Scala analysis: 072_E7
Enharmonic tetrachord 30/29 * 58/57 * 19/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 30/29 58.691521 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: 30/29 58.6915 2: 58/57 30.1092 3: 19/15 409.2443 undevicesimal ditone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 58/57 30.109 cents 1: 1 30/29 58.692 cents 1: 1 19/15 409.244 cents undevicesimal ditone 2: 1 20/19 88.801 cents small undevicesimal semitone 2: 1 58/45 439.353 cents 2: 1 38/29 467.936 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 : 58.7 88.8 498.0 58.7 : 30.1 439.4 498.0 88.8 : 409.2 467.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 30.1092 .. 409.2443 cents 361/290, 379.1351 cents 58/57, 30.1092 cents 2: 88.8007 .. 467.9358 cents 361/290, 379.1351 cents 300/361,-320.4436 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 58/57, 30.1092 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/15, 409.2443 cents Average / Smallest step : 5.513767 Largest / Average step : 2.465104 Largest / Smallest step : 13.592012 Median interval of one step : 30/29, 58.6915 cents, amount: 1 Least squares average step : 123.60199 cents, oct.: 370.80598 cents Scale is not proper Scale has trivalence property 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 30.10918 cents Scale diversity : 0.316083 Lumma stability : 0.120909 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 : 855/841, 28.5823 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 -- Rational properties -- Prime limit : 29 Odd number limit : 57 (O: 29 U: 57) Highest odd numerator or denominator: 29 Scale harmonicity : 0.009813 Average absolute harmonicity : 0.084468 Specific harmonicity : 0.051098 Fundamental : 1/1653, -10.6909 octaves, 0.1583 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 9.918000E+04, 16.59776 octaves Euler's gradus suavitatis : 57 Sum of Mann's harmonic distance : 52.5, average 17.50000 Mersenne's string divisions : 16107 Sum of van Prooijen's expressibility: 3.21827, average 1.07276 Sum of Tenney's harmonic distance : 6.59848, average 2.19949 Vogel's harmonic complexity : 40.00000 Wille's k value : 427 Wilson's harmonic complexity : 59 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.06336, average 2.17723 Lattice compactness (without 2's) : 10.05986, average 1.67664 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.66667 2 19: -1 .. 0 -0.33333 1 1 29: -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 34| Scale is weakly epimorphic with val: <6 10 19 28 37| Scale is weakly epimorphic with val: <6 10 19 30 32| Scale is weakly epimorphic with val: <6 11 18 28 32| Scale is weakly epimorphic with val: <6 11 18 31 32| Scale is weakly epimorphic with val: <6 11 19 28 34| Scale is weakly epimorphic with val: <6 11 19 28 37| Scale is weakly epimorphic with val: <6 11 19 29 33| Scale is weakly epimorphic with val: <6 11 19 32 33| Scale is weakly epimorphic with val: <7 10 17 28 32| Scale is weakly epimorphic with val: <7 10 17 28 35| Scale is weakly epimorphic with val: <7 10 17 28 38| Scale is weakly epimorphic with val: <7 10 18 29 33| Scale is weakly epimorphic with val: <7 10 18 29 36| Scale is weakly epimorphic with val: <7 10 18 30 32| Scale is weakly epimorphic with val: <7 10 19 28 33| Scale is weakly epimorphic with val: <7 10 19 30 34| Scale is weakly epimorphic with val: <7 10 19 30 37| Scale is weakly epimorphic with val: <7 10 19 31 33| Scale is weakly epimorphic with val: <7 11 15 28 34| Scale is weakly epimorphic with val: <7 11 15 28 37| Scale is weakly epimorphic with val: <7 11 15 30 32| Scale is weakly epimorphic with val: <7 11 15 30 35| Scale is weakly epimorphic with val: <7 11 15 30 38| Scale is weakly epimorphic with val: <7 11 15 31 34| Scale is weakly epimorphic with val: <7 11 15 31 37| Scale is weakly epimorphic with val: <7 11 15 33 35| Scale