Scala analysis: 073_E7
Enharmonic tetrachord 60/59 * 59/57 * 19/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60/59 29.097055 2: 20/19 88.800698 small undevicesimal semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/15 409.2443 undevicesimal ditone 1: 60/59 29.0971 2: 59/57 59.7036 3: 19/15 409.2443 undevicesimal ditone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 60/59 29.097 cents 1: 1 59/57 59.704 cents 1: 1 19/15 409.244 cents undevicesimal ditone 2: 1 20/19 88.801 cents small undevicesimal semitone 2: 1 76/59 438.341 cents 2: 1 59/45 468.948 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 : 29.1 88.8 498.0 29.1 : 59.7 468.9 498.0 88.8 : 409.2 438.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.0971 .. 409.2443 cents 1121/900, 380.1472 cents 60/59, 29.0971 cents 2: 88.8007 .. 468.9479 cents 1121/900, 380.1472 cents 300/361,-320.4436 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 60/59, 29.0971 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/15, 409.2443 cents Average / Smallest step : 5.705560 Largest / Average step : 2.465104 Largest / Smallest step : 14.064801 Median interval of one step : 59/57, 59.7036 cents, amount: 1 Least squares average step : 121.48810 cents, oct.: 364.46431 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1318-tone equal temperament with octave 4/3 degrees: 77 235 1318 Least number of segments generator : 661 of 249.778 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 793 of 299.658 cents and inv. generated superset size: 49 = 46 more = 1633.333% 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 29.09706 cents Scale diversity : 0.313026 Lumma stability : 0.116845 Lumma impropriety factor : 0.643403 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 : 60/59, 29.0971 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% -- Rational properties -- Prime limit : 59 Odd number limit : 59 (O: 59 U: 59) Highest odd numerator or denominator: 59 Scale harmonicity : 0.020904 Fundamental : 1/3363, -11.7155 octaves, 0.0778 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 2.017800E+05, 17.62242 octaves Euler's gradus suavitatis : 87 Sum of Mann's harmonic distance : 82.5, average 27.50000 Mersenne's string divisions : 4641 Sum of van Prooijen's expressibility: 3.52673, average 1.17558 Sum of Tenney's harmonic distance : 7.20797, average 2.40266 Vogel's harmonic complexity : 60.33333 Wille's k value : 560 Wilson's harmonic complexity : 89 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.51738, average 2.08623 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.66667 2 19: -1 .. 