Scala analysis: 050_E2
Enharmonic tetrachord 69/67 * 67/66 * 88/69
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 69/67 50.922320 2: 23/22 76.956405 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 88/69 421.0886 1: 69/67 50.9223 2: 67/66 26.0341 3: 88/69 421.0886
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 67/66 26.034 cents 1: 1 69/67 50.922 cents 1: 1 88/69 421.089 cents 2: 1 23/22 76.956 cents 2: 1 268/207 447.123 cents 2: 1 88/67 472.011 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 : 50.9 77.0 498.0 50.9 : 26.0 447.1 498.0 77.0 : 421.1 472.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.0341 .. 421.0886 cents 1936/1541, 395.0545 cents 67/66, 26.0341 cents 2: 76.9564 .. 472.0109 cents 1936/1541, 395.0545 cents 1587/1936,-344.1322 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 67/66, 26.0341 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 88/69, 421.0886 cents Average / Smallest step : 6.376832 Largest / Average step : 2.536449 Largest / Smallest step : 16.174511 Median interval of one step : 69/67, 50.9223 cents, amount: 1 Least squares average step : 121.35501 cents, oct.: 364.06503 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1702-tone equal temperament with octave 4/3 degrees: 174 263 1702 Least number of segments generator : 853 of 249.608 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1511 of 442.154 cents and inv. generated superset size: 62 = 59 more = 2066.667% 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 26.03409 cents Scale diversity : 0.232736 Lumma stability : 0.104545 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 : 4554/4489, 24.8882 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% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions with margin 395.0545 cents: 2 -- Rational properties -- Prime limit : 67 Odd number limit : 207 (O: 69 U: 207) Highest odd numerator or denominator: 69 Scale harmonicity : 0.014577 Fundamental : 1/4422, -12.1105 octaves, 0.0592 Hz. Guide tone : 276, 8.1085 octaves, 72208.656 Hz. Exponens Consonantiae : 1.220472E+06, 20.21901 octaves Euler's gradus suavitatis : 106 Sum of Mann's harmonic distance : 94.0, average 31.33333 Mersenne's string divisions : 42840 Sum of van Prooijen's expressibility: 3.67770, average 1.22590 Sum of Tenney's harmonic distance : 7.44826, average 2.48275 Vogel's harmonic complexity : 71.66667 Wille's k value : 2311 Wilson's harmonic complexity : 107 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.57848, average 2.26308 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 1 0.00000 2 1 11: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 1 67: -1 .. 0 -0.33333 1 1 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 32 44| Scale is weakly epimorphic with val: <6 10 23 36 43| Scale is weakly epimorphic with val: <6 10 24 33 45| Scale is weakly epimorphic with val: <6 10 25 34 43| Scale is weakly epimorphic with val: <6 10 26 35 44| Scale is weakly epimorphic with val: <6 10 26 36 43| Scale is weakly epimorphic with val: <6 10 27 36 45| Scale is weakly epimorphic with val: <6 11 23 32 44| Scale is weakly epimorphic with val: <6 11 24 33 45| Scale is weakly epimorphic with val: <6 11 24 35 43| Scale is weakly epimorphic with val: <6 11 25 34 43| Scale is weakly epimorphic with val: <6 11 25 36 44| Scale is weakly epimorphic with val: <6 11 26 35 44| Scale is weakly epimorphic with val: <6 11 27 35 43| Scale is weakly epimorphic with val: <6 11 27 36 45| Scale is weakly epimorphic with val: <7 10 23 33 44| Scale is weakly epimorphic with val: <7 10 24 34 45| Scale is weakly epimorphic with val: <7 10 24 36 43| Scale is weakly epimorphic with val: <7 10 25 35 43| Scale is weakly epimorphic with val: <7 10 26 36 44| Scale is weakly epimorphic with val: <7 10 27 36 43| Scale is weakly epimorphic with val: <7 11 23 31 43| Scale is weakly epimorphic with val: <7 11 23 32 45| Scale is weakly epimorphic with val: <7 11 23 34 43| Scale is weakly epimorphic with val: <7 11 23 35 45| Scale is weakly epimorphic with val: <7 11 24 30 43| Scale is weakly epimorphic with val: <7 11 24 32 44| Scale is JI-epimorphic with val: <7 11 24 33 43| Scale is weakly epimorphic with val: <7 11 24 35 44| Scale is weakly epimorphic with val: <7 11 24 