Scala analysis: 065_E6
Enharmonic tetrachord 208/203 * 203/198 * 33/26
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 208/203 42.124561 2: 104/99 85.299718 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 33/26 412.7453 tridecimal major third 1: 208/203 42.1246 2: 203/198 43.1752 3: 33/26 412.7453 tridecimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 208/203 42.125 cents 1: 1 203/198 43.175 cents 1: 1 33/26 412.745 cents tridecimal major third 2: 1 104/99 85.300 cents 2: 1 264/203 454.870 cents 2: 1 203/156 455.920 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 : 42.1 85.3 498.0 42.1 : 43.2 455.9 498.0 85.3 : 412.7 454.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 42.1246 .. 412.7453 cents 6699/5408, 370.6207 cents 208/203, 42.1246 cents 2: 85.2997 .. 455.9204 cents 6699/5408, 370.6207 cents 2704/3267,-327.4456 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 208/203, 42.1246 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 33/26, 412.7453 cents Average / Smallest step : 3.941050 Largest / Average step : 2.486193 Largest / Smallest step : 9.798210 Median interval of one step : 203/198, 43.1752 cents, amount: 1 Least squares average step : 121.91850 cents, oct.: 365.75550 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1880-tone equal temperament with octave 4/3 degrees: 159 322 1880 Least number of segments generator : 941 of 249.287 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1097 of 290.615 cents and inv. generated superset size: 27 = 24 more = 900.000% 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 42.12456 cents Scale diversity : 0.319332 Lumma stability : 0.169160 Lumma impropriety factor : 0.657462 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 : 41209/41184, 1.0506 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 369.5701 cents: 2 -- Rational properties -- Prime limit : 29 Odd number limit : 203 (O: 203 U: 203) Highest odd numerator or denominator: 203 Scale harmonicity : 0.008770 Average absolute harmonicity : 0.081960 Specific harmonicity : 0.043491 Fundamental : 1/20097, -14.2947 octaves, 0.0130 Hz. Guide tone : 208, 7.7004 octaves, 54418.118 Hz. Exponens Consonantiae : 4.180176E+06, 21.99513 octaves Euler's gradus suavitatis : 65 Sum of Mann's harmonic distance : 310.5, average 103.50000 Mersenne's string divisions : 83433 Sum of van Prooijen's expressibility: 4.78025, average 1.59342 Sum of Tenney's harmonic distance : 9.71741, average 3.23914 Vogel's harmonic complexity : 46.00000 Wille's k value : 3349 Wilson's harmonic complexity : 66 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 18.12480, average 3.02080 Lattice compactness (without 2's) : 11.55934, average 1.92656 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -2 .. 0 -1.00000 3 1 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 13: 0 .. 1 0.66667 2 1 29: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 19 24 26 33| Scale is weakly epimorphic with val: <7 11 19 24 26 36| Scale is JI-epimorphic with val: <7 11 19 24 27 35| Scale is weakly epimorphic with val: <7 11 19 25 27 34| Scale is weakly epimorphic with val: <7 11 19 25 27 37| Scale is weakly epimorphic with val: <7 11 19 25 28 33| Scale is JI-epimorphic with val: <7 11 19 25 28 36| Scale is weakly epimorphic with val: <7 11 19 26 26 34| Scale is weakly epimorphic with val: <7 11 19 26 26 37| Scale is weakly epimorphic with val: <7 11 19 26 28 35| Scale is weakly epimorphic with val: <7 11 20 24 26 35| Scale is JI-epimorphic with val: <7 11 20 24 27 34| Scale is weakly epimorphic with val: <7 11 20 24 27 37| Scale is weakly epimorphic with val: <7 11 20 25 27 33| Scale is weakly epimorphic with val: <7 11 20 25 27 36| Scale is JI-epimorphic with val: <7 11 20 25 28 35| Scale is weakly epimorphic with val: <7 11 20 26 26 33| Scale is weakly epimorphic with val: <7 11 20 26 26 36| Scale is weakly epimorphic with val: <7 11 20 26 28 34| Scale is weakly epimorphic with val: <7 11 20 26 28 37| Scale is weakly epimorphic with val: <7 11 21 24 26 34| Scale is weakly