Scala analysis: 306_C23
Chromatic tetrachord 16/15 * 75/64 * 16/15, Helmholtz
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 16/15 111.7313 minor diatonic semitone 2: 75/64 274.5824 classic augmented second 3: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 75/64 274.582 cents classic augmented second 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 2 5/4 386.314 cents major third Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 111.7 386.3 498.0 111.7: 274.6 386.3 498.0 386.3: 111.7 223.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 274.5824 cents 1125/1024, 162.8511 cents 16/15, 111.7313 cents 2: 223.4626 .. 386.3137 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 75/64, 274.5824 cents Average / Smallest step : 1.485842 Largest / Average step : 1.653962 Largest / Smallest step : 2.457525 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Most common interval of one step : 16/15, 111.7313 cents, amount: 2 Least squares average step : 169.89241 cents, oct.: 509.67722 cents Scale is not proper Scale has Myhill's property chromas: 1125/1024, 162.8511 cents and 16875/16384, 51.1199 cents, ratio: 3.185673 generators: 1 of 111.73129 cents and 2 of 386.31371 cents ET pair of linear temperament : 98&214 Scale is distributional even Scale is a mode of a 263-tone equal temperament with octave 4/3 degrees: 59 204 263 generators: 59 and 204 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Scale is a Constant Structure, by a margin of 51.11986 cents Scale diversity : 1.121851 Lumma stability : 0.448679 Lumma impropriety factor : 0.102641 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 16875/16384, 51.1199 cents Most common intervals : 16/15, 111.7313 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 5 Odd number limit : 225 (O: 75 U: 225) Highest odd numerator or denominator: 15 Scale harmonicity : 0.046584 Average absolute harmonicity : 0.136621 Specific harmonicity : 0.231660 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 80, 6.3219 octaves, 20930.045 Hz. Exponens Consonantiae : 4.800000E+03, 12.22882 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 23.5, average 7.83333 Mersenne's string divisions : 1953 Sum of van Prooijen's expressibility: 2.35218, average 0.78406 Sum of Tenney's harmonic distance : 4.76042, average 1.58681 Vogel's harmonic complexity : 9.33333 Wille's k value : 37 Wilson's harmonic complexity : 13 Rectangular lattice diameter : 3 Triangular lattice diameter : 3 Lattice compactness : 21.59661, average 3.59943 Lattice compactness (without 2's) : 8.06450, average 1.34408 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.33333 8 3: -1 .. 0 -0.66667 2 1 5: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <7 11 15| Scale is JI-epimorphic with val: <7 11 16| Scale is weakly epimorphic with val: <7 11 18| Scale is weakly epimorphic with val: <7 11 19|
FIT/MODE
3: 1 1 1 SP B ME I SD: 44.3225 c. M: 54.2837 c. 4: 1 2 1 P M ME I SD: 10.4348 c. M: 12.7800 c. 5: 1 3 1 N M DE I SD: 9.8978 c. M: 12.1223 c. 9: 2 5 2 N M DE I SD: 0.8611 c. M: 1.0546 c. 31: 7 17 7 N M DE I SD: 0.5964 c. M: 0.7305 c. 40: 9 22 9 N M DE I SD: 0.2685 c. M: 0.3288 c. 49: 11 27 11 N M DE I SD: 0.0610 c. M: 0.0747 c. 107: 24 59 24 N M DE I SD: 0.0165 c. M: 0.0203 c. 156: 35 86 35 N M DE I SD: 0.0078 c. M:-0.0096 c. 263: 59 145 59 N M DE I SD: 0.0021 c. M: 0.0026 c. 419: 94 231 94 N M DE I SD: 0.0016 c. M: 0.0020 c. 682: 153 376 153 N M DE I SD: 0.0002 c. M: 0.0002 c. 2309: 518 1273 518 N M DE I SD: 0.0001 c. M: 0.0001 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: 0.0000 cents 5 x 6:7 S SD: 55.0665 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 64.5080 cents 8:9:10:11 H SD: 35.4885 cents 9:10:11:12 H SD: 26.8912 cents 10:11 x 13 SD: 34.4934 cents 11:12:14:15 S SD: 21.0829 cents 12:13:15:16 SD: 8.9471 cents 15:16:19:20 SD: 7.6435 cents 27:29:34:36 SD: 5.8384 cents 28:30:35:37 SD: 5.7788 cents 32:34:40:43 SD: 5.0269 cents 33:35:41:44 SD: 4.8082 cents 43:46:54:57 SD: 4.6151 cents 44:47:55:59 SD: 3.3706 cents 45:48:56:60 S SD: 2.5705 cents 48:51:60:64 SD: 2.2586 cents 60:64:75:80 SD: 0.0000 cents