Scala analysis: 447_D14
Diatonic tetrachord 90/83 * 83/76 * 152/135
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 90/83 140.176398 2: 45/38 292.710699 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 152/135 205.3343 1: 90/83 140.1764 2: 83/76 152.5343 3: 152/135 205.3343
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 90/83 140.176 cents 1: 1 83/76 152.534 cents 1: 1 152/135 205.334 cents 2: 1 45/38 292.711 cents 2: 1 304/249 345.511 cents 2: 1 166/135 357.869 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 : 140.2 292.7 498.0 140.2: 152.5 357.9 498.0 292.7: 205.3 345.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 140.1764 .. 205.3343 cents 6308/6075, 65.1579 cents 90/83, 140.1764 cents 2: 292.7107 .. 357.8686 cents 6308/6075, 65.1579 cents 6075/5776, 87.3764 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 90/83, 140.1764 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 152/135, 205.3343 cents Average / Smallest step : 1.184329 Largest / Average step : 1.236842 Largest / Smallest step : 1.464828 Median interval of one step : 83/76, 152.5343 cents, amount: 1 Least squares average step : 158.55234 cents, oct.: 475.65703 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1613-tone equal temperament with octave 4/3 degrees: 454 948 1613 Least number of segments generator : 807 of 249.177 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1151 of 355.394 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 87.37640 cents Scale diversity : 1.354443 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.738345 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 : 6889/6840, 12.3579 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle 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 52.8000 cents: 2 -- Rational properties -- Prime limit : 83 Odd number limit : 249 (O: 83 U: 249) Highest odd numerator or denominator: 83 Scale harmonicity : 0.019415 Fundamental : 1/9462, -13.2079 octaves, 0.0277 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 1.703160E+06, 20.69978 octaves Euler's gradus suavitatis : 114 Sum of Mann's harmonic distance : 131.5, average 43.83333 Mersenne's string divisions : 100513 Sum of van Prooijen's expressibility: 4.04941, average 1.34980 Sum of Tenney's harmonic distance : 8.18550, average 2.72850 Vogel's harmonic complexity : 79.00000 Wille's k value : 5602 Wilson's harmonic complexity : 116 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 17.35614, average 2.89269 Lattice compactness (without 2's) : 13.16446, average 2.19408 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 2 1.00000 5 1 5: 0 .. 1 0.66667 2 19: -1 .. 0 -0.33333 1 1 83: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 3 / 3 = 1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 17 28 45| Scale is weakly epimorphic with val: <6 10 18 29 46| Scale is weakly epimorphic with val: <6 10 19 30 47| Scale is weakly epimorphic with val: <6 11 15 28 47| Scale is weakly epimorphic with val: <6 11 16 29 45| Scale is weakly epimorphic with val: <6 11 17 30 46| Scale is weakly epimorphic with val: <6 11 18 31 47| Scale is weakly epimorphic with val: <6 11 19 32 45| Scale is weakly epimorphic with val: <7 10 18 28 46| Scale is weakly epimorphic with val: <7 10 19 29 47| Scale is weakly epimorphic with val: <7 11 15 28 46| Scale is weakly epimorphic with val: <7 11 15 29 45| Scale is weakly epimorphic with val: <7 11 15 31 46| Scale is weakly epimorphic with val: <7 11 15 32 45| Scale is weakly epimorphic with val: <7 11 15 34 46| Scale is weakly epimorphic with val: <7 11 16 29 47| Scale is weakly epimorphic with val: <7 11 16 30 46| Scale is weakly epimorphic with val: <7 11 16 32 47| Scale is weakly epimorphic with val: <7 11 16 33 46| Scale is weakly epimorphic with val: <7 11 17 28 47| Scale is JI-epimorphic with val: <7 11 17 30 45| Scale is weakly epimorphic with val: <7 