Scala analysis: 126_E15
Enharmonic tetrachord 60/59 * 59/56 * 56/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60/59 29.097055 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: 60/59 29.0971 2: 59/56 90.3458 3: 56/45 378.6022 septimal narrow major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 60/59 29.097 cents 1: 1 59/56 90.346 cents 1: 1 56/45 378.602 cents septimal narrow major third 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 224/177 407.699 cents 2: 1 59/45 468.948 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 : 29.1 119.4 498.0 29.1 : 90.3 468.9 498.0 119.4: 378.6 407.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.0971 .. 378.6022 cents 826/675, 349.5051 cents 60/59, 29.0971 cents 2: 119.4428 .. 468.9479 cents 826/675, 349.5051 cents 675/784,-259.1594 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 60/59, 29.0971 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 56/45, 378.6022 cents Average / Smallest step : 5.705560 Largest / Average step : 2.280530 Largest / Smallest step : 13.011701 Median interval of one step : 59/56, 90.3458 cents, amount: 1 Least squares average step : 125.86555 cents, oct.: 377.59664 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1301-tone equal temperament with octave 4/3 degrees: 76 312 1301 Least number of segments generator : 651 of 249.214 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 738 of 282.519 cents and inv. generated superset size: 26 = 23 more = 866.667% 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 29.09706 cents Scale diversity : 0.482591 Lumma stability : 0.116845 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 : 60/59, 29.0971 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% -- Rational properties -- Prime limit : 59 Odd number limit : 177 (O: 59 U: 177) Highest odd numerator or denominator: 59 Scale harmonicity : 0.039970 Fundamental : 1/2478, -11.2750 octaves, 0.1056 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 1.486800E+05, 17.18185 octaves Euler's gradus suavitatis : 76 Sum of Mann's harmonic distance : 77.5, average 25.83333 Mersenne's string divisions : 3451 Sum of van Prooijen's expressibility: 3.42406, average 1.14135 Sum of Tenney's harmonic distance : 6.95040, average 2.31680 Vogel's harmonic complexity : 53.33333 Wille's k value : 1327 Wilson's harmonic complexity : 77 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.95689, average 2.65948 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.33333 1 1 59: -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 44| Scale is weakly epimorphic with val: <6 10 18 19 42| Scale is weakly epimorphic with val: <6 10 19 20 43| Scale is weakly epimorphic with val: <6 11 16 18 43| Scale is weakly epimorphic with val: <6 11 17 19 44| Scale is weakly epimorphic with val: <6 11 18 20 42| Scale is weakly epimorphic with val: <6 11 19 21 43| Scale is weakly epimorphic with val: <7 10 18 18 43| Scale is weakly epimorphic with val: <7 10 19 19 44| Scale is weakly epimorphic with val: <7 11 15 18 44| Scale is weakly epimorphic with val: <7 11 15 20 42| Scale is weakly epimorphic with val: <7 11 15 21 44| Scale is weakly epimorphic with val: <7 11 16 18 43| Scale is weakly epimorphic with val: <7 11 16 19 42| Scale is weakly epimorphic with val: <7 11 