Scala analysis: 313_C24
Chromatic tetrachord 92/91 * 26/23 * 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 92/91 18.920779 2: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 92/91 18.9208 2: 26/23 212.2533 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 92/91 18.921 cents 1: 1 26/23 212.253 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 46/39 285.792 cents 2: 1 91/69 479.124 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 : 18.9 231.2 498.0 18.9 : 212.3 479.1 498.0 231.2: 266.9 285.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 18.9208 .. 266.8709 cents 637/552, 247.9501 cents 92/91, 18.9208 cents 2: 231.1741 .. 479.1242 cents 637/552, 247.9501 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 92/91, 18.9208 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 8.774216 Largest / Average step : 1.607511 Largest / Smallest step : 14.104647 Median interval of one step : 26/23, 212.2533 cents, amount: 1 Least squares average step : 141.10028 cents, oct.: 423.30085 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2079-tone equal temperament with octave 4/3 degrees: 79 965 2079 Least number of segments generator : 1040 of 249.142 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1420 of 340.175 cents and inv. generated superset size: 146 = 143 more = 4866.667% 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 18.92078 cents Scale diversity : 0.449902 Lumma stability : 0.075980 Lumma impropriety factor : 0.071674 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 : 92/91, 18.9208 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 : 91 (O: 91 U: 91) Highest odd numerator or denominator: 91 Scale harmonicity : 0.012470 Average absolute harmonicity : 0.100874 Specific harmonicity : 0.063779 Fundamental : 1/273, -8.0928 octaves, 0.9583 Hz. Guide tone : 184, 7.5236 octaves, 48139.104 Hz. Exponens Consonantiae : 5.023200E+04, 15.61632 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 102.5, average 34.16667 Mersenne's string divisions : 6405 Sum of van Prooijen's expressibility: 3.28126, average 1.09375 Sum of Tenney's harmonic distance : 6.75020, average 2.25007 Vogel's harmonic complexity : 23.00000 Wille's k value : 45 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.50820, average 2.25137 Lattice compactness (without 2's) : 8.56048, average 1.42675 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 0 -0.33333 1 1 7: -1 .. 0 -0.66667 2 1 13: -1 .. 0 -0.33333 1 23: 0 .. 1 0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 20 25 36| Scale is weakly epimorphic with val: <6 11 19 25 35| Scale is weakly epimorphic with val: <6 11 19 26 36| Scale is weakly epimorphic with val: <7 10 18 25 31| Scale is weakly epimorphic with val: <7 10 18 25 34| Scale is weakly epimorphic with val: <7 10 18 26 32| Scale is weakly epimorphic with val: <7 10 18 26 35| Scale is weakly epimorphic with val: <7 10 18 27 30| Scale is weakly epimorphic with val: <7 10 18 27 33| Scale is weakly epimorphic with val: <7 10 18 27 36| Scale is weakly epimorphic with val: <7 10 18 28 31| Scale is weakly epimorphic with val: <7 10 18 28 34| Scale is weakly epimorphic with val: <7 10 18 29 32| Scale is weakly epimorphic with val: <7 10 18 29 35| Scale is weakly epimorphic with val: <7 10 18 30 30| Scale is weakly epimorphic with val: <7 10 18 30 33| Scale is weakly epimorphic with val: <7 10 18 30 36| Scale is weakly epimorphic with val: <7 10 19 25 33| Scale is weakly epimorphic with val: <7 10 19 26 34| Scale is weakly epimorphic with val: <7 10 19 27 35| Scale is weakly epimorphic with val: <7 10 19 28 36| Scale is weakly epimorphic with val: <7 10 22 25 36| Scale is JI-epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 25 34| Scale is JI-epimorphic with val: <7 11 19 26 32| Scale is weakly epimorphic with val: <7 11 19 26 35| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is JI-epimorphic with val: <7 11 19 27 33| Scale is weakly epimorphic with val: <7 11 19 27 36| Scale is weakly epimorphic with val: <7 11 19 28 31| Scale is JI-epimorphic with val: <7 11 19 28 34| Scale is weakly epimorphic with val: <7 11 19 29 32| Scale is JI-epimorphic with val: <7 11 19 29 35| Scale is weakly epimorphic with val: <7 11 19 30 30| Scale is weakly epimorphic with val: <7 11 19 30 33| Scale is JI-epimorphic with val: <7 11 19 30 36| Scale is weakly epimorphic with val: <7 11 20 25 30| Scale is weakly epimorphic with val: <7 11 20 25 33| Scale is weakly epimorphic with val: <7 11 20 25 36| Scale is weakly epimorphic with val: <7 11 20 26 31| Scale is weakly epimorphic with val: <7 11 20 26 34| Scale is weakly epimorphic with val: <7 11 20 27 32| Scale is weakly epimorphic with val: <7 11 20 27 35| Scale is weakly epimorphic with val: <7 11 20 28 30| Scale is weakly epimorphic with val: <7 11 20 28 33| Scale is weakly epimorphic with val: <7 11 20 28 36| Scale is weakly epimorphic with val: <7 11 20 29 31| Scale is weakly epimorphic with val: <7 11 20 29 34| Scale is weakly epimorphic with val: <7 11 20 30 32| Scale is weakly epimorphic with val: <7 11 20 30 35| Scale is weakly epimorphic with val: <7 11 22 25 31| Scale is weakly epimorphic with val: <7 11 22 25 34| Scale is weakly epimorphic with val: <7 11 22 26 32| Scale is weakly epimorphic with val: <7 11 22 26 35| Scale is weakly epimorphic with val: <7 11 22 27 30| Scale is weakly epimorphic with val: <7 11 22 27 33| Scale is weakly epimorphic with val: <7 11 22 27 36| Scale is weakly epimorphic with val: <7 11 22 28 31| Scale is weakly epimorphic with val: <7 11 22 28 34| Scale is weakly epimorphic with val: <7 11 22 29 32| Scale is weakly epimorphic with val: <7 11 22 29 35| Scale is weakly epimorphic with val: <7 11 22 30 30| Scale is weakly epimorphic with val: <7 11 22 30 33| Scale is weakly epimorphic with val: <7 11 22 30 36| Scale is weakly epimorphic with val: <7 12 18 25 30| Scale is weakly epimorphic with val: <7 12 18 25 33| Scale is weakly epimorphic with val: <7 12 18 25 36| Scale is weakly epimorphic with val: <7 12 18 26 31| Scale is weakly epimorphic with val: <7 12 18 26 34| Scale is weakly epimorphic with val: <7 12 18 27 32| Scale is weakly epimorphic with val: <7 12 18 27 35| Scale is weakly epimorphic with val: <7 12 18 28 30| Scale is weakly epimorphic with val: <7 12 18 28 33| Scale is weakly epimorphic with val: <7 12 18 28 36| Scale is weakly epimorphic with val: <7 12 18 29 31| Scale is weakly epimorphic with val: <7 12 18 29 34| Scale is weakly epimorphic with val: <7 12 18 30 32| Scale is weakly epimorphic with val: <7 12 18 30 35| Scale is weakly epimorphic with val: <7 12 20 25 34| Scale is weakly epimorphic with val: <7 12 20 26 35| Scale is weakly epimorphic with val: <7 12 20 27 36| Scale is weakly epimorphic with val: <8 11 20 25 32| Scale is weakly epimorphic with val: <8 11 20 26 33| Scale is weakly epimorphic with val: <8 11 20 27 34| Scale is weakly epimorphic with val: <8 11 20 28 35| Scale is weakly epimorphic with val: <8 11 20 29 36| Scale is weakly epimorphic with val: <8 11 21 25 31| Scale is weakly epimorphic with val: <8 11 21 25 34| Scale is weakly epimorphic with val: <8 11 21 26 32| Scale is weakly epimorphic with val: <8 11 21 26 35| Scale is weakly epimorphic with val: <8 11 21 27 30| Scale is weakly epimorphic with val: <8 11 21 27 33| Scale is weakly epimorphic with val: <8 11 21 27 36| Scale is weakly epimorphic with val: <8 11 21 28 31| Scale is weakly epimorphic with val: <8 11 21 28 34| Scale is weakly epimorphic with val: <8 11 21 29 32| Scale is weakly epimorphic with val: <8 11 21 29 35| Scale is weakly epimorphic with val: <8 11 21 30 30| Scale is weakly epimorphic with