Scala analysis: 067_E6
Enharmonic tetrachord 156/151 * 302/297 * 33/26
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 156/151 56.396975 2: 104/99 85.299718 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 33/26 412.7453 tridecimal major third 1: 156/151 56.3970 2: 302/297 28.9027 3: 33/26 412.7453 tridecimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 302/297 28.903 cents 1: 1 156/151 56.397 cents 1: 1 33/26 412.745 cents tridecimal major third 2: 1 104/99 85.300 cents 2: 1 151/117 441.648 cents 2: 1 198/151 469.142 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 : 56.4 85.3 498.0 56.4 : 28.9 441.6 498.0 85.3 : 412.7 469.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 28.9027 .. 412.7453 cents 9801/7852, 383.8425 cents 302/297, 28.9027 cents 2: 85.2997 .. 469.1423 cents 9801/7852, 383.8425 cents 2704/3267,-327.4456 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 302/297, 28.9027 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 33/26, 412.7453 cents Average / Smallest step : 5.743919 Largest / Average step : 2.486193 Largest / Smallest step : 14.280489 Median interval of one step : 156/151, 56.3970 cents, amount: 1 Least squares average step : 122.93796 cents, oct.: 368.81387 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1051-tone equal temperament with octave 4/3 degrees: 119 180 1051 Least number of segments generator : 526 of 249.259 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 961 of 455.396 cents and inv. generated superset size: 14 = 11 more = 466.667% 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 28.90274 cents Scale diversity : 0.291326 Lumma stability : 0.116065 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 : 23166/22801, 27.4942 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% Limited inverse transpositions with margin 383.8425 cents: 2 -- Rational properties -- Prime limit : 151 Odd number limit : 297 (O: 151 U: 297) Highest odd numerator or denominator: 151 Scale harmonicity : 0.019480 Fundamental : 1/14949, -13.8678 octaves, 0.0175 Hz. Guide tone : 312, 8.2854 octaves, 81627.176 Hz. Exponens Consonantiae : 4.664088E+06, 22.15316 octaves Euler's gradus suavitatis : 182 Sum of Mann's harmonic distance : 258.5, average 86.16667 Mersenne's string divisions : 62321 Sum of van Prooijen's expressibility: 4.65173, average 1.55058 Sum of Tenney's harmonic distance : 9.46395, average 3.15465 Vogel's harmonic complexity : 123.00000 Wille's k value : 2491 Wilson's harmonic complexity : 184 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 16.11123, average 2.68521 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -2 .. 1 -0.66667 4 1 11: -1 .. 0 -0.33333 1 13: 0 .. 1 0.66667 2 1 151: -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 23 28 52| Scale is weakly epimorphic with val: <6 10 24 29 53| Scale is weakly epimorphic with val: <6 10 25 30 51| Scale is weakly epimorphic with val: <6 11 23 30 51| Scale is weakly epimorphic with val: <7 10 23 25 53| Scale is weakly epimorphic with val: <7 10 23 30 51| Scale is weakly epimorphic with val: <7 10 24 26 51| Scale is weakly epimorphic with val: <7 10 25 27 52| Scale is weakly epimorphic with val: <7 10 26 28 53| Scale is weakly epimorphic with val: <7 10 26 30 51| Scale is weakly epimorphic with val: <7 10 27 29 51| Scale is weakly epimorphic with val: <7 11 23 25 51| Scale is weakly epimorphic with val: <7 11 23 26 53| Scale is weakly epimorphic with val: <7 11 23 28 51| Scale is weakly epimorphic with val: <7 11 23 29 53| Scale is weakly epimorphic with val: <7 11 24 26 52| Scale is JI-epimorphic with val: <7 11 24 27 51| Scale is weakly epimorphic with val: <7 11 24 29 52| Scale is weakly epimorphic with val: <7 11 24 30 51| Scale is weakly epimorphic with val: <7 11 25 25 52| Scale is weakly epimorphic