Scala analysis: 123_E15
Enharmonic tetrachord 45/44 * 22/21 * 56/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 45/44 38.905773 1/5-tone 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: 45/44 38.9058 1/5-tone 2: 22/21 80.5370 undecimal minor semitone 3: 56/45 378.6022 septimal narrow major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 45/44 38.906 cents 1/5-tone 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 56/45 378.602 cents septimal narrow major third 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 176/135 459.139 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 : 38.9 119.4 498.0 38.9 : 80.5 459.1 498.0 119.4: 378.6 417.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.9058 .. 378.6022 cents 2464/2025, 339.6964 cents 45/44, 38.9058 cents 2: 119.4428 .. 459.1392 cents 2464/2025, 339.6964 cents 675/784,-259.1594 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 45/44, 38.9058 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 56/45, 378.6022 cents Average / Smallest step : 4.267104 Largest / Average step : 2.280530 Largest / Smallest step : 9.731260 Median interval of one step : 22/21, 80.5370 cents, amount: 1 Least squares average step : 126.56617 cents, oct.: 379.69851 cents Scale is not proper Scale has trivalence property Scale is a mode of a 909-tone equal temperament with octave 4/3 degrees: 71 218 909 Least number of segments generator : 455 of 249.296 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 860 of 471.198 cents and inv. generated superset size: 24 = 21 more = 800.000% 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 38.90577 cents Scale diversity : 0.527869 Lumma stability : 0.156234 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 : 45/44, 38.9058 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.021337 Average absolute harmonicity : 0.098251 Specific harmonicity : 0.106192 Fundamental : 1/924, -9.8517 octaves, 0.2831 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 1.663200E+05, 17.34360 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 62.5, average 20.83333 Mersenne's string divisions : 18067 Sum of van Prooijen's expressibility: 3.30643, average 1.10214 Sum of Tenney's harmonic distance : 6.69807, average 2.23269 Vogel's harmonic complexity : 22.00000 Wille's k value : 472 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 18.46748, average 3.07791 Lattice compactness (without 2's) : 12.67971, average 2.11328 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.33333 5 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.33333 1 1 11: -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 24| Scale is weakly epimorphic with val: <6 10 17 18 27| Scale is weakly epimorphic with val: <6 10 18 18 23| Scale is weakly epimorphic with val: <6 10 18 19 25| Scale is weakly epimorphic with val: <6 10 18 21 23| Scale is weakly epimorphic with val: <6 10 19 19 24| Scale is weakly epimorphic with val: <6 10 19 20 23| Scale is weakly epimorphic with val: <6 10 19 20 26| Scale is weakly epimorphic with val: <6 10 19 22 24| Scale is weakly epimorphic with val: <6 11 16 18 24| Scale is weakly epimorphic with val: <6 11 16 18 27| Scale is weakly epimorphic with val: <6 11 16 19 23| Scale is weakly epimorphic with val: <6 11 16 22 23| Scale is weakly epimorphic with val: <6 11 17 19 25| Scale is weakly epimorphic with val: <6 11 17 20 24| Scale is weakly epimorphic with val: <6 11 18 18 25| 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 18 21 25| Scale is weakly epimorphic with val: <6 11 19 19 26| Scale is weakly epimorphic with val: <6 11 19 21 24| Scale is weakly epimorphic with val: <6 11 19 21 27| Scale is weakly epimorphic with val: <6 11 19 22 26| Scale is weakly epimorphic with val: <7 10 18 18 25| 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 11 15 18 24| Scale is weakly epimorphic with val: <7 11 15 18 27| Scale is weakly epimorphic with val: <7 11 15 20 25| Scale is weakly epimorphic with val: <7 11 15 