val: <8 11 21 30 33| Scale is weakly epimorphic with val: <8 11 21 30 36| Scale is weakly epimorphic with val: <8 12 19 25 31| Scale is weakly epimorphic with val: <8 12 19 26 32| Scale is weakly epimorphic with val: <8 12 19 27 33| Scale is weakly epimorphic with val: <8 12 19 28 34| Scale is weakly epimorphic with val: <8 12 19 29 35| Scale is weakly epimorphic with val: <8 12 19 30 36| Scale is weakly epimorphic with val: <8 12 21 25 32| Scale is weakly epimorphic with val: <8 12 21 25 35| Scale is weakly epimorphic with val: <8 12 21 26 30| Scale is weakly epimorphic with val: <8 12 21 26 33| Scale is weakly epimorphic with val: <8 12 21 26 36| Scale is weakly epimorphic with val: <8 12 21 27 31| Scale is weakly epimorphic with val: <8 12 21 27 34| Scale is weakly epimorphic with val: <8 12 21 28 32| Scale is weakly epimorphic with val: <8 12 21 28 35| Scale is weakly epimorphic with val: <8 12 21 29 30| Scale is weakly epimorphic with val: <8 12 21 29 33| Scale is weakly epimorphic with val: <8 12 21 29 36| Scale is weakly epimorphic with val: <8 12 21 30 31| Scale is weakly epimorphic with val: <8 12 21 30 34| Scale is weakly epimorphic with val: <8 12 22 25 34| Scale is weakly epimorphic with val: <8 12 22 26 35| Scale is weakly epimorphic with val: <8 12 22 27 36|
FIT/MODE
3: 0 1 2 N G T3 SD: 39.1736 c. M: 65.1591 c. 4: 0 2 2 P M DE S SD: 15.0173 c. M: 18.9208 c. 7: 0 3 4 N G T3 SD: 14.9690 c. M: 18.9208 c. 9: 0 4 5 N G T3 SD: 12.3078 c. M: 18.9208 c. 11: 0 5 6 N G T3 SD: 11.2685 c. M: 18.9208 c. 13: 0 6 7 N G T3 SD: 10.9500 c. M: 18.9208 c. 15: 1 6 8 N T3 SD: 8.2772 c. M:-14.2822 c. 16: 1 6 9 N T3 SD: 10.4140 c. M: 13.2794 c. 17: 1 7 9 N T3 SD: 6.2690 c. M:-10.3760 c. 18: 1 7 10 N T3 SD: 7.5935 c. M: 9.8208 c. 19: 1 8 10 N T3 SD: 5.0220 c. M:-7.2921 c. 20: 1 8 11 N T3 SD: 5.3396 c. M: 7.0538 c. 21: 1 9 11 N T3 SD: 4.4302 c. M:-5.9902 c. 22: 1 9 12 N T3 SD: 3.5007 c. M: 4.7900 c. 24: 1 10 13 N T3 SD: 1.9818 c. M: 2.9035 c. 26: 1 11 14 N T3 SD: 0.7668 c. M: 1.3072 c. 28: 1 12 15 N T3 SD: 0.6554 c. M: 1.1335 c. 54: 2 23 29 N T3 SD: 0.4407 c. M: 0.5977 c. 127: 5 54 68 N T3 SD: 0.4135 c. M:-0.6873 c. 129: 5 55 69 N T3 SD: 0.3523 c. M:-0.4747 c. 155: 6 66 83 N T3 SD: 0.2305 c. M:-0.3584 c. 181: 7 77 97 N T3 SD: 0.1978 c. M:-0.3406 c. 183: 7 78 98 N T3 SD: 0.1183 c. M:-0.1583 c. 209: 8 89 112 N T3 SD: 0.0838 c. M:-0.1431 c. 237: 9 101 127 N T3 SD: 0.0092 c. M: 0.0140 c. 1368: 52 583 733 N T3 SD: 0.0081 c. M:-0.0108 c. 1605: 61 684 860 N T3 SD: 0.0057 c. M:-0.0080 c. 1842: 70 785 987 N T3 SD: 0.0039 c. M:-0.0060 c. 2079: 79 886 1114 N T3 SD: 0.0027 c. M:-0.0045 c. 2316: 88 987 1241 N T3 SD: 0.0019 c. M:-0.0032 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: 59.7273 cents 6 x 7:8 S SD: 17.8484 cents 7 x 8:9 S SD: 31.4805 cents 8 x 9:11 SD: 29.9221 cents 9 x 10:12 S SD: 24.3852 cents 10 x 11:13 SD: 39.6850 cents 11 x 13:15 SD: 34.9349 cents 12 x 14:16 S SD: 17.8484 cents 13 x 15:17 SD: 18.7389 cents 26:27:30:35 S SD: 17.3315 cents 27:28:31:36 SD: 14.9201 cents 28:29:32:37 SD: 14.8731 cents 29:30:33:39 SD: 14.3700 cents 30:31:34:40 SD: 13.5081 cents 33:34:38:44 SD: 11.7570 cents 34:35:39:45 SD: 11.4553 cents 35:36:40:47 SD: 10.7643 cents 36:37:41:48 SD: 9.7141 cents 40:41:46:53 SD: 9.4395 cents 41:42:47:55 SD: 8.5523 cents 42:43:48:56 SD: 7.2720 cents 47:48:54:63 S SD: 7.2719 cents 48:49:55:64 SD: 5.7899 cents 51:52:58:68 SD: 5.6604 cents 54:55:62:72 SD: 5.0438 cents 55:56:63:73 SD: 5.0364 cents 56:57:64:75 SD: 4.6769 cents 57:58:65:76 SD: 3.9388 cents 62:63:71:83 SD: 3.9126 cents 63:64:72:84 S SD: 2.7811 cents 69:70:79:92 SD: 2.2532 cents 77:78:88:103 SD: 2.1903 cents 78:79:89:104 SD: 1.3956 cents 84:85:96:112 SD: 0.5225 cents 174:176:199:232 SD: 0.5048 cents 183:185:209:244 SD: 0.3958 cents 189:191:216:252 SD: 0.2324 cents 273:276:312:364 SD: 0.0000 cents