Scala analysis: 122_E15
Enharmonic tetrachord 45/43 * 43/42 * 56/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 45/43 78.706010 2: 15/14 119.442808 major diatonic semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 56/45 378.6022 septimal narrow major third 1: 45/43 78.7060 2: 43/42 40.7368 3: 56/45 378.6022 septimal narrow major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 43/42 40.737 cents 1: 1 45/43 78.706 cents 1: 1 56/45 378.602 cents septimal narrow major third 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 172/135 419.339 cents 2: 1 56/43 457.308 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 : 78.7 119.4 498.0 78.7 : 40.7 419.3 498.0 119.4: 378.6 457.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.7368 .. 378.6022 cents 784/645, 337.8654 cents 43/42, 40.7368 cents 2: 119.4428 .. 457.3082 cents 784/645, 337.8654 cents 675/784,-259.1594 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 43/42, 40.7368 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 56/45, 378.6022 cents Average / Smallest step : 4.075308 Largest / Average step : 2.280530 Largest / Smallest step : 9.293862 Median interval of one step : 45/43, 78.7060 cents, amount: 1 Least squares average step : 129.40904 cents, oct.: 388.22713 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2164-tone equal temperament with octave 4/3 degrees: 342 519 2164 Least number of segments generator : 1083 of 249.253 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1993 of 458.689 cents and inv. generated superset size: 42 = 39 more = 1400.000% 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 40.73680 cents Scale diversity : 0.534886 Lumma stability : 0.163587 Lumma impropriety factor : 0.520353 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 : 1890/1849, 37.9692 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% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 43 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.036120 Fundamental : 1/1806, -10.8186 octaves, 0.1449 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 3.250800E+05, 18.31044 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 62.0, average 20.66667 Mersenne's string divisions : 17864 Sum of van Prooijen's expressibility: 3.30643, average 1.10214 Sum of Tenney's harmonic distance : 6.68808, average 2.22936 Vogel's harmonic complexity : 43.00000 Wille's k value : 967 Wilson's harmonic complexity : 64 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 15.81883, average 2.63647 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.33333 1 1 43: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 17 18 36| Scale is weakly epimorphic with val: <6 10 17 18 39| Scale is weakly epimorphic with val: <6 10 17 18 42| Scale is weakly epimorphic with val: <6 10 18 19 37| Scale is weakly epimorphic with val: <6 10 18 19 40| Scale is weakly epimorphic with val: <6 10 19 19 36| Scale is weakly epimorphic with val: <6 10 19 20 38| Scale is weakly epimorphic with val: <6 10 19 20 41| Scale is weakly epimorphic with val: <6 10 19 22 36| Scale is weakly epimorphic with val: <6 11 16 18 36| Scale is weakly epimorphic with val: <6 11 16 18 39| Scale is weakly epimorphic with val: <6 11 16 18 42| Scale is weakly epimorphic with val: <6 11 17 19 37| Scale is weakly epimorphic with val: <6 11 17 19 40| Scale is weakly epimorphic with val: <6 11 17 20 36| Scale is weakly epimorphic with val: <6 11 18 18 37| Scale is weakly epimorphic with val: <6 11 18 20 38| Scale is weakly epimorphic with val: <6 11 18 20 41| Scale is weakly epimorphic with val: <6 11 18 21 37| Scale is weakly epimorphic with val: <6 11 19 19 38| Scale is weakly epimorphic with val: <6 11 19 21 36| Scale is weakly epimorphic with val: <6 11 19 21 39| Scale is weakly epimorphic with val: <6 11 19 21 42| Scale is weakly epimorphic with val: <6 11 19 22 38| Scale is weakly epimorphic with val: <7 10 18 18 36| Scale is weakly epimorphic with val: <7 10 18 18 39| Scale is weakly epimorphic with val: <7 10 18 18 42| Scale is weakly epimorphic with val: <7 10 19 19 37| Scale is weakly epimorphic with val: <7 10 19 19 40| Scale is weakly epimorphic with val: <7 10 19 20 36| Scale is weakly epimorphic with val: <7 11 15 18 38| Scale is weakly epimorphic with val: <7 11 15 18 41| Scale is weakly epimorphic with val: <7 11 15 20 36| Scale is weakly epimorphic with val: <7 11 15 20 39| Scale is weakly epimorphic with val: <7 11 15 20 42| Scale is weakly epimorphic with val: <7 11 15 21 38| Scale is weakly epimorphic with val: <7 11 15 21 41| Scale is JI-epimorphic with val: <7 11 16 18 37| Scale is weakly epimorphic with val: <7 11 16 18 40| Scale is weakly epimorphic with val: <7 11 16 19 36| Scale is weakly epimorphic with val: <7 11 16 19 39| Scale is weakly epimorphic with val: <7 11 16 19 42| Scale is weakly epimorphic with val: <7 11 16 21 37| Scale is weakly epimorphic with val: <7 11 16 21 40| Scale is weakly epimorphic with val: <7 11 16 22 36| Scale is weakly epimorphic with val: <7 11 16 22 39| Scale is weakly epimorphic with val: <7 11 16 22 42| Scale is JI-epimorphic with val: <7 11 17 19 38| Scale is weakly epimorphic with val: <7 11 17 19 41| Scale is weakly epimorphic with val: <7 11 17 20 37| Scale is weakly epimorphic with val: <7 11 17 20 40| Scale is weakly epimorphic with val: <7 11 17 22 38| Scale is weakly epimorphic with val: <7 11 17 22 41| Scale is weakly epimorphic with val: <7 11 18 18 38| Scale is weakly epimorphic with val: <7 11 18 18 41| Scale is weakly epimorphic with val: <7 11 18 20 36| Scale is JI-epimorphic with val: <7 11 18 20 39| Scale is weakly epimorphic with val: <7 11 18 20 42| Scale is weakly epimorphic with val: <7 11 18 21 38| Scale is weakly epimorphic with val: <7 11 18 21 41| Scale is weakly epimorphic with val: <7 11 19 19 36| Scale is weakly epimorphic with val: <7 11 19 19 39| Scale is weakly epimorphic with val: <7 11 19 19 42| Scale is weakly epimorphic with val: <7 11 19 21 37| Scale is JI-epimorphic with val: <7 11 19 21 40| Scale is weakly epimorphic with val: <7 11 19 22 36| Scale is weakly epimorphic with val: <7 11 19 22 39| Scale is weakly epimorphic with val: <7 11 19 22 42| Scale is weakly epimorphic with val: <7 12 15 19 36| Scale is weakly epimorphic with val: <7 12 15 22 36| Scale is weakly epimorphic with val: <7 12 16 18 36| Scale is weakly epimorphic with val: <7 12 16 18 39| Scale is weakly epimorphic with val: <7 12 16 18 42| Scale is weakly epimorphic with val: <7 12 16 20 37| Scale is weakly epimorphic with val: <7 12 17 18 38| Scale is weakly epimorphic with val: <7 12 17 19 37| Scale is weakly epimorphic with val: <7 12 17 19 40| Scale is weakly epimorphic with val: <7 12 17 21 38| Scale is weakly epimorphic with val: <7 12 18 19 39| Scale is weakly epimorphic with val: <7 12 18 20 38| Scale is weakly epimorphic with val: <7 12 18 20 41| Scale is weakly epimorphic with val: <7 12 18 22 39| Scale is weakly epimorphic with val: <7 12 19 20 40| Scale is weakly epimorphic with val: <7 12 19 21 36| Scale is weakly epimorphic with val: <7 12 19 21 39| Scale is weakly epimorphic with val: <7 12 19 21 42| Scale is weakly epimorphic with val: <8 11 17 19 36| Scale is weakly epimorphic with val: <8 11 17 22 36| Scale is weakly epimorphic with