with val: <7 11 25 27 53| Scale is JI-epimorphic with val: <7 11 25 28 52| Scale is weakly epimorphic with val: <7 11 25 30 53| Scale is weakly epimorphic with val: <7 11 26 26 53| Scale is weakly epimorphic with val: <7 11 26 28 51| Scale is JI-epimorphic with val: <7 11 26 29 53| Scale is weakly epimorphic with val: <7 11 27 27 51| Scale is weakly epimorphic with val: <7 11 27 29 52| Scale is weakly epimorphic with val: <7 11 27 30 51| Scale is weakly epimorphic with val: <7 12 23 29 51| Scale is weakly epimorphic with val: <7 12 23 30 53| Scale is weakly epimorphic with val: <7 12 24 28 51| Scale is weakly epimorphic with val: <7 12 24 30 52| Scale is weakly epimorphic with val: <7 12 25 29 52| Scale is weakly epimorphic with val: <7 12 26 30 53| Scale is weakly epimorphic with val: <7 12 27 28 51| Scale is weakly epimorphic with val: <8 11 23 28 52| Scale is weakly epimorphic with val: <8 11 24 25 51| Scale is weakly epimorphic with val: <8 11 24 29 53| Scale is weakly epimorphic with val: <8 11 25 26 52| Scale is weakly epimorphic with val: <8 11 25 27 51| Scale is weakly epimorphic with val: <8 11 26 27 53| Scale is weakly epimorphic with val: <8 11 26 28 52| Scale is weakly epimorphic with val: <8 11 27 28 51| Scale is weakly epimorphic with val: <8 11 27 29 53| Scale is weakly epimorphic with val: <8 12 23 26 52| Scale is weakly epimorphic with val: <8 12 23 28 53| Scale is weakly epimorphic with val: <8 12 24 26 51| Scale is weakly epimorphic with val: <8 12 24 27 53| Scale is weakly epimorphic with val: <8 12 25 27 52| Scale is weakly epimorphic with val: <8 12 25 28 51| Scale is weakly epimorphic with val: <8 12 26 28 53| Scale is weakly epimorphic with val: <8 12 26 29 52| Scale is weakly epimorphic with val: <8 12 27 30 53|
FIT/MODE
3: 0 0 3 N M DE S SD: 59.0386 c. M: 85.2997 c. 4: 0 1 3 N G T3 SD: 39.6575 c. M: 56.3970 c. 5: 1 0 4 N G T3 SD: 26.2808 c. M:-43.2120 c. 6: 1 0 5 N G T3 SD: 15.4205 c. M:-26.6105 c. 7: 1 0 6 N G T3 SD: 11.8021 c. M:-14.7523 c. 10: 1 1 8 N M DE S SD: 9.0961 c. M:-14.3093 c. 11: 1 1 9 N M DE S SD: 7.1007 c. M: 11.1202 c. 16: 2 1 13 N T3 SD: 5.7640 c. M:-8.0837 c. 17: 2 1 14 N T3 SD: 1.9609 c. M:-2.5906 c. 18: 2 1 15 N T3 SD: 1.4577 c. M: 2.2922 c. 35: 4 2 29 N T3 SD: 0.3051 c. M:-0.5225 c. 88: 10 5 73 N T3 SD: 0.2609 c. M: 0.4057 c. 123: 14 7 102 N T3 SD: 0.2283 c. M:-0.2911 c. 158: 18 9 131 N T3 SD: 0.2263 c. M:-0.3423 c. 204: 23 12 169 N T3 SD: 0.1655 c. M: 0.2448 c. 222: 25 13 184 N T3 SD: 0.1817 c. M: 0.3108 c. 239: 27 14 198 N T3 SD: 0.1108 c. M:-0.1390 c. 257: 29 15 213 N T3 SD: 0.1154 c. M: 0.1973 c. 274: 31 16 227 N T3 SD: 0.0809 c. M:-0.1314 c. 292: 33 17 242 N T3 SD: 0.0650 c. M: 0.1111 c. 327: 37 19 271 N T3 SD: 0.0254 c. M: 0.0433 c. 362: 41 21 300 N T3 SD: 0.0066 c. M:-0.0114 c. 1051: 119 61 871 N T3 SD: 0.0034 c. M: 0.0056 c. 1413: 160 82 1171 N T3 SD: 0.0010 c. M: 0.0012 c. 1775: 201 103 1471 N T3 SD: 0.0009 c. M:-0.0014 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 24:25 x 32 SD: 7.1377 cents 25:26 x 33 SD: 10.4291 cents 26:27 x 35 SD: 9.4127 cents 27:28 x 36 SD: 3.2820 cents 28:29 x 37 SD: 8.0629 cents 29:30 x 39 SD: 7.5183 cents 33:34:35:44 SD: 5.7416 cents 36:37:38:48 SD: 4.0727 cents 46 x 48:61 SD: 7.4835 cents 47 x 49:63 SD: 8.0217 cents 48:50 x 64 SD: 7.1377 cents 49:51 x 65 SD: 7.8077 cents 50:52:53:67 SD: 7.0674 cents 51:53:54:68 SD: 5.6807 cents 52:54:55:69 SD: 5.6655 cents 53:55:56:71 SD: 5.0173 cents 54:56:57:72 SD: 3.5281 cents 56:58:59:75 SD: 3.3975 cents 57:59:60:76 SD: 1.6052 cents 60:62:63:80 SD: 0.3037 cents 333:344:350:444 SD: 0.3031 cents 336:347:353:448 SD: 0.2150 cents 393:406:413:524 SD: 0.2126 cents 396:409:416:528 SD: 0.1588 cents 453:468:476:604 SD: 0.1470 cents 456:471:479:608 SD: 0.1271 cents 513:530:539:684 SD: 0.0984 cents 573:592:602:764 SD: 0.0636 cents