Scala analysis: 121_E15
Enharmonic tetrachord 30/29 * 29/28 * 56/45, Ptolemy
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 30/29 58.691521 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: 30/29 58.6915 2: 29/28 60.7513 3: 56/45 378.6022 septimal narrow major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 30/29 58.692 cents 1: 1 29/28 60.751 cents 1: 1 56/45 378.602 cents septimal narrow major third 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 112/87 437.294 cents 2: 1 58/45 439.353 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 : 58.7 119.4 498.0 58.7 : 60.8 439.4 498.0 119.4: 378.6 437.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.6915 .. 378.6022 cents 812/675, 319.9107 cents 30/29, 58.6915 cents 2: 119.4428 .. 439.3535 cents 812/675, 319.9107 cents 675/784,-259.1594 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 30/29, 58.6915 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 56/45, 378.6022 cents Average / Smallest step : 2.828603 Largest / Average step : 2.280530 Largest / Smallest step : 6.450714 Median interval of one step : 29/28, 60.7513 cents, amount: 1 Least squares average step : 127.97944 cents, oct.: 383.93831 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1205-tone equal temperament with octave 4/3 degrees: 142 289 1205 Least number of segments generator : 603 of 249.229 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 916 of 378.597 cents and inv. generated superset size: 14 = 11 more = 466.667% 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 58.69152 cents Scale diversity : 0.576753 Lumma stability : 0.235688 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 : 841/840, 2.0598 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 : 2 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 Limited inverse transpositions with margin 317.8509 cents: 2 -- Rational properties -- Prime limit : 29 Odd number limit : 87 (O: 29 U: 87) Highest odd numerator or denominator: 29 Scale harmonicity : 0.012644 Average absolute harmonicity : 0.093004 Specific harmonicity : 0.064690 Fundamental : 1/1218, -10.2503 octaves, 0.2148 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 7.308000E+04, 16.15719 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 47.5, average 15.83333 Mersenne's string divisions : 11977 Sum of van Prooijen's expressibility: 3.11561, average 1.03854 Sum of Tenney's harmonic distance : 6.34092, average 2.11364 Vogel's harmonic complexity : 33.00000 Wille's k value : 652 Wilson's harmonic complexity : 47 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.20429, average 2.53405 Lattice compactness (without 2's) : 10.77729, average 1.79622 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.33333 1 1 29: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 17 18 32| Scale is weakly epimorphic with val: <6 10 17 18 35| Scale is weakly epimorphic with val: <6 10 17 18 38| Scale is weakly epimorphic with val: <6 10 18 19 33| Scale is weakly epimorphic with val: <6 10 18 19 36| Scale is weakly epimorphic with val: <6 10 19 19 32| Scale is weakly epimorphic with val: <6 10 19 20 34| Scale is weakly epimorphic with val: <6 10 19 20 37| Scale is weakly epimorphic with val: <6 10 19 22 32| Scale is weakly epimorphic with val: <6 11 16 18 34| Scale is