Scala analysis: 439_D12
Diatonic tetrachord 99/94 * 47/42 * 112/99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99/94 89.721322 2: 33/28 284.447037 undecimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 112/99 213.5980 1: 99/94 89.7213 2: 47/42 194.7257 3: 112/99 213.5980
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 99/94 89.721 cents 1: 1 47/42 194.726 cents 1: 1 112/99 213.598 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 1 56/47 303.319 cents 2: 1 376/297 408.324 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 : 89.7 284.4 498.0 89.7 : 194.7 408.3 498.0 284.4: 213.6 303.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.7213 .. 213.5980 cents 10528/9801, 123.8766 cents 99/94, 89.7213 cents 2: 284.4470 .. 408.3237 cents 10528/9801, 123.8766 cents 3267/3136, 70.8491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 99/94, 89.7213 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 112/99, 213.5980 cents Average / Smallest step : 1.850341 Largest / Average step : 1.286618 Largest / Smallest step : 2.380682 Median interval of one step : 47/42, 194.7257 cents, amount: 1 Least squares average step : 153.76789 cents, oct.: 461.30366 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 977-tone equal temperament with octave 4/3 degrees: 176 558 977 Least number of segments generator : 489 of 249.277 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 595 of 303.313 cents and inv. generated superset size: 21 = 18 more = 700.000% 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 70.84907 cents Scale diversity : 1.070951 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.502548 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 : 1568/1551, 18.8722 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 105.0044 cents: 1 -- Rational properties -- Prime limit : 47 Odd number limit : 297 (O: 99 U: 297) Highest odd numerator or denominator: 99 Scale harmonicity : 0.024711 Fundamental : 1/3948, -11.9469 octaves, 0.0663 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 1.563408E+06, 20.57626 octaves Euler's gradus suavitatis : 73 Sum of Mann's harmonic distance : 130.5, average 43.50000 Mersenne's string divisions : 82411 Sum of van Prooijen's expressibility: 3.99127, average 1.33042 Sum of Tenney's harmonic distance : 8.01362, average 2.67121 Vogel's harmonic complexity : 50.00000 Wille's k value : 2326 Wilson's harmonic complexity : 74 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 18.11267, average 3.01878 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.33333 5 3: -1 .. 2 0.66667 4 1 7: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 1 47: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 18 23 39| Scale is weakly epimorphic with val: <6 10 18 23 42| Scale is weakly epimorphic with val: <6 10 18 27 38| Scale is weakly epimorphic with val: <6 10 19 24 37| Scale is weakly epimorphic with val: <6 10 19 24 40| Scale is weakly epimorphic with val: <6 10 19 24 43| Scale is weakly epimorphic with val: <6 10 20 25 38| Scale is weakly epimorphic with val: <6 10 20 25 41| Scale is weakly epimorphic with val: <6 10 20 26 37| Scale is weakly epimorphic with val: <6 10 21 26 39| Scale is weakly epimorphic with val: <6 10 21 26 42| Scale is weakly epimorphic with val: <6 10 21 27 38| Scale is weakly epimorphic with val: <6 10 22 27 37| Scale is weakly epimorphic with val: <6 10 22 27 40| Scale is weakly epimorphic with val: <6 10 22 27 43| Scale is weakly epimorphic with val: <6 11 18 24 37| Scale is weakly epimorphic with val: <6 11 18 27 40| Scale is weakly epimorphic with val: <6 11 19 23 37| Scale is weakly epimorphic with val: <6 11 19 