Scala analysis: 230_C14
Chromatic tetrachord 6/5 * 35/32 * 64/63
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6/5 315.641287 minor third 2: 21/16 470.780907 narrow fourth 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/63 27.2641 septimal comma, Archytas' comma 1: 6/5 315.6413 minor third 2: 35/32 155.1396 septimal neutral second 3: 64/63 27.2641 septimal comma, Archytas' comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 35/32 155.140 cents septimal neutral second 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 128/105 342.905 cents septimal neutral third 2: 1 21/16 470.781 cents narrow fourth 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 : 315.6 470.8 498.0 315.6: 155.1 182.4 498.0 470.8: 27.3 342.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 315.6413 cents 189/160, 288.3772 cents 64/63, 27.2641 cents 2: 182.4037 .. 470.7809 cents 189/160, 288.3772 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 6.089145 Largest / Average step : 1.901282 Largest / Smallest step : 11.577180 Median interval of one step : 35/32, 155.1396 cents, amount: 1 Least squares average step : 196.52415 cents, oct.: 589.57245 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1297-tone equal temperament with octave 4/3 degrees: 822 1226 1297 Least number of segments generator : 649 of 249.214 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 730 of 280.318 cents and inv. generated superset size: 27 = 24 more = 900.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LMS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 27.26409 cents Scale diversity : 0.642771 Lumma stability : 0.109484 Lumma impropriety factor : 0.267521 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 : 64/63, 27.2641 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly decreasing 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 : 7 Odd number limit : 105 (O: 35 U: 105) Highest odd numerator or denominator: 21 Scale harmonicity : 0.035690 Average absolute harmonicity : 0.124204 Specific harmonicity : 0.182390 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 2.016000E+04, 14.29921 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 27.5, average 9.16667 Mersenne's string divisions : 2849 Sum of van Prooijen's expressibility: 2.49831, average 0.83277 Sum of Tenney's harmonic distance : 5.08264, average 1.69421 Vogel's harmonic complexity : 13.33333 Wille's k value : 157 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 22.25953, average 3.70992 Lattice compactness (without 2's) : 9.71478, average 1.61913 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.33333 7 3: -1 .. 1 0.33333 3 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 1 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: <7 10 15 21| Scale is weakly epimorphic with val: <7 10 18 21| Scale is weakly epimorphic with val: <7 11 16 18| Scale is weakly epimorphic with val: <7 11 16 21| Scale is JI-epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 11 17 22| Scale is weakly epimorphic with val: <7 11 19 21| Scale is weakly epimorphic with val: <7 12 15 19| Scale is weakly epimorphic with val: <7 12 16 20| Scale is weakly epimorphic with val: <7 12 18 19| Scale is weakly epimorphic with val: <8 11 16 19| Scale is weakly epimorphic with val: <8 11 16 22| Scale is weakly epimorphic with val: <8 12 17 19| Scale is weakly epimorphic with val: <8 12 17 22|
FIT/MODE
3: 2 1 0 N G T3 SD: 18.3659 c. M:-27.2641 c. 5: 3 2 0 N G T3 SD: 18.4937 c. M:-27.2641 c. 6: 4 2 0 N G T3 SD: 18.3659 c. M:-27.2641 c. 8: 5 3 0 N G T3 SD: 15.9412 c. M:-27.2641 c. 10: 6 3 1 N T3 SD: 16.2357 c. M: 22.5404 c. 11: 7 3 1 N T3 SD: 10.4266 c. M: 18.0127 c. 13: 8 4 1 N T3 SD: 8.2825 c. M: 11.0471 c. 14: 9 4 1 N T3 SD: 5.4648 c. M: 8.3106 c. 16: 10 5 1 N T3 SD: 3.3648 c. M: 4.3632 c. 19: 12 6 1 N T3 SD: 0.8729 c. M: 1.0866 c. 52: 33 16 3 N T3 SD: 0.8832 c. M: 1.4693 c. 55: 35 17 3 N T3 SD: 0.7506 c. M:-1.2964 c. 71: 45 22 4 N T3 SD: 0.4590 c. M: 0.7948 c. 74: 47 23 4 N T3 SD: 0.4420 c. M:-0.6846 c. 90: 57 28 5 N T3 SD: 0.2642 c. M: 0.4051 c. 109: 69 34 6 N T3 SD: 0.2282 c. M: 0.3651 c. 145: 92 45 8 N T3 SD: 0.2417 c. M:-0.3597 c. 164: 104 51 9 N T3 SD: 0.1176 c. M:-0.1921 c. 183: 116 57 10 N T3 SD: 0.0443 c. M:-0.0594 c. 456: 289 142 25 N T3 SD: 0.0239 c. M: 0.0410 c. 475: 301 148 26 N T3 SD: 0.0220 c. M: 0.0380 c. 639: 405 199 35 N T3 SD: 0.0150 c. M:-0.0210 c. 658: 417 205 36 N T3 SD: 0.0109 c. M:-0.0154 c. 1114: 706 347 61 N T3 SD: 0.0050 c. M: 0.0077 c. 1297: 822 404 71 N T3 SD: 0.0028 c. M:-0.0048 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 4:5 x x S SD: 70.6724 cents 5:6 x 7 S SD: 42.2336 cents 6:7 x 8 S SD: 24.3852 cents 7:8:9 x S SD: 45.8502 cents 8:10 x 11 S SD: 44.2510 cents 9:11 x 12 SD: 15.8833 cents 10:12:13 x S SD: 8.2835 cents 12:14 x 16 S SD: 24.3852 cents 13:16:17 x SD: 22.1445 cents 14:17:18:19 SD: 17.1042 cents 15:18 x 20 S SD: 0.0000 cents 16:19:21 x SD: 9.0641 cents 18:22 x 24 SD: 15.8833 cents 19:23:25 x SD: 7.8644 cents 21:25 x 28 SD: 6.8974 cents 22:26:29 x SD: 13.7346 cents 23:28:30:31 SD: 10.9907 cents 24:29 x 32 SD: 5.9905 cents 25:30:33 x S SD: 4.9323 cents 28:34:37 x SD: 11.8060 cents 29:35:38:39 SD: 6.0310 cents 30:36:39:40 S SD: 5.5223 cents 31:37:41 x SD: 8.1018 cents 32:38:42:43 SD: 7.5288 cents 33:40:43:44 SD: 7.1484 cents 34:41 x 45 SD: 7.6634 cents 35:42:46:47 SD: 4.1816 cents 36:43:47:48 SD: 4.0673 cents 37:44 x 49 SD: 9.7881 cents 38:46:50:51 SD: 6.4659 cents 39:47:51:52 SD: 3.2466 cents 40:48 x 53 SD: 5.4271 cents 41:49:54:55 SD: 4.6756 cents 44:53:58:59 SD: 4.6545 cents 45:54:59:60 SD: 0.6110 cents 150:180:197:200 SD: 0.3663 cents 195:234:256:260 SD: 0.1409 cents 240:288:315:320 SD: 0.0000 cents