Scala analysis: 104_E13
Enharmonic tetrachord 46/45 * 24/23 * 5/4, Ptolemy
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/45 38.050632 23rd-partial chroma 2: 16/15 111.731285 minor diatonic semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 5/4 386.3137 major third 1: 46/45 38.0506 23rd-partial chroma 2: 24/23 73.6807 vicesimotertial minor semitone 3: 5/4 386.3137 major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 46/45 38.051 cents 23rd-partial chroma 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 23/18 424.364 cents vicesimotertial major third 2: 1 30/23 459.994 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 : 38.1 111.7 498.0 38.1 : 73.7 460.0 498.0 111.7: 386.3 424.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 386.3137 cents 225/184, 348.2631 cents 46/45, 38.0506 cents 2: 111.7313 .. 459.9944 cents 225/184, 348.2631 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 46/45, 38.0506 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 4.363002 Largest / Average step : 2.326981 Largest / Smallest step : 10.152623 Median interval of one step : 24/23, 73.6807 cents, amount: 1 Least squares average step : 125.40344 cents, oct.: 376.21033 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2055-tone equal temperament with octave 4/3 degrees: 157 461 2055 Least number of segments generator : 1028 of 249.144 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1079 of 261.504 cents and inv. generated superset size: 35 = 32 more = 1166.667% 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 38.05063 cents Scale diversity : 0.479752 Lumma stability : 0.152800 Lumma impropriety factor : 0.551321 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 : 540/529, 35.6300 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) Steps are strictly increasing 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 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 23 Odd number limit : 45 (O: 23 U: 45) Highest odd numerator or denominator: 45 Scale harmonicity : 0.017295 Average absolute harmonicity : 0.103019 Specific harmonicity : 0.088465 Fundamental : 1/45, -5.4919 octaves, 5.8139 Hz. Guide tone : 368, 8.5236 octaves, 96278.208 Hz. Exponens Consonantiae : 1.656000E+04, 14.01542 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 64.5, average 21.50000 Mersenne's string divisions : 2821 Sum of van Prooijen's expressibility: 3.30643, average 1.10214 Sum of Tenney's harmonic distance : 6.77536, average 2.25845 Vogel's harmonic complexity : 13.66667 Wille's k value : 11 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 16.67715, average 2.77953 Lattice compactness (without 2's) : 9.00997, average 1.50166 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 4 2.33333 7 3: -2 ..-1 -1.33333 4 1 5: -1 .. 0 -0.66667 2 1 23: 0 .. 1 0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 16 33| Scale is weakly epimorphic with val: <6 10 19 36| Scale is weakly epimorphic with val: <6 11 17 36| Scale is weakly epimorphic with val: <7 10 15 30| Scale is weakly epimorphic with val: <7 10 15 33| Scale is weakly epimorphic with val: <7 10 15 36| Scale is weakly epimorphic with val: <7 10 16 32| Scale is weakly epimorphic with val: <7 10 19 35| Scale is JI-epimorphic with val: <7 11 15 31| Scale is weakly epimorphic with val: <7 11 15 34| Scale is weakly epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 16 33| Scale is weakly epimorphic with val: <7 11 16 36| Scale is weakly epimorphic with val: <7 11 18 31| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 19 33| Scale is weakly epimorphic with val: <7 11 19 36| Scale is weakly epimorphic with val: <7 12 15 35| Scale is weakly epimorphic with val: <8 11 17 34| Scale is weakly epimorphic with val: <8 11 18 30| Scale is weakly epimorphic with val: <8 11 18 33| Scale is weakly epimorphic with val: <8 11 18 36| Scale is weakly epimorphic with val: <8 12 15 34| Scale is weakly epimorphic with val: <8 12 17 32| Scale is weakly epimorphic with val: <8 12 17 35|
FIT/MODE
3: 0 1 2 N G T3 SD: 38.2735 c. M:-54.2837 c. 4: 0 1 3 N G T3 SD: 23.1745 c. M: 38.0506 c. 5: 0 1 4 N G T3 SD: 23.0565 c. M: 38.0506 c. 8: 1 1 6 N M DE S SD: 15.8031 c. M:-24.2050 c. 9: 1 1 7 N M DE S SD: 9.9996 c. M:-17.2877 c. 10: 1 1 8 N M DE S SD: 9.7486 c. M: 12.1223 c. 12: 1 2 9 N T3 SD: 7.6431 c. M:-12.7800 c. 13: 1 2 10 N T3 SD: 1.8549 c. M:-3.2022 c. 27: 2 4 21 N T3 SD: 0.9045 c. M: 1.1584 c. 40: 3 6 31 N T3 SD: 0.4451 c. M: 0.6973 c. 67: 5 10 52 N T3 SD: 0.5267 c. M: 0.8831 c. 103: 8 15 80 N T3 SD: 0.4718 c. M:-0.6325 c. 107: 8 16 83 N T3 SD: 0.4699 c. M: 0.8136 c. 116: 9 17 90 N T3 SD: 0.3460 c. M:-0.5908 c. 129: 10 19 100 N T3 SD: 0.3487 c. M:-0.5575 c. 142: 11 21 110 N T3 SD: 0.4225 c. M:-0.5303 c. 143: 11 21 111 N T3 SD: 0.2211 c. M: 0.2807 c. 156: 12 23 121 N T3 SD: 0.1505 c. M:-0.2605 c. 183: 14 27 142 N T3 SD: 0.0901 c. M: 0.1474 c. 196: 15 29 152 N T3 SD: 0.0572 c. M:-0.0747 c. 379: 29 56 294 N T3 SD: 0.0386 c. M:-0.0584 c. 419: 32 62 325 N T3 SD: 0.0080 c. M: 0.0138 c. 1217: 93 180 944 N T3 SD: 0.0071 c. M: 0.0088 c. 1453: 111 215 1127 N T3 SD: 0.0070 c. M:-0.0118 c. 1636: 125 242 1269 N T3 SD: 0.0039 c. M: 0.0060 c. 2055: 157 304 1594 N T3 SD: 0.0026 c. M: 0.0044 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 x 5 S SD: 111.7313 cents 5 x x 7 SD: 84.4672 cents 6 x 7:8 S SD: 77.5698 cents 7 x 8:9 S SD: 67.5105 cents 8 x 9:11 SD: 53.2328 cents 9 x 10:12 S SD: 35.3362 cents 10 x 11:13 SD: 34.4934 cents 11 x 12:15 S SD: 27.5105 cents 12 x 13:16 SD: 13.4207 cents 13 x 14:17 SD: 18.7389 cents 14 x 15:19 SD: 15.7988 cents 15 x 16:20 S SD: 0.0000 cents 16 x 17:21 SD: 14.0467 cents 17 x 18:23 SD: 14.1599 cents 18 x 19:24 SD: 9.0641 cents 19 x 20:25 S SD: 16.2144 cents 20 x 21:27 SD: 17.3627 cents 21 x 22:28 SD: 15.5971 cents 22 x 23:29 SD: 20.0048 cents 23:24:25:31 SD: 17.2690 cents 24:25:26:32 SD: 14.0817 cents 25:26:27:33 SD: 13.5657 cents 26:27:28:35 S SD: 11.9884 cents 27:28:29:36 SD: 9.2139 cents 29:30:31:39 SD: 8.5685 cents 30:31:32:40 S SD: 6.2387 cents 33:34:35:44 SD: 5.6089 cents 41:42:44:55 S SD: 5.1096 cents 42:43:45:56 SD: 2.7220 cents 45:46:48:60 S SD: 0.0000 cents