23 40| Scale is weakly epimorphic with val: <6 11 19 23 43| Scale is weakly epimorphic with val: <6 11 19 25 38| Scale is weakly epimorphic with val: <6 11 20 24 38| Scale is weakly epimorphic with val: <6 11 20 24 41| Scale is weakly epimorphic with val: <6 11 20 26 39| Scale is weakly epimorphic with val: <6 11 21 24 37| Scale is weakly epimorphic with val: <6 11 21 25 39| Scale is weakly epimorphic with val: <6 11 21 25 42| Scale is weakly epimorphic with val: <6 11 21 27 40| Scale is weakly epimorphic with val: <6 11 22 25 38| Scale is weakly epimorphic with val: <6 11 22 26 37| Scale is weakly epimorphic with val: <6 11 22 26 40| Scale is weakly epimorphic with val: <6 11 22 26 43| Scale is weakly epimorphic with val: <7 10 18 25 39| Scale is weakly epimorphic with val: <7 10 18 25 42| Scale is weakly epimorphic with val: <7 10 18 27 37| Scale is weakly epimorphic with val: <7 10 19 26 37| Scale is weakly epimorphic with val: <7 10 19 26 40| Scale is weakly epimorphic with val: <7 10 19 26 43| Scale is weakly epimorphic with val: <7 10 20 27 38| Scale is weakly epimorphic with val: <7 10 20 27 41| Scale is weakly epimorphic with val: <7 10 21 27 37| Scale is JI-epimorphic with val: <7 11 18 23 37| Scale is weakly epimorphic with val: <7 11 18 23 40| Scale is weakly epimorphic with val: <7 11 18 23 43| Scale is weakly epimorphic with val: <7 11 18 25 38| Scale is weakly epimorphic with val: <7 11 18 25 41| Scale is weakly epimorphic with val: <7 11 18 26 37| Scale is weakly epimorphic with val: <7 11 18 26 40| Scale is weakly epimorphic with val: <7 11 18 26 43| Scale is weakly epimorphic with val: <7 11 19 23 39| Scale is weakly epimorphic with val: <7 11 19 23 42| Scale is JI-epimorphic with val: <7 11 19 24 38| Scale is weakly epimorphic with val: <7 11 19 24 41| Scale is weakly epimorphic with val: <7 11 19 26 39| Scale is weakly epimorphic with val: <7 11 19 26 42| Scale is weakly epimorphic with val: <7 11 19 27 38| Scale is weakly epimorphic with val: <7 11 19 27 41| Scale is weakly epimorphic with val: <7 11 20 24 37| Scale is weakly epimorphic with val: <7 11 20 24 40| Scale is weakly epimorphic with val: <7 11 20 24 43| Scale is JI-epimorphic with val: <7 11 20 25 39| Scale is weakly epimorphic with val: <7 11 20 25 42| Scale is weakly epimorphic with val: <7 11 20 27 37| Scale is weakly epimorphic with val: <7 11 20 27 40| Scale is weakly epimorphic with val: <7 11 20 27 43| Scale is weakly epimorphic with val: <7 11 21 23 37| Scale is weakly epimorphic with val: <7 11 21 23 40| Scale is weakly epimorphic with val: <7 11 21 23 43| Scale is weakly epimorphic with val: <7 11 21 25 38| Scale is weakly epimorphic with val: <7 11 21 25 41| Scale is weakly epimorphic with val: <7 11 21 26 37| Scale is JI-epimorphic with val: <7 11 21 26 40| Scale is weakly epimorphic with val: <7 11 21 26 43| Scale is weakly epimorphic with val: <7 11 22 23 39| Scale is weakly epimorphic with val: <7 11 22 23 42| Scale is weakly epimorphic with val: <7 11 22 24 38| Scale is weakly epimorphic with val: <7 11 22 24 41| Scale is weakly epimorphic with val: <7 11 22 26 39| Scale is weakly epimorphic with val: <7 11 22 26 42| Scale is weakly epimorphic with val: <7 11 22 27 38| Scale is JI-epimorphic with val: <7 11 22 27 41| Scale is weakly epimorphic with val: <7 12 18 23 39| Scale is weakly epimorphic with val: <7 12 18 23 42| Scale is weakly epimorphic with val: <7 12 18 24 38| Scale is weakly epimorphic with val: <7 12 18 27 41| Scale is weakly epimorphic with val: <7 12 19 24 37| Scale is weakly epimorphic with val: <7 12 19 24 40| Scale is weakly epimorphic with val: <7 12 19 24 43| Scale is weakly