weakly epimorphic with val: <6 11 16 18 37| Scale is weakly epimorphic with val: <6 11 17 19 32| Scale is weakly epimorphic with val: <6 11 17 19 35| Scale is weakly epimorphic with val: <6 11 17 19 38| Scale is weakly epimorphic with val: <6 11 18 18 32| Scale is weakly epimorphic with val: <6 11 18 20 33| Scale is weakly epimorphic with val: <6 11 18 20 36| Scale is weakly epimorphic with val: <6 11 18 21 32| Scale is weakly epimorphic with val: <6 11 19 19 33| Scale is weakly epimorphic with val: <6 11 19 21 34| Scale is weakly epimorphic with val: <6 11 19 21 37| Scale is weakly epimorphic with val: <6 11 19 22 33| Scale is weakly epimorphic with val: <7 10 18 18 33| Scale is weakly epimorphic with val: <7 10 18 18 36| Scale is weakly epimorphic with val: <7 10 18 19 32| Scale is weakly epimorphic with val: <7 10 18 22 32| Scale is weakly epimorphic with val: <7 10 19 19 34| Scale is weakly epimorphic with val: <7 10 19 19 37| Scale is weakly epimorphic with val: <7 10 19 20 33| Scale is weakly epimorphic with val: <7 11 15 18 34| Scale is weakly epimorphic with val: <7 11 15 18 37| 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 20 38| Scale is weakly epimorphic with val: <7 11 15 21 34| Scale is weakly epimorphic with val: <7 11 15 21 37| Scale is JI-epimorphic with val: <7 11 16 18 33| Scale is weakly epimorphic with val: <7 11 16 18 36| Scale is weakly 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 19 38| 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 16 22 38| Scale is JI-epimorphic with val: <7 11 17 19 34| Scale is weakly epimorphic with val: <7 11 17 19 37| Scale is weakly epimorphic with val: <7 11 17 20 33| Scale is weakly epimorphic with val: <7 11 17 20 36| Scale is weakly epimorphic with val: <7 11 17 22 34| Scale is weakly epimorphic with val: <7 11 17 22 37| Scale is weakly epimorphic with val: <7 11 18 18 34| Scale is weakly epimorphic with val: <7 11 18 18 37| Scale is weakly epimorphic with val: <7 11 18 20 32| Scale is JI-epimorphic with val: <7 11 18 20 35| Scale is weakly epimorphic with val: <7 11 18 20 38| Scale is weakly epimorphic with val: <7 11 18 21 34| Scale is weakly epimorphic with val: <7 11 18 21 37| 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 19 38| Scale is weakly epimorphic with val: <7 11 19 21 33| Scale is JI-epimorphic with val: <7 11 19 21 36| Scale is weakly epimorphic with val: <7 11 19 22 32| Scale is weakly epimorphic with val: <7 11 19 22 35| Scale is weakly epimorphic with val: <7 11 19 22 38| Scale is weakly epimorphic with val: <7 12 16 18 34| Scale is weakly epimorphic with val: <7 12 16 18 37| Scale is weakly epimorphic with val: <7 12 16 20 32| Scale is weakly epimorphic with val: <7 12 17 18 33| Scale is weakly epimorphic with val: <7 12 17 19 32| Scale is weakly epimorphic with val: <7 12 17 19 35| Scale is weakly epimorphic with val: <7 12 17 19 38| Scale is weakly epimorphic with val: <7 12 17 21 33| Scale is weakly epimorphic with val: <7 12 18 19 34| Scale is weakly epimorphic with val: <7 12 18 20 33| Scale is weakly epimorphic with val: <7 12 18 20 36| Scale is weakly epimorphic with val: <7 12 18 22 34| Scale is weakly epimorphic with val: <7 12 19 20 35| Scale is weakly epimorphic with val: <7 12 19 21 34| Scale is weakly epimorphic with val: <7 12 19 21 