Scala analysis: 148_C4
Chromatic tetrachord 81/77 * 77/75 * 100/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/77 87.676155 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: 81/77 87.6762 2: 77/75 45.5614 3: 100/81 364.8074 grave major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 77/75 45.561 cents 1: 1 81/77 87.676 cents 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: 1 308/243 410.369 cents 2: 1 100/77 452.484 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 : 87.7 133.2 498.0 87.7 : 45.6 410.4 498.0 133.2: 364.8 452.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 45.5614 .. 364.8074 cents 2500/2079, 319.2460 cents 77/75, 45.5614 cents 2: 133.2376 .. 452.4836 cents 2500/2079, 319.2460 cents 2187/2500,-231.5698 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 77/75, 45.5614 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 100/81, 364.8074 cents Average / Smallest step : 3.643763 Largest / Average step : 2.197437 Largest / Smallest step : 8.006937 Median interval of one step : 81/77, 87.6762 cents, amount: 1 Least squares average step : 132.02045 cents, oct.: 396.06135 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1869-tone equal temperament with octave 4/3 degrees: 329 500 1869 Least number of segments generator : 935 of 249.156 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1382 of 368.271 cents and inv. generated superset size: 23 = 20 more = 766.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 45.56142 cents Scale diversity : 0.632539 Lumma stability : 0.182961 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 : 6075/5929, 42.1147 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 11 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.017668 Average absolute harmonicity : 0.095971 Specific harmonicity : 0.089987 Fundamental : 1/5775, -12.4956 octaves, 0.0453 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 1.871100E+06, 20.83546 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 108.5, average 36.16667 Mersenne's string divisions : 28756 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.70346, average 2.56782 Vogel's harmonic complexity : 28.33333 Wille's k value : 3118 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 23.19676, average 3.86613 Lattice compactness (without 2's) : 21.16223, average 3.52704 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 4 2.00000 8 1 5: -2 .. 0 -0.66667 2 1 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 12 / 3 = 4.00000 Scale is weakly epimorphic with val: <6 11 15 18 24| Scale is weakly epimorphic with val: <6 11 15 18 27| Scale is weakly epimorphic with val: <6 11 15 19 23| Scale is weakly epimorphic with val: <6 11 15 19 26| Scale is weakly epimorphic with val: <6 11 15 20 25| Scale is weakly epimorphic with val: <6 11 15 21 24| Scale is weakly epimorphic with val: <6 11 15 21 27| Scale is weakly epimorphic with val: <6 11 15 22 23| Scale is weakly epimorphic with val: <6 11 15 22 26| Scale is weakly epimorphic with val: <6 11 17 18 23| Scale is weakly epimorphic with val: <7 11 16 18 24| Scale is weakly epimorphic with val: <7 11 16 18 27| Scale is weakly epimorphic with val: <7 11 16 19 23| Scale is weakly epimorphic with val: <7 11 16 19 26| Scale is weakly epimorphic with val: <7 11 16 20 25| Scale is weakly epimorphic with val: <7 11 16 21 24| Scale is weakly epimorphic with val: <7 11 16 21 27| Scale is weakly epimorphic with val: <7 11 16 22 23| Scale is weakly epimorphic with val: <7 11 16 22 26| Scale is weakly epimorphic with val: <7 11 17 18 25| Scale is weakly epimorphic with val: <7 11 17 19 24| Scale is weakly epimorphic with val: <7 11 17 19 27| Scale is weakly epimorphic with val: <7 11 17 20 23| Scale is weakly