Scala analysis: 314_C24
Chromatic tetrachord 256/243 * 243/224 * 7/6, Hipkins
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 256/243 90.2250 limma, Pythagorean minor second 2: 243/224 140.9491 Archytas' 2/3-tone 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 243/224 140.949 cents Archytas' 2/3-tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 896/729 357.096 cents 2: 1 81/64 407.820 cents Pythagorean major third 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 : 90.2 231.2 498.0 90.2 : 140.9 407.8 498.0 231.2: 266.9 357.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 266.8709 cents 567/512, 176.6459 cents 256/243, 90.2250 cents 2: 231.1741 .. 407.8200 cents 567/512, 176.6459 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.840011 Largest / Average step : 1.607511 Largest / Smallest step : 2.957838 Median interval of one step : 243/224, 140.9491 cents, amount: 1 Least squares average step : 146.19344 cents, oct.: 438.58032 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2219-tone equal temperament with octave 4/3 degrees: 402 1030 2219 Least number of segments generator : 1110 of 249.135 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1457 of 327.017 cents and inv. generated superset size: 19 = 16 more = 633.333% 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 35.69681 cents Scale diversity : 1.134974 Lumma stability : 0.362317 Lumma impropriety factor : 0.071674 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 : 49/48, 35.6968 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 7 Odd number limit : 729 (O: 243 U: 729) Highest odd numerator or denominator: 243 Scale harmonicity : 0.031627 Average absolute harmonicity : 0.112143 Specific harmonicity : 0.162397 Fundamental : 1/1701, -10.7322 octaves, 0.1538 Hz. Guide tone : 256, 8.0000 octaves, 66976.145 Hz. Exponens Consonantiae : 4.354560E+05, 18.73217 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 260.5, average 86.83333 Mersenne's string divisions : 52395 Sum of van Prooijen's expressibility: 3.70783, average 1.23594 Sum of Tenney's harmonic distance : 7.62122, average 2.54041 Vogel's harmonic complexity : 18.00000 Wille's k value : 283 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 30.91691, average 5.15282 Lattice compactness (without 2's) : 17.51323, average 2.91887 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 4.33333 13 3: -5 .. 0 -2.00000 6 2 7: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-7 / 3 =-2.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is JI-epimorphic with val: <7 11 19| Scale is weakly epimorphic with val: <7 11 22|
FIT/MODE
3: 0 1 2 N G T3 SD: 64.2554 c. M: 90.2250 c. 4: 1 1 2 P M ME S SD: 22.3168 c. M:-34.2863 c. 5: 1 1 3 N M DE S SD: 19.2289 c. M: 31.9561 c. 6: 1 2 3 P T3 SD: 11.1154 c. M:-17.8484 c. 10: 2 3 5 P T3 SD: 11.6422 c. M:-17.8484 c. 11: 2 3 6 N T3 SD: 2.7720 c. M: 4.7900 c. 17: 3 5 9 N T3 SD: 2.2870 c. M:-3.2000 c. 28: 5 8 15 N T3 SD: 0.7447 c. M: 1.2884 c. 60: 11 17 32 N T3 SD: 0.9536 c. M:-1.2469 c. 67: 12 19 36 N T3 SD: 0.7273 c. M: 1.0229 c. 71: 13 20 38 N T3 SD: 0.5862 c. M:-0.9663 c. 82: 15 23 44 N T3 SD: 0.5522 c. M:-0.8808 c. 88: 16 25 47 N T3 SD: 0.5367 c. M:-0.8696 c. 99: 18 28 53 N T3 SD: 0.2352 c. M:-0.3286 c. 127: 23 36 68 N T3 SD: 0.1172 c. M:-0.2011 c. 138: 25 39 74 N T3 SD: 0.1136 c. M: 0.1967 c. 237: 43 67 127 N T3 SD: 0.0799 c. M:-0.1376 c. 265: 48 75 142 N T3 SD: 0.0083 c. M: 0.0131 c. 1424: 258 403 763 N T3 SD: 0.0089 c. M:-0.0111 c. 1562: 283 442 837 N T3 SD: 0.0070 c. M:-0.0098 c. 1689: 306 478 905 N T3 SD: 0.0063 c. M:-0.0084 c. 1827: 331 517 979 N T3 SD: 0.0055 c. M: 0.0071 c. 1954: 354 553 1047 N T3 SD: 0.0045 c. M:-0.0065 c. 2219: 402 628 1189 N T3 SD: 0.0031 c. M:-0.0050 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: 59.7273 cents 6 x 7:8 S SD: 17.8484 cents 7 x 8:9 S SD: 31.4805 cents 8 x 9:11 SD: 29.9221 cents 9 x 10:12 S SD: 24.3852 cents 10 x 11:13 SD: 39.6850 cents 11:12:13:15 SD: 30.7885 cents 12:13:14:16 S SD: 20.0326 cents 13:14:15:17 SD: 17.8081 cents 14:15:16:19 SD: 14.1131 cents 15:16:17:20 SD: 8.6436 cents 20:21:23:27 SD: 8.2464 cents 21:22:24:28 S SD: 3.2293 cents 36:38:41:48 SD: 2.3015 cents 57:60:65:76 SD: 1.3529 cents 111:117:127:148 SD: 0.7174 cents 132:139:151:176 SD: 0.6033 cents 147:155:168:196 SD: 0.5058 cents 168:177:192:224 SD: 0.0403 cents