic with val: <7 11 19 19 23| Scale is weakly epimorphic with val: <7 11 19 19 26| Scale is weakly epimorphic with val: <7 11 19 21 24| Scale is weakly epimorphic with val: <7 11 19 21 27| Scale is weakly epimorphic with val: <7 11 19 22 23| Scale is weakly epimorphic with val: <7 11 19 22 26| Scale is weakly epimorphic with val: <7 12 15 19 23| Scale is weakly epimorphic with val: <7 12 15 20 25| Scale is weakly epimorphic with val: <7 12 15 22 23| Scale is weakly epimorphic with val: <7 12 16 18 23| Scale is weakly epimorphic with val: <7 12 16 19 25| Scale is weakly epimorphic with val: <7 12 16 21 23| Scale is weakly epimorphic with val: <7 12 17 18 25| Scale is weakly epimorphic with val: <7 12 17 20 23| Scale is weakly epimorphic with val: <7 12 18 19 23| Scale is weakly epimorphic with val: <7 12 18 22 23| Scale is weakly epimorphic with val: <7 12 19 21 23| Scale is weakly epimorphic with val: <8 11 15 19 24| Scale is weakly epimorphic with val: <8 11 15 20 23| Scale is weakly epimorphic with val: <8 11 15 20 26| Scale is weakly epimorphic with val: <8 11 15 22 24| Scale is weakly epimorphic with val: <8 11 16 18 24| Scale is weakly epimorphic with val: <8 11 16 19 23| Scale is weakly epimorphic with val: <8 11 16 19 26| Scale is weakly epimorphic with val: <8 11 16 21 24| Scale is weakly epimorphic with val: <8 11 17 18 23| Scale is weakly epimorphic with val: <8 11 17 18 26| Scale is weakly epimorphic with val: <8 11 17 20 24| Scale is weakly epimorphic with val: <8 11 18 19 24| Scale is weakly epimorphic with val: <8 11 18 22 24| Scale is weakly epimorphic with val: <8 11 19 21 24| Scale is weakly epimorphic with val: <8 12 15 20 25| Scale is weakly epimorphic with val: <8 12 15 22 23| Scale is weakly epimorphic with val: <8 12 15 22 26| Scale is weakly epimorphic with val: <8 12 16 19 25| Scale is weakly epimorphic with val: <8 12 16 21 23| Scale is weakly epimorphic with val: <8 12 16 21 26| Scale is weakly epimorphic with val: <8 12 16 22 25| Scale is weakly epimorphic with val: <8 12 17 18 25| Scale is weakly epimorphic with val: <8 12 17 20 23| Scale is weakly epimorphic with val: <8 12 17 20 26| Scale is weakly epimorphic with val: <8 12 17 21 25| Scale is weakly epimorphic with val: <8 12 18 19 23| Scale is weakly epimorphic with val: <8 12 18 19 26| Scale is weakly epimorphic with val: <8 12 18 20 25| Scale is weakly epimorphic with val: <8 12 19 19 25| Scale is weakly epimorphic with val: <8 12 19 22 25|
FIT/MODE
3: 0 1 2 N G T3 SD: 29.5242 c. M: 48.7704 c. 4: 0 1 3 N G T3 SD: 31.9432 c. M: 48.7704 c. 6: 1 1 4 N M DE S SD: 21.6692 c. M:-34.2371 c. 7: 1 1 5 N M DE S SD: 13.7882 c. M:-22.3789 c. 9: 1 2 6 N T3 SD: 9.6543 c. M:-15.3779 c. 10: 1 2 7 N T3 SD: 0.9249 c. M: 1.2236 c. 53: 5 11 37 N T3 SD: 1.0435 c. M: 1.7850 c. 63: 6 13 44 N T3 SD: 0.8117 c. M: 1.3375 c. 73: 7 15 51 N T3 SD: 0.6629 c. M: 1.0126 c. 83: 8 17 58 N T3 SD: 0.5703 c. M: 0.7660 c. 92: 9 19 64 N T3 SD: 0.5445 c. M:-0.9419 c. 93: 9 19 65 N T3 SD: 0.5168 c. M: 0.6880 c. 102: 10 21 71 N T3 SD: 0.4225 c. M:-0.7296 c. 112: 11 23 78 N T3 SD: 0.3312 c. M:-0.5552 c. 122: 12 25 85 N T3 SD: 0.2677 c. M:-0.4094 c. 132: 13 27 92 N T3 SD: 0.2307 c. M:-0.2857 c. 142: 14 29 99 N T3 SD: 0.2182 c. M:-0.3326 c. 185: 18 38 129 N T3 SD: 0.1935 c. M: 0.3119 c. 195: 19 40 136 N T3 SD: 0.1436 c. M: 0.2429 c. 205: 20 42 143 N T3 SD: 0.1044 c. M: 0.1806 c. 215: 21 44 150 N T3 SD: 0.0810 c. M: 0.1241 c. 225: 22 46 157 N T3 SD: 0.0794 c. M: 0.1168 c. 337: 33 69 235 N T3 SD: 0.0615 c. M:-0.1065 c. 347: 34 71 242 N T3 SD: 0.0429 c. M:-0.0682 c. 357: 35 73 249 N T3 SD: 0.0380 c. M:-0.0576 c. 552: 54 113 385 N T3 SD: 0.0362 c. M: 0.0486 c. 562: 55 115 392 N T3 SD: 0.0196 c. M: 0.0293 c. 572: 56 117 399 N T3 SD: 0.0067 c. M: 0.0107 c. 1501: 147 307 1047 N T3 SD: 0.0040 c. M:-0.0055 c. 2073: 203 424 1446 N T3 SD: 0.0012 c. M:-0.0017 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: 92.6837 cents 6 x 7:8 S SD: 58.1169 cents 7 x 8:9 S SD: 51.1133 cents 8 x 9:11 SD: 37.6697 cents 9 x 10:12 S SD: 15.8833 cents 10 x 11:13 SD: 23.0628 cents 11 x 12:15 S SD: 19.4529 cents 12 x 13:16 SD: 6.0322 cents 13 x 14:17 SD: 20.1813 cents 14 x 15:19 SD: 21.8633 cents 15 x 16:20 S SD: 19.4529 cents 16 x 17:21 SD: 26.5995 cents 17:18:19:23 SD: 23.3680 cents 18:19:20:24 S SD: 18.3154 cents 19:20:21:25 SD: 17.1283 cents 20:21:22:27 SD: 14.6939 cents 21:22:23:28 SD: 10.8327 cents 23:24:25:31 SD: 10.5951 cents 24:25:26:32 SD: 8.3350 cents 30:31:33:40 SD: 5.4809 cents 32:33:35:43 SD: 4.9672 cents 33:34:36:44 SD: 0.9707 cents 111:114:121:148 SD: 0.9694 cents 141:145:154:188 SD: 0.6911 cents 144:148:157:192 SD: 0.5568 cents 177:182:193:236 SD: 0.3266 cents 210:216:229:280 SD: 0.2290 cents 318:327:347:424 SD: 0.2139 cents 351:361:383:468 SD: 0.1444 cents 384:395:419:512 SD: 0.1320 cents 528:543:576:704 SD: 0.0911 cents 561:577:612:748 SD: 0.0286 cents 594:611:648:792 SD: 0.0270 cents