epimorphic with val: <7 11 21 24 26 37| Scale is JI-epimorphic with val: <7 11 21 24 27 33| Scale is weakly epimorphic with val: <7 11 21 24 27 36| Scale is weakly epimorphic with val: <7 11 21 25 27 35| Scale is JI-epimorphic with val: <7 11 21 25 28 34| Scale is weakly epimorphic with val: <7 11 21 25 28 37| Scale is weakly epimorphic with val: <7 11 21 26 26 35| Scale is weakly epimorphic with val: <7 11 21 26 28 33| Scale is weakly epimorphic with val: <7 11 21 26 28 36| Scale is weakly epimorphic with val: <7 12 19 24 28 34| Scale is weakly epimorphic with val: <7 12 19 26 27 33| Scale is weakly epimorphic with val: <7 12 20 24 28 33|
FIT/MODE
3: 0 0 3 N M DE S SD: 54.9258 c. M: 85.2997 c. 4: 0 1 3 N G T3 SD: 33.2266 c. M: 42.1246 c. 5: 0 1 4 N G T3 SD: 25.6855 c. M: 42.1246 c. 6: 0 1 5 N G T3 SD: 24.3566 c. M: 42.1246 c. 7: 0 1 6 N G T3 SD: 25.6561 c. M: 42.1246 c. 8: 0 1 7 N G T3 SD: 27.7219 c. M: 42.1246 c. 9: 1 1 7 N M DE S SD: 16.5186 c. M:-25.3769 c. 10: 1 1 8 N M DE S SD: 9.3762 c. M:-14.3093 c. 11: 1 1 9 N M DE S SD: 3.5374 c. M:-5.2539 c. 12: 1 1 10 N M DE S SD: 1.3711 c. M: 2.2922 c. 23: 2 2 19 N M DE S SD: 1.0223 c. M:-1.3168 c. 35: 3 3 29 N M DE S SD: 0.3294 c. M:-0.5650 c. 47: 4 4 39 N M DE S SD: 0.3394 c. M: 0.5261 c. 82: 7 7 68 N M DE S SD: 0.2738 c. M:-0.3915 c. 117: 10 10 97 N M DE S SD: 0.2729 c. M:-0.4434 c. 129: 11 11 107 N M DE S SD: 0.2884 c. M: 0.3618 c. 152: 13 13 126 N M DE S SD: 0.2792 c. M:-0.4714 c. 187: 16 16 155 N M DE S SD: 0.2854 c. M:-0.4889 c. 199: 17 17 165 N M DE S SD: 0.2713 c. M:-0.4220 c. 222: 19 19 184 N M DE S SD: 0.2906 c. M:-0.5009 c. 239: 20 21 198 N T3 SD: 0.2703 c. M: 0.4472 c. 250: 21 22 207 N T3 SD: 0.2683 c. M:-0.3640 c. 251: 21 22 208 N T3 SD: 0.2633 c. M: 0.4555 c. 262: 22 23 217 N T3 SD: 0.2245 c. M: 0.3040 c. 274: 23 24 227 N T3 SD: 0.1986 c. M: 0.3179 c. 286: 24 25 237 N T3 SD: 0.1916 c. M: 0.3306 c. 297: 25 26 246 N T3 SD: 0.1736 c. M:-0.2232 c. 298: 25 26 247 N T3 SD: 0.2010 c. M: 0.3423 c. 309: 26 27 256 N T3 SD: 0.1452 c. M: 0.2179 c. 321: 27 28 266 N T3 SD: 0.1360 c. M: 0.2329 c. 332: 28 29 275 N T3 SD: 0.1389 c. M:-0.2080 c. 333: 28 29 276 N T3 SD: 0.1453 c. M: 0.2469 c. 344: 29 30 285 N T3 SD: 0.1060 c. M: 0.1382 c. 356: 30 31 295 N T3 SD: 0.0921 c. M: 0.1545 c. 368: 31 32 305 N T3 SD: 0.1002 c. M: 0.1697 c. 379: 32 33 314 N T3 SD: 0.0797 c. M:-0.1170 c. 391: 33 34 324 N T3 SD: 0.0576 c. M: 0.0901 c. 403: 34 35 334 N T3 SD: 0.0630 c. M: 0.1059 c. 426: 36 37 353 N T3 SD: 0.0338 c. M:-0.0460 c. 438: 37 38 363 N T3 SD: 0.0319 c. M: 0.0523 c. 461: 39 40 382 N T3 SD: 0.0286 c. M:-0.0486 c. 473: 40 41 392 N T3 SD: 0.0073 c. M: 0.0108 c. 1407: 119 122 1166 N T3 SD: 0.0050 c. M:-0.0086 c. 1880: 159 163 1558 N T3 SD: 0.0027 c. M:-0.0037 c. 2353: 199 204 1950 N T3 SD: 0.0021 c. M: 0.0035 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: 90.7856 cents 7 x 8:9 S SD: 79.4409 cents 8 x 9:11 SD: 65.0123 cents 9 x 10:12 S SD: 48.5520 cents 10 x 11:13 SD: 45.4807 cents 11 x 12:15 S SD: 38.0218 cents 12 x 13:16 SD: 26.6365 cents 13 x 14:17 SD: 27.2901 cents 14 x 15:19 SD: 22.9384 cents 15 x 16:20 S SD: 13.2158 cents 16 x 17:21 SD: 16.8053 cents 17 x 18:23 SD: 14.3634 cents 18 x 19:24 SD: 4.1516 cents 19 x 20:25 S SD: 11.5982 cents 20 x 21:27 SD: 10.7612 cents 21 x 22:28 SD: 2.3813 cents 22 x 23:29 SD: 10.7365 cents 23 x 24:31 SD: 11.0148 cents 24 x 25:32 SD: 7.3136 cents 25 x 26:33 SD: 12.3033 cents 26 x 27:35 SD: 12.9707 cents 27:28 x 36 SD: 10.4182 cents 28:29 x 37 SD: 12.1248 cents 29:30 x 39 SD: 11.1276 cents 30:31:32:40 S SD: 10.0721 cents 31:32:33:41 SD: 9.9304 cents 32:33:34:43 SD: 8.7696 cents 33:34:35:44 SD: 6.3755 cents 35:36:37:47 SD: 5.9152 cents 36:37:38:48 SD: 3.2852 cents 39:40:41:52 SD: 0.7111 cents 81:83:85:108 SD: 0.6178 cents 120:123:126:160 SD: 0.3468 cents 159:163:167:212 SD: 0.3145 cents 279:286:293:372 SD: 0.3144 cents 414:424:435:552 SD: 0.2940 cents 453:464:476:604 SD: 0.2450 cents 492:504:517:656 SD: 0.2166 cents 531:544:558:708 SD: 0.2058 cents 534:547:561:712 SD: 0.1641 cents 573:587:602:764 SD: 0.1256 cents