16 21 43| Scale is weakly epimorphic with val: <7 11 16 22 42| Scale is weakly epimorphic with val: <7 11 17 19 44| Scale is weakly epimorphic with val: <7 11 17 20 43| = patent Scale is weakly epimorphic with val: <7 11 17 22 44| Scale is weakly epimorphic with val: <7 11 18 18 44| Scale is JI-epimorphic with val: <7 11 18 20 42| Scale is weakly epimorphic with val: <7 11 18 21 44| Scale is weakly epimorphic with val: <7 11 19 19 42| Scale is JI-epimorphic with val: <7 11 19 21 43| Scale is weakly epimorphic with val: <7 11 19 22 42| Scale is weakly epimorphic with val: <7 12 16 18 44| Scale is weakly epimorphic with val: <7 12 17 19 42| Scale is weakly epimorphic with val: <7 12 18 20 43| Scale is weakly epimorphic with val: <7 12 19 20 42| Scale is weakly epimorphic with val: <7 12 19 21 44| Scale is weakly epimorphic with val: <8 11 18 18 44| Scale is weakly epimorphic with val: <8 11 18 20 42| Scale is weakly epimorphic with val: <8 11 19 19 42| Scale is weakly epimorphic with val: <8 11 19 21 43| Scale is weakly epimorphic with val: <8 12 17 18 43| Scale is weakly epimorphic with val: <8 12 17 19 42| Scale is weakly epimorphic with val: <8 12 17 22 42| Scale is weakly epimorphic with val: <8 12 18 19 44| Scale is weakly epimorphic with val: <8 12 18 20 43| Scale is weakly epimorphic with val: <8 12 19 20 42| Scale is weakly epimorphic with val: <8 12 19 21 44|
FIT/MODE
3: 0 1 2 N G T3 SD: 31.7049 c. M:-46.5722 c. 4: 0 1 3 N G T3 SD: 17.0522 c. M: 29.0971 c. 5: 0 1 4 N G T3 SD: 20.3308 c. M: 29.0971 c. 8: 0 2 6 N G T3 SD: 17.0522 c. M: 29.0971 c. 11: 1 2 8 N T3 SD: 13.2959 c. M:-16.3876 c. 12: 1 2 9 N T3 SD: 7.7377 c. M:-12.4067 c. 13: 1 2 10 N T3 SD: 5.9227 c. M:-9.2141 c. 16: 1 3 12 N T3 SD: 3.1524 c. M:-5.0684 c. 17: 1 3 13 N T3 SD: 1.3075 c. M: 2.2557 c. 33: 2 6 25 N T3 SD: 0.9765 c. M:-1.2954 c. 50: 3 9 38 N T3 SD: 0.4564 c. M:-0.7856 c. 67: 4 12 51 N T3 SD: 0.4699 c. M:-0.6370 c. 104: 6 19 79 N T3 SD: 0.2648 c. M: 0.3637 c. 121: 7 22 92 N T3 SD: 0.1701 c. M: 0.2845 c. 154: 9 28 117 N T3 SD: 0.1256 c. M:-0.2174 c. 171: 10 31 130 N T3 SD: 0.0232 c. M: 0.0285 c. 667: 39 121 507 N T3 SD: 0.0214 c. M:-0.0283 c. 788: 46 143 599 N T3 SD: 0.0152 c. M: 0.0234 c. 838: 49 152 637 N T3 SD: 0.0173 c. M:-0.0249 c. 959: 56 174 729 N T3 SD: 0.0086 c. M: 0.0141 c. 1130: 66 205 859 N T3 SD: 0.0044 c. M: 0.0077 c. 1301: 76 236 989 N T3 SD: 0.0028 c. M: 0.0039 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 x 20:25 S SD: 19.1360 cents 20 x 21:27 SD: 20.5293 cents 21 x 23:28 SD: 19.0253 cents 22 x 24:29 SD: 18.4700 cents 23:24:25:31 SD: 18.1307 cents 24:25:26:32 SD: 15.2551 cents 25:26:27:33 SD: 14.9024 cents 26:27:28:35 S SD: 13.6065 cents 27:28:29:36 SD: 11.3773 cents 29:30:31:39 SD: 11.1183 cents 30:31:32:40 S SD: 9.5748 cents 33:34:35:44 SD: 9.5395 cents 36:37:39:48 SD: 8.8330 cents 37:38:40:49 SD: 8.6300 cents 38:39:41:51 SD: 7.6550 cents 39:40:42:52 SD: 5.7301 cents 41:42:44:55 S SD: 5.5575 cents 42:43:45:56 SD: 3.8799 cents 53:54:57:71 SD: 3.6445 cents 54:55:58:72 SD: 1.6784 cents 57:58:61:76 SD: 0.7549 cents 111:113:119:148 SD: 0.6983 cents 126:128:135:168 SD: 0.6110 cents 168:171:180:224 SD: 0.5150 cents 180:183:193:240 SD: 0.4564 cents 183:186:196:244 SD: 0.3791 cents 237:241:254:316 SD: 0.1673 cents 294:299:315:392 SD: 0.0327 cents