Scala analysis: 527_M35
Miscellaneous tetrachord 36/35 * 135/128 * 896/729
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: 243/224 140.949098 Archytas' 2/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 896/729 357.0959 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 135/128 92.1787 major chroma, major limma 3: 896/729 357.0959
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 135/128 92.179 cents major chroma, major limma 1: 1 896/729 357.096 cents 2: 1 243/224 140.949 cents Archytas' 2/3-tone 2: 1 512/405 405.866 cents narrow diminished fourth 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 : 48.8 140.9 498.0 48.8 : 92.2 449.3 498.0 140.9: 357.1 405.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 357.0959 cents 7840/6561, 308.3255 cents 36/35, 48.7704 cents 2: 140.9491 .. 449.2746 cents 7840/6561, 308.3255 cents 177147/200704,-216.1468 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 : 896/729, 357.0959 cents Average / Smallest step : 3.404013 Largest / Average step : 2.150986 Largest / Smallest step : 7.321983 Median interval of one step : 135/128, 92.1787 cents, amount: 1 Least squares average step : 130.34311 cents, oct.: 391.02934 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1583-tone equal temperament with octave 4/3 degrees: 155 448 1583 Least number of segments generator : 792 of 249.180 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1034 of 325.318 cents and inv. generated superset size: 33 = 30 more = 1100.000% 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 48.77038 cents Scale diversity : 0.688192 Lumma stability : 0.195847 Lumma impropriety factor : 0.433991 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 : 525/512, 43.4083 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 : 7 Odd number limit : 729 (O: 243 U: 729) Highest odd numerator or denominator: 243 Scale harmonicity : 0.025198 Average absolute harmonicity : 0.096953 Specific harmonicity : 0.117065 Fundamental : 1/3360, -11.7142 octaves, 0.0779 Hz. Guide tone : 972, 9.9248 octaves, 254300.049 Hz. Exponens Consonantiae : 3.265920E+06, 21.63906 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 272.5, average 90.83333 Mersenne's string divisions : 232099 Sum of van Prooijen's expressibility: 4.40680, average 1.46893 Sum of Tenney's harmonic distance : 8.91541, average 2.97180 Vogel's harmonic complexity : 19.33333 Wille's k value : 1822 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 32.81116, average 5.46853 Lattice compactness (without 2's) : 21.11017, average 3.51836 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -0.33333 9 3: -1 .. 5 2.00000 8 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.66667 2 2 Average exponent except 2's : 3 / 3 = 1.00000 Average absolute exponent except 2's: 11 / 3 = 3.66667 Scale is weakly epimorphic with val: <6 11 16 22| Scale is weakly epimorphic with val: <6 11 19 22| Scale is weakly epimorphic with val: <7 11 15 19| Scale is weakly epimorphic with val: <7 11 15 22| Scale is JI-epimorphic with val: <7 11 17 18| Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 11 18 19| Scale is weakly epimorphic with val: <7 11 18 22| Scale is weakly epimorphic with val: <7 12 15 22| Scale is weakly epimorphic with val: <7 12 17 18| Scale is weakly epimorphic with val: <7 12 18 22| Scale is weakly epimorphic with val: <8 11 15 20| Scale is weakly epimorphic with val: <8 12 16 21|
FIT/MODE
3: 0 1 2 N G T3 SD: 31.6589 c. M: 48.7704 c. 4: 0 1 3 N G T3 SD: 29.7139 c. M: 48.7704 c. 6: 1 1 4 N M DE S SD: 24.4982 c. M:-34.2371 c. 7: 1 1 5 N M DE S SD: 12.9439 c. M:-22.3789 c. 8: 1 1 6 N M DE S SD: 12.2754 c. M: 16.4378 c. 10: 1 2 7 N T3 SD: 4.9233 c. M:-8.4644 c. 11: 1 2 8 N T3 SD: 3.5780 c. M: 5.1186 c. 21: 2 4 15 N T3 SD: 1.0970 c. M:-1.3495 c. 32: 3 6 23 N T3 SD: 1.3019 c. M: 2.0787 c. 49: 5 9 35 N T3 SD: 1.4172 c. M:-2.0505 c. 50: 5 9 36 N T3 SD: 1.0502 c. M: 1.4965 c. 53: 5 10 38 N T3 SD: 1.0306 c. M: 1.7850 c. 60: 6 11 43 N T3 SD: 0.6045 c. M:-1.0341 c. 71: 7 13 51 N T3 SD: 0.4240 c. M: 0.6547 c. 81: 8 15 58 N T3 SD: 0.3641 c. M:-0.4711 c. 92: 9 17 66 N T3 SD: 0.1173 c. M: 0.1973 c. 173: 17 32 124 N T3 SD: 0.1189 c. M:-0.1705 c. 205: 20 38 147 N T3 SD: 0.1067 c. M: 0.1806 c. 265: 26 49 190 N T3 SD: 0.0547 c. M:-0.0944 c. 357: 35 66 256 N T3 SD: 0.0424 c. M:-0.0576 c. 378: 37 70 271 N T3 SD: 0.0217 c. M:-0.0319 c. 470: 46 87 337 N T3 SD: 0.0165 c. M: 0.0256 c. 735: 72 136 527 N T3 SD: 0.0107 c. M:-0.0177 c. 1113: 109 206 798 N T3 SD: 0.0050 c. M:-0.0070 c. 1583: 155 293 1135 N T3 SD: 0.0025 c. M: 0.0041 c. 2318: 227 429 1662 N T3 SD: 0.0017 c. M:-0.0028 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: 97.0207 cents 6 x 7:8 S SD: 62.9609 cents 7 x 8:9 S SD: 55.0105 cents 8 x 9:11 SD: 41.2374 cents 9 x 10:12 S SD: 20.7273 cents 10 x 11:13 SD: 24.9991 cents 11 x 12:15 S SD: 20.0469 cents 12 x 13:16 SD: 1.1882 cents 13 x 14:17 SD: 17.9594 cents 14 x 15:19 SD: 18.7180 cents 15 x 16:20 S SD: 14.6089 cents 16 x 17:21 SD: 22.5770 cents 17 x 18:23 SD: 24.5067 cents 18:19:20:24 S SD: 20.3537 cents 19:20:21:25 SD: 18.7757 cents 20:21:22:27 SD: 16.0396 cents 21:22:23:28 SD: 11.9389 cents 22:23:24:29 SD: 11.9247 cents 23:24:25:31 SD: 10.4478 cents 24:25:26:32 SD: 7.3435 cents 32:33:35:43 SD: 6.6929 cents 33:34:36:44 SD: 3.3721 cents 36:37:39:48 SD: 0.9088 cents 105:108:114:140 SD: 0.4748 cents 141:145:153:188 SD: 0.1895 cents 177:182:192:236 SD: 0.1856 cents 318:327:345:424 SD: 0.1577 cents