Scala analysis: 248_C17
Chromatic tetrachord 28/27 * 243/224 * 32/27, Archytas
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 32/27 294.1350 Pythagorean minor third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 243/224 140.9491 Archytas' 2/3-tone 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 243/224 140.949 cents Archytas' 2/3-tone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 896/729 357.096 cents 2: 1 9/7 435.084 cents septimal major third, BP 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 : 63.0 203.9 498.0 63.0 : 140.9 435.1 498.0 203.9: 294.1 357.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 294.1350 cents 8/7, 231.1741 cents 28/27, 62.9609 cents 2: 203.9100 .. 435.0841 cents 8/7, 231.1741 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 2.636795 Largest / Average step : 1.771737 Largest / Smallest step : 4.671709 Median interval of one step : 243/224, 140.9491 cents, amount: 1 Least squares average step : 140.35114 cents, oct.: 421.05341 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1424-tone equal temperament with octave 4/3 degrees: 180 583 1424 Least number of segments generator : 713 of 249.372 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 897 of 313.726 cents and inv. generated superset size: 84 = 81 more = 2800.000% 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 62.96090 cents Scale diversity : 0.981798 Lumma stability : 0.252832 Lumma impropriety factor : 0.181158 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 : 28/27, 62.9609 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% -- Rational properties -- Prime limit : 7 Odd number limit : 729 (O: 243 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.034942 Average absolute harmonicity : 0.127860 Specific harmonicity : 0.176749 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 5.443200E+04, 15.73217 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 39.5, average 13.16667 Mersenne's string divisions : 6545 Sum of van Prooijen's expressibility: 2.86273, average 0.95424 Sum of Tenney's harmonic distance : 5.81504, average 1.93835 Vogel's harmonic complexity : 12.66667 Wille's k value : 121 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 24.79172, average 4.13195 Lattice compactness (without 2's) : 16.49737, average 2.74956 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.33333 7 3: -3 .. 2 -0.66667 6 2 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 10 19| Scale is weakly epimorphic with val: <7 11 18| Scale is weakly epimorphic with val: <7 11 21| Scale is weakly epimorphic with val: <7 12 20| Scale is weakly epimorphic with val: <8 11 20|
FIT/MODE
3: 0 1 2 N G T3 SD: 42.4268 c. M: 62.9609 c. 5: 1 1 3 N M DE S SD: 21.3315 c. M:-36.6481 c. 7: 1 2 4 N T3 SD: 7.2576 c. M:-9.5379 c. 15: 2 4 9 N T3 SD: 3.3607 c. M: 4.6920 c. 17: 2 5 10 N T3 SD: 2.6100 c. M: 4.3674 c. 22: 3 6 13 N T3 SD: 2.8620 c. M:-4.9543 c. 24: 3 7 14 N T3 SD: 2.1229 c. M:-3.6087 c. 32: 4 9 19 N T3 SD: 0.9986 c. M: 1.5792 c. 39: 5 11 23 N T3 SD: 0.5678 c. M:-0.8910 c. 56: 7 16 33 N T3 SD: 0.5515 c. M: 0.7053 c. 71: 9 20 42 N T3 SD: 0.2960 c. M: 0.4832 c. 95: 12 27 56 N T3 SD: 0.3192 c. M:-0.5506 c. 110: 14 31 65 N T3 SD: 0.2640 c. M:-0.4266 c. 127: 16 36 75 N T3 SD: 0.1244 c. M: 0.2151 c. 166: 21 47 98 N T3 SD: 0.0677 c. M:-0.1084 c. 237: 30 67 140 N T3 SD: 0.0621 c. M:-0.0828 c. 293: 37 83 173 N T3 SD: 0.0552 c. M: 0.0678 c. 364: 46 103 215 N T3 SD: 0.0261 c. M: 0.0399 c. 530: 67 150 313 N T3 SD: 0.0038 c. M:-0.0065 c. 1424: 180 403 841 N T3 SD: 0.0045 c. M: 0.0058 c. 1954: 247 553 1154 N T3 SD: 0.0028 c. M: 0.0043 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: 70.0332 cents 6 x 7:8 S SD: 31.4805 cents 7 x 8:9 S SD: 34.3053 cents 8 x 9:11 SD: 26.6365 cents 9 x 10:12 S SD: 10.7531 cents 10 x 11:13 SD: 29.3037 cents 11 x 12:15 S SD: 32.9836 cents 12 x 14:16 S SD: 31.4805 cents 13:14:15:17 SD: 28.5195 cents 14:15:16:19 SD: 23.2677 cents 15:16:17:20 SD: 16.8054 cents 16:17:18:21 S SD: 16.6895 cents 17:18:19:23 SD: 15.1408 cents 18:19:20:24 S SD: 12.4787 cents 21:22:24:28 S SD: 10.8128 cents 22:23:25:29 SD: 9.9448 cents 23:24:26:31 SD: 7.7087 cents 24:25:27:32 SD: 2.5705 cents 54:56:61:72 SD: 2.3699 cents 57:59:64:76 SD: 1.5642 cents 81:84:91:108 SD: 0.7921 cents 135:140:152:180 SD: 0.4748 cents 192:199:216:256 SD: 0.3221 cents 216:224:243:288 SD: 0.0000 cents