Scala analysis: 441_D12
Diatonic tetrachord 10/9 * 297/280 * 112/99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 33/28 284.447037 undecimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 112/99 213.5980 1: 10/9 182.4037 minor whole tone 2: 297/280 102.0433 3: 112/99 213.5980
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 297/280 102.043 cents 1: 1 10/9 182.404 cents minor whole tone 1: 1 112/99 213.598 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 1 6/5 315.641 cents minor third 2: 1 1120/891 396.002 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 : 182.4 284.4 498.0 182.4: 102.0 315.6 498.0 284.4: 213.6 396.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 102.0433 .. 213.5980 cents 31360/29403, 111.5546 cents 297/280, 102.0433 cents 2: 284.4470 .. 396.0017 cents 31360/29403, 111.5546 cents 3267/3136, 70.8491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 297/280, 102.0433 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 112/99, 213.5980 cents Average / Smallest step : 1.626907 Largest / Average step : 1.286618 Largest / Smallest step : 2.093209 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 160.38806 cents, oct.: 481.16417 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 942-tone equal temperament with octave 4/3 degrees: 345 538 942 Least number of segments generator : 473 of 250.080 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 799 of 422.439 cents and inv. generated superset size: 26 = 23 more = 866.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 70.84907 cents Scale diversity : 1.203387 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.552030 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 : 56/55, 31.1943 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 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% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 11 Odd number limit : 891 (O: 297 U: 891) Highest odd numerator or denominator: 33 Scale harmonicity : 0.021337 Average absolute harmonicity : 0.107666 Specific harmonicity : 0.110903 Fundamental : 1/252, -7.9773 octaves, 1.0382 Hz. Guide tone : 660, 9.3663 octaves, 172672.873 Hz. Exponens Consonantiae : 1.663200E+05, 17.34360 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 43.5, average 14.50000 Mersenne's string divisions : 8113 Sum of van Prooijen's expressibility: 2.94988, average 0.98329 Sum of Tenney's harmonic distance : 5.99910, average 1.99970 Vogel's harmonic complexity : 16.33333 Wille's k value : 148 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 18.33635, average 3.05606 Lattice compactness (without 2's) : 12.29592, average 2.04932 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -2 .. 1 -0.66667 4 1 5: 0 .. 1 0.33333 1 1 7: -1 .. 0 -0.33333 1 11: 0 .. 1 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: <6 10 15 18 23| Scale is weakly epimorphic with val: <6 10 15 19 24| Scale is weakly epimorphic with val: <6 10 15 20 25| Scale is weakly epimorphic with val: <6 10 15 21 26| Scale is weakly epimorphic with val: <6 10 15 22 27| Scale is weakly epimorphic with val: <6 10 17 18 24| Scale is weakly epimorphic with val: <6 10 17 18 27| Scale is weakly epimorphic with val: <6 10 17 19 25| Scale is weakly epimorphic with val: <6 10 17 20 23| Scale is weakly epimorphic with val: <6 10 17 20 26| Scale is weakly epimorphic with val: <6 10 17 21 24| Scale is weakly epimorphic with val: <6 10 17 21 27| Scale is weakly epimorphic with val: <6 10 17 22 25| Scale is weakly epimorphic with val: <6 10 18 18 23| Scale is weakly epimorphic with val: <6 10 18 19 24| Scale is weakly epimorphic with val: <6 10 18 20 25| Scale is weakly epimorphic with val: <6 10 18 21 26| Scale is weakly epimorphic with val: <6 10 18 22 27| Scale is weakly epimorphic with val: <6 11 15 19 23| Scale is weakly epimorphic with val: <6 11 15 20 24| Scale is weakly epimorphic with val: <6 11 15 21 25| Scale is weakly epimorphic with val: <6 11 15 22 26| Scale is weakly epimorphic with val: <6 11 18 19 23| Scale is weakly epimorphic with val: <6 11 18 20 24| Scale is weakly epimorphic with val: <6 11 18 21 25| Scale is weakly epimorphic with val: <6 11 18 22 26| Scale is weakly epimorphic with val: <6 11 19 19 25| Scale is weakly epimorphic with val: <6 11 19 20 23| Scale is weakly epimorphic with val: <6 11 19 20 26| Scale is weakly epimorphic with val: <6 11 19 21 24| Scale is weakly epimorphic with val: <6 11 19 21 27| Scale is weakly epimorphic with val: <6 11 19 22 25| Scale is weakly epimorphic with val: <7 10 15 18 25| Scale is weakly epimorphic with val: <7 10 15 19 26| Scale is weakly epimorphic with val: <7 10 15 20 27| Scale is weakly epimorphic with val: <7 10 16 18 24| Scale is weakly epimorphic with val: <7 10 16 18 27| Scale is