val: <8 11 18 18 36| Scale is weakly epimorphic with val: <8 11 18 18 39| Scale is weakly epimorphic with val: <8 11 18 18 42| Scale is weakly epimorphic with val: <8 11 18 20 37| Scale is weakly epimorphic with val: <8 11 19 19 37| Scale is weakly epimorphic with val: <8 11 19 19 40| Scale is weakly epimorphic with val: <8 11 19 21 38| Scale is weakly epimorphic with val: <8 12 15 20 36| Scale is weakly epimorphic with val: <8 12 16 18 37| Scale is weakly epimorphic with val: <8 12 16 21 37| Scale is weakly epimorphic with val: <8 12 17 18 36| Scale is weakly epimorphic with val: <8 12 17 18 39| Scale is weakly epimorphic with val: <8 12 17 18 42| Scale is weakly epimorphic with val: <8 12 17 19 38| Scale is weakly epimorphic with val: <8 12 17 22 38| Scale is weakly epimorphic with val: <8 12 18 19 37| Scale is weakly epimorphic with val: <8 12 18 19 40| Scale is weakly epimorphic with val: <8 12 18 20 39| Scale is weakly epimorphic with val: <8 12 19 20 38| Scale is weakly epimorphic with val: <8 12 19 20 41| Scale is weakly epimorphic with val: <8 12 19 21 40|
FIT/MODE
3: 1 0 2 N G T3 SD: 57.1309 c. M:-87.3090 c. 4: 1 0 3 N G T3 SD: 26.6071 c. M:-45.8052 c. 5: 1 0 4 N G T3 SD: 16.6365 c. M:-20.9030 c. 7: 1 1 5 N M DE S SD: 13.8983 c. M:-22.8558 c. 8: 1 1 6 N M DE S SD: 9.9382 c. M: 16.4504 c. 11: 2 1 8 N T3 SD: 11.6751 c. M:-16.3876 c. 12: 2 1 9 N T3 SD: 3.8381 c. M:-5.0684 c. 13: 2 1 10 N T3 SD: 2.8680 c. M: 4.5093 c. 25: 4 2 19 N T3 SD: 0.5688 c. M:-0.9812 c. 63: 10 5 48 N T3 SD: 0.5362 c. M: 0.8607 c. 83: 13 7 63 N T3 SD: 0.5200 c. M: 0.6990 c. 88: 14 7 67 N T3 SD: 0.4578 c. M: 0.5912 c. 96: 15 8 73 N T3 SD: 0.5164 c. M: 0.8865 c. 108: 17 9 82 N T3 SD: 0.3188 c. M:-0.4569 c. 121: 19 10 92 N T3 SD: 0.2924 c. M: 0.5006 c. 133: 21 11 101 N T3 SD: 0.2271 c. M:-0.3876 c. 146: 23 12 111 N T3 SD: 0.1452 c. M: 0.2469 c. 171: 27 14 130 N T3 SD: 0.0422 c. M: 0.0673 c. 196: 31 16 149 N T3 SD: 0.0391 c. M:-0.0664 c. 367: 58 30 279 N T3 SD: 0.0121 c. M: 0.0206 c. 905: 143 74 688 N T3 SD: 0.0139 c. M: 0.0221 c. 930: 147 76 707 N T3 SD: 0.0149 c. M: 0.0191 c. 1234: 195 101 938 N T3 SD: 0.0137 c. M:-0.0234 c. 1272: 201 104 967 N T3 SD: 0.0129 c. M: 0.0216 c. 1405: 222 115 1068 N T3 SD: 0.0118 c. M:-0.0171 c. 1430: 226 117 1087 N T3 SD: 0.0111 c. M:-0.0183 c. 1601: 253 131 1217 N T3 SD: 0.0078 c. M:-0.0133 c. 1772: 280 145 1347 N T3 SD: 0.0071 c. M:-0.0093 c. 1797: 284 147 1366 N T3 SD: 0.0068 c. M:-0.0104 c. 1968: 311 161 1496 N T3 SD: 0.0041 c. M:-0.0070 c. 2139: 338 175 1626 N T3 SD: 0.0042 c. M: 0.0061 c. 2164: 342 177 1645 N T3 SD: 0.0043 c. M:-0.0054 c. 2335: 369 191 1775 N T3 SD: 0.0015 c. M:-0.0027 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: 73.7140 cents 7 x 8:9 S SD: 64.1248 cents 8 x 9:11 SD: 49.9317 cents 9 x 10:12 S SD: 31.4805 cents 10 x 11:13 SD: 31.6109 cents 11 x 12:15 S SD: 24.9336 cents 12 x 13:16 SD: 9.5649 cents 13 x 14:17 SD: 17.3820 cents 14 x 15:19 SD: 15.3211 cents 15 x 16:20 S SD: 3.8558 cents 16 x 17:21 SD: 15.4371 cents 17:18 x 23 SD: 16.1924 cents 18:19 x 24 SD: 7.4485 cents 19:20 x 25 S SD: 12.5271 cents 20:21 x 27 SD: 11.1323 cents 23:24:25:31 SD: 10.5202 cents 24:25:26:32 SD: 6.9161 cents 27:28:29:36 SD: 5.4379 cents 33 x 35:44 SD: 8.7881 cents 34:36 x 45 S SD: 11.9713 cents 35:37:38:47 SD: 10.4554 cents 36:38:39:48 SD: 8.0820 cents 37:39:40:49 SD: 7.6986 cents 38:40:41:51 SD: 6.4752 cents 39:41:42:52 SD: 3.9499 cents 41:43:44:55 SD: 3.8403 cents 42:44:45:56 SD: 0.6103 cents 153:160:164:204 SD: 0.4888 cents 195:204:209:260 SD: 0.2790 cents 237:248:254:316 SD: 0.1711 cents 279:292:299:372 SD: 0.1453 cents 561:587:601:748 SD: 0.1143 cents