Scala analysis: 125_E15
Enharmonic tetrachord 80/77 * 33/32 * 56/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 80/77 66.169865 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: 80/77 66.1699 2: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 3: 56/45 378.6022 septimal narrow major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 80/77 66.170 cents 1: 1 56/45 378.602 cents septimal narrow major third 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 77/60 431.875 cents 2: 1 128/99 444.772 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 : 66.2 119.4 498.0 66.2 : 53.3 431.9 498.0 119.4: 378.6 444.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.2729 .. 378.6022 cents 1792/1485, 325.3292 cents 33/32, 53.2729 cents 2: 119.4428 .. 444.7721 cents 1792/1485, 325.3292 cents 675/784,-259.1594 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 33/32, 53.2729 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 56/45, 378.6022 cents Average / Smallest step : 3.116310 Largest / Average step : 2.280530 Largest / Smallest step : 7.106838 Median interval of one step : 80/77, 66.1699 cents, amount: 1 Least squares average step : 128.51361 cents, oct.: 385.54082 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2160-tone equal temperament with octave 4/3 degrees: 287 518 2160 Least number of segments generator : 1081 of 249.253 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1889 of 435.559 cents and inv. generated superset size: 40 = 37 more = 1333.333% 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 53.27294 cents Scale diversity : 0.569489 Lumma stability : 0.213928 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 : 2560/2541, 12.8969 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 Limited inverse transpositions with margin 325.3292 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 77 U: 99) Highest odd numerator or denominator: 77 Scale harmonicity : 0.022123 Average absolute harmonicity : 0.096382 Specific harmonicity : 0.103702 Fundamental : 1/462, -8.8517 octaves, 0.5663 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 1.108800E+05, 16.75864 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 96.5, average 32.16667 Mersenne's string divisions : 31871 Sum of van Prooijen's expressibility: 3.53970, average 1.17990 Sum of Tenney's harmonic distance : 7.19098, average 2.39699 Vogel's harmonic complexity : 18.66667 Wille's k value : 247 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 20.49253, average 3.41542 Lattice compactness (without 2's) : 10.32780, average 1.72130 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.66667 7 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.66667 2 1 11: -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 25| Scale is weakly epimorphic with val: <6 10 18 19 25| Scale is weakly epimorphic with val: <6 10 19 20 25| Scale is weakly epimorphic with val: <6 11 16 18 23| Scale is weakly epimorphic with val: <6 11 16 18 26| Scale is weakly epimorphic with val: <6 11 17 19 23| Scale is weakly epimorphic with val: <6 11 17 19 26| Scale is weakly epimorphic with val: <6 11 18 20 23| Scale is weakly epimorphic with val: <6 11 18 20 26| Scale is weakly epimorphic with val: <6 11 19 21 23| Scale is weakly epimorphic with val: <6 11 19 21 26| Scale is weakly epimorphic with val: <7 10 17 18 24| Scale is weakly epimorphic with val: <7 10 18 18 23| Scale is weakly epimorphic with val: <7 10 18 18 26| Scale is weakly epimorphic with val: <7 10 18 19 24| Scale is weakly epimorphic with val: <7 10 19 19 23| Scale is weakly epimorphic with val: <7 10 19 19 26| Scale is weakly epimorphic with val: <7 10 19 20 24| Scale is weakly epimorphic with val: <7 11 15 18 23| Scale is weakly epimorphic with val: <7 11 15 18 26| Scale is weakly epimorphic with val: <7 11 15 20 25| Scale is weakly epimorphic with val: <7 11 15 21 23| Scale is weakly epimorphic with val: <7 11 15 21 