0 -0.33333 1 1 59: -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 19 28 43| Scale is weakly epimorphic with val: <6 11 19 28 43| Scale is weakly epimorphic with val: <7 10 17 28 42| Scale is weakly epimorphic with val: <7 10 18 29 43| Scale is weakly epimorphic with val: <7 10 19 30 44| Scale is weakly epimorphic with val: <7 11 15 28 44| Scale is weakly epimorphic with val: <7 11 15 30 42| Scale is weakly epimorphic with val: <7 11 15 31 44| Scale is weakly epimorphic with val: <7 11 15 33 42| Scale is weakly epimorphic with val: <7 11 15 34 44| Scale is weakly epimorphic with val: <7 11 16 28 43| Scale is weakly epimorphic with val: <7 11 16 29 42| Scale is weakly epimorphic with val: <7 11 16 31 43| Scale is weakly epimorphic with val: <7 11 16 32 42| Scale is weakly epimorphic with val: <7 11 16 34 43| Scale is weakly epimorphic with val: <7 11 17 29 44| Scale is weakly epimorphic with val: <7 11 17 30 43| Scale is weakly epimorphic with val: <7 11 17 32 44| Scale is weakly epimorphic with val: <7 11 17 33 43| Scale is weakly epimorphic with val: <7 11 18 28 44| Scale is JI-epimorphic with val: <7 11 18 30 42| Scale is weakly epimorphic with val: <7 11 18 31 44| Scale is weakly epimorphic with val: <7 11 18 33 42| Scale is weakly epimorphic with val: <7 11 18 34 44| Scale is weakly epimorphic with val: <7 11 19 28 43| Scale is weakly epimorphic with val: <7 11 19 29 42| Scale is JI-epimorphic with val: <7 11 19 31 43| Scale is weakly epimorphic with val: <7 11 19 32 42| Scale is weakly epimorphic with val: <7 11 19 34 43| Scale is weakly epimorphic with val: <7 12 17 28 42| Scale is weakly epimorphic with val: <7 12 18 29 43| Scale is weakly epimorphic with val: <7 12 19 29 42| Scale is weakly epimorphic with val: <7 12 19 30 44| Scale is weakly epimorphic with val: <7 12 19 32 42| Scale is weakly epimorphic with val: <8 11 15 28 44| Scale is weakly epimorphic with val: <8 11 16 29 42| Scale is weakly epimorphic with val: <8 11 17 30 43| Scale is weakly epimorphic with val: <8 11 18 30 42| Scale is weakly epimorphic with val: <8 11 18 31 44| Scale is weakly epimorphic with val: <8 11 18 33 42| Scale is weakly epimorphic with val: <8 11 19 28 43| Scale is weakly epimorphic with val: <8 11 19 31 43| Scale is weakly epimorphic with val: <8 11 19 32 42| Scale is weakly epimorphic with val: <8 11 19 34 43| Scale is weakly epimorphic with val: <8 12 15 28 44| Scale is weakly epimorphic with val: <8 12 16 29 42| Scale is weakly epimorphic with val: <8 12 17 28 42| Scale is weakly epimorphic with val: <8 12 17 30 43| Scale is weakly epimorphic with val: <8 12 17 31 42| Scale is weakly epimorphic with val: <8 12 17 34 42| Scale is weakly epimorphic with val: <8 12 18 29 43| Scale is weakly epimorphic with val: <8 12 18 31 44| Scale is weakly epimorphic with val: <8 12 18 32 43| Scale is weakly epimorphic with val: <8 12 19 30 44| Scale is weakly epimorphic with val: <8 12 19 32 42| Scale is weakly epimorphic with val: <8 12 19 33 44|
FIT/MODE
