Scala analysis: 164_C6
Chromatic tetrachord 65/64 * 16/15 * 16/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 65/64 26.841376 13th-partial chroma 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: 65/64 26.8414 13th-partial chroma 2: 16/15 111.7313 minor diatonic semitone 3: 16/13 359.4723 tridecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 65/64 26.841 cents 13th-partial chroma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 16/13 359.472 cents tridecimal neutral third 2: 1 13/12 138.573 cents tridecimal 2/3-tone 2: 1 5/4 386.314 cents major third 2: 1 256/195 471.204 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 : 26.8 138.6 498.0 26.8 : 111.7 471.2 498.0 138.6: 359.5 386.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.8414 .. 359.4723 cents 1024/845, 332.6310 cents 65/64, 26.8414 cents 2: 138.5727 .. 471.2036 cents 1024/845, 332.6310 cents 169/192,-220.8997 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 65/64, 26.8414 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 16/13, 359.4723 cents Average / Smallest step : 6.185041 Largest / Average step : 2.165300 Largest / Smallest step : 13.392471 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 128.43726 cents, oct.: 385.31179 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1373-tone equal temperament with octave 4/3 degrees: 74 382 1373 Least number of segments generator : 687 of 249.204 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 745 of 270.243 cents and inv. generated superset size: 31 = 28 more = 1033.333% 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 26.84138 cents Scale diversity : 0.551530 Lumma stability : 0.107787 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 : 65/64, 26.8414 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 Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 13 Odd number limit : 195 (O: 65 U: 195) Highest odd numerator or denominator: 65 Scale harmonicity : 0.025497 Average absolute harmonicity : 0.093503 Specific harmonicity : 0.110740 Fundamental : 1/192, -7.5850 octaves, 1.3626 Hz. Guide tone : 260, 8.0224 octaves, 68022.647 Hz. Exponens Consonantiae : 4.992000E+04, 15.60733 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 80.5, average 26.83333 Mersenne's string divisions : 22575 Sum of van Prooijen's expressibility: 3.40398, average 1.13466 Sum of Tenney's harmonic distance : 6.89140, average 2.29713 Vogel's harmonic complexity : 15.33333 Wille's k value : 97 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 3 Triangular lattice diameter : 3 Lattice compactness : 27.40107, average 4.56685 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 2 -2.00000 10 3: -1 .. 0 -0.66667 2 1 5: 0 .. 1 0.33333 1 13: 0 .. 1 0.66667 2 2 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 15 25| Scale is weakly epimorphic with val: <6 10 18 25| Scale is weakly epimorphic with val: <6 11 15 26| Scale is weakly epimorphic with val: <6 11 18 26| Scale is weakly epimorphic with val: <7 10 16 29| Scale is weakly epimorphic with val: <7 10 17 27| Scale is weakly epimorphic with val: <7 10 19 26| Scale is weakly epimorphic with val: <7 11 15 26| Scale is weakly epimorphic with val: <7 11 15 29| Scale is JI-epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 18 29| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 12 15 30| Scale is weakly epimorphic with val: <7 12 17 29| Scale is weakly epimorphic with val: <7 12 18 27| Scale is weakly epimorphic with val: <8 11 16 30| Scale is weakly epimorphic with val: <8 11 19 30|
FIT/MODE
3: 0 1 2 N G T3 SD: 22.1626 c. M:-27.4423 c. 4: 0 1 3 N G T3 SD: 17.4946 c. M: 26.8414 c. 7: 0 2 5 N G T3 SD: 15.6455 c. M: 26.8414 c. 10: 1 2 7 N T3 SD: 14.6609 c. M:-22.9631 c. 11: 1 2 8 N T3 SD: 10.7608 c. M:-18.4354 c. 13: 1 3 9 N T3 SD: 10.7521 c. M:-14.6720 c. 14: 1 3 10 N T3 SD: 5.4819 c. M:-8.7333 c. 15: 1 3 11 N T3 SD: 4.9550 c. M:-6.3616 c. 17: 1 4 12 N T3 SD: 4.7824 c. M:-7.9112 c. 18: 1 4 13 N T3 SD: 0.4955 c. M:-0.8278 c. 93: 5 21 67 N T3 SD: 0.3862 c. M:-0.6657 c. 111: 6 25 80 N T3 SD: 0.3043 c. M:-0.5210 c. 129: 7 29 93 N T3 SD: 0.2630 c. M:-0.4166 c. 147: 8 33 106 N T3 SD: 0.2472 c. M:-0.3378 c. 165: 9 37 119 N T3 SD: 0.2461 c. M:-0.3247 c. 169: 9 38 122 N T3 SD: 0.1873 c. M: 0.3183 c. 187: 10 42 135 N T3 SD: 0.1284 c. M: 0.2080 c. 205: 11 46 148 N T3 SD: 0.0859 c. M: 0.1170 c. 223: 12 50 161 N T3 SD: 0.0638 c. M: 0.1028 c. 334: 18 75 241 N T3 SD: 0.0604 c. M:-0.1045 c. 352: 19 79 254 N T3 SD: 0.0560 c. M:-0.0876 c. 370: 20 83 267 N T3 SD: 0.0622 c. M:-0.0800 c. 464: 25 104 335 N T3 SD: 0.0622 c. M: 0.1076 c. 521: 28 117 376 N T3 SD: 0.0488 c. M: 0.0750 c. 539: 29 121 389 N T3 SD: 0.0311 c. M: 0.0449 c. 557: 30 125 402 N T3 SD: 0.0157 c. M:-0.0215 c. 575: 31 129 415 N T3 SD: 0.0097 c. M:-0.0138 c. 1355: 73 304 978 N T3 SD: 0.0056 c. M: 0.0094 c. 1373: 74 308 991 N T3 SD: 0.0031 c. M: 0.0052 c. 1930: 104 433 1393 N T3 SD: 0.0026 c. M: 0.0037 c. 1948: 105 437 1406 N T3 SD: 0.0023 c. M:-0.0040 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 x 22:27 SD: 17.0378 cents 23:24:25:31 SD: 16.9234 cents 24:25:26:32 SD: 14.6104 cents 26:27:28:35 S SD: 14.3835 cents 27:28:29:36 SD: 13.0190 cents 31:32:34:41 SD: 12.6628 cents 32:33:35:43 SD: 11.3265 cents 33:34:36:44 SD: 9.2052 cents 35:36:38:47 SD: 8.4798 cents 36:37:39:48 SD: 6.8642 cents 39:40:42:52 SD: 6.6183 cents 44:45:48:59 SD: 6.5601 cents 45:46:49:60 SD: 4.7617 cents 47:48:51:63 SD: 4.5297 cents 48:49:52:64 SD: 2.9518 cents 57:58:62:76 SD: 2.5735 cents 60:61:65:80 SD: 0.5916 cents 132:134:143:176 SD: 0.2691 cents 192:195:208:256 SD: 0.0000 cents