26| Scale is JI-epimorphic with val: <7 11 16 18 25| 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 21 25| Scale is weakly epimorphic with val: <7 11 16 22 23| Scale is weakly epimorphic with val: <7 11 16 22 26| Scale is JI-epimorphic with val: <7 11 17 19 25| 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 22 25| Scale is weakly epimorphic with val: <7 11 18 18 23| Scale is weakly epimorphic with val: <7 11 18 18 26| Scale is JI-epimorphic with val: <7 11 18 20 25| Scale is weakly epimorphic with val: <7 11 18 21 23| Scale is weakly epimorphic with val: <7 11 18 21 26| Scale is weakly epimorphic with val: <7 11 19 19 23| Scale is weakly epimorphic with val: <7 11 19 19 26| Scale is JI-epimorphic with val: <7 11 19 21 25| 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 25| Scale is weakly epimorphic with val: <7 12 17 18 24| Scale is weakly epimorphic with val: <7 12 17 19 25| Scale is weakly epimorphic with val: <7 12 18 19 24| Scale is weakly epimorphic with val: <7 12 18 20 25| Scale is weakly epimorphic with val: <7 12 19 20 24| Scale is weakly epimorphic with val: <7 12 19 21 25| Scale is weakly epimorphic with val: <8 11 15 20 24| Scale is weakly epimorphic with val: <8 11 16 18 27| Scale is weakly epimorphic with val: <8 11 16 21 24| Scale is weakly epimorphic with val: <8 11 17 19 27| Scale is weakly epimorphic with val: <8 11 17 22 24| Scale is weakly epimorphic with val: <8 11 18 18 25| Scale is weakly epimorphic with val: <8 11 18 20 27| Scale is weakly epimorphic with val: <8 11 19 19 25| Scale is weakly epimorphic with val: <8 11 19 21 27| Scale is weakly epimorphic with val: <8 12 15 20 24| Scale is weakly epimorphic with val: <8 12 16 18 27| Scale is weakly epimorphic with val: <8 12 16 21 24| Scale is weakly epimorphic with val: <8 12 17 18 23| Scale is weakly epimorphic with val: <8 12 17 18 26| Scale is weakly epimorphic with val: <8 12 17 19 27| Scale is weakly epimorphic with val: <8 12 17 22 24| Scale is weakly epimorphic with val: <8 12 18 19 23| Scale is weakly epimorphic with val: <8 12 18 19 26| Scale is weakly epimorphic with val: <8 12 18 20 27| Scale is weakly epimorphic with val: <8 12 19 20 23| Scale is weakly epimorphic with val: <8 12 19 20 26| Scale is weakly epimorphic with val: <8 12 19 21 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 46.7169 c. M: 66.1699 c. 4: 1 0 3 N G T3 SD: 33.8103 c. M:-58.3414 c. 5: 1 0 4 N G T3 SD: 22.4466 c. M:-33.4391 c. 7: 1 1 5 N M DE S SD: 13.5053 c. M:-22.8558 c. 8: 1 1 6 N M DE S SD: 3.6973 c. M:-5.0684 c. 21: 3 2 16 N T3 SD: 2.9175 c. M:-4.9794 c. 29: 4 3 22 N T3 SD: 1.5255 c. M:-2.5260 c. 37: 5 4 28 N T3 SD: 1.1812 c. M:-1.7033 c. 38: 5 4 29 N T3 SD: 0.9329 c. M: 1.4848 c. 46: 6 5 35 N T3 SD: 0.7250 c. M: 1.2075 c. 67: 9 7 51 N T3 SD: 0.5138 c. M:-0.7317 c. 75: 10 8 57 N T3 SD: 0.1455 c. M:-0.2361 c. 188: 25 20 143 N T3 SD: 0.1371 c. M: 0.2299 c. 196: 26 21 149 N T3 SD: 0.0598 c. M: 0.1027 c. 271: 36 29 206 N T3 SD: 0.0098 c. M:-0.0145 c. 1430: 190 153 1087 N T3 SD: 0.0108 c. M:-0.0183 c. 1543: 205 165 1173 N T3 SD: 0.0088 c. M: 0.0153 c. 1618: 215 173 1230 N T3 SD: 0.0085 c. M: 0.0105 c. 1814: 241 194 1379 N T3 SD: 0.0064 c. M: 0.0108 c. 1889: 251 202 1436 N T3 SD: 0.0060 c. M:-0.0076 c. 2085: 277 223 1585 N T3 SD: 0.0046 c. M: 0.0076 c. 2160: 287 231 1642 N T3 SD: 0.0040 c. M:-0.0056 c. 2356: 313 252 1791 N T3 SD: 0.0035 c. M: 0.0050 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: 16.1087 cents 20:21 x 27 SD: 14.1184 cents 21:22:23:28 SD: 13.5576 cents 22:23:24:29 SD: 12.8275 cents 23:24:25:31 SD: 10.6835 cents 24:25:26:32 SD: 6.5509 cents 26:27:28:35 S SD: 6.2679 cents 27:28:29:36 SD: 1.7803 cents 96:100:103:128 SD: 1.7012 cents 99:103:106:132 SD: 0.8903 cents 126:131:135:168 SD: 0.4006 cents 153:159:164:204 SD: 0.2884 cents 282:293:302:376 SD: 0.2741 cents 309:321:331:412 SD: 0.1429 cents 435:452:466:580 SD: 0.1106 cents 462:480:495:616 SD: 0.0000 cents