Scala analysis: 092_E11
Enharmonic tetrachord 240/233 * 233/226 * 113/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 240/233 51.245341 2: 120/113 104.053960 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 113/90 393.9910 1: 240/233 51.2453 2: 233/226 52.8086 3: 113/90 393.9910
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 240/233 51.245 cents 1: 1 233/226 52.809 cents 1: 1 113/90 393.991 cents 2: 1 120/113 104.054 cents 2: 1 904/699 445.236 cents 2: 1 233/180 446.800 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 : 51.2 104.1 498.0 51.2 : 52.8 446.8 498.0 104.1: 394.0 445.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.2453 .. 393.9910 cents 26329/21600, 342.7457 cents 240/233, 51.2453 cents 2: 104.0540 .. 446.7997 cents 26329/21600, 342.7457 cents 10800/12769,-289.9371 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 240/233, 51.2453 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 113/90, 393.9910 cents Average / Smallest step : 3.239612 Largest / Average step : 2.373226 Largest / Smallest step : 7.688329 Median interval of one step : 233/226, 52.8086 cents, amount: 1 Least squares average step : 125.24916 cents, oct.: 375.74748 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1905-tone equal temperament with octave 4/3 degrees: 196 398 1905 Least number of segments generator : 953 of 249.153 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1103 of 288.369 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 51.24534 cents Scale diversity : 0.460327 Lumma stability : 0.205786 Lumma impropriety factor : 0.582150 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 : 54289/54240, 1.5633 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 341.1824 cents: 2 -- Rational properties -- Prime limit : 233 Odd number limit : 699 (O: 233 U: 699) Highest odd numerator or denominator: 233 Scale harmonicity : 0.063559 Fundamental : 1/78987, -16.2693 octaves, 0.0033 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 1.895688E+07, 24.17622 octaves Euler's gradus suavitatis : 357 Sum of Mann's harmonic distance : 356.5, average 118.83333 Mersenne's string divisions : 771463 Sum of van Prooijen's expressibility: 4.89756, average 1.63252 Sum of Tenney's harmonic distance : 9.95901, average 3.31967 Vogel's harmonic complexity : 241.00000 Wille's k value : 13164 Wilson's harmonic complexity : 357 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.24482, average 2.70747 Lattice compactness (without 2's) : 8.30056, average 1.38343 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 113: -1 .. 0 -0.33333 1 1 233: -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: <7 11 15 48 56| Scale is weakly epimorphic with val: <7 11 15 49 58| Scale is weakly epimorphic with val: <7 11 16 49 57| Scale is weakly epimorphic with val: <7 11 16 50 56| Scale is weakly epimorphic with val: <7 11 17 48 57| Scale is weakly epimorphic with val: <7 11 17 50 58| Scale is JI-epimorphic with val: <7 11 18 48 56| Scale is weakly epimorphic with val: <7 11 18 49 58| Scale is JI-epimorphic with val: <7 11 19 49 57| Scale is weakly epimorphic with val: <7 11 19 50 56| Scale is weakly epimorphic with val: <7 12 18 48 57| Scale is weakly epimorphic with val: <7 12 19 48 56| Scale is weakly epimorphic with val: <7 12 19 49 58| Scale is weakly epimorphic with val: <8 11 16 48 58| Scale is weakly epimorphic with val: <8 11 16 50 56| Scale is weakly epimorphic with val: <8 11 17 48 57| Scale is weakly epimorphic with val: <8 11 17 49 56| Scale is weakly epimorphic with val: <8 11 18 49 58| Scale is weakly epimorphic with val: <8 11 18 50 57| Scale is weakly epimorphic with val: <8 12 15 48 57| Scale is weakly epimorphic with val: <8 12 15 49 56| Scale is weakly epimorphic with val: <8 12 16 49 58| Scale is weakly epimorphic with val: <8 12 16 50 57| Scale is weakly epimorphic with val: <8 12 17 48 58| Scale is weakly epimorphic with val: <8 12 17 50 56|
