Scala analysis: 129_E16
Enharmonic tetrachord 88/85 * 85/82 * 41/33
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/85 60.048819 2: 44/41 122.255537 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 41/33 375.7895 1: 88/85 60.0488 2: 85/82 62.2067 3: 41/33 375.7895
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 88/85 60.049 cents 1: 1 85/82 62.207 cents 1: 1 41/33 375.789 cents 2: 1 44/41 122.256 cents 2: 1 328/255 435.838 cents 2: 1 85/66 437.996 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 : 60.0 122.3 498.0 60.0 : 62.2 438.0 498.0 122.3: 375.8 435.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 60.0488 .. 375.7895 cents 3485/2904, 315.7406 cents 88/85, 60.0488 cents 2: 122.2555 .. 437.9962 cents 3485/2904, 315.7406 cents 1452/1681,-253.5339 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 88/85, 60.0488 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 41/33, 375.7895 cents Average / Smallest step : 2.764667 Largest / Average step : 2.263587 Largest / Smallest step : 6.258066 Median interval of one step : 85/82, 62.2067 cents, amount: 1 Least squares average step : 128.47821 cents, oct.: 385.43462 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2314-tone equal temperament with octave 4/3 degrees: 279 568 2314 Least number of segments generator : 1159 of 249.453 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2025 of 435.843 cents and inv. generated superset size: 43 = 40 more = 1433.333% 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 60.04882 cents Scale diversity : 0.597947 Lumma stability : 0.241138 Lumma impropriety factor : 0.509058 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 : 7225/7216, 2.1579 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 313.5827 cents: 2 -- Rational properties -- Prime limit : 41 Odd number limit : 255 (O: 85 U: 255) Highest odd numerator or denominator: 85 Scale harmonicity : 0.016566 Fundamental : 1/10455, -13.3519 octaves, 0.0250 Hz. Guide tone : 88, 6.4594 octaves, 23023.050 Hz. Exponens Consonantiae : 9.200400E+05, 19.81134 octaves Euler's gradus suavitatis : 76 Sum of Mann's harmonic distance : 132.5, average 44.16667 Mersenne's string divisions : 102935 Sum of van Prooijen's expressibility: 4.01932, average 1.33977 Sum of Tenney's harmonic distance : 8.20932, average 2.73644 Vogel's harmonic complexity : 53.66667 Wille's k value : 1742 Wilson's harmonic complexity : 77 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 13.31857, average 2.21976 Lattice compactness (without 2's) : 8.56048, average 1.42675 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 0 -0.33333 1 1 5: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 41: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 11 16 24 30 37| Scale is weakly epimorphic with val: <7 11 16 24 30 40| Scale is weakly epimorphic with val: <7 11 16 24 31 39| Scale is JI-epimorphic with val: <7 11 16 25 29 37| Scale is weakly epimorphic with val: <7 11 16 25 29 40| Scale is weakly epimorphic with val: <7 11 16 25 31 38| Scale is weakly epimorphic with val: <7 11 16 25 31 41| Scale is weakly epimorphic with val: <7 11 16 26 29 39| Scale is JI-epimorphic with val: <7 11 16 26 30 38| Scale is weakly epimorphic with val: <7 11 16 26 30 41| Scale is weakly epimorphic with val: <7 11 17 24 29 37| Scale is weakly epimorphic with val: <7 11 17 24 29 40| Scale is weakly epimorphic with val: <7 11 17 24 30 39| Scale is weakly epimorphic with val: <7 11 17 25 30 38| Scale is weakly epimorphic with val: <7 11 17 25 30 41| Scale is weakly epimorphic with val: <7 11 17 25 31 37| Scale is