Scala analysis: 051_E2
Enharmonic tetrachord 69/68 * 34/33 * 88/69
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 69/68 25.273939 2: 23/22 76.956405 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 88/69 421.0886 1: 69/68 25.2739 2: 34/33 51.6825 3: 88/69 421.0886
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 69/68 25.274 cents 1: 1 34/33 51.682 cents 1: 1 88/69 421.089 cents 2: 1 23/22 76.956 cents 2: 1 22/17 446.363 cents 2: 1 272/207 472.771 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 : 25.3 77.0 498.0 25.3 : 51.7 472.8 498.0 77.0 : 421.1 446.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.2739 .. 421.0886 cents 5984/4761, 395.8147 cents 69/68, 25.2739 cents 2: 76.9564 .. 472.7711 cents 5984/4761, 395.8147 cents 1587/1936,-344.1322 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 69/68, 25.2739 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 88/69, 421.0886 cents Average / Smallest step : 6.568624 Largest / Average step : 2.536449 Largest / Smallest step : 16.660980 Median interval of one step : 34/33, 51.6825 cents, amount: 1 Least squares average step : 119.52298 cents, oct.: 358.56895 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2168-tone equal temperament with octave 4/3 degrees: 110 335 2168 Least number of segments generator : 1085 of 249.252 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2101 of 482.653 cents and inv. generated superset size: 35 = 32 more = 1166.667% 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 25.27394 cents Scale diversity : 0.230640 Lumma stability : 0.101493 Lumma impropriety factor : 0.690966 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 : 69/68, 25.2739 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 369.4061 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 207 (O: 69 U: 207) Highest odd numerator or denominator: 69 Scale harmonicity : 0.010028 Average absolute harmonicity : 0.081205 Specific harmonicity : 0.046750 Fundamental : 1/2244, -11.1319 octaves, 0.1166 Hz. Guide tone : 276, 8.1085 octaves, 72208.656 Hz. Exponens Consonantiae : 6.193440E+05, 19.24038 octaves Euler's gradus suavitatis : 57 Sum of Mann's harmonic distance : 94.5, average 31.50000 Mersenne's string divisions : 43155 Sum of van Prooijen's expressibility: 3.67770, average 1.22590 Sum of Tenney's harmonic distance : 7.45469, average 2.48490 Vogel's harmonic complexity : 38.66667 Wille's k value : 1138 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.76839, average 2.79473 Lattice compactness (without 2's) : 10.05986, average 1.67664 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.33333 5 3: -1 .. 1 0.00000 2 1 11: -1 .. 0 -0.33333 1 17: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 2 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 23 28 33| Scale is weakly epimorphic with val: <6 10 23 29 32| Scale is weakly epimorphic with val: <6 10 23 31 36| Scale is weakly epimorphic with val: <6 10 23 32 32| Scale is weakly epimorphic with val: <6 10 24 27 33| Scale is weakly epimorphic with val: <6 10 24 29 34| Scale is weakly epimorphic with val: <6 10 24 30 33| Scale is weakly epimorphic with val: <6 10 24 33 33| Scale is weakly epimorphic with val: <6 10 25 27 32| Scale is weakly epimorphic with val: <6 10 25 28 34| Scale