FIT/MODE
3: 0 0 3 N M DE S SD: 66.9659 c. M: 104.0540 c. 4: 0 1 3 N G T3 SD: 31.8569 c. M: 51.2453 c. 5: 0 1 4 N G T3 SD: 29.6976 c. M: 51.2453 c. 6: 0 1 5 N G T3 SD: 31.9846 c. M: 51.2453 c. 7: 1 0 6 N G T3 SD: 22.2027 c. M: 32.9047 c. 8: 1 1 6 N M DE S SD: 13.4130 c. M:-20.4573 c. 9: 1 1 7 N M DE S SD: 4.4949 c. M:-6.6227 c. 10: 1 1 8 N M DE S SD: 2.6978 c. M: 4.4450 c. 19: 2 2 15 N M DE S SD: 0.8225 c. M:-1.1804 c. 29: 3 3 23 N M DE S SD: 0.6047 c. M: 1.0102 c. 48: 5 5 38 N M DE S SD: 0.4038 c. M:-0.6343 c. 67: 7 7 53 N M DE S SD: 0.4557 c. M:-0.7892 c. 77: 8 8 61 N M DE S SD: 0.4350 c. M: 0.5641 c. 115: 12 12 91 N M DE S SD: 0.4235 c. M:-0.7246 c. 125: 13 13 99 N M DE S SD: 0.4148 c. M:-0.5513 c. 163: 17 17 129 N M DE S SD: 0.4144 c. M:-0.6980 c. 167: 17 18 132 N T3 SD: 0.3674 c. M: 0.5461 c. 177: 18 19 140 N T3 SD: 0.3461 c. M: 0.5967 c. 186: 19 20 147 N T3 SD: 0.3040 c. M:-0.3748 c. 196: 20 21 155 N T3 SD: 0.2561 c. M: 0.4244 c. 206: 21 22 163 N T3 SD: 0.2788 c. M: 0.4738 c. 215: 22 23 170 N T3 SD: 0.1960 c. M: 0.2826 c. 225: 23 24 178 N T3 SD: 0.1932 c. M: 0.3341 c. 234: 24 25 185 N T3 SD: 0.1666 c. M:-0.2375 c. 244: 25 26 193 N T3 SD: 0.1275 c. M: 0.2161 c. 263: 27 28 208 N T3 SD: 0.0881 c. M: 0.1152 c. 273: 28 29 216 N T3 SD: 0.1021 c. M: 0.1638 c. 282: 29 30 223 N T3 SD: 0.0864 c. M:-0.1469 c. 292: 30 31 231 N T3 SD: 0.0445 c. M: 0.0763 c. 311: 32 33 246 N T3 SD: 0.0225 c. M:-0.0390 c. 603: 62 64 477 N T3 SD: 0.0229 c. M: 0.0367 c. 632: 65 67 500 N T3 SD: 0.0225 c. M: 0.0319 c. 651: 67 69 515 N T3 SD: 0.0086 c. M:-0.0127 c. 943: 97 100 746 N T3 SD: 0.0099 c. M: 0.0148 c. 962: 99 102 761 N T3 SD: 0.0066 c. M:-0.0088 c. 1594: 164 169 1261 N T3 SD: 0.0051 c. M: 0.0082 c. 1905: 196 202 1507 N T3 SD: 0.0017 c. M: 0.0029 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: 81.4085 cents 7 x 8:9 S SD: 70.9288 cents 8 x 9:11 SD: 56.5889 cents 9 x 10:12 S SD: 39.1749 cents 10 x 11:13 SD: 37.5370 cents 11 x 12:15 S SD: 30.3465 cents 12 x 13:16 SD: 17.2594 cents 13 x 14:17 SD: 20.7238 cents 14 x 15:19 SD: 17.1446 cents 15 x 16:20 S SD: 3.8387 cents 16 x 17:21 SD: 13.6395 cents 17 x 18:23 SD: 12.8916 cents 18 x 19:24 SD: 5.2255 cents 19 x 20:25 S SD: 13.7702 cents 20 x 21:27 SD: 14.5444 cents 21 x 22:28 SD: 11.7585 cents 22:23 x 29 SD: 16.2214 cents 23:24 x 31 SD: 14.6086 cents 24:25 x 32 SD: 9.7135 cents 27:28:29:36 SD: 7.6282 cents 29:30:31:39 SD: 6.7193 cents 30:31:32:40 S SD: 3.1522 cents 33:34:35:44 SD: 0.7435 cents 96:99:102:128 SD: 0.7397 cents 129:133:137:172 SD: 0.5416 cents 162:167:172:216 SD: 0.4750 cents 195:201:207:260 SD: 0.4634 cents 273:281:290:364 SD: 0.4500 cents 306:315:325:408 SD: 0.3623 cents 336:346:357:448 SD: 0.3392 cents 339:349:360:452 SD: 0.3051 cents 369:380:392:492 SD: 0.2459 cents 402:414:427:536 SD: 0.1700 cents 435:448:462:580 SD: 0.1106 cents 468:482:497:624 SD: 0.0727 cents 501:516:532:668 SD: 0.0692 cents 597:615:634:796 SD: 0.0625 cents