3: 0 0 3 N M DE S SD: 53.9512 c. M: 88.8007 c. 4: 0 1 3 N G T3 SD: 26.5950 c. M:-35.7106 c. 5: 0 1 4 N G T3 SD: 17.9207 c. M: 29.0971 c. 6: 0 1 5 N G T3 SD: 17.1289 c. M: 29.0971 c. 7: 0 1 6 N G T3 SD: 19.6487 c. M: 29.0971 c. 10: 1 1 8 N M DE S SD: 13.4860 c. M:-20.7074 c. 11: 1 1 9 N M DE S SD: 9.3961 c. M:-16.1798 c. 12: 1 1 10 N M DE S SD: 7.9054 c. M:-12.4067 c. 13: 1 1 11 N M DE S SD: 8.8169 c. M: 12.1784 c. 15: 1 2 12 N T3 SD: 6.6753 c. M:-10.8083 c. 16: 1 2 13 N T3 SD: 2.8940 c. M:-4.5827 c. 17: 1 2 14 N T3 SD: 0.5381 c. M: 0.9104 c. 50: 3 6 41 N T3 SD: 0.6672 c. M:-0.8474 c. 67: 4 8 55 N T3 SD: 0.4347 c. M:-0.6370 c. 84: 5 10 69 N T3 SD: 0.3262 c. M:-0.5485 c. 101: 6 12 83 N T3 SD: 0.2837 c. M:-0.4898 c. 118: 7 14 97 N T3 SD: 0.2757 c. M:-0.4480 c. 135: 8 16 111 N T3 SD: 0.2834 c. M:-0.4167 c. 152: 9 18 125 N T3 SD: 0.2969 c. M:-0.3925 c. 169: 10 20 139 N T3 SD: 0.3117 c. M: 0.3903 c. 174: 10 21 143 N T3 SD: 0.2764 c. M: 0.4738 c. 190: 11 23 156 N T3 SD: 0.2405 c. M:-0.3231 c. 191: 11 23 157 N T3 SD: 0.2529 c. M: 0.4138 c. 207: 12 25 170 N T3 SD: 0.1824 c. M: 0.2249 c. 224: 13 27 184 N T3 SD: 0.1361 c. M: 0.1927 c. 241: 14 29 198 N T3 SD: 0.1018 c. M: 0.1650 c. 258: 15 31 212 N T3 SD: 0.0814 c. M: 0.1410 c. 275: 16 33 226 N T3 SD: 0.0769 c. M: 0.1199 c. 292: 17 35 240 N T3 SD: 0.0854 c. M: 0.1078 c. 308: 18 37 253 N T3 SD: 0.0787 c. M:-0.1359 c. 325: 19 39 267 N T3 SD: 0.0482 c. M:-0.0812 c. 342: 20 41 281 N T3 SD: 0.0246 c. M:-0.0319 c. 359: 21 43 295 N T3 SD: 0.0223 c. M:-0.0365 c. 617: 36 74 507 N T3 SD: 0.0223 c. M: 0.0377 c. 701: 41 84 576 N T3 SD: 0.0195 c. M:-0.0325 c. 942: 55 113 774 N T3 SD: 0.0167 c. M:-0.0226 c. 959: 56 115 788 N T3 SD: 0.0089 c. M: 0.0141 c. 976: 57 117 802 N T3 SD: 0.0083 c. M: 0.0104 c. 1301: 76 156 1069 N T3 SD: 0.0076 c. M:-0.0129 c. 1318: 77 158 1083 N T3 SD: 0.0006 c. M:-0.0010 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: 89.0351 cents 7 x 8:9 S SD: 77.8368 cents 8 x 9:11 SD: 63.4196 cents 9 x 10:12 S SD: 46.8015 cents 10 x 11:13 SD: 43.9549 cents 11 x 12:15 S SD: 36.5287 cents 12 x 13:16 SD: 24.8860 cents 13 x 14:17 SD: 25.9335 cents 14 x 15:19 SD: 21.6672 cents 15 x 16:20 S SD: 11.4653 cents 16 x 17:21 SD: 15.8454 cents 17 x 18:23 SD: 13.6187 cents 18 x 19:24 SD: 2.4012 cents 19 x 20:25 S SD: 11.4653 cents 20 x 21:27 SD: 10.9693 cents 21 x 22:28 SD: 4.1318 cents 22 x 23:29 SD: 11.5300 cents 23 x 24:31 SD: 12.0303 cents 24 x 25:32 SD: 9.0641 cents 25 x 26:33 SD: 13.5975 cents 26 x 27:35 SD: 14.3613 cents 27 x 28:36 SD: 12.9199 cents 28 x 29:37 SD: 16.0301 cents 29:30:31:39 SD: 14.1708 cents 30:31:32:40 S SD: 11.9788 cents 31:32:33:41 SD: 11.7540 cents 32:33:34:43 SD: 10.6821 cents 33:34:35:44 SD: 8.6975 cents 35:36:37:47 SD: 8.1219 cents 36:37:38:48 SD: 6.3185 cents 39:40:41:52 SD: 4.9668 cents 42:43:44:56 SD: 4.7583 cents 51:52:54:68 SD: 3.7049 cents 53:54:56:71 SD: 3.6445 cents 54:55:57:72 SD: 1.8315 cents 57:58:60:76 SD: 0.3374 cents 303:308:319:404 SD: 0.2713 cents 360:366:379:480 SD: 0.1792 cents 417:424:439:556 SD: 0.1153 cents 474:482:499:632 SD: 0.0732 cents 531:540:559:708 SD: 0.0543 cents