Scala analysis: 147_C4
Chromatic tetrachord 27/26 * 26/25 * 100/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/26 65.337341 tridecimal comma 2: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 100/81 364.8074 grave major third 1: 27/26 65.3373 tridecimal comma 2: 26/25 67.9002 tridecimal 1/3-tone 3: 100/81 364.8074 grave major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 27/26 65.337 cents tridecimal comma 1: 1 26/25 67.900 cents tridecimal 1/3-tone 1: 1 100/81 364.807 cents grave major third 2: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 1 50/39 430.145 cents 2: 1 104/81 432.708 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 : 65.3 133.2 498.0 65.3 : 67.9 432.7 498.0 133.2: 364.8 430.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 65.3373 .. 364.8074 cents 2600/2187, 299.4701 cents 27/26, 65.3373 cents 2: 133.2376 .. 432.7077 cents 2600/2187, 299.4701 cents 2187/2500,-231.5698 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 27/26, 65.3373 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 100/81, 364.8074 cents Average / Smallest step : 2.540890 Largest / Average step : 2.197437 Largest / Smallest step : 5.583445 Median interval of one step : 26/25, 67.9002 cents, amount: 1 Least squares average step : 130.42482 cents, oct.: 391.27446 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1555-tone equal temperament with octave 4/3 degrees: 204 416 1555 Least number of segments generator : 778 of 249.183 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1233 of 394.913 cents and inv. generated superset size: 48 = 45 more = 1600.000% 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 65.33734 cents Scale diversity : 0.679958 Lumma stability : 0.262375 Lumma impropriety factor : 0.464958 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 : 676/675, 2.5629 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 : 2 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 296.9072 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.020567 Average absolute harmonicity : 0.098153 Specific harmonicity : 0.103989 Fundamental : 1/1950, -10.9293 octaves, 0.1342 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 2.106000E+05, 17.68415 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 56.0, average 18.66667 Mersenne's string divisions : 19292 Sum of van Prooijen's expressibility: 3.33985, average 1.11328 Sum of Tenney's harmonic distance : 6.75482, average 2.25161 Vogel's harmonic complexity : 24.66667 Wille's k value : 1012 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 21.60573, average 3.60096 Lattice compactness (without 2's) : 18.59914, average 3.09986 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 3 1.66667 7 1 5: -2 .. 0 -0.66667 2 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 11 15 25| Scale is weakly epimorphic with val: <6 11 15 28| Scale is weakly 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 17 25| Scale is weakly epimorphic with val: <7 11 17 28| 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 16 26| Scale is weakly epimorphic with val: <7 12 19 26| Scale is weakly epimorphic with val: <8 11 15 27| Scale is weakly epimorphic with val: <8 11 15 30| Scale is weakly epimorphic with val: <8 12 17 25|
FIT/MODE
3: 0 1 2 N G T3 SD: 42.2032 c. M: 65.3373 c. 4: 0 1 3 N G T3 SD: 38.0575 c. M: 65.3373 c. 5: 0 1 4 N G T3 SD: 42.4258 c. M: 65.3373 c. 6: 1 1 4 N M DE S SD: 21.4988 c. M:-32.7774 c. 7: 1 1 5 N M DE S SD: 6.2150 c. M:-9.0610 c. 8: 1 1 6 N M DE S SD: 5.3431 c. M: 8.7263 c. 15: 2 2 11 N M DE S SD: 0.6641 c. M:-1.0687 c. 101: 13 14 74 N T3 SD: 0.7138 c. M: 1.2325 c. 108: 14 15 79 N T3 SD: 0.5319 c. M: 0.7760 c. 116: 15 16 85 N T3 SD: 0.5458 c. M: 0.9350 c. 123: 16 17 90 N T3 SD: 0.3878 c. M: 0.5510 c. 131: 17 18 96 N T3 SD: 0.4193 c. M: 0.7055 c. 138: 18 19 101 N T3 SD: 0.2759 c. M: 0.3749 c. 146: 19 20 107 N T3 SD: 0.3230 c. M: 0.5233 c. 153: 20 21 112 N T3 SD: 0.1874 c. M: 0.2334 c. 168: 22 23 123 N T3 SD: 0.1179 c. M:-0.1673 c. 183: 24 25 134 N T3 SD: 0.0695 c. M:-0.1187 c. 198: 26 27 145 N T3 SD: 0.0575 c. M:-0.0775 c. 389: 51 53 285 N T3 SD: 0.0540 c. M: 0.0842 c. 557: 73 76 408 N T3 SD: 0.0372 c. M: 0.0639 c. 572: 75 78 419 N T3 SD: 0.0227 c. M: 0.0342 c. 587: 77 80 430 N T3 SD: 0.0175 c. M: 0.0296 c. 770: 101 105 564 N T3 SD: 0.0063 c. M: 0.0094 c. 785: 103 107 575 N T3 SD: 0.0067 c. M:-0.0112 c. 1357: 178 185 994 N T3 SD: 0.0072 c. M: 0.0096 c. 1555: 204 212 1139 N T3 SD: 0.0010 c. M:-0.0015 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: 100.5060 cents 6 x 7:8 S SD: 66.8167 cents 7 x 8:9 S SD: 58.2143 cents 8 x 9:11 SD: 44.2510 cents 9 x 10:12 S SD: 24.5831 cents 10 x 11:13 SD: 27.0660 cents 11 x 12:15 S SD: 21.3096 cents 12 x 13:16 SD: 2.6675 cents 13 x 14:17 SD: 16.9891 cents 14 x 15:19 SD: 16.8020 cents 15 x 16:20 S SD: 10.7531 cents 16 x 17:21 SD: 19.6419 cents 17:18 x 23 SD: 21.0291 cents 18:19 x 24 SD: 14.1328 cents 21:22:23:28 SD: 9.5416 cents 23:24:25:31 SD: 7.7708 cents 24:25:26:32 SD: 2.5150 cents 51:53:55:68 SD: 0.9376 cents 75:78:81:100 SD: 0.8543 cents 126:131:136:168 SD: 0.7583 cents 186:193:201:248 SD: 0.5746 cents 210:218:227:280 SD: 0.5479 cents 213:221:230:284 SD: 0.5119 cents 237:246:256:316 SD: 0.2852 cents 261:271:282:348 SD: 0.2589 cents 288:299:311:384 SD: 0.1660 cents 312:324:337:416 SD: 0.0685 cents