weakly epimorphic with val: <7 10 16 19 25| Scale is weakly epimorphic with val: <7 10 16 20 23| Scale is weakly epimorphic with val: <7 10 16 20 26| Scale is weakly epimorphic with val: <7 10 16 21 24| Scale is weakly epimorphic with val: <7 10 16 21 27| Scale is weakly epimorphic with val: <7 10 16 22 25| Scale is weakly epimorphic with val: <7 10 18 18 25| Scale is weakly epimorphic with val: <7 10 18 19 26| Scale is weakly epimorphic with val: <7 10 18 20 27| Scale is JI-epimorphic with val: <7 11 16 18 23| Scale is weakly epimorphic with val: <7 11 16 18 26| Scale is JI-epimorphic with val: <7 11 16 19 24| Scale is weakly epimorphic with val: <7 11 16 19 27| Scale is JI-epimorphic with val: <7 11 16 20 25| Scale is weakly epimorphic with val: <7 11 16 21 23| Scale is JI-epimorphic with val: <7 11 16 21 26| Scale is weakly epimorphic with val: <7 11 16 22 24| Scale is JI-epimorphic with val: <7 11 16 22 27| Scale is weakly epimorphic with val: <7 11 17 18 25| Scale is weakly epimorphic with val: <7 11 17 19 23| Scale is weakly epimorphic with val: <7 11 17 19 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 25| Scale is weakly epimorphic with val: <7 11 17 22 23| Scale is weakly epimorphic with val: <7 11 17 22 26| Scale is weakly epimorphic with val: <7 11 19 19 24| Scale is weakly epimorphic with val: <7 11 19 19 27| Scale is weakly epimorphic with val: <7 11 19 20 25| Scale is weakly epimorphic with val: <7 11 19 21 23| Scale is weakly epimorphic with val: <7 11 19 21 26| Scale is weakly epimorphic with val: <7 11 19 22 24| Scale is weakly epimorphic with val: <7 11 19 22 27| Scale is weakly epimorphic with val: <7 12 15 18 23| Scale is weakly epimorphic with val: <7 12 15 19 24| Scale is weakly epimorphic with val: <7 12 15 20 25| Scale is weakly epimorphic with val: <7 12 15 21 26| Scale is weakly epimorphic with val: <7 12 15 22 27| Scale is weakly epimorphic with val: <7 12 18 18 23| Scale is weakly epimorphic with val: <7 12 18 19 24| Scale is weakly epimorphic with val: <7 12 18 20 25| Scale is weakly epimorphic with val: <7 12 18 21 26| Scale is weakly epimorphic with val: <7 12 18 22 27| Scale is weakly epimorphic with val: <8 11 15 18 26| Scale is weakly epimorphic with val: <8 11 15 19 27| Scale is weakly epimorphic with val: <8 11 17 18 24| Scale is weakly epimorphic with val: <8 11 17 18 27| Scale is weakly epimorphic with val: <8 11 17 19 25| Scale is weakly epimorphic with val: <8 11 17 20 23| Scale is weakly epimorphic with val: <8 11 17 20 26| Scale is weakly epimorphic with val: <8 11 17 21 24| Scale is weakly epimorphic with val: <8 11 17 21 27| Scale is weakly epimorphic with val: <8 11 17 22 25| Scale is weakly epimorphic with val: <8 11 18 18 26| Scale is weakly epimorphic with val: <8 11 18 19 27| Scale is weakly epimorphic with val: <8 12 15 18 25| Scale is weakly epimorphic with val: <8 12 15 19 26| Scale is weakly epimorphic with val: <8 12 15 20 27| Scale is weakly epimorphic with val: <8 12 18 18 25| Scale is weakly epimorphic with val: <8 12 18 19 26| Scale is weakly epimorphic with val: <8 12 18 20 27| Scale is weakly epimorphic with val: <8 12 19 19 25| Scale is weakly epimorphic with val: <8 12 19 20 23| Scale is weakly epimorphic with val: <8 12 19 20 26| Scale is weakly epimorphic with val: <8 12 19 21 24| Scale is weakly epimorphic with val: <8 12 19 21 27| Scale is weakly epimorphic with val: <8 12 19 22 25|
FIT/MODE
3: 1 1 1 SP B ME I SD: 29.0559 c. M:-47.5830 c. 5: 2 1 2 SP M ME I SD: 12.7737 c. M:-16.8143 c. 9: 3 2 4 SP T3 SD: 10.4680 c. M: 16.3887 c. 11: 4 2 5 SP T3 SD: 7.4199 c. M: 12.7861 c. 14: 5 3 6 SP T3 SD: 2.6171 c. M: 4.5305 c. 16: 6 3 7 SP T3 SD: 3.5355 c. M:-4.3632 c. 19: 7 4 8 SP T3 SD: 2.3345 c. M:-3.8948 c. 30: 11 6 13 SP T3 SD: 1.2885 c. M: 2.2215 c. 44: 16 9 19 SP T3 SD: 1.1303 c. M: 1.4669 c. 49: 18 10 21 SP T3 SD: 0.3300 c. M:-0.5516 c. 112: 41 23 48 SP T3 SD: 0.0992 c. M:-0.1501 c. 161: 59 33 69 SP T3 SD: 0.1073 c. M:-0.1501 c. 254: 93 52 109 SP T3 SD: 0.0801 c. M: 0.1300 c. 303: 111 62 130 SP T3 SD: 0.0563 c. M: 0.0847 c. 366: 134 75 157 SP T3 SD: 0.0428 c. M: 0.0594 c. 415: 152 85 178 SP T3 SD: 0.0144 c. M: 0.0213 c. 527: 193 108 226 SP T3 SD: 0.0098 c. M:-0.0151 c. 942: 345 193 404 SP T3 SD: 0.0009 c. M:-0.0013 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 7:8 x 9 S SD: 39.8203 cents 8:9 x 11 SD: 28.7251 cents 9:10:11:12 H SD: 20.9870 cents 10:11:12:13 H SD: 18.8473 cents 11:12:13:15 SD: 16.8175 cents 12:13:14:16 S SD: 15.7412 cents 15:17:18:20 SD: 15.4503 cents 16:18:19:21 SD: 12.3674 cents 17:19:20:23 SD: 9.1373 cents 18:20:21:24 S SD: 5.8587 cents 27:30:32:36 S SD: 3.2293 cents 45:50:53:60 SD: 0.3887 cents 162:180:191:216 SD: 0.2159 cents 207:230:244:276 SD: 0.0845 cents 252:280:297:336 SD: 0.0000 cents