Scala analysis: 295_C21
Chromatic tetrachord 68/67 * 67/57 * 19/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/67 25.648381 2: 68/57 305.487393 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/17 192.5576 quasi-meantone 1: 68/67 25.6484 2: 67/57 279.8390 3: 19/17 192.5576 quasi-meantone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68/67 25.648 cents 1: 1 19/17 192.558 cents quasi-meantone 1: 1 67/57 279.839 cents 2: 1 76/67 218.206 cents 2: 1 68/57 305.487 cents 2: 1 67/51 472.397 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 : 25.6 305.5 498.0 25.6 : 279.8 472.4 498.0 305.5: 192.6 218.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.6484 .. 279.8390 cents 4489/3876, 254.1906 cents 68/67, 25.6484 cents 2: 218.2060 .. 472.3966 cents 4489/3876, 254.1906 cents 4332/4489,-61.6330 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 68/67, 25.6484 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 67/57, 279.8390 cents Average / Smallest step : 6.472728 Largest / Average step : 1.685625 Largest / Smallest step : 10.910592 Median interval of one step : 19/17, 192.5576 cents, amount: 1 Least squares average step : 152.19701 cents, oct.: 456.59104 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1107-tone equal temperament with octave 4/3 degrees: 57 679 1107 Least number of segments generator : 554 of 249.247 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1010 of 454.404 cents and inv. generated superset size: 13 = 10 more = 433.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 25.64838 cents Scale diversity : 0.573647 Lumma stability : 0.102996 Lumma impropriety factor : 0.123750 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 : 68/67, 25.6484 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 67 Odd number limit : 67 (O: 67 U: 67) Highest odd numerator or denominator: 67 Scale harmonicity : 0.014516 Fundamental : 1/3819, -11.8990 octaves, 0.0685 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 2.596920E+05, 17.98644 octaves Euler's gradus suavitatis : 105 Sum of Mann's harmonic distance : 133.5, average 44.50000 Mersenne's string divisions : 23625 Sum of van Prooijen's expressibility: 4.05907, average 1.35302 Sum of Tenney's harmonic distance : 8.32615, average 2.77538 Vogel's harmonic complexity : 71.66667 Wille's k value : 636 Wilson's harmonic complexity : 106 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 11.36053, average 1.89342 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 0 -0.66667 2 1 17: 0 .. 1 0.66667 2 19: -1 .. 0 -0.33333 1 1 67: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 27 28 45| Scale is weakly epimorphic with val: <7 10 28 29 43| Scale is weakly epimorphic with val: <7 10 29 30 44| Scale is weakly epimorphic with val: <7 10 30 31 45| Scale is weakly epimorphic with val: <7 10 31 32 43| Scale is weakly epimorphic with val: <7 10 32 33 44| Scale is weakly epimorphic with val: <7 10 32 34 43| Scale is weakly epimorphic with val: <7 10 33 34 45| Scale is weakly epimorphic with val: <7 11 27 28 43| Scale is weakly epimorphic with val: <7 11 27 29 45| Scale is weakly epimorphic with val: <7 11 27 31 43| Scale is weakly epimorphic with val: <7 11 27 32 45| Scale is weakly epimorphic with val: <7 11 27 34 43| Scale is weakly epimorphic with val: <7 11 28 29 44| Scale is weakly epimorphic with val: <7 11 28 30 43| Scale is weakly epimorphic with val: <7 11 28 32 44| Scale is weakly epimorphic with val: <7 11 28 33 43| Scale is weakly epimorphic with val: <7 11 29 30 45| Scale is weakly epimorphic