Scala analysis: 135_C2
Chromatic tetrachord 28/27 * 27/26 * 26/21, Schlesinger
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: 14/13 128.298245 2/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 26/21 369.7468 1: 28/27 62.9609 Archytas' 1/3-tone 2: 27/26 65.3373 tridecimal comma 3: 26/21 369.7468
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 27/26 65.337 cents tridecimal comma 1: 1 26/21 369.747 cents 2: 1 14/13 128.298 cents 2/3-tone 2: 1 104/81 432.708 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 : 63.0 128.3 498.0 63.0 : 65.3 435.1 498.0 128.3: 369.7 432.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 369.7468 cents 117/98, 306.7859 cents 28/27, 62.9609 cents 2: 128.2982 .. 435.0841 cents 117/98, 306.7859 cents 147/169,-241.4485 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 : 26/21, 369.7468 cents Average / Smallest step : 2.636795 Largest / Average step : 2.227189 Largest / Smallest step : 5.872641 Median interval of one step : 27/26, 65.3373 cents, amount: 1 Least squares average step : 129.54946 cents, oct.: 388.64837 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1052-tone equal temperament with octave 4/3 degrees: 133 271 1052 Least number of segments generator : 527 of 249.496 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 611 of 289.264 cents and inv. generated superset size: 18 = 15 more = 600.000% 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 : 0.643251 Lumma stability : 0.252832 Lumma impropriety factor : 0.484793 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 : 729/728, 2.3764 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 304.4094 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.023563 Average absolute harmonicity : 0.097828 Specific harmonicity : 0.113257 Fundamental : 1/351, -8.4553 octaves, 0.7454 Hz. Guide tone : 28, 4.8074 octaves, 7325.516 Hz. Exponens Consonantiae : 9.828000E+03, 13.26268 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 44.5, average 14.83333 Mersenne's string divisions : 10395 Sum of van Prooijen's expressibility: 3.02243, average 1.00748 Sum of Tenney's harmonic distance : 6.21777, average 2.07259 Vogel's harmonic complexity : 20.00000 Wille's k value : 94 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.26247, average 2.54374 Lattice compactness (without 2's) : 12.70689, average 2.11781 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -3 .. 0 -1.33333 4 1 7: 0 .. 1 0.66667 2 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 21 26| Scale is weakly epimorphic with val: <6 10 21 29| Scale is weakly epimorphic with val: <6 10 22 25| Scale is weakly epimorphic with val: <7 10 19 27| Scale is weakly epimorphic with val: <7 10 19 30| Scale is weakly epimorphic with val: <7 10 21 25| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 30| Scale is JI-epimorphic with val: <7 11 20 25| Scale is weakly epimorphic with val: <7 11 20 28| Scale is weakly epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <8 11 20 27| Scale is weakly epimorphic with val: <8 11 20 30| Scale is weakly epimorphic with val: <8 11 21 26| Scale is weakly epimorphic with val: <8 12 22 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 42.3738 c. M: 62.9609 c. 4: 0 1 3 N G T3 SD: 36.4162 c. M: 62.9609 c. 5: 0 1 4 N G T3 SD: 39.9464 c. M: 62.9609 c. 6: 1 1 4 N M DE S SD: 24.6605 c. M:-37.7168 c. 7: 1 1 5 N M DE S SD: 9.3641 c. M:-14.0003 c. 8: 1 1 6 N M DE S SD: 2.2240 c. M: 3.7870 c. 23: 3 3 17 N M DE S SD: 1.4890 c. M:-2.0015 c. 31: 4 4 23 N M DE S SD: 0.7638 c. M:-1.3030 c. 39: 5 5 29 N M DE S SD: 0.6184 c. M:-0.8910 c. 101: 13 13 75 N M DE S SD: 0.6624 c. M:-1.1439 c. 109: 14 14 81 N M DE S SD: 0.6181 c. M:-1.0082 c. 112: 14 15 83 N T3 SD: 0.5576 c. M: 0.7053 c. 120: 15 16 89 N T3 SD: 0.4581 c. M: 0.7053 c. 128: 16 17 95 N T3 SD: 0.4116 c. M: 0.7053 c. 136: 17 18 101 N T3 SD: 0.4135 c. M: 0.7053 c. 143: 18 19 106 N T3 SD: 0.3623 c. M:-0.5665 c. 151: 19 20 112 N T3 SD: 0.2573 c. M:-0.3359 c. 159: 20 21 118 N T3 SD: 0.1957 c. M: 0.3137 c. 167: 21 22 124 N T3 SD: 0.1950 c. M: 0.3325 c. 182: 23 24 135 N T3 SD: 0.1839 c. M:-0.3178 c. 190: 24 25 141 N T3 SD: 0.0885 c. M:-0.1449 c. 198: 25 26 147 N T3 SD: 0.0449 c. M: 0.0764 c. 388: 49 51 288 N T3 SD: 0.0520 c. M:-0.0639 c. 419: 53 55 311 N T3 SD: 0.0490 c. M:-0.0761 c. 427: 54 56 317 N T3 SD: 0.0139 c. M:-0.0237 c. 625: 79 82 464 N T3 SD: 0.0048 c. M: 0.0080 c. 1052: 133 138 781 N T3 SD: 0.0028 c. M:-0.0049 c. 1677: 212 220 1245 N T3 SD: 0.0002 c. M: 0.0004 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 69.2863 cents 7 x 8:9 S SD: 60.3065 cents 8 x 9:11 SD: 46.2470 cents 9 x 10:12 S SD: 27.0527 cents 10 x 11:13 SD: 28.5854 cents 11 x 12:15 S SD: 22.4315 cents 12 x 13:16 SD: 5.1372 cents 13 x 14:17 SD: 16.8086 cents 14 x 15:19 SD: 15.9480 cents 15 x 16:20 S SD: 8.2835 cents 16 x 17:21 SD: 17.9459 cents 17 x 18:23 SD: 19.3638 cents 18:19 x 24 SD: 15.3211 cents 19:20 x 25 S SD: 17.2736 cents 20:21:22:27 SD: 15.8898 cents 21:22:23:28 SD: 11.3592 cents 22:23:24:29 SD: 10.9867 cents 23:24:25:31 SD: 8.9627 cents 24:25:26:32 SD: 4.2821 cents 27:28:29:36 SD: 1.5287 cents 51:53:55:68 SD: 1.4557 cents 78:81:84:104 SD: 0.7921 cents 105:109:113:140 SD: 0.7075 cents 195:202:210:260 SD: 0.6345 cents 219:227:236:292 SD: 0.4705 cents 246:255:265:328 SD: 0.3021 cents 273:283:294:364 SD: 0.2265 cents 324:336:349:432 SD: 0.1272 cents 351:364:378:468 SD: 0.0000 cents