weakly epimorphic with val: <7 11 17 25 31 40| Scale is JI-epimorphic with val: <7 11 17 26 29 38| Scale is weakly epimorphic with val: <7 11 17 26 29 41| Scale is weakly epimorphic with val: <7 11 17 26 31 39| Scale is weakly epimorphic with val: <7 11 18 24 29 39| Scale is weakly epimorphic with val: <7 11 18 24 31 37| Scale is weakly epimorphic with val: <7 11 18 24 31 40| Scale is weakly epimorphic with val: <7 11 18 25 29 38| Scale is weakly epimorphic with val: <7 11 18 25 29 41| Scale is weakly epimorphic with val: <7 11 18 25 30 37| Scale is weakly epimorphic with val: <7 11 18 25 30 40| Scale is weakly epimorphic with val: <7 11 18 26 30 39| Scale is weakly epimorphic with val: <7 11 18 26 31 38| Scale is weakly epimorphic with val: <7 11 18 26 31 41| Scale is weakly epimorphic with val: <7 12 16 26 30 37| Scale is weakly epimorphic with val: <7 12 17 26 29 37| Scale is weakly epimorphic with val: <7 12 18 26 31 37|
FIT/MODE
3: 0 1 2 N G T3 SD: 42.8981 c. M: 60.0488 c. 4: 0 1 3 N G T3 SD: 34.6937 c. M: 60.0488 c. 5: 0 1 4 N G T3 SD: 37.0528 c. M: 60.0488 c. 6: 1 1 4 N M DE S SD: 28.5306 c. M:-43.7595 c. 7: 1 1 5 N M DE S SD: 13.2280 c. M:-20.0430 c. 8: 1 1 6 N M DE S SD: 1.8219 c. M:-2.2557 c. 25: 3 3 19 N M DE S SD: 1.5816 c. M: 2.7247 c. 33: 4 4 25 N M DE S SD: 0.8953 c. M: 1.5174 c. 41: 5 5 31 N M DE S SD: 0.6011 c. M: 0.7811 c. 49: 6 6 37 N M DE S SD: 0.5651 c. M:-0.9363 c. 57: 7 7 43 N M DE S SD: 0.6448 c. M:-1.1146 c. 90: 11 11 68 N M DE S SD: 0.5595 c. M:-0.8233 c. 118: 14 15 89 N T3 SD: 0.5599 c. M: 0.9587 c. 126: 15 16 95 N T3 SD: 0.4663 c. M: 0.7577 c. 134: 16 17 101 N T3 SD: 0.4063 c. M: 0.5808 c. 142: 17 18 107 N T3 SD: 0.3793 c. M:-0.5020 c. 151: 18 19 114 N T3 SD: 0.4119 c. M: 0.6792 c. 158: 19 20 119 N T3 SD: 0.4028 c. M:-0.6796 c. 159: 19 20 120 N T3 SD: 0.3130 c. M: 0.5340 c. 167: 20 21 126 N T3 SD: 0.2328 c. M: 0.4027 c. 175: 21 22 132 N T3 SD: 0.1780 c. M: 0.2834 c. 183: 22 23 138 N T3 SD: 0.1597 c. M:-0.2145 c. 208: 25 26 157 N T3 SD: 0.1347 c. M: 0.1876 c. 216: 26 27 163 N T3 SD: 0.0640 c. M: 0.0990 c. 224: 27 28 169 N T3 SD: 0.0210 c. M:-0.0323 c. 705: 85 88 532 N T3 SD: 0.0232 c. M: 0.0402 c. 713: 86 89 538 N T3 SD: 0.0161 c. M:-0.0239 c. 929: 112 116 701 N T3 SD: 0.0134 c. M: 0.0227 c. 937: 113 117 707 N T3 SD: 0.0084 c. M:-0.0142 c. 1153: 139 144 870 N T3 SD: 0.0080 c. M: 0.0121 c. 1161: 140 145 876 N T3 SD: 0.0052 c. M:-0.0083 c. 1385: 167 173 1045 N T3 SD: 0.0053 c. M:-0.0082 c. 2090: 252 261 1577 N T3 SD: 0.0049 c. M: 0.0081 c. 2314: 279 289 1746 N T3 SD: 0.0025 c. M: 0.0042 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: 72.3077 cents 7 x 8:9 S SD: 62.9034 cents 8 x 9:11 SD: 48.7480 cents 9 x 10:12 S SD: 30.0741 cents 10 x 11:13 SD: 30.6130 cents 11 x 12:15 S SD: 24.0789 cents 12 x 13:16 SD: 8.1586 cents 13 x 14:17 SD: 17.0780 cents 14 x 15:19 SD: 15.3855 cents 15 x 16:20 S SD: 5.2621 cents 16 x 17:21 SD: 16.1449 cents 17 x 18:23 SD: 17.1880 cents 18 x 19:24 SD: 14.3263 cents 19:20 x 25 S SD: 18.3881 cents 20:21 x 27 SD: 16.2694 cents 21:22:23:28 SD: 13.5871 cents 22:23:24:29 SD: 12.8359 cents 23:24:25:31 SD: 10.6689 cents 24:25:26:32 SD: 6.4902 cents 26:27:28:35 S SD: 6.1368 cents 27:28:29:36 SD: 1.0854 cents 84:87:90:112 SD: 0.9664 cents 111:115:119:148 SD: 0.7213 cents 138:143:148:184 SD: 0.6462 cents 165:171:177:220 SD: 0.6418 cents 204:211:219:272 SD: 0.5797 cents 231:239:248:308 SD: 0.4334 cents 258:267:277:344 SD: 0.3419 cents 285:295:306:380 SD: 0.2991 cents 312:323:335:416 SD: 0.2949 cents 315:326:338:420 SD: 0.2243 cents 342:354:367:456 SD: 0.1213 cents 369:382:396:492 SD: 0.0355 cents