37| Scale is weakly epimorphic with val: <8 11 16 18 32| Scale is weakly epimorphic with val: <8 11 16 21 32| Scale is weakly epimorphic with val: <8 11 17 19 33| Scale is weakly epimorphic with val: <8 11 17 22 33| Scale is weakly epimorphic with val: <8 11 18 18 33| Scale is weakly epimorphic with val: <8 11 18 18 36| Scale is weakly epimorphic with val: <8 11 18 20 34| Scale is weakly epimorphic with val: <8 11 19 19 34| Scale is weakly epimorphic with val: <8 11 19 19 37| Scale is weakly epimorphic with val: <8 11 19 21 35| Scale is weakly epimorphic with val: <8 12 15 20 32| Scale is weakly epimorphic with val: <8 12 16 18 33| Scale is weakly epimorphic with val: <8 12 16 21 33| Scale is weakly epimorphic with val: <8 12 17 18 32| Scale is weakly epimorphic with val: <8 12 17 18 35| Scale is weakly epimorphic with val: <8 12 17 18 38| Scale is weakly epimorphic with val: <8 12 17 19 34| Scale is weakly epimorphic with val: <8 12 17 22 34| Scale is weakly epimorphic with val: <8 12 18 19 33| Scale is weakly epimorphic with val: <8 12 18 19 36| Scale is weakly epimorphic with val: <8 12 18 20 35| Scale is weakly epimorphic with val: <8 12 19 20 34| Scale is weakly epimorphic with val: <8 12 19 20 37| Scale is weakly epimorphic with val: <8 12 19 21 36|
FIT/MODE
3: 0 1 2 N G T3 SD: 43.2576 c. M: 58.6915 c. 4: 0 1 3 N G T3 SD: 34.0117 c. M: 58.6915 c. 5: 0 1 4 N G T3 SD: 35.7681 c. M: 58.6915 c. 6: 1 0 5 N G T3 SD: 25.2903 c. M: 36.4353 c. 7: 1 1 5 N M DE S SD: 15.0287 c. M:-22.8558 c. 8: 1 1 6 N M DE S SD: 3.5773 c. M:-5.0684 c. 17: 2 2 13 N M DE S SD: 1.3036 c. M: 2.2557 c. 25: 3 3 19 N M DE S SD: 0.6221 c. M:-1.0739 c. 42: 5 5 32 N M DE S SD: 0.6056 c. M: 0.8607 c. 67: 8 8 51 N M DE S SD: 0.5353 c. M:-0.7765 c. 92: 11 11 70 N M DE S SD: 0.5336 c. M:-0.8573 c. 109: 13 13 83 N M DE S SD: 0.5524 c. M:-0.7083 c. 117: 14 14 89 N M DE S SD: 0.5417 c. M:-0.9036 c. 121: 14 15 92 N T3 SD: 0.6173 c. M: 1.0665 c. 129: 15 16 98 N T3 SD: 0.4712 c. M: 0.7793 c. 137: 16 17 104 N T3 SD: 0.4286 c. M: 0.5257 c. 146: 17 18 111 N T3 SD: 0.4051 c. M: 0.7000 c. 154: 18 19 117 N T3 SD: 0.3034 c. M: 0.4785 c. 162: 19 20 123 N T3 SD: 0.3090 c. M:-0.4569 c. 171: 20 21 130 N T3 SD: 0.2549 c. M: 0.4406 c. 179: 21 22 136 N T3 SD: 0.1899 c. M: 0.2617 c. 196: 23 24 149 N T3 SD: 0.1431 c. M: 0.2475 c. 204: 24 25 155 N T3 SD: 0.1212 c. M:-0.1856 c. 221: 26 27 168 N T3 SD: 0.0566 c. M: 0.0980 c. 246: 29 30 187 N T3 SD: 0.0128 c. M:-0.0211 c. 713: 84 87 542 N T3 SD: 0.0094 c. M: 0.0158 c. 959: 113 117 729 N T3 SD: 0.0046 c. M: 0.0063 c. 1205: 142 147 916 N T3 SD: 0.0031 c. M:-0.0053 c. 1451: 171 177 1103 N T3 SD: 0.0037 c. M:-0.0056 c. 2164: 255 264 1645 N T3 SD: 0.0035 c. M:-0.0051 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 x 18:23 SD: 16.2676 cents 18 x 19:24 SD: 12.9199 cents 19:20 x 25 S SD: 18.9234 cents 20:21 x 27 SD: 16.7847 cents 21:22:23:28 SD: 14.6252 cents 22:23:24:29 SD: 13.7363 cents 23:24:25:31 SD: 11.5253 cents 24:25:26:32 SD: 7.5240 cents 26:27:28:35 S SD: 6.6420 cents 27:28:29:36 SD: 2.0126 cents 57:59:61:76 SD: 0.7549 cents 84:87:90:112 SD: 0.6866 cents 141:146:151:188 SD: 0.6099 cents 237:245:254:316 SD: 0.4372 cents 264:273:283:352 SD: 0.3643 cents 294:304:315:392 SD: 0.2618 cents 321:332:344:428 SD: 0.1695 cents 378:391:405:504 SD: 0.0509 cents