11 17 31 47| Scale is weakly epimorphic with val: <7 11 17 33 45| Scale is weakly epimorphic with val: <7 11 17 34 47| Scale is weakly epimorphic with val: <7 11 18 28 46| Scale is weakly epimorphic with val: <7 11 18 29 45| Scale is JI-epimorphic with val: <7 11 18 31 46| Scale is weakly epimorphic with val: <7 11 18 32 45| Scale is weakly epimorphic with val: <7 11 18 34 46| Scale is weakly epimorphic with val: <7 11 19 29 47| Scale is weakly epimorphic with val: <7 11 19 30 46| Scale is JI-epimorphic with val: <7 11 19 32 47| Scale is weakly epimorphic with val: <7 11 19 33 46| Scale is weakly epimorphic with val: <7 12 15 29 45| Scale is weakly epimorphic with val: <7 12 16 30 46| Scale is weakly epimorphic with val: <7 12 17 30 45| Scale is weakly epimorphic with val: <7 12 17 31 47| Scale is weakly epimorphic with val: <7 12 17 33 45| Scale is weakly epimorphic with val: <7 12 18 28 46| Scale is weakly epimorphic with val: <7 12 18 31 46| Scale is weakly epimorphic with val: <7 12 18 32 45| Scale is weakly epimorphic with val: <7 12 18 34 46| Scale is weakly epimorphic with val: <7 12 19 29 47| Scale is weakly epimorphic with val: <7 12 19 32 47| Scale is weakly epimorphic with val: <7 12 19 33 46| Scale is weakly epimorphic with val: <8 11 17 28 46| Scale is weakly epimorphic with val: <8 11 18 28 45| Scale is weakly epimorphic with val: <8 11 18 29 47| Scale is weakly epimorphic with val: <8 11 18 31 45| Scale is weakly epimorphic with val: <8 11 18 34 45| Scale is weakly epimorphic with val: <8 11 19 29 46| Scale is weakly epimorphic with val: <8 11 19 30 45| Scale is weakly epimorphic with val: <8 11 19 32 46| Scale is weakly epimorphic with val: <8 12 15 28 45| Scale is weakly epimorphic with val: <8 12 16 29 46| Scale is weakly epimorphic with val: <8 12 16 30 45| Scale is weakly epimorphic with val: <8 12 16 33 45| Scale is weakly epimorphic with val: <8 12 17 28 46| Scale is weakly epimorphic with val: <8 12 17 30 47| Scale is weakly epimorphic with val: <8 12 17 31 46| Scale is weakly epimorphic with val: <8 12 17 34 46| Scale is weakly epimorphic with val: <8 12 18 29 47| Scale is weakly epimorphic with val: <8 12 18 31 45| Scale is weakly epimorphic with val: <8 12 18 32 47| Scale is weakly epimorphic with val: <8 12 19 32 46|
FIT/MODE
3: 1 1 1 SP B ME I SD: 27.1640 c. M:-39.3193 c. 4: 1 1 2 P M ME S SD: 26.7959 c. M: 43.6882 c. 5: 1 2 2 SP M ME S SD: 23.6863 c. M: 40.5674 c. 7: 2 2 3 SP M ME S SD: 4.8419 c. M: 8.1136 c. 15: 4 5 6 SP T3 SD: 5.5270 c. M: 7.3644 c. 17: 5 5 7 SP M DE S SD: 3.6446 c. M:-6.3074 c. 22: 6 7 9 SP T3 SD: 2.6715 c. M: 4.3459 c. 29: 8 9 12 SP T3 SD: 1.6655 c. M: 2.7847 c. 36: 10 11 15 SP T3 SD: 1.6455 c. M: 2.1844 c. 39: 11 12 16 SP T3 SD: 0.6069 c. M:-1.0081 c. 46: 13 14 19 SP T3 SD: 0.3981 c. M:-0.5754 c. 85: 24 26 35 SP T3 SD: 0.2982 c. M:-0.4481 c. 114: 32 35 47 SP T3 SD: 0.2161 c. M: 0.3743 c. 153: 43 47 63 SP T3 SD: 0.1890 c. M:-0.2569 c. 160: 45 49 66 SP T3 SD: 0.0860 c. M: 0.1093 c. 199: 56 61 82 SP T3 SD: 0.0647 c. M:-0.1097 c. 245: 69 75 101 SP T3 SD: 0.0526 c. M:-0.0893 c. 359: 101 110 148 SP T3 SD: 0.0341 c. M: 0.0579 c. 405: 114 124 167 SP T3 SD: 0.0204 c. M: 0.0324 c. 604: 170 185 249 SP T3 SD: 0.0084 c. M:-0.0144 c. 1009: 284 309 416 SP T3 SD: 0.0046 c. M:-0.0067 c. 1613: 454 494 665 SP T3 SD: 0.0032 c. M:-0.0049 c. 2377: 669 728 980 SP T3 SD: 0.0021 c. M: 0.0030 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 8:9 x 11 SD: 41.5331 cents 9:10:11:12 H SD: 23.0336 cents 10:11:12:13 H SD: 18.4493 cents 11:12:13:15 SD: 13.4798 cents 12:13:14:16 S SD: 8.6298 cents 21:23:25:28 SD: 6.5264 cents 27:29:32:36 SD: 5.5086 cents 33:36:39:44 SD: 3.6770 cents 48:52:57:64 SD: 1.6877 cents 60:65:71:80 SD: 0.6846 cents 141:153:167:188 SD: 0.4191 cents 201:218:238:268 SD: 0.1427 cents 450:488:533:600 SD: 0.1274 cents 462:501:547:616 SD: 0.1186 cents 510:553:604:680 SD: 0.0518 cents