36 43| Scale is weakly epimorphic with val: <7 11 25 30 45| Scale is weakly epimorphic with val: <7 11 25 31 44| Scale is weakly epimorphic with val: <7 11 25 33 45| Scale is JI-epimorphic with val: <7 11 25 34 44| Scale is weakly epimorphic with val: <7 11 25 36 45| Scale is weakly epimorphic with val: <7 11 26 31 43| Scale is weakly epimorphic with val: <7 11 26 32 45| Scale is weakly epimorphic with val: <7 11 26 34 43| Scale is JI-epimorphic with val: <7 11 26 35 45| Scale is weakly epimorphic with val: <7 11 27 30 43| Scale is weakly epimorphic with val: <7 11 27 32 44| Scale is weakly epimorphic with val: <7 11 27 33 43| Scale is weakly epimorphic with val: <7 11 27 35 44| Scale is weakly epimorphic with val: <7 11 27 36 43| Scale is weakly epimorphic with val: <7 12 23 33 44| Scale is weakly epimorphic with val: <7 12 23 34 43| Scale is weakly epimorphic with val: <7 12 24 34 45| Scale is weakly epimorphic with val: <7 12 24 35 44| Scale is weakly epimorphic with val: <7 12 25 35 43| Scale is weakly epimorphic with val: <7 12 25 36 45| Scale is weakly epimorphic with val: <7 12 26 34 43| Scale is weakly epimorphic with val: <7 12 26 36 44| Scale is weakly epimorphic with val: <7 12 27 35 44| Scale is weakly epimorphic with val: <8 11 23 34 44| Scale is weakly epimorphic with val: <8 11 23 35 43| Scale is weakly epimorphic with val: <8 11 24 35 45| Scale is weakly epimorphic with val: <8 11 24 36 44| Scale is weakly epimorphic with val: <8 11 25 36 43| Scale is weakly epimorphic with val: <8 11 26 35 43| Scale is weakly epimorphic with val: <8 11 27 36 44| Scale is weakly epimorphic with val: <8 12 23 34 44| Scale is weakly epimorphic with val: <8 12 23 36 45| Scale is weakly epimorphic with val: <8 12 24 34 43| Scale is weakly epimorphic with val: <8 12 24 35 45| Scale is weakly epimorphic with val: <8 12 25 35 44| Scale is weakly epimorphic with val: <8 12 25 36 43| Scale is weakly epimorphic with val: <8 12 26 36 45| Scale is weakly epimorphic with val: <8 12 27 34 43|
FIT/MODE
3: 0 0 3 N M DE S SD: 53.2772 c. M: 76.9564 c. 4: 0 1 3 N G T3 SD: 40.2266 c. M: 50.9223 c. 5: 1 0 4 N G T3 SD: 31.0029 c. M:-48.6867 c. 6: 1 0 5 N G T3 SD: 18.8509 c. M:-32.0852 c. 7: 1 0 6 N G T3 SD: 12.1498 c. M:-20.2270 c. 8: 1 0 7 N G T3 SD: 10.7169 c. M: 14.7008 c. 11: 1 1 9 N M DE S SD: 8.5001 c. M:-13.5972 c. 12: 1 1 10 N M DE S SD: 6.4634 c. M: 9.4186 c. 13: 1 1 11 N M DE S SD: 7.2836 c. M: 12.6112 c. 17: 2 1 14 N T3 SD: 7.7114 c. M:-10.9339 c. 18: 2 1 15 N T3 SD: 4.3250 c. M:-6.0511 c. 19: 2 1 16 N T3 SD: 1.3026 c. M:-1.6823 c. 39: 4 2 33 N T3 SD: 0.2137 c. M: 0.3341 c. 97: 10 5 82 N T3 SD: 0.2465 c. M:-0.4225 c. 136: 14 7 115 N T3 SD: 0.2026 c. M:-0.3470 c. 175: 18 9 148 N T3 SD: 0.1883 c. M:-0.3052 c. 214: 22 11 181 N T3 SD: 0.1841 c. M:-0.2786 c. 226: 23 12 191 N T3 SD: 0.1696 c. M: 0.2363 c. 245: 25 13 207 N T3 SD: 0.1781 c. M:-0.2914 c. 246: 25 13 208 N T3 SD: 0.1783 c. M: 0.3080 c. 265: 27 14 224 N T3 SD: 0.1178 c. M: 0.1781 c. 304: 31 16 257 N T3 SD: 0.0819 c. M: 0.1348 c. 343: 35 18 290 N T3 SD: 0.0585 c. M: 0.1014 c. 362: 37 19 306 N T3 SD: 0.0525 c. M:-0.0892 c. 382: 39 20 323 N T3 SD: 0.0473 c. M: 0.0748 c. 401: 41 21 339 N T3 SD: 0.0277 c. M:-0.0481 c. 440: 45 23 372 N T3 SD: 0.0115 c. M:-0.0142 c. 1262: 129 66 1067 N T3 SD: 0.0074 c. M: 0.0128 c. 1301: 133 68 1100 N T3 SD: 0.0073 c. M: 0.0102 c. 1702: 174 89 1439 N T3 SD: 0.0039 c. M: 0.0059 c. 1741: 178 91 1472 N T3 SD: 0.0026 c. M: 0.0040 c. 2181: 223 114 1844 N T3 SD: 0.0007 c. M:-0.0011 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 27:28 x 36 SD: 6.0193 cents 28:29 x 37 SD: 9.1882 cents 29:30 x 39 SD: 8.3844 cents 30:31 x 40 SD: 2.9223 cents 31:32 x 41 SD: 7.2946 cents 32:33 x 43 SD: 6.8381 cents 36:37:38:48 SD: 5.6694 cents 39:40:41:52 SD: 3.9846 cents 42:43:44:56 SD: 3.5989 cents 51 x 53:68 SD: 5.1811 cents 52 x 54:69 SD: 7.1522 cents 53 x 55:71 SD: 7.5988 cents 54:56 x 72 SD: 6.0193 cents 57:59:60:76 SD: 4.9148 cents 59:61:62:79 SD: 4.4603 cents 60:62:63:80 SD: 3.1723 cents 62:64:65:83 SD: 3.1339 cents 63:65:66:84 SD: 1.5970 cents 66:68:69:88 SD: 0.2534 cents 333:343:348:444 SD: 0.2474 cents 372:383:389:496 SD: 0.2073 cents 438:451:458:584 SD: 0.1491 cents 504:519:527:672 SD: 0.1113 cents 570:587:596:760 SD: 0.0892 cents