is weakly epimorphic with val: <6 10 25 30 35| Scale is weakly epimorphic with val: <6 10 25 31 34| Scale is weakly epimorphic with val: <6 10 26 28 33| Scale is weakly epimorphic with val: <6 10 26 29 35| Scale is weakly epimorphic with val: <6 10 26 31 36| Scale is weakly epimorphic with val: <6 10 26 32 35| Scale is weakly epimorphic with val: <6 10 27 27 36| Scale is weakly epimorphic with val: <6 10 27 29 34| Scale is weakly epimorphic with val: <6 10 27 30 36| Scale is weakly epimorphic with val: <6 10 27 33 36| Scale is weakly epimorphic with val: <6 11 23 27 31| Scale is weakly epimorphic with val: <6 11 23 29 32| Scale is weakly epimorphic with val: <6 11 23 30 34| Scale is weakly epimorphic with val: <6 11 23 32 32| Scale is weakly epimorphic with val: <6 11 24 27 33| Scale is weakly epimorphic with val: <6 11 24 28 32| Scale is weakly epimorphic with val: <6 11 24 30 33| Scale is weakly epimorphic with val: <6 11 24 31 35| Scale is weakly epimorphic with val: <6 11 24 33 33| Scale is weakly epimorphic with val: <6 11 25 28 34| Scale is weakly epimorphic with val: <6 11 25 29 33| Scale is weakly epimorphic with val: <6 11 25 31 34| Scale is weakly epimorphic with val: <6 11 25 32 36| Scale is weakly epimorphic with val: <6 11 26 27 31| Scale is weakly epimorphic with val: <6 11 26 29 35| Scale is weakly epimorphic with val: <6 11 26 30 34| Scale is weakly epimorphic with val: <6 11 26 32 35| Scale is weakly epimorphic with val: <6 11 27 27 36| Scale is weakly epimorphic with val: <6 11 27 28 32| Scale is weakly epimorphic with val: <6 11 27 30 36| Scale is weakly epimorphic with val: <6 11 27 31 35| Scale is weakly epimorphic with val: <6 11 27 33 36| Scale is weakly epimorphic with val: <7 10 23 27 33| Scale is weakly epimorphic with val: <7 10 23 28 35| Scale is weakly epimorphic with val: <7 10 23 30 33| Scale is weakly epimorphic with val: <7 10 23 33 33| Scale is weakly epimorphic with val: <7 10 24 28 34| Scale is weakly epimorphic with val: <7 10 24 29 36| Scale is weakly epimorphic with val: <7 10 24 31 34| Scale is weakly epimorphic with val: <7 10 25 27 34| Scale is weakly epimorphic with val: <7 10 25 29 35| Scale is weakly epimorphic with val: <7 10 25 32 35| Scale is weakly epimorphic with val: <7 10 26 27 36| Scale is weakly epimorphic with val: <7 10 26 28 35| Scale is weakly epimorphic with val: <7 10 26 30 36| Scale is weakly epimorphic with val: <7 10 26 33 36| Scale is weakly epimorphic with val: <7 10 27 29 36| Scale is JI-epimorphic with val: <7 11 23 28 32| Scale is weakly epimorphic with val: <7 11 23 28 35| Scale is weakly epimorphic with val: <7 11 23 29 31| Scale is weakly epimorphic with val: <7 11 23 29 34| Scale is weakly epimorphic with val: <7 11 23 31 32| Scale is weakly epimorphic with val: <7 11 23 31 35| Scale is weakly epimorphic with val: <7 11 23 32 34| Scale is weakly epimorphic with val: <7 11 24 27 32| Scale is weakly epimorphic with val: <7 11 24 27 35| Scale is weakly epimorphic with val: <7 11 24 29 30| Scale is JI-epimorphic with val: <7 11 24 29 33| Scale is weakly epimorphic with val: <7 11 24 29 36| Scale is weakly epimorphic with val: <7 11 24 30 32| Scale is weakly epimorphic with val: <7 11 24 30 35| Scale is weakly epimorphic with val: <7 11 24 32 33| Scale is weakly