is weakly epimorphic with val: <7 11 15 33 38| Scale is weakly epimorphic with val: <7 11 15 34 34| Scale is weakly epimorphic with val: <7 11 15 34 37| Scale is JI-epimorphic with val: <7 11 16 28 33| Scale is weakly epimorphic with val: <7 11 16 28 36| Scale is weakly epimorphic with val: <7 11 16 29 32| Scale is weakly epimorphic with val: <7 11 16 29 35| Scale is weakly epimorphic with val: <7 11 16 29 38| Scale is weakly epimorphic with val: <7 11 16 31 33| Scale is weakly epimorphic with val: <7 11 16 31 36| Scale is weakly epimorphic with val: <7 11 16 32 32| Scale is weakly epimorphic with val: <7 11 16 32 35| Scale is weakly epimorphic with val: <7 11 16 32 38| Scale is weakly epimorphic with val: <7 11 16 34 36| Scale is JI-epimorphic with val: <7 11 17 29 34| Scale is weakly epimorphic with val: <7 11 17 29 37| Scale is weakly epimorphic with val: <7 11 17 30 33| Scale is weakly epimorphic with val: <7 11 17 30 36| Scale is weakly epimorphic with val: <7 11 17 32 34| Scale is weakly epimorphic with val: <7 11 17 32 37| Scale is weakly epimorphic with val: <7 11 17 33 33| Scale is weakly epimorphic with val: <7 11 17 33 36| Scale is weakly epimorphic with val: <7 11 18 28 34| Scale is weakly epimorphic with val: <7 11 18 28 37| Scale is weakly epimorphic with val: <7 11 18 30 32| Scale is JI-epimorphic with val: <7 11 18 30 35| Scale is weakly epimorphic with val: <7 11 18 30 38| Scale is weakly epimorphic with val: <7 11 18 31 34| Scale is weakly epimorphic with val: <7 11 18 31 37| Scale is weakly epimorphic with val: <7 11 18 33 35| Scale is weakly epimorphic with val: <7 11 18 33 38| Scale is weakly epimorphic with val: <7 11 18 34 34| Scale is weakly epimorphic with val: <7 11 18 34 37| Scale is weakly epimorphic with val: <7 11 19 28 33| Scale is weakly epimorphic with val: <7 11 19 28 36| Scale is weakly epimorphic with val: <7 11 19 29 32| Scale is weakly epimorphic with val: <7 11 19 29 35| Scale is weakly epimorphic with val: <7 11 19 29 38| Scale is weakly epimorphic with val: <7 11 19 31 33| Scale is JI-epimorphic with val: <7 11 19 31 36| Scale is weakly epimorphic with val: <7 11 19 32 32| Scale is weakly epimorphic with val: <7 11 19 32 35| Scale is weakly epimorphic with val: <7 11 19 32 38| Scale is weakly epimorphic with val: <7 11 19 34 36| Scale is weakly epimorphic with val: <7 12 16 29 32| Scale is weakly epimorphic with val: <7 12 16 32 32| Scale is weakly epimorphic with val: <7 12 17 28 32| Scale is weakly epimorphic with val: <7 12 17 28 35| Scale is weakly epimorphic with val: <7 12 17 28 38| Scale is weakly epimorphic with val: <7 12 17 30 33| Scale is weakly epimorphic with val: <7 12 17 33 33| Scale is weakly epimorphic with val: <7 12 18 28 34| Scale is weakly epimorphic with val: <7 12 18 29 33| Scale is weakly epimorphic with val: <7 12 18 29 36| Scale is weakly epimorphic with val: <7 12 18 31 34| Scale is weakly epimorphic with val: <7 12 18 34 34| Scale is weakly epimorphic with val: <7 12 19 29 35| Scale is weakly epimorphic with val: <7 12 19 30 34| Scale is weakly epimorphic with val: <7 12 19 30 37| Scale is weakly epimorphic with val: <7 12 19 32 35| Scale is weakly epimorphic with val: <8 11 15 28 33| Scale is weakly epimorphic with val: <8 11 15 28 36| Scale is weakly epimorphic with val: <8 11 16 28 32| Scale is weakly epimorphic with val: <8 11 16 29 34| Scale is weakly epimorphic with val: <8 11 16 29 37| Scale is weakly epimorphic with val: <8 11 16 31 32| Scale is weakly epimorphic with val: <8 11 17 29 33| Scale is weakly epimorphic with val: <8 11 17 30 32| Scale is weakly epimorphic with val: <8 11 17 30 35| Scale is weakly epimorphic with val: <8 11 17 30 38| Scale is weakly epimorphic with val: <8 11 17 32 33| Scale is weakly epimorphic with val: <8 11 18 30 34| Scale is weakly epimorphic with val: <8 11 18 31 33| Scale is