epimorphic with val: <7 12 19 25 39| Scale is weakly epimorphic with val: <7 12 20 23 37| Scale is weakly epimorphic with val: <7 12 20 25 38| Scale is weakly epimorphic with val: <7 12 20 25 41| Scale is weakly epimorphic with val: <7 12 20 26 40| Scale is weakly epimorphic with val: <7 12 21 24 38| Scale is weakly epimorphic with val: <7 12 21 26 39| Scale is weakly epimorphic with val: <7 12 21 26 42| Scale is weakly epimorphic with val: <7 12 21 27 41| Scale is weakly epimorphic with val: <7 12 22 25 39| Scale is weakly epimorphic with val: <7 12 22 27 37| Scale is weakly epimorphic with val: <7 12 22 27 40| Scale is weakly epimorphic with val: <7 12 22 27 43| Scale is weakly epimorphic with val: <8 11 18 26 39| Scale is weakly epimorphic with val: <8 11 18 26 42| Scale is weakly epimorphic with val: <8 11 18 27 38| Scale is weakly epimorphic with val: <8 11 19 27 37| Scale is weakly epimorphic with val: <8 11 19 27 40| Scale is weakly epimorphic with val: <8 11 19 27 43| Scale is weakly epimorphic with val: <8 11 20 26 37| Scale is weakly epimorphic with val: <8 11 21 27 38| Scale is weakly epimorphic with val: <8 12 18 24 37| Scale is weakly epimorphic with val: <8 12 18 25 39| Scale is weakly epimorphic with val: <8 12 18 25 42| Scale is weakly epimorphic with val: <8 12 18 27 40| Scale is weakly epimorphic with val: <8 12 19 25 38| Scale is weakly epimorphic with val: <8 12 19 26 37| Scale is weakly epimorphic with val: <8 12 19 26 40| Scale is weakly epimorphic with val: <8 12 19 26 43| Scale is weakly epimorphic with val: <8 12 20 26 39| Scale is weakly epimorphic with val: <8 12 20 27 38| Scale is weakly epimorphic with val: <8 12 20 27 41| Scale is weakly epimorphic with val: <8 12 21 24 37| Scale is weakly epimorphic with val: <8 12 21 27 40| Scale is weakly epimorphic with val: <8 12 22 25 38|
FIT/MODE
3: 0 1 2 N G T3 SD: 85.7828 c. M: 118.4320 c. 4: 1 1 2 P M ME S SD: 28.6661 c. M: 35.4245 c. 5: 1 2 2 SP M ME S SD: 10.0755 c. M:-14.3800 c. 11: 2 4 5 SP T3 SD: 7.3977 c. M: 12.7861 c. 12: 2 5 5 SP M DE S SD: 5.2292 c. M: 6.7138 c. 16: 3 6 7 SP T3 SD: 3.2595 c. M: 4.2967 c. 21: 4 8 9 SP T3 SD: 2.9714 c. M:-5.1444 c. 23: 4 9 10 SP T3 SD: 2.4700 c. M: 3.1048 c. 28: 5 11 12 SP T3 SD: 0.4613 c. M: 0.7847 c. 77: 14 30 33 SP T3 SD: 0.4883 c. M:-0.8323 c. 100: 18 39 43 SP T3 SD: 0.3269 c. M: 0.5614 c. 105: 19 41 45 SP T3 SD: 0.2473 c. M:-0.4011 c. 133: 24 52 57 SP T3 SD: 0.1231 c. M:-0.1515 c. 161: 29 63 69 SP T3 SD: 0.0869 c. M:-0.1501 c. 261: 47 102 112 SP T3 SD: 0.0736 c. M: 0.1225 c. 289: 52 113 124 SP T3 SD: 0.0833 c. M: 0.1077 c. 366: 66 143 157 SP T3 SD: 0.0579 c. M:-0.0901 c. 394: 71 154 169 SP T3 SD: 0.0239 c. M: 0.0305 c. 422: 76 165 181 SP T3 SD: 0.0184 c. M: 0.0260 c. 555: 100 217 238 SP T3 SD: 0.0158 c. M:-0.0219 c. 816: 147 319 350 SP T3 SD: 0.0140 c. M: 0.0243 c. 949: 171 371 407 SP T3 SD: 0.0123 c. M:-0.0212 c. 977: 176 382 419 SP T3 SD: 0.0028 c. M:-0.0045 c. 2348: 423 918 1007 SP T3 SD: 0.0020 c. M:-0.0031 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: 101.8667 cents 5 x 6:7 S SD: 45.0216 cents 6 x 7:8 S SD: 8.7881 cents 7 x 8:9 S SD: 41.2374 cents 8 x 9:11 SD: 48.2810 cents 9:10:11:12 H SD: 37.3484 cents 10:11:12:13 H SD: 30.8433 cents 11:12:13:15 SD: 24.1456 cents 12:13:14:16 S SD: 17.3057 cents 15:16:18:20 S SD: 12.7258 cents 16:17:19:21 SD: 11.2848 cents 17:18:20:23 SD: 9.0281 cents 18:19:21:24 SD: 5.9999 cents 33:35:39:44 SD: 4.3486 cents 39:41:46:52 SD: 1.1391 cents 96:101:113:128 SD: 0.9490 cents 111:117:131:148 SD: 0.9181 cents 129:136:152:172 SD: 0.6026 cents 168:177:198:224 SD: 0.2081 cents 207:218:244:276 SD: 0.0890 cents 582:613:686:776 SD: 0.0722 cents