Scala analysis: 193_C10
Chromatic tetrachord 46/45 * 15/14 * 28/23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/45 38.050632 23rd-partial chroma 2: 23/21 157.493440 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 28/23 340.5516 1: 46/45 38.0506 23rd-partial chroma 2: 15/14 119.4428 major diatonic semitone 3: 28/23 340.5516
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 46/45 38.051 cents 23rd-partial chroma 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 28/23 340.552 cents 2: 1 23/21 157.493 cents 2: 1 56/45 378.602 cents septimal narrow major third 2: 1 30/23 459.994 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 : 38.1 157.5 498.0 38.1 : 119.4 460.0 498.0 157.5: 340.6 378.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 340.5516 cents 630/529, 302.5009 cents 46/45, 38.0506 cents 2: 157.4934 .. 459.9944 cents 630/529, 302.5009 cents 529/588,-183.0581 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 46/45, 38.0506 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 28/23, 340.5516 cents Average / Smallest step : 4.363002 Largest / Average step : 2.051330 Largest / Smallest step : 8.949958 Median interval of one step : 15/14, 119.4428 cents, amount: 1 Least squares average step : 131.94089 cents, oct.: 395.82268 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1597-tone equal temperament with octave 4/3 degrees: 122 505 1597 Least number of segments generator : 799 of 249.178 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1031 of 321.531 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 38.05063 cents Scale diversity : 0.697659 Lumma stability : 0.152800 Lumma impropriety factor : 0.367553 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 : 46/45, 38.0506 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 -- Rational properties -- Prime limit : 23 Odd number limit : 45 (O: 23 U: 45) Highest odd numerator or denominator: 45 Scale harmonicity : 0.015127 Average absolute harmonicity : 0.083565 Specific harmonicity : 0.066278 Fundamental : 1/315, -8.2992 octaves, 0.8306 Hz. Guide tone : 92, 6.5236 octaves, 24069.552 Hz. Exponens Consonantiae : 2.898000E+04, 14.82277 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 71.0, average 23.66667 Mersenne's string divisions : 4004 Sum of van Prooijen's expressibility: 3.49206, average 1.16402 Sum of Tenney's harmonic distance : 7.07910, average 2.35970 Vogel's harmonic complexity : 26.33333 Wille's k value : 172 Wilson's harmonic complexity : 41 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 13.06336, average 2.17723 Lattice compactness (without 2's) : 10.05986, average 1.67664 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 3 3: -2 ..-1 -1.33333 4 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 18 32| Scale is weakly epimorphic with val: <6 10 15 20 33| Scale is weakly epimorphic with val: <6 10 15 21 32| Scale is weakly epimorphic with val: <6 10 16 18 31| Scale is weakly epimorphic with val: <6 10 16 19 33| Scale is weakly epimorphic with val: <6 10 16 21 34| Scale is weakly epimorphic with val: <6 10 16 22 33| Scale is weakly epimorphic with val: <6 10 17 19 32| Scale is weakly epimorphic with val: <6 10 17 20 34| Scale is weakly epimorphic with val: <6 10 17 22 35| Scale is weakly epimorphic with val: <6 10 18 18 35| Scale is weakly epimorphic with val: <6 10 18 20 33| Scale is weakly epimorphic with val: <6 10 18 21 35| Scale is weakly epimorphic with val: <6 10 19 19 36| Scale is weakly epimorphic with val: <6 10 19 21 34| Scale is weakly epimorphic with val: <6 10 19 22 36| Scale is weakly epimorphic with val: <6 11 15 18 34| Scale is weakly epimorphic with val: <6 11 15 19 33| Scale is weakly epimorphic with val: <6 11 15 21 34| Scale is weakly epimorphic with val: <6 11 15 22 36| Scale is weakly epimorphic with val: <6 11 16 19 35| Scale is weakly epimorphic with val: <6 11 16 20 34| Scale is weakly epimorphic with val: <6 11 16 22 35| Scale is weakly epimorphic with val: <6 11 17 18 32| Scale is weakly epimorphic with val: <6 11 17 20 36| Scale is weakly epimorphic with val: <6 11 17 21 35| Scale is weakly epimorphic with val: <6 11 18 19 33| Scale is weakly epimorphic with val: <6 11 18 22 36| Scale is weakly epimorphic with val: <6 11 19 20 34| Scale is weakly epimorphic with val: <7 10 15 19 31| Scale is weakly epimorphic with val: <7 10 15 20 33| Scale is weakly epimorphic with val: <7 10 15 22 31| Scale is weakly epimorphic with val: <7 10 16 18 31| Scale is weakly epimorphic with val: <7 10 16 20 32| Scale is weakly epimorphic with val: <7 10 16 21 34| Scale is weakly epimorphic with val: <7 10 17 18 33| Scale is weakly epimorphic with val: <7 10 17 19 32| Scale is weakly epimorphic with val: <7 10 17 21 33| Scale is weakly epimorphic with val: <7 10 17 22 35| Scale is weakly epimorphic with val: <7 10 18 19 34| Scale is weakly epimorphic with val: <7 10 18 20 33| Scale is weakly epimorphic with val: <7 10 18 22 34| Scale is weakly epimorphic with val: <7 10 19 20 35| Scale is weakly epimorphic with val: <7 10 19 21 34| Scale is JI-epimorphic with val: <7 11 15 18 31| Scale is weakly epimorphic with val: <7 11 15 18 34| Scale is weakly epimorphic with val: <7 11 15 20 32| Scale is weakly epimorphic with val: <7 11 15 20 35| Scale is weakly epimorphic with val: <7 11 15 21 31| Scale is weakly epimorphic with val: <7 11 15 21 34| Scale is weakly epimorphic with val: <7 11 16 18 30| Scale is weakly epimorphic with val: <7 11 16 18 33| Scale is weakly epimorphic with val: <7 11 16 18 36| Scale is JI-epimorphic with val: <7 11 16 19 32| Scale is weakly epimorphic with val: <7 11 16 19 35| Scale is weakly epimorphic with val: <7 11 16 21 30| Scale is weakly epimorphic with val: <7 11 16 21 33| Scale is weakly epimorphic with val: <7 11 16 21 36| Scale is weakly epimorphic with val: <7 11 16 22 32| Scale is weakly epimorphic with val: <7 11 16 22 35| Scale is weakly epimorphic with val: <7 11 17 19 31| Scale is weakly epimorphic with val: <7 11 17 19 34| Scale is weakly epimorphic with val: <7 11 17 20 30| Scale is JI-epimorphic with val: <7 11 17 20 33| = patent Scale is weakly epimorphic with val: <7 11 17 20 36| Scale is weakly epimorphic with val: <7 11 17 22 31| Scale is weakly epimorphic with val: <7 11 17 22 34| Scale is weakly epimorphic with val: <7 11 18 18 31| Scale is weakly epimorphic with val: <7 11 18 18 34| Scale is weakly epimorphic with val: <7 11 18 20 32| Scale is weakly epimorphic with val: <7 11 18 20 35| Scale is weakly epimorphic with val: <7 11 18 21 31| Scale is JI-epimorphic with val: <7 11 18 21 34| Scale is weakly epimorphic with val: <7 11 19 19 32| Scale is weakly epimorphic with val: <7 11 19 19 35| Scale is weakly epimorphic with val: <7 11 19 21 30| Scale is weakly epimorphic with val: <7 11 19 21 33| Scale is weakly epimorphic with val: <7 11 19 21 36| Scale is weakly epimorphic with val: <7 11 19 22 32| Scale is JI-epimorphic with val: <7 11 19 22 35| Scale is weakly epimorphic with val: <7 12 15 18 33| Scale is weakly epimorphic with val: <7 12 15 19 35| Scale is weakly epimorphic with val: <7 12 15 21 36| Scale is weakly epimorphic with val: <7 12 15 22 35| Scale is weakly epimorphic with val: <7 12 16 19 34| Scale is weakly epimorphic with val: <7 12 16 20 36| Scale is weakly epimorphic with val: <7 12 17 20 