epimorphic with val: <7 11 24 32 36| Scale is weakly epimorphic with val: <7 11 24 33 35| Scale is weakly epimorphic with val: <7 11 25 27 31| Scale is weakly epimorphic with val: <7 11 25 27 34| Scale is weakly 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 28 36| Scale is weakly epimorphic with val: <7 11 25 30 31| Scale is JI-epimorphic with val: <7 11 25 30 34| Scale is weakly epimorphic with val: <7 11 25 31 33| Scale is weakly epimorphic with val: <7 11 25 31 36| Scale is weakly epimorphic with val: <7 11 25 33 34| Scale is weakly epimorphic with val: <7 11 26 28 32| Scale is weakly epimorphic with val: <7 11 26 28 35| Scale is weakly epimorphic with val: <7 11 26 29 31| Scale is weakly epimorphic with val: <7 11 26 29 34| Scale is weakly epimorphic with val: <7 11 26 31 32| Scale is JI-epimorphic with val: <7 11 26 31 35| Scale is weakly epimorphic with val: <7 11 26 32 34| Scale is weakly epimorphic with val: <7 11 27 27 32| Scale is weakly epimorphic with val: <7 11 27 27 35| Scale is weakly epimorphic with val: <7 11 27 29 30| Scale is weakly epimorphic with val: <7 11 27 29 33| Scale is weakly epimorphic with val: <7 11 27 29 36| Scale is weakly epimorphic with val: <7 11 27 30 32| Scale is weakly epimorphic with val: <7 11 27 30 35| Scale is weakly epimorphic with val: <7 11 27 32 33| Scale is JI-epimorphic with val: <7 11 27 32 36| Scale is weakly epimorphic with val: <7 11 27 33 35| Scale is weakly epimorphic with val: <7 12 23 27 33| Scale is weakly epimorphic with val: <7 12 23 29 34| Scale is weakly epimorphic with val: <7 12 23 30 33| Scale is weakly epimorphic with val: <7 12 23 33 33| Scale is weakly epimorphic with val: <7 12 24 27 32| Scale is weakly epimorphic with val: <7 12 24 28 34| Scale is weakly epimorphic with val: <7 12 24 30 35| Scale is weakly epimorphic with val: <7 12 24 31 34| Scale is weakly epimorphic with val: <7 12 25 28 33| Scale is weakly epimorphic with val: <7 12 25 29 35| Scale is weakly epimorphic with val: <7 12 25 31 36| Scale is weakly epimorphic with val: <7 12 25 32 35| Scale is weakly epimorphic with val: <7 12 26 27 36| Scale is weakly epimorphic with val: <7 12 26 29 34| Scale is weakly epimorphic with val: <7 12 26 30 36| Scale is weakly epimorphic with val: <7 12 26 33 36| Scale is weakly epimorphic with val: <7 12 27 27 32| Scale is weakly epimorphic with val: <7 12 27 30 35| Scale is weakly epimorphic with val: <8 11 23 27 35| Scale is weakly epimorphic with val: <8 11 23 28 34| Scale is weakly epimorphic with val: <8 11 23 31 34| Scale is weakly epimorphic with val: <8 11 24 28 36| Scale is weakly epimorphic with val: <8 11 24 29 35| Scale is weakly epimorphic with val: <8 11 24 32 35| Scale is weakly epimorphic with val: <8 11 25 27 36| Scale is weakly epimorphic with val: <8 11 25 30 36| Scale is weakly epimorphic with val: <8 11 25 33 36| Scale is weakly epimorphic with val: <8 11 26 27 35| Scale is weakly epimorphic with val: <8 11 27 28 36| Scale is weakly epimorphic with val: <8 12 23 28 34| Scale is weakly epimorphic with val: <8 12 23 29 36| Scale is weakly epimorphic with val: <8 12 23 31 34| Scale is weakly epimorphic with val: <8 12 24 27 34| Scale is weakly epimorphic with val: <8 12 24 29 35| Scale is weakly epimorphic with val: <8 12 24 32 35| Scale is weakly epimorphic with val: <8 12 25 27 36| Scale is weakly epimorphic with val: <8 12 25 28 35| Scale is weakly epimorphic with val: <8 12 25 30 36| Scale is weakly epimorphic with val: <8 12 25 33 36| Scale is weakly epimorphic with val: <8 12 26 29 36| Scale is weakly epimorphic with val: <8 12 27 27 34|