with val: <7 11 29 31 44| Scale is weakly epimorphic with val: <7 11 29 33 45| Scale is weakly epimorphic with val: <7 11 29 34 44| Scale is JI-epimorphic with val: <7 11 30 31 43| Scale is weakly epimorphic with val: <7 11 30 32 45| Scale is weakly epimorphic with val: <7 11 30 34 43| Scale is JI-epimorphic with val: <7 11 31 32 44| Scale is weakly epimorphic with val: <7 11 31 33 43| Scale is JI-epimorphic with val: <7 11 32 33 45| Scale is weakly epimorphic with val: <7 11 32 34 44| Scale is weakly epimorphic with val: <7 11 33 34 43| Scale is weakly epimorphic with val: <7 12 32 33 43| Scale is weakly epimorphic with val: <7 12 33 34 44| Scale is weakly epimorphic with val: <8 11 27 29 45| Scale is weakly epimorphic with val: <8 11 28 30 43| Scale is weakly epimorphic with val: <8 11 29 31 44| Scale is weakly epimorphic with val: <8 11 30 31 43| Scale is weakly epimorphic with val: <8 11 30 32 45| Scale is weakly epimorphic with val: <8 11 30 34 43| Scale is weakly epimorphic with val: <8 11 31 32 44| Scale is weakly epimorphic with val: <8 11 31 33 43| Scale is weakly epimorphic with val: <8 11 32 33 45| Scale is weakly epimorphic with val: <8 11 32 34 44| Scale is weakly epimorphic with val: <8 12 27 28 44| Scale is weakly epimorphic with val: <8 12 28 29 45| Scale is weakly epimorphic with val: <8 12 29 30 43| Scale is weakly epimorphic with val: <8 12 30 31 44| Scale is weakly epimorphic with val: <8 12 30 32 43| Scale is weakly epimorphic with val: <8 12 31 32 45| Scale is weakly epimorphic with val: <8 12 31 33 44| Scale is weakly epimorphic with val: <8 12 32 33 43| Scale is weakly epimorphic with val: <8 12 32 34 45| Scale is weakly epimorphic with val: <8 12 33 34 44|
FIT/MODE
3: 0 2 1 N G T3 SD: 21.3100 c. M:-26.5426 c. 5: 0 3 2 N G T3 SD: 15.2992 c. M: 25.6484 c. 8: 0 5 3 N G T3 SD: 15.1808 c. M: 25.6484 c. 11: 1 6 4 N T3 SD: 13.1198 c. M:-19.6284 c. 13: 1 7 5 N T3 SD: 7.3337 c. M:-12.6628 c. 15: 1 8 6 N T3 SD: 5.8147 c. M:-7.5546 c. 16: 1 9 6 N T3 SD: 4.6028 c. M:-5.7907 c. 18: 1 10 7 N T3 SD: 1.3358 c. M:-2.0208 c. 39: 2 22 15 N T3 SD: 0.5817 c. M:-1.0018 c. 57: 3 32 22 N T3 SD: 0.3774 c. M:-0.5645 c. 98: 5 55 38 N T3 SD: 0.3523 c. M: 0.5619 c. 119: 6 67 46 N T3 SD: 0.3107 c. M: 0.5369 c. 137: 7 77 53 N T3 SD: 0.1341 c. M: 0.2008 c. 176: 9 99 68 N T3 SD: 0.1287 c. M: 0.1802 c. 194: 10 109 75 N T3 SD: 0.0162 c. M:-0.0240 c. 719: 37 404 278 N T3 SD: 0.0125 c. M: 0.0188 c. 913: 47 513 353 N T3 SD: 0.0064 c. M: 0.0097 c. 1107: 57 622 428 N T3 SD: 0.0024 c. M: 0.0038 c. 1301: 67 731 503 N T3 SD: 0.0004 c. M:-0.0006 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 5 x S SD: 80.8263 cents 5 x 6:7 S SD: 42.5377 cents 6 x 7:8 S SD: 19.3082 cents 7 x 8:9 S SD: 48.6994 cents 8 x 10:11 S SD: 48.4017 cents 9 x 11:12 SD: 20.9603 cents 21:22:25:28 SD: 18.3364 cents 24:25:29:32 SD: 16.7236 cents 25:26:30:33 SD: 15.6029 cents 26:27:31:35 SD: 14.3397 cents 27:28:32:36 S SD: 13.0004 cents 30:31:36:40 SD: 10.9111 cents 31:32:37:41 SD: 10.8352 cents 32:33:38:43 SD: 10.5842 cents 33:34:39:44 SD: 10.2347 cents 35:36:42:47 SD: 9.3664 cents 36:37:43:48 SD: 7.2962 cents 41:42:49:55 SD: 6.4861 cents 42:43:50:56 SD: 5.1738 cents 46:47:55:61 SD: 5.1443 cents 47:48:56:63 S SD: 4.7807 cents 48:49:57:64 SD: 4.2761 cents 51:52:61:68 SD: 3.0484 cents 57:58:68:76 SD: 1.4869 cents 63:64:75:84 SD: 1.3278 cents 72:73:86:96 SD: 0.9204 cents 129:131:154:172 SD: 0.5136 cents 135:137:161:180 SD: 0.1988 cents 264:268:315:352 SD: 0.1607 cents 399:405:476:532 SD: 0.0638 cents 534:542:637:712 SD: 0.0573 cents