Scala analysis: 165_C6
Chromatic tetrachord 52/51 * 17/16 * 16/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 52/51 33.617251 2: 13/12 138.572661 tridecimal 2/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 16/13 359.4723 tridecimal neutral third 1: 52/51 33.6173 2: 17/16 104.9554 17th harmonic 3: 16/13 359.4723 tridecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 52/51 33.617 cents 1: 1 17/16 104.955 cents 17th harmonic 1: 1 16/13 359.472 cents tridecimal neutral third 2: 1 13/12 138.573 cents tridecimal 2/3-tone 2: 1 64/51 393.090 cents 2: 1 17/13 464.428 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 : 33.6 138.6 498.0 33.6 : 105.0 464.4 498.0 138.6: 359.5 393.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6173 .. 359.4723 cents 204/169, 325.8551 cents 52/51, 33.6173 cents 2: 138.5727 .. 464.4277 cents 204/169, 325.8551 cents 169/192,-220.8997 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 52/51, 33.6173 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 16/13, 359.4723 cents Average / Smallest step : 4.938387 Largest / Average step : 2.165300 Largest / Smallest step : 10.693091 Median interval of one step : 17/16, 104.9554 cents, amount: 1 Least squares average step : 128.92126 cents, oct.: 386.76377 cents Scale is not proper Scale has trivalence property Scale is a mode of a 726-tone equal temperament with octave 4/3 degrees: 49 202 726 Least number of segments generator : 365 of 250.395 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 595 of 408.177 cents and inv. generated superset size: 22 = 19 more = 733.333% 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 33.61725 cents Scale diversity : 0.596644 Lumma stability : 0.134997 Lumma impropriety factor : 0.443534 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 : 52/51, 33.6173 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 17 Odd number limit : 51 (O: 17 U: 51) Highest odd numerator or denominator: 51 Scale harmonicity : 0.016967 Average absolute harmonicity : 0.089711 Specific harmonicity : 0.079614 Fundamental : 1/204, -7.6724 octaves, 1.2825 Hz. Guide tone : 52, 5.7004 octaves, 13604.529 Hz. Exponens Consonantiae : 1.060800E+04, 13.37287 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 67.5, average 22.50000 Mersenne's string divisions : 18025 Sum of van Prooijen's expressibility: 3.29863, average 1.09954 Sum of Tenney's harmonic distance : 6.69588, average 2.23196 Vogel's harmonic complexity : 22.66667 Wille's k value : 110 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 3 Triangular lattice diameter : 1 Lattice compactness : 16.99173, average 2.83196 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.66667 6 3: -1 ..-1 -1.00000 3 1 13: 0 .. 1 0.66667 2 1 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 25 29| Scale is weakly epimorphic with val: <6 10 25 32| Scale is weakly epimorphic with val: <6 11 26 28| Scale is weakly epimorphic with val: <6 11 26 31| Scale is weakly epimorphic with val: <7 10 26 27| Scale is weakly epimorphic with val: <7 10 27 29| Scale is weakly epimorphic with val: <7 10 27 32| Scale is weakly epimorphic with val: <7 10 29 30| Scale is weakly epimorphic with val: <7 11 26 27| Scale is weakly epimorphic with val: <7 11 26 30| Scale is weakly epimorphic with val: <7 11 26 33| Scale is JI-epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <7 11 27 32| Scale is weakly epimorphic with val: <7 11 29 30| Scale is weakly epimorphic with val: <7 11 29 33| Scale is weakly epimorphic with val: <7 11 30 32| Scale is weakly epimorphic with val: <7 12 29 30| Scale is weakly epimorphic with val: <7 12 29 33| Scale is weakly epimorphic with val: <8 11 25 27| Scale is weakly epimorphic with val: <8 11 28 30| Scale is weakly epimorphic with val: <8 11 30 31| Scale is weakly epimorphic with val: <8 12 27 28| Scale is weakly epimorphic with val: <8 12 30 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 25.0546 c. M: 33.6173 c. 4: 0 1 3 N G T3 SD: 21.0384 c. M: 33.6173 c. 7: 0 2 5 N G T3 SD: 19.5278 c. M: 33.6173 c. 10: 1 2 7 N T3 SD: 11.2480 c. M:-16.1872 c. 11: 1 2 8 N T3 SD: 6.9153 c. M:-11.6596 c. 14: 1 3 10 N T3 SD: 2.4299 c. M:-3.7259 c. 29: 2 6 21 N T3 SD: 0.8018 c. M: 1.1809 c. 43: 3 9 31 N T3 SD: 0.6954 c. M:-1.1301 c. 61: 4 13 44 N T3 SD: 0.5687 c. M: 0.9586 c. 75: 5 16 54 N T3 SD: 0.5615 c. M:-0.8799 c. 90: 6 19 65 N T3 SD: 0.2727 c. M: 0.4143 c. 104: 7 22 75 N T3 SD: 0.1846 c. M:-0.3053 c. 133: 9 28 96 N T3 SD: 0.0503 c. M:-0.0850 c. 356: 24 75 257 N T3 SD: 0.0476 c. M: 0.0714 c. 370: 25 78 267 N T3 SD: 0.0462 c. M:-0.0723 c. 460: 31 97 332 N T3 SD: 0.0318 c. M: 0.0533 c. 489: 33 103 353 N T3 SD: 0.0332 c. M: 0.0571 c. 503: 34 106 363 N T3 SD: 0.0392 c. M:-0.0482 c. 593: 40 125 428 N T3 SD: 0.0134 c. M: 0.0223 c. 726: 49 153 524 N T3 SD: 0.0019 c. M: 0.0026 c. 2311: 156 487 1668 N T3 SD: 0.0014 c. M:-0.0024 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 6:7 S SD: 98.0918 cents 6 x 7:8 S SD: 64.1491 cents 7 x 8:9 S SD: 55.9891 cents 8 x 9:11 SD: 42.1514 cents 9 x 10:12 S SD: 21.9155 cents 10 x 11:13 SD: 25.5919 cents 11 x 12:15 S SD: 20.3667 cents 12 x 13:16 SD: 0.0000 cents 13 x 14:17 SD: 17.5761 cents 14 x 15:19 SD: 18.0616 cents 15 x 16:20 S SD: 13.4207 cents 16 x 17:21 SD: 21.6417 cents 17 x 18:23 SD: 23.4966 cents 18 x 20:24 S SD: 21.9155 cents 19 x 21:25 SD: 20.7941 cents 20:21:22:27 SD: 20.4039 cents 21:22:23:28 SD: 16.8637 cents 22:23:24:29 SD: 16.3819 cents 23:24:25:31 SD: 14.8653 cents 24:25:26:32 SD: 12.3517 cents 27:28:29:36 SD: 10.9640 cents 32:33:35:43 SD: 9.6743 cents 33:34:36:44 SD: 7.2411 cents 35:36:38:47 SD: 6.6324 cents 36:37:39:48 SD: 4.6056 cents 45:46:49:60 SD: 3.3011 cents 48:49:52:64 SD: 0.6932 cents 108:110:117:144 SD: 0.6169 cents 156:159:169:208 SD: 0.2135 cents 204:208:221:272 SD: 0.0000 cents