weakly epimorphic with val: <8 11 18 31 36| Scale is weakly epimorphic with val: <8 11 18 33 34| Scale is weakly epimorphic with val: <8 11 19 28 35| Scale is weakly epimorphic with val: <8 11 19 31 35| Scale is weakly epimorphic with val: <8 11 19 32 34| Scale is weakly epimorphic with val: <8 11 19 32 37| Scale is weakly epimorphic with val: <8 11 19 34 35| Scale is weakly epimorphic with val: <8 12 15 28 33| Scale is weakly epimorphic with val: <8 12 15 28 36| Scale is weakly epimorphic with val: <8 12 15 29 32| Scale is weakly epimorphic with val: <8 12 15 32 32| Scale is weakly epimorphic with val: <8 12 16 29 34| Scale is weakly epimorphic with val: <8 12 16 29 37| Scale is weakly epimorphic with val: <8 12 16 30 33| Scale is weakly epimorphic with val: <8 12 16 33 33| Scale is weakly epimorphic with val: <8 12 17 28 34| Scale is weakly epimorphic with val: <8 12 17 30 32| Scale is weakly epimorphic with val: <8 12 17 30 35| Scale is weakly epimorphic with val: <8 12 17 30 38| Scale is weakly epimorphic with val: <8 12 17 31 34| Scale is weakly epimorphic with val: <8 12 17 34 34| Scale is weakly epimorphic with val: <8 12 18 29 35| Scale is weakly epimorphic with val: <8 12 18 31 33| Scale is weakly epimorphic with val: <8 12 18 31 36| Scale is weakly epimorphic with val: <8 12 18 32 35| Scale is weakly epimorphic with val: <8 12 19 30 36| Scale is weakly epimorphic with val: <8 12 19 32 34| Scale is weakly epimorphic with val: <8 12 19 32 37| Scale is weakly epimorphic with val: <8 12 19 33 36|
FIT/MODE
3: 0 0 3 N M DE S SD: 61.4553 c. M: 88.8007 c. 4: 1 0 3 N G T3 SD: 43.2338 c. M:-65.8197 c. 5: 1 0 4 N G T3 SD: 24.4340 c. M:-40.9175 c. 6: 1 0 5 N G T3 SD: 14.4318 c. M:-24.3160 c. 7: 1 0 6 N G T3 SD: 12.4735 c. M: 17.6514 c. 9: 1 1 7 N M DE S SD: 12.7776 c. M:-21.8760 c. 10: 1 1 8 N M DE S SD: 8.0787 c. M:-10.8083 c. 11: 1 1 9 N M DE S SD: 7.8108 c. M: 13.4147 c. 15: 2 1 12 N T3 SD: 7.6667 c. M:-10.8083 c. 16: 2 1 13 N T3 SD: 3.3518 c. M:-4.5827 c. 17: 2 1 14 N T3 SD: 0.5287 c. M: 0.9104 c. 67: 8 4 55 N T3 SD: 0.5047 c. M:-0.7765 c. 84: 10 5 69 N T3 SD: 0.3549 c. M:-0.5996 c. 101: 12 6 83 N T3 SD: 0.2793 c. M:-0.4821 c. 118: 14 7 97 N T3 SD: 0.2492 c. M:-0.3986 c. 135: 16 8 111 N T3 SD: 0.2451 c. M:-0.3360 c. 152: 18 9 125 N T3 SD: 0.2536 c. M: 0.3322 c. 179: 21 11 147 N T3 SD: 0.2032 c. M: 0.2617 c. 196: 23 12 161 N T3 SD: 0.1630 c. M: 0.2475 c. 213: 25 13 175 N T3 SD: 0.1393 c. M: 0.2355 c. 230: 27 14 189 N T3 SD: 0.1306 c. M: 0.2254 c. 247: 29 15 203 N T3 SD: 0.1333 c. M: 0.2166 c. 263: 31 16 216 N T3 SD: 0.1178 c. M:-0.2035 c. 280: 33 17 230 N T3 SD: 0.0786 c. M:-0.1359 c. 297: 35 18 244 N T3 SD: 0.0439 c. M:-0.0760 c. 314: 37 19 258 N T3 SD: 0.0133 c. M:-0.0226 c. 331: 39 20 272 N T3 SD: 0.0156 c. M: 0.0253 c. 645: 76 39 530 N T3 SD: 0.0043 c. M: 0.0071 c. 959: 113 58 788 N T3 SD: 0.0051 c. M: 0.0063 c. 1604: 189 97 1318 N T3 SD: 0.0042 c. M: 0.0067 c. 2249: 265 136 1848 N T3 SD: 0.0040 c. M: 0.0068 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 23:24 x 31 SD: 11.9893 cents 24:25 x 32 SD: 5.9905 cents 25:26 x 33 SD: 9.8430 cents 26:27 x 35 SD: 8.9251 cents 27:28 x 36 SD: 2.1347 cents 28:29 x 37 SD: 7.8314 cents 30:31:32:40 S SD: 7.6704 cents 32:33:34:43 SD: 7.2407 cents 33:34:35:44 SD: 4.9424 cents 36:37:38:48 SD: 4.0797 cents 44 x 46:59 SD: 7.6892 cents 45 x 47:60 SD: 6.7589 cents 46:48 x 61 SD: 8.8556 cents 47:49 x 63 SD: 8.1448 cents 48:50:51:64 SD: 6.7042 cents 49:51:52:65 SD: 6.5675 cents 50:52:53:67 SD: 5.8233 cents 51:53:54:68 SD: 4.2889 cents 53:55:56:71 SD: 3.9220 cents 54:56:57:72 SD: 2.1419 cents 57:59:60:76 SD: 0.3374 cents 264:273:278:352 SD: 0.3091 cents 321:332:338:428 SD: 0.2160 cents 378:391:398:504 SD: 0.1609 cents 435:450:458:580 SD: 0.1326 cents 492:509:518:656 SD: 0.1236 cents 495:512:521:660 SD: 0.0972 cents 552:571:581:736 SD: 0.0628 cents