Scala analysis: 173_C7
Chromatic tetrachord 28/27 * 22/21 * 27/22
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: 88/81 143.497939 2nd undecimal neutral second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 27/22 354.5471 neutral third, Zalzal wosta of al-Farabi 1: 28/27 62.9609 Archytas' 1/3-tone 2: 22/21 80.5370 undecimal minor semitone 3: 27/22 354.5471 neutral third, Zalzal wosta of al-Farabi
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 88/81 143.498 cents 2nd undecimal neutral second 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 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 : 63.0 143.5 498.0 63.0 : 80.5 435.1 498.0 143.5: 354.5 417.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 354.5471 cents 729/616, 291.5862 cents 28/27, 62.9609 cents 2: 143.4979 .. 435.0841 cents 729/616, 291.5862 cents 1936/2187,-211.0491 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 : 27/22, 354.5471 cents Average / Smallest step : 2.636795 Largest / Average step : 2.135633 Largest / Smallest step : 5.631226 Median interval of one step : 22/21, 80.5370 cents, amount: 1 Least squares average step : 131.72084 cents, oct.: 395.16252 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1843-tone equal temperament with octave 4/3 degrees: 233 531 1843 Least number of segments generator : 922 of 249.158 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1175 of 317.527 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 62.96090 cents Scale diversity : 0.746736 Lumma stability : 0.252832 Lumma impropriety factor : 0.423755 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 : 99/98, 17.5761 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 Limited inverse transpositions with margin 274.0100 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.023734 Average absolute harmonicity : 0.098326 Specific harmonicity : 0.121455 Fundamental : 1/81, -6.3399 octaves, 3.2299 Hz. Guide tone : 616, 9.2668 octaves, 161161.348 Hz. Exponens Consonantiae : 4.989600E+04, 15.60664 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 115.5, average 38.50000 Mersenne's string divisions : 65065 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.81067, average 2.60356 Vogel's harmonic complexity : 12.33333 Wille's k value : 13 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 18.62944, average 3.10491 Lattice compactness (without 2's) : 15.41578, average 2.56930 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -4 ..-1 -2.66667 8 1 7: 0 .. 1 0.33333 1 1 11: 0 .. 1 0.33333 1 1 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 10 19 25| Scale is weakly epimorphic with val: <6 10 21 23| Scale is weakly epimorphic with val: <6 10 21 26| Scale is weakly epimorphic with val: <6 10 22 25| Scale is weakly epimorphic with val: <7 10 19 24| Scale is weakly epimorphic with val: <7 10 19 27| Scale is weakly epimorphic with val: <7 11 18 24| Scale is weakly epimorphic with val: <7 11 18 27| Scale is JI-epimorphic with val: <7 11 20 25| = patent Scale is weakly epimorphic with val: <7 11 21 24| Scale is weakly epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <8 11 18 23| Scale is weakly epimorphic with val: <8 11 20 24| Scale is weakly epimorphic with val: <8 11 20 27| Scale is weakly epimorphic with val: <8 11 21 23| Scale is weakly epimorphic with val: <8 12 19 27| Scale is weakly epimorphic with val: <8 12 22 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 38.6052 c. M: 62.9609 c. 4: 0 1 3 N G T3 SD: 37.9674 c. M: 62.9609 c. 5: 1 0 4 N G T3 SD: 33.0117 c. M: 43.8889 c. 6: 1 1 4 N M DE S SD: 17.4058 c. M:-22.5171 c. 7: 1 1 5 N M DE S SD: 4.7780 c. M:-8.1884 c. 17: 2 3 12 N T3 SD: 3.0545 c. M: 4.3674 c. 24: 3 4 17 N T3 SD: 1.0975 c. M:-1.7652 c. 31: 4 5 22 N T3 SD: 0.9829 c. M:-1.3030 c. 55: 7 9 39 N T3 SD: 0.8383 c. M:-1.3879 c. 56: 7 9 40 N T3 SD: 0.8033 c. M: 1.1994 c. 63: 8 10 45 N T3 SD: 0.7115 c. M: 1.1994 c. 80: 10 13 57 N T3 SD: 0.4448 c. M: 0.7053 c. 87: 11 14 62 N T3 SD: 0.2204 c. M: 0.3816 c. 111: 14 18 79 N T3 SD: 0.0961 c. M: 0.1444 c. 198: 25 32 141 N T3 SD: 0.0828 c. M: 0.1213 c. 229: 29 37 163 N T3 SD: 0.0684 c. M:-0.1103 c. 309: 39 50 220 N T3 SD: 0.0645 c. M: 0.1009 c. 316: 40 51 225 N T3 SD: 0.0639 c. M:-0.0828 c. 340: 43 55 242 N T3 SD: 0.0360 c. M:-0.0562 c. 427: 54 69 304 N T3 SD: 0.0235 c. M: 0.0330 c. 538: 68 87 383 N T3 SD: 0.0082 c. M: 0.0110 c. 1305: 165 211 929 N T3 SD: 0.0059 c. M:-0.0103 c. 1416: 179 229 1008 N T3 SD: 0.0039 c. M:-0.0066 c. 1843: 233 298 1312 N T3 SD: 0.0028 c. M:-0.0041 c. 1954: 247 316 1391 N T3 SD: 0.0028 c. M: 0.0043 c. 2381: 301 385 1695 N T3 SD: 0.0024 c. M: 0.0041 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: 95.8750 cents 6 x 7:8 S SD: 61.6865 cents 7 x 8:9 S SD: 53.9703 cents 8 x 9:11 SD: 40.2729 cents 9 x 10:12 S SD: 19.4529 cents 10 x 11:13 SD: 24.4115 cents 11 x 12:15 S SD: 19.7777 cents 12 x 13:16 SD: 2.4626 cents 13 x 14:17 SD: 18.4469 cents 14 x 15:19 SD: 19.4781 cents 15 x 16:20 S SD: 15.8833 cents 16 x 17:21 SD: 23.6054 cents 17:18 x 23 SD: 21.9904 cents 18:19:20:24 S SD: 16.5079 cents 19:20:21:25 SD: 15.2015 cents 20:21:22:27 SD: 12.4167 cents 21:22:23:28 SD: 7.4892 cents 23:24:25:31 SD: 7.1952 cents 24:25:26:32 SD: 3.0501 cents 57:59:62:76 SD: 1.2864 cents 81:84:88:108 SD: 0.0000 cents