21 24| Scale is weakly epimorphic with val: <7 11 15 21 27| Scale is JI-epimorphic with val: <7 11 16 18 23| Scale is weakly epimorphic with val: <7 11 16 18 26| Scale is weakly epimorphic with val: <7 11 16 19 25| Scale is weakly epimorphic with val: <7 11 16 21 23| Scale is weakly epimorphic with val: <7 11 16 21 26| Scale is weakly epimorphic with val: <7 11 16 22 25| Scale is JI-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 22 24| Scale is weakly epimorphic with val: <7 11 17 22 27| Scale is weakly epimorphic with val: <7 11 18 18 24| Scale is weakly epimorphic with val: <7 11 18 18 27| Scale is JI-epimorphic with val: <7 11 18 20 25| Scale is weakly epimorphic with val: <7 11 18 21 24| Scale is weakly epimorphic with val: <7 11 18 21 27| Scale is weakly epimorphic with val: <7 11 19 19 25| Scale is weakly epimorphic with val: <7 11 19 21 23| Scale is JI-epimorphic with val: <7 11 19 21 26| Scale is weakly epimorphic with val: <7 11 19 22 25| Scale is weakly epimorphic with val: <7 12 16 18 25| Scale is weakly epimorphic with val: <7 12 16 20 23| Scale is weakly epimorphic with val: <7 12 17 18 24| Scale is weakly epimorphic with val: <7 12 17 19 23| Scale is weakly epimorphic with val: <7 12 17 19 26| Scale is weakly epimorphic with val: <7 12 17 21 24| Scale is weakly epimorphic with val: <7 12 18 19 25| Scale is weakly epimorphic with val: <7 12 18 20 24| Scale is weakly epimorphic with val: <7 12 18 20 27| Scale is weakly epimorphic with val: <7 12 18 22 25| Scale is weakly epimorphic with val: <7 12 19 20 26| Scale is weakly epimorphic with val: <7 12 19 21 25| Scale is weakly epimorphic with val: <8 11 18 18 23| Scale is weakly epimorphic with val: <8 11 18 18 26| Scale is weakly epimorphic with val: <8 11 19 19 24| Scale is weakly epimorphic with val: <8 11 19 19 27| 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 18 19 24| Scale is weakly epimorphic with val: <8 12 18 19 27| Scale is weakly epimorphic with val: <8 12 18 20 23| Scale is weakly epimorphic with val: <8 12 19 20 25| Scale is weakly epimorphic with val: <8 12 19 21 24|
FIT/MODE
3: 0 1 2 N G T3 SD: 35.0363 c. M:-46.5722 c. 4: 0 1 3 N G T3 SD: 22.6521 c. M: 38.9058 c. 5: 0 1 4 N G T3 SD: 25.2127 c. M: 38.9058 c. 8: 1 1 6 N M DE S SD: 13.7950 c. M:-23.3499 c. 9: 1 1 7 N M DE S SD: 10.7529 c. M:-16.4326 c. 11: 1 2 8 N T3 SD: 10.1513 c. M:-16.3876 c. 12: 1 2 9 N T3 SD: 3.2883 c. M:-5.0684 c. 13: 1 2 10 N T3 SD: 2.6260 c. M: 4.5093 c. 25: 2 4 19 N T3 SD: 0.5438 c. M:-0.9378 c. 63: 5 10 48 N T3 SD: 0.6130 c. M: 0.8607 c. 88: 7 14 67 N T3 SD: 0.5340 c. M:-0.7114 c. 92: 7 15 70 N T3 SD: 0.6168 c. M: 1.0110 c. 104: 8 17 79 N T3 SD: 0.3793 c. M: 0.5946 c. 117: 9 19 89 N T3 SD: 0.3730 c. M: 0.5946 c. 129: 10 21 98 N T3 SD: 0.2216 c. M: 0.2976 c. 142: 11 23 108 N T3 SD: 0.2180 c. M: 0.3248 c. 154: 12 25 117 N T3 SD: 0.1374 c. M:-0.2174 c. 167: 13 27 127 N T3 SD: 0.1171 c. M: 0.1506 c. 192: 15 31 146 N T3 SD: 0.0690 c. M: 0.1195 c. 217: 17 35 165 N T3 SD: 0.0848 c. M:-0.1116 c. 321: 25 52 244 N T3 SD: 0.0693 c. M: 0.1172 c. 346: 27 56 263 N T3 SD: 0.0295 c. M: 0.0410 c. 371: 29 60 282 N T3 SD: 0.0245 c. M:-0.0343 c. 538: 42 87 409 N T3 SD: 0.0196 c. M: 0.0249 c. 563: 44 91 428 N T3 SD: 0.0147 c. M: 0.0182 c. 909: 71 147 691 N T3 SD: 0.0026 c. M: 0.0046 c. 2381: 186 385 1810 N T3 SD: 0.0024 c. M: 0.0040 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 22:23:24:29 SD: 17.6774 cents 23:24:25:31 SD: 15.5639 cents 24:25:26:32 SD: 12.3607 cents 25:26:27:33 SD: 12.1734 cents 26:27:28:35 S SD: 10.8090 cents 27:28:29:36 SD: 8.1437 cents 30:31:32:40 S SD: 6.4849 cents 38:39:41:51 SD: 5.8899 cents 39:40:42:52 SD: 3.3777 cents 42:43:45:56 SD: 0.6103 cents 180:184:193:240 SD: 0.5137 cents 222:227:238:296 SD: 0.3652 cents 225:230:241:300 SD: 0.3324 cents 264:270:283:352 SD: 0.2914 cents 267:273:286:356 SD: 0.2038 cents 309:316:331:412 SD: 0.1313 cents 351:359:376:468 SD: 0.1155 cents 531:543:569:708 SD: 0.1025 cents 573:586:614:764 SD: 0.0708 cents