Scala analysis: 068_E6
Enharmonic tetrachord 52/51 * 34/33 * 33/26
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 52/51 33.617251 2: 104/99 85.299718 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 33/26 412.7453 tridecimal major third 1: 52/51 33.6173 2: 34/33 51.6825 3: 33/26 412.7453 tridecimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 52/51 33.617 cents 1: 1 34/33 51.682 cents 1: 1 33/26 412.745 cents tridecimal major third 2: 1 104/99 85.300 cents 2: 1 22/17 446.363 cents 2: 1 17/13 464.428 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 : 33.6 85.3 498.0 33.6 : 51.7 464.4 498.0 85.3 : 412.7 446.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6173 .. 412.7453 cents 1683/1352, 379.1280 cents 52/51, 33.6173 cents 2: 85.2997 .. 464.4277 cents 1683/1352, 379.1280 cents 2704/3267,-327.4456 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 52/51, 33.6173 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 33/26, 412.7453 cents Average / Smallest step : 4.938387 Largest / Average step : 2.486193 Largest / Smallest step : 12.277782 Median interval of one step : 34/33, 51.6825 cents, amount: 1 Least squares average step : 121.31083 cents, oct.: 363.93250 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1378-tone equal temperament with octave 4/3 degrees: 93 236 1378 Least number of segments generator : 691 of 249.745 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1283 of 463.710 cents and inv. generated superset size: 60 = 57 more = 2000.000% 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 33.61725 cents Scale diversity : 0.303676 Lumma stability : 0.134997 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 : 289/286, 18.0652 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 Limited inverse transpositions with margin 361.0628 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 99 (O: 33 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.012693 Average absolute harmonicity : 0.084131 Specific harmonicity : 0.061892 Fundamental : 1/1683, -10.7168 octaves, 0.1555 Hz. Guide tone : 104, 6.7004 octaves, 27209.059 Hz. Exponens Consonantiae : 1.750320E+05, 17.41726 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 156.5, average 52.16667 Mersenne's string divisions : 20909 Sum of van Prooijen's expressibility: 4.18033, average 1.39344 Sum of Tenney's harmonic distance : 8.51542, average 2.83847 Vogel's harmonic complexity : 31.66667 Wille's k value : 280 Wilson's harmonic complexity : 47 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 14.16902, average 2.36150 Lattice compactness (without 2's) : 10.05986, average 1.67664 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -2 ..-1 -1.33333 4 1 11: -1 .. 0 -0.33333 1 13: 0 .. 1 0.66667 2 1 17: -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: <6 10 23 28 29| Scale is weakly epimorphic with val: <6 10 23 28 32| Scale is weakly epimorphic with val: <6 10 24 29 30| Scale is weakly epimorphic with val: <6 10 24 29 33| Scale is weakly epimorphic with val: <6 10 25 30 31| Scale is weakly epimorphic with val: <6 11 23 30 32| Scale is weakly epimorphic with val: <7 10 23 25 27| Scale is weakly epimorphic with val: <7 10 23 25 30| Scale is weakly epimorphic with val: <7 10 23 25 33| Scale is weakly epimorphic with val: <7 10 23 27 28| Scale is weakly epimorphic with val: <7 10 23 30 31| Scale is weakly epimorphic with val: <7 10 24 26 28| Scale is weakly epimorphic with val: <7 10 24 26 31| Scale is weakly epimorphic with val: <7 10 24 28 29| Scale is weakly epimorphic with val: <7 10 25 26 27| Scale is weakly epimorphic with val: <7 10 25 27 29| Scale is weakly epimorphic with val: <7 10 25 27 32| Scale is weakly epimorphic with val: <7 10 25 29 30| Scale is weakly epimorphic with val: <7 10 26 27 28| Scale is weakly epimorphic with val: <7 10 26 28 30| Scale is weakly epimorphic with val: <7 10 26 28 33| Scale is weakly epimorphic with val: <7 10 26 30 31| Scale is weakly epimorphic with val: <7 10 27 28 29| Scale is weakly epimorphic with val: <7 10 27 29 31| Scale is weakly epimorphic with val: <7 11 23 25 29| Scale is weakly epimorphic with val: <7 11 23 25 32| Scale is JI-epimorphic with val: <7 11 23 26 28| Scale is weakly epimorphic with val: <7 11 23 26 31| Scale is weakly epimorphic with val: <7 11 23 28 29| Scale is weakly epimorphic with val: <7 11 23 28 32| Scale is weakly epimorphic with val: <7 11 23 29 31| Scale is weakly epimorphic with val: <7 11 24 26 27| Scale is weakly epimorphic with val: <7 11 24 26 30| Scale is weakly epimorphic with val: <7 11 24 26 33| Scale is JI-epimorphic with val: <7 11 24 27 29| Scale is weakly epimorphic with val: <7 11 