FIT/MODE
3: 0 0 3 N M DE S SD: 46.7656 c. M: 76.9564 c. 4: 0 1 3 N G T3 SD: 31.0925 c. M:-47.5548 c. 5: 0 1 4 N G T3 SD: 19.5952 c. M: 25.2739 c. 6: 0 1 5 N G T3 SD: 15.0043 c. M: 25.2739 c. 7: 0 1 6 N G T3 SD: 14.9721 c. M: 25.2739 c. 8: 0 1 7 N G T3 SD: 16.8808 c. M: 25.2739 c. 12: 1 1 10 N M DE S SD: 10.0004 c. M:-16.2298 c. 13: 1 1 11 N M DE S SD: 7.5295 c. M:-13.0372 c. 14: 1 1 12 N M DE S SD: 6.8271 c. M:-10.3007 c. 17: 1 2 14 N T3 SD: 6.7264 c. M:-10.9339 c. 18: 1 2 15 N T3 SD: 3.7573 c. M:-6.0511 c. 19: 1 2 16 N T3 SD: 1.1123 c. M:-1.6823 c. 39: 2 4 33 N T3 SD: 0.2469 c. M: 0.3341 c. 97: 5 10 82 N T3 SD: 0.2327 c. M:-0.3985 c. 136: 7 14 115 N T3 SD: 0.2105 c. M:-0.3607 c. 175: 9 18 148 N T3 SD: 0.2071 c. M:-0.3398 c. 214: 11 22 181 N T3 SD: 0.2087 c. M:-0.3265 c. 239: 12 25 202 N T3 SD: 0.1762 c. M: 0.2675 c. 258: 13 27 218 N T3 SD: 0.1821 c. M:-0.2599 c. 259: 13 27 219 N T3 SD: 0.1606 c. M: 0.2755 c. 278: 14 29 235 N T3 SD: 0.1202 c. M: 0.1925 c. 297: 15 31 251 N T3 SD: 0.1259 c. M:-0.1819 c. 298: 15 31 252 N T3 SD: 0.1262 c. M: 0.2046 c. 317: 16 33 268 N T3 SD: 0.0802 c. M: 0.1360 c. 336: 17 35 284 N T3 SD: 0.0827 c. M:-0.1220 c. 356: 18 37 301 N T3 SD: 0.0534 c. M: 0.0919 c. 375: 19 39 317 N T3 SD: 0.0488 c. M:-0.0746 c. 395: 20 41 334 N T3 SD: 0.0410 c. M: 0.0565 c. 414: 21 43 350 N T3 SD: 0.0217 c. M:-0.0361 c. 453: 23 47 383 N T3 SD: 0.0079 c. M:-0.0131 c. 1301: 66 135 1100 N T3 SD: 0.0075 c. M: 0.0102 c. 1715: 87 178 1450 N T3 SD: 0.0050 c. M: 0.0087 c. 1754: 89 182 1483 N T3 SD: 0.0040 c. M: 0.0065 c. 2168: 110 225 1833 N T3 SD: 0.0026 c. M: 0.0041 c. 2207: 112 229 1866 N T3 SD: 0.0025 c. M: 0.0043 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: 94.9573 cents 7 x 8:9 S SD: 83.2874 cents 8 x 9:11 SD: 68.8390 cents 9 x 10:12 S SD: 52.7237 cents 10 x 11:13 SD: 49.1772 cents 11 x 12:15 S SD: 41.6608 cents 12 x 13:16 SD: 30.8081 cents 13 x 14:17 SD: 30.6843 cents 14 x 15:19 SD: 26.1918 cents 15 x 16:20 S SD: 17.3874 cents 16 x 17:21 SD: 19.5402 cents 17 x 18:23 SD: 16.7533 cents 18 x 19:24 SD: 8.3233 cents 19 x 20:25 S SD: 12.9044 cents 20 x 21:27 SD: 11.3900 cents 21 x 22:28 SD: 1.7903 cents 22 x 23:29 SD: 9.8929 cents 23 x 24:31 SD: 9.5004 cents 24 x 25:32 SD: 3.1420 cents 25 x 26:33 SD: 9.8076 cents 26 x 27:35 SD: 10.1176 cents 27 x 28:36 SD: 6.9978 cents 28 x 29:37 SD: 11.2215 cents 29 x 30:39 SD: 11.7733 cents 30 x 31:40 SD: 10.0948 cents 31 x 32:41 SD: 13.0399 cents 32 x 33:43 SD: 13.6237 cents 33 x 35:44 SD: 12.4551 cents 34:35:36:45 S SD: 11.8682 cents 35:36:37:47 SD: 10.9260 cents 36:37:38:48 SD: 9.2387 cents 38:39:40:51 SD: 8.5446 cents 39:40:41:52 SD: 6.9680 cents 41:42:43:55 SD: 6.7612 cents 42:43:44:56 SD: 5.2907 cents 45:46:47:60 SD: 4.2953 cents 48:49:50:64 SD: 4.0569 cents 59:60:62:79 SD: 4.0489 cents 60:61:63:80 SD: 2.7403 cents 63:64:66:84 SD: 1.3655 cents 66:67:69:88 SD: 0.2534 cents 417:423:436:556 SD: 0.1903 cents 483:490:505:644 SD: 0.1319 cents 549:557:574:732 SD: 0.0888 cents