epimorphic with val: <7 11 17 20 26| Scale is weakly epimorphic with val: <7 11 17 21 25| Scale is weakly epimorphic with val: <7 11 17 22 24| Scale is weakly epimorphic with val: <7 11 17 22 27| Scale is weakly epimorphic with val: <7 11 19 19 23| Scale is weakly epimorphic with val: <7 11 19 19 26| Scale is weakly epimorphic with val: <7 11 19 20 25| Scale is weakly epimorphic with val: <7 11 19 21 24| Scale is weakly epimorphic with val: <7 11 19 21 27| Scale is weakly epimorphic with val: <7 11 19 22 23| Scale is weakly epimorphic with val: <7 11 19 22 26| Scale is weakly epimorphic with val: <7 12 16 18 27| Scale is weakly epimorphic with val: <7 12 16 19 26| Scale is weakly epimorphic with val: <7 12 16 20 25| Scale is weakly epimorphic with val: <7 12 16 21 24| Scale is weakly epimorphic with val: <7 12 16 22 23| Scale is weakly epimorphic with val: <7 12 19 19 26| Scale is weakly epimorphic with val: <7 12 19 20 25| Scale is weakly epimorphic with val: <7 12 19 21 24| Scale is weakly epimorphic with val: <7 12 19 22 23| Scale is weakly epimorphic with val: <8 11 15 18 25| Scale is weakly epimorphic with val: <8 11 15 19 24| Scale is weakly epimorphic with val: <8 11 15 19 27| Scale is weakly epimorphic with val: <8 11 15 20 23| Scale is weakly epimorphic with val: <8 11 15 20 26| Scale is weakly epimorphic with val: <8 11 15 21 25| Scale is weakly epimorphic with val: <8 11 15 22 24| Scale is weakly epimorphic with val: <8 11 15 22 27| Scale is weakly epimorphic with val: <8 11 16 18 23| Scale is weakly epimorphic with val: <8 12 17 18 27| Scale is weakly epimorphic with val: <8 12 17 19 26| Scale is weakly epimorphic with val: <8 12 17 20 25| Scale is weakly epimorphic with val: <8 12 17 21 24| Scale is weakly epimorphic with val: <8 12 17 22 23|
FIT/MODE
3: 1 0 2 N G T3 SD: 49.0283 c. M:-78.3388 c. 4: 1 0 3 N G T3 SD: 21.8554 c. M:-36.8351 c. 5: 1 0 4 N G T3 SD: 20.6016 c. M: 33.6286 c. 6: 1 1 4 N M DE S SD: 19.1151 c. M:-32.7774 c. 7: 1 1 5 N M DE S SD: 10.8818 c. M: 16.5269 c. 10: 2 1 7 N T3 SD: 11.6054 c. M:-16.1759 c. 11: 2 1 8 N T3 SD: 2.2363 c. M:-2.8775 c. 23: 4 2 17 N T3 SD: 2.0081 c. M: 3.3128 c. 34: 6 3 25 N T3 SD: 0.8189 c. M: 1.4021 c. 45: 8 4 33 N T3 SD: 0.5567 c. M:-0.8652 c. 79: 14 7 58 N T3 SD: 0.5938 c. M: 0.8459 c. 86: 15 8 63 N T3 SD: 0.4670 c. M: 0.8078 c. 97: 17 9 71 N T3 SD: 0.2703 c. M: 0.3899 c. 108: 19 10 79 N T3 SD: 0.2887 c. M:-0.4967 c. 131: 23 12 96 N T3 SD: 0.1673 c. M: 0.2331 c. 142: 25 13 104 N T3 SD: 0.0247 c. M:-0.0421 c. 602: 106 55 441 N T3 SD: 0.0254 c. M: 0.0395 c. 699: 123 64 512 N T3 SD: 0.0216 c. M: 0.0373 c. 744: 131 68 545 N T3 SD: 0.0170 c. M: 0.0239 c. 841: 148 77 616 N T3 SD: 0.0179 c. M: 0.0297 c. 886: 156 81 649 N T3 SD: 0.0119 c. M:-0.0157 c. 1028: 181 94 753 N T3 SD: 0.0091 c. M:-0.0146 c. 1170: 206 107 857 N T3 SD: 0.0080 c. M:-0.0138 c. 1312: 231 120 961 N T3 SD: 0.0081 c. M:-0.0132 c. 1443: 254 132 1057 N T3 SD: 0.0085 c. M: 0.0114 c. 1585: 279 145 1161 N T3 SD: 0.0058 c. M: 0.0077 c. 1727: 304 158 1265 N T3 SD: 0.0040 c. M: 0.0064 c. 1869: 329 171 1369 N T3 SD: 0.0031 c. M: 0.0053 c. 2011: 354 184 1473 N T3 SD: 0.0033 c. M: 0.0044 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 16:17 x 21 SD: 16.1393 cents 17:18 x 23 SD: 13.8381 cents 18:19 x 24 SD: 2.9634 cents 29 x 31:39 SD: 11.5859 cents 30 x 32:40 S SD: 10.7531 cents 31:33 x 41 SD: 12.4426 cents 32:34:35:43 SD: 10.3268 cents 33:35:36:44 SD: 7.4842 cents 34:36:37:45 SD: 7.1756 cents 35:37:38:47 SD: 5.8502 cents 36:38:39:48 SD: 2.6581 cents 39:41:42:52 SD: 1.6865 cents 75:79:81:100 SD: 0.7594 cents 114:120:123:152 SD: 0.6761 cents 174:183:188:232 SD: 0.2746 cents 213:224:230:284 SD: 0.1951 cents 288:303:311:384 SD: 0.1050 cents 462:486:499:616 SD: 0.0463 cents