Scala analysis: 448_D14
Diatonic tetrachord 135/128 * 64/57 * 152/135
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/128 92.178716 major chroma, major limma 2: 45/38 292.710699 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 152/135 205.3343 1: 135/128 92.1787 major chroma, major limma 2: 64/57 200.5320 3: 152/135 205.3343
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 135/128 92.179 cents major chroma, major limma 1: 1 64/57 200.532 cents 1: 1 152/135 205.334 cents 2: 1 45/38 292.711 cents 2: 1 19/16 297.513 cents 19th harmonic 2: 1 512/405 405.866 cents narrow diminished fourth 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 : 92.2 292.7 498.0 92.2 : 200.5 405.9 498.0 292.7: 205.3 297.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 205.3343 cents 19456/18225, 113.1556 cents 135/128, 92.1787 cents 2: 292.7107 .. 405.8663 cents 19456/18225, 113.1556 cents 6075/5776, 87.3764 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 152/135, 205.3343 cents Average / Smallest step : 1.801012 Largest / Average step : 1.236842 Largest / Smallest step : 2.227567 Median interval of one step : 64/57, 200.5320 cents, amount: 1 Least squares average step : 155.12394 cents, oct.: 465.37181 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1140-tone equal temperament with octave 4/3 degrees: 211 670 1140 Least number of segments generator : 571 of 249.459 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 751 of 328.098 cents and inv. generated superset size: 62 = 59 more = 2066.667% 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 87.37640 cents Scale diversity : 1.037764 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.545601 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 : 361/360, 4.8023 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 108.3533 cents: 1 -- Rational properties -- Prime limit : 19 Odd number limit : 405 (O: 135 U: 405) Highest odd numerator or denominator: 135 Scale harmonicity : 0.016619 Average absolute harmonicity : 0.094121 Specific harmonicity : 0.082794 Fundamental : 1/7296, -12.8329 octaves, 0.0359 Hz. Guide tone : 540, 9.0768 octaves, 141277.805 Hz. Exponens Consonantiae : 3.939840E+06, 21.90971 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 176.5, average 58.83333 Mersenne's string divisions : 152803 Sum of van Prooijen's expressibility: 4.26067, average 1.42022 Sum of Tenney's harmonic distance : 8.54972, average 2.84991 Vogel's harmonic complexity : 28.00000 Wille's k value : 3847 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 33.09901, average 5.51650 Lattice compactness (without 2's) : 15.46571, average 2.57762 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -7 .. 2 -2.00000 10 3: -1 .. 3 1.33333 6 1 5: 0 .. 1 0.66667 2 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 5 / 3 = 1.66667 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 28| Scale is weakly epimorphic with val: <6 10 15 31| Scale is weakly epimorphic with val: <6 10 15 34| Scale is weakly epimorphic with val: <6 10 19 30| Scale is weakly epimorphic with val: <6 11 17 30| Scale is weakly epimorphic with val: <7 10 18 28| Scale is weakly epimorphic with val: <7 11 15 29| Scale is weakly epimorphic with val: <7 11 15 32| Scale is JI-epimorphic with val: <7 11 17 30| Scale is weakly epimorphic with val: <7 11 17 33| Scale is weakly epimorphic with val: <7 11 18 29| Scale is weakly epimorphic with val: <7 11 18 32| Scale is weakly epimorphic with val: <7 12 16 29| Scale is weakly epimorphic with val: <7 12 16 32| Scale is weakly epimorphic with val: <7 12 17 31| Scale is weakly epimorphic with val: <8 11 18 29| Scale is weakly epimorphic with val: <8 12 16 29| Scale is weakly epimorphic with val: <8 12 19 32|
FIT/MODE
3: 1 1 1 SP B ME I SD: 48.2970 c. M:-73.8363 c. 4: 1 1 2 P M ME S SD: 31.3797 c. M: 43.6882 c. 5: 1 2 2 SP M ME S SD: 5.5563 c. M:-7.4303 c. 12: 2 5 5 SP M DE S SD: 5.4431 c. M: 9.1712 c. 17: 3 7 7 SP M DE S SD: 2.4804 c. M: 4.2884 c. 22: 4 9 9 SP M DE S SD: 1.3121 c. M: 1.6251 c. 27: 5 11 11 SP M DE S SD: 1.4016 c. M:-2.4271 c. 49: 9 20 20 SP M DE S SD: 1.2512 c. M:-2.0506 c. 60: 11 24 25 SP T3 SD: 1.3576 c. M: 2.1844 c. 65: 12 26 27 SP T3 SD: 0.9025 c. M: 1.5459 c. 70: 13 28 29 SP T3 SD: 0.6046 c. M: 0.9986 c. 75: 14 30 31 SP T3 SD: 0.5473 c. M:-0.7897 c. 87: 16 35 36 SP T3 SD: 0.5504 c. M: 0.7533 c. 92: 17 37 38 SP T3 SD: 0.2356 c. M: 0.3799 c. 97: 18 39 40 SP T3 SD: 0.1421 c. M:-0.2420 c. 189: 35 76 78 SP T3 SD: 0.1238 c. M: 0.2081 c. 211: 39 85 87 SP T3 SD: 0.0720 c. M: 0.1230 c. 216: 40 87 89 SP T3 SD: 0.0762 c. M:-0.1213 c. 308: 57 124 127 SP T3 SD: 0.0170 c. M: 0.0284 c. 735: 136 296 303 SP T3 SD: 0.0170 c. M: 0.0235 c. 832: 154 335 343 SP T3 SD: 0.0074 c. M:-0.0105 c. 1140: 211 459 470 SP T3 SD: 0.0019 c. M:-0.0033 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 5 x S SD: 93.6030 cents 5 x 6:7 S SD: 43.7622 cents 6 x 7:8 S SD: 12.9199 cents 7 x 8:9 S SD: 44.0194 cents 8 x 9:11 SD: 51.7773 cents 9:10:11:12 H SD: 35.1700 cents 10:11:12:13 H SD: 29.3457 cents 11:12:13:15 SD: 23.4362 cents 12:13:14:16 S SD: 17.7015 cents 15:16:18:20 S SD: 10.0450 cents 17:18:20:23 SD: 9.5077 cents 18:19:21:24 SD: 8.6263 cents 21:22:25:28 SD: 4.9328 cents 33:35:39:44 SD: 3.4337 cents 39:41:46:52 SD: 2.9669 cents 54:57:64:72 SD: 0.6714 cents 147:155:174:196 SD: 0.2995 cents 201:212:238:268 SD: 0.0673 cents