24 27 32| Scale is weakly epimorphic with val: <7 11 24 29 30| Scale is weakly epimorphic with val: <7 11 24 29 33| Scale is weakly epimorphic with val: <7 11 24 30 32| Scale is weakly epimorphic with val: <7 11 25 25 27| Scale is weakly epimorphic with val: <7 11 25 25 30| Scale is weakly epimorphic with val: <7 11 25 25 33| Scale is weakly epimorphic with val: <7 11 25 27 28| Scale is weakly epimorphic with val: <7 11 25 27 31| Scale is JI-epimorphic with val: <7 11 25 28 30| Scale is weakly epimorphic with val: <7 11 25 28 33| Scale is weakly epimorphic with val: <7 11 25 30 31| Scale is weakly epimorphic with val: <7 11 26 26 28| Scale is weakly epimorphic with val: <7 11 26 26 31| Scale is weakly epimorphic with val: <7 11 26 28 29| Scale is weakly epimorphic with val: <7 11 26 28 32| Scale is JI-epimorphic with val: <7 11 26 29 31| Scale is weakly epimorphic with val: <7 11 27 27 29| Scale is weakly epimorphic with val: <7 11 27 27 32| Scale is weakly epimorphic with val: <7 11 27 29 30| Scale is weakly epimorphic with val: <7 11 27 29 33| Scale is JI-epimorphic with val: <7 11 27 30 32| Scale is weakly epimorphic with val: <7 12 23 29 30| Scale is weakly epimorphic with val: <7 12 23 29 33| Scale is weakly epimorphic with val: <7 12 24 30 31| Scale is weakly epimorphic with val: <8 11 23 25 27| Scale is weakly epimorphic with val: <8 11 23 28 30| Scale is weakly epimorphic with val: <8 11 24 25 29| Scale is weakly epimorphic with val: <8 11 24 25 32| Scale is weakly epimorphic with val: <8 11 24 26 28| Scale is weakly epimorphic with val: <8 11 24 29 31| Scale is weakly epimorphic with val: <8 11 25 26 27| Scale is weakly epimorphic with val: <8 11 25 26 30| Scale is weakly epimorphic with val: <8 11 25 26 33| Scale is weakly epimorphic with val: <8 11 25 27 29| Scale is weakly epimorphic with val: <8 11 25 30 32| Scale is weakly epimorphic with val: <8 11 26 27 28| Scale is weakly epimorphic with val: <8 11 26 27 31| Scale is weakly epimorphic with val: <8 11 26 28 30| Scale is weakly epimorphic with val: <8 11 27 28 29| Scale is weakly epimorphic with val: <8 11 27 28 32| Scale is weakly epimorphic with val: <8 11 27 29 31| Scale is weakly epimorphic with val: <8 12 23 26 28| Scale is weakly epimorphic with val: <8 12 23 26 31| Scale is weakly epimorphic with val: <8 12 23 28 29| Scale is weakly epimorphic with val: <8 12 24 26 27| Scale is weakly epimorphic with val: <8 12 24 27 29| Scale is weakly epimorphic with val: <8 12 24 27 32| Scale is weakly epimorphic with val: <8 12 24 29 30| Scale is weakly epimorphic with val: <8 12 25 27 28| Scale is weakly epimorphic with val: <8 12 25 28 30| Scale is weakly epimorphic with val: <8 12 25 28 33| Scale is weakly epimorphic with val: <8 12 25 30 31| Scale is weakly epimorphic with val: <8 12 26 28 29| Scale is weakly epimorphic with val: <8 12 26 29 31| Scale is weakly epimorphic with val: <8 12 27 29 30| Scale is weakly epimorphic with val: <8 12 27 30 32|
FIT/MODE
3: 0 0 3 N M DE S SD: 52.9344 c. M: 85.2997 c. 4: 0 1 3 N G T3 SD: 29.8198 c. M:-39.2115 c. 5: 0 1 4 N G T3 SD: 21.0940 c. M: 33.6173 c. 6: 0 1 5 N G T3 SD: 19.4540 c. M: 33.6173 c. 7: 0 1 6 N G T3 SD: 21.0583 c. M: 33.6173 c. 10: 1 1 8 N M DE S SD: 12.4737 c. M:-16.1872 c. 11: 1 1 9 N M DE S SD: 7.3835 c. M:-11.6596 c. 12: 1 1 10 N M DE S SD: 4.7417 c. M:-7.8865 c. 17: 1 2 14 N T3 SD: 2.9085 c. M: 4.3205 c. 28: 2 3 23 N T3 SD: 2.3846 c. M:-3.6369 c. 29: 2 3 24 N T3 SD: 0.5351 c. M:-0.7307 c. 59: 4 6 49 N T3 SD: 0.5183 c. M: 0.8853 c. 76: 5 8 63 N T3 SD: 0.4953 c. M: 0.8511 c. 88: 6 9 73 N T3 SD: 0.3057 c. M: 0.4057 c. 105: 7 11 87 N T3 SD: 0.2435 c. M: 0.4143 c. 134: 9 14 111 N T3 SD: 0.1440 c. M:-0.1856 c. 163: 11 17 135 N T3 SD: 0.1467 c. M:-0.2540 c. 193: 13 20 160 N T3 SD: 0.0913 c. M: 0.1418 c. 222: 15 23 184 N T3 SD: 0.0345 c. M: 0.0488 c. 356: 24 37 295 N T3 SD: 0.0329 c. M: 0.0412 c. 549: 37 57 455 N T3 SD: 0.0328 c. M: 0.0514 c. 578: 39 60 479 N T3 SD: 0.0077 c. M: 0.0121 c. 800: 54 83 663 N T3 SD: 0.0055 c. M: 0.0095 c. 1378: 93 143 1142 N T3 SD: 0.0032 c. M: 0.0046 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 x 28:36 SD: 11.1694 cents 28 x 29:37 SD: 14.5233 cents 29:30 x 39 SD: 14.5735 cents 30:31:32:40 S SD: 11.7120 cents 31:32:33:41 SD: 11.4424 cents 32:33:34:43 SD: 10.2967 cents 33:34:35:44 SD: 8.1705 cents 35:36:37:47 SD: 7.4563 cents 36:37:38:48 SD: 5.3733 cents 39:40:41:52 SD: 3.4312 cents 42:43:44:56 SD: 2.8552 cents 54:55:57:72 SD: 2.8357 cents 57:58:60:76 SD: 1.6521 cents 96:98:101:128 SD: 1.1095 cents 99:101:104:132 SD: 0.3362 cents 255:260:268:340 SD: 0.2611 cents 258:263:271:344 SD: 0.1443 cents 357:364:375:476 SD: 0.0466 cents