35| Scale is weakly epimorphic with val: <7 12 18 18 33| Scale is weakly epimorphic with val: <7 12 18 21 36| Scale is weakly epimorphic with val: <7 12 19 19 34| Scale is weakly epimorphic with val: <8 11 15 19 33| Scale is weakly epimorphic with val: <8 11 15 20 32| Scale is weakly epimorphic with val: <8 11 15 22 36| Scale is weakly epimorphic with val: <8 11 16 18 33| Scale is weakly epimorphic with val: <8 11 16 20 34| Scale is weakly epimorphic with val: <8 11 16 21 33| Scale is weakly epimorphic with val: <8 11 17 18 32| Scale is weakly epimorphic with val: <8 11 17 19 34| Scale is weakly epimorphic with val: <8 11 17 21 35| Scale is weakly epimorphic with val: <8 11 17 22 34| Scale is weakly epimorphic with val: <8 11 18 19 33| Scale is weakly epimorphic with val: <8 11 18 20 35| Scale is weakly epimorphic with val: <8 11 18 22 36| Scale is weakly epimorphic with val: <8 11 19 20 34| Scale is weakly epimorphic with val: <8 11 19 21 36| Scale is weakly epimorphic with val: <8 12 15 18 33| Scale is weakly epimorphic with val: <8 12 15 20 34| Scale is weakly epimorphic with val: <8 12 15 21 36| Scale is weakly epimorphic with val: <8 12 16 18 35| Scale is weakly epimorphic with val: <8 12 16 19 34| Scale is weakly epimorphic with val: <8 12 16 21 35| Scale is weakly epimorphic with val: <8 12 17 19 36| Scale is weakly epimorphic with val: <8 12 17 20 35| Scale is weakly epimorphic with val: <8 12 17 22 36| Scale is weakly epimorphic with val: <8 12 18 18 33| Scale is weakly epimorphic with val: <8 12 18 21 36| Scale is weakly epimorphic with val: <8 12 19 19 34|
FIT/MODE
3: 0 1 2 N G T3 SD: 22.5127 c. M: 38.0506 c. 7: 0 2 5 N G T3 SD: 23.6554 c. M: 38.0506 c. 9: 1 2 6 N T3 SD: 11.1278 c. M:-17.2877 c. 10: 1 2 7 N T3 SD: 8.2349 c. M:-11.7539 c. 12: 1 3 8 N T3 SD: 5.3085 c. M:-8.5216 c. 13: 1 3 9 N T3 SD: 2.4577 c. M: 4.2488 c. 25: 2 6 17 N T3 SD: 1.5003 c. M:-1.8810 c. 38: 3 9 26 N T3 SD: 0.7430 c. M:-1.2687 c. 51: 4 12 35 N T3 SD: 0.9258 c. M: 1.2440 c. 54: 4 13 37 N T3 SD: 0.7819 c. M: 1.1584 c. 66: 5 16 45 N T3 SD: 0.5927 c. M:-0.9754 c. 79: 6 19 54 N T3 SD: 0.1458 c. M: 0.2244 c. 117: 9 28 80 N T3 SD: 0.1505 c. M:-0.2605 c. 171: 13 41 117 N T3 SD: 0.1652 c. M: 0.2161 c. 196: 15 47 134 N T3 SD: 0.0479 c. M:-0.0651 c. 275: 21 66 188 N T3 SD: 0.0417 c. M:-0.0699 c. 471: 36 113 322 N T3 SD: 0.0372 c. M:-0.0622 c. 484: 37 116 331 N T3 SD: 0.0337 c. M: 0.0536 c. 563: 43 135 385 N T3 SD: 0.0185 c. M: 0.0298 c. 759: 58 182 519 N T3 SD: 0.0069 c. M: 0.0089 c. 1034: 79 248 707 N T3 SD: 0.0070 c. M:-0.0121 c. 1597: 122 383 1092 N T3 SD: 0.0025 c. M: 0.0034 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: 89.6458 cents 6 x 7:8 S SD: 54.6887 cents 7 x 8:9 S SD: 48.4585 cents 8 x 9:11 SD: 35.3288 cents 9 x 10:12 S SD: 12.4551 cents 10 x 11:13 SD: 22.2350 cents 11 x 12:15 S SD: 19.7527 cents 12 x 13:16 SD: 9.4604 cents 13 x 14:17 SD: 22.2625 cents 14 x 15:19 SD: 24.4274 cents 15 x 16:20 S SD: 22.8811 cents 16 x 18:21 S SD: 26.9157 cents 17 x 19:23 SD: 21.6117 cents 18:19:20:24 S SD: 20.2939 cents 19:20:21:25 SD: 19.2937 cents 20:21:22:27 SD: 17.2351 cents 21:22:23:28 SD: 14.1621 cents 23:24:25:31 SD: 14.1125 cents 24:25:26:32 SD: 12.5706 cents 27:28:30:36 S SD: 11.7428 cents 28:29:31:37 SD: 11.0890 cents 29:30:32:39 SD: 9.5105 cents 30:31:33:40 SD: 6.7223 cents 33:34:36:44 SD: 5.0863 cents 39:40:43:52 SD: 4.3027 cents 41:42:45:55 SD: 3.9110 cents 42:43:46:56 SD: 0.8954 cents 135:138:148:180 SD: 0.5573 cents 177:181:194:236 SD: 0.4753 cents 180:184:197:240 SD: 0.4183 cents 222:227:243:296 SD: 0.3792 cents 231:236:253:308 SD: 0.3259 cents 273:279:299:364 SD: 0.1379 cents 315:322:345:420 SD: 0.0000 cents