Scala analysis: 098_E12
Enharmonic tetrachord 34/33 * 33/32 * 64/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/33 51.682466 2: 17/16 104.955410 17th harmonic 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/51 393.0896 1: 34/33 51.6825 2: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 3: 64/51 393.0896
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 34/33 51.682 cents 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 64/51 393.090 cents 2: 1 17/16 104.955 cents 17th harmonic 2: 1 128/99 444.772 cents 2: 1 22/17 446.363 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 : 51.7 105.0 498.0 51.7 : 53.3 446.4 498.0 105.0: 393.1 444.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.6825 .. 393.0896 cents 352/289, 341.4071 cents 34/33, 51.6825 cents 2: 104.9554 .. 446.3625 cents 352/289, 341.4071 cents 867/1024,-288.1342 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 34/33, 51.6825 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 64/51, 393.0896 cents Average / Smallest step : 3.212211 Largest / Average step : 2.367796 Largest / Smallest step : 7.605860 Median interval of one step : 33/32, 53.2729 cents, amount: 1 Least squares average step : 125.40916 cents, oct.: 376.22749 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2178-tone equal temperament with octave 4/3 degrees: 226 459 2178 Least number of segments generator : 1091 of 249.480 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1435 of 328.143 cents and inv. generated superset size: 57 = 54 more = 1900.000% 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 51.68247 cents Scale diversity : 0.467148 Lumma stability : 0.207541 Lumma impropriety factor : 0.578530 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 : 1089/1088, 1.5905 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 : 2 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 339.8166 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 99 (O: 33 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.017554 Average absolute harmonicity : 0.087613 Specific harmonicity : 0.078169 Fundamental : 1/528, -9.0444 octaves, 0.4955 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 3.590400E+04, 15.13186 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 53.5, average 17.83333 Mersenne's string divisions : 15477 Sum of van Prooijen's expressibility: 3.22608, average 1.07536 Sum of Tenney's harmonic distance : 6.56374, average 2.18791 Vogel's harmonic complexity : 23.33333 Wille's k value : 280 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 21.45179, average 3.57530 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.33333 7 3: -1 .. 0 -0.66667 2 1 11: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 24 31| Scale is weakly epimorphic with val: <6 10 25 27| Scale is weakly epimorphic with val: <6 11 23 27| Scale is weakly epimorphic with val: <6 11 24 32| Scale is weakly epimorphic with val: <6 11 26 27| Scale is weakly epimorphic with val: <7 10 23 31| Scale is weakly epimorphic with val: <7 10 24 30| Scale is weakly epimorphic with val: <7 10 26 31| Scale is weakly epimorphic with val: <7 10 27 33| Scale is weakly epimorphic with val: <7 11 23 29| Scale is weakly epimorphic with val: <7 11 23 32| Scale is weakly epimorphic with val: <7 11 25 27| Scale is JI-epimorphic with val: <7 11 25 30| = patent Scale is weakly epimorphic with val: <7 11 25 33| Scale is weakly epimorphic with val: <7 11 26 29| Scale is weakly epimorphic with val: <7 11 26 32| Scale is weakly epimorphic with val: <7 12 24 32| Scale is weakly epimorphic with val: <7 12 25 31| Scale is weakly epimorphic with val: <8 11 24 30| Scale is weakly epimorphic with val: <8 11 27 33| Scale is weakly epimorphic with val: <8 12 24 31|
FIT/MODE
3: 0 0 3 N M DE S SD: 67.5443 c. M: 104.9554 c. 4: 0 1 3 N G T3 SD: 31.9035 c. M: 51.6825 c. 5: 0 1 4 N G T3 SD: 29.9981 c. M: 51.6825 c. 6: 0 1 5 N G T3 SD: 32.4180 c. M: 51.6825 c. 7: 1 1 5 N M DE S SD: 24.3137 c. M:-37.3432 c. 8: 1 1 6 N M DE S SD: 12.8351 c. M:-19.5558 c. 9: 1 1 7 N M DE S SD: 3.9200 c. M:-5.7213 c. 10: 1 1 8 N M DE S SD: 3.2716 c. M: 5.3464 c. 19: 2 2 15 N M DE S SD: 0.4333 c. M:-0.7433 c. 86: 9 9 68 N M DE S SD: 0.4835 c. M: 0.7134 c. 105: 11 11 83 N M DE S SD: 0.4500 c. M: 0.6031 c. 124: 13 13 98 N M DE S SD: 0.4322 c. M:-0.5319 c. 143: 15 15 113 N M DE S SD: 0.4223 c. M:-0.5600 c. 156: 16 17 123 N T3 SD: 0.4169 c. M: 0.6009 c. 162: 17 17 128 N M DE S SD: 0.4167 c. M:-0.5815 c. 166: 17 18 131 N T3 SD: 0.3926 c. M: 0.6779 c. 175: 18 19 138 N T3 SD: 0.3298 c. M: 0.4550 c. 185: 19 20 146 N T3 SD: 0.3079 c. M: 0.5319 c. 194: 20 21 153 N T3 SD: 0.2613 c. M: 0.3376 c. 204: 21 22 161 N T3 SD: 0.2389 c. M: 0.4131 c. 213: 22 23 168 N T3 SD: 0.2070 c. M:-0.2654 c. 223: 23 24 176 N T3 SD: 0.1818 c. M: 0.3146 c. 232: 24 25 183 N T3 SD: 0.1644 c. M:-0.2351 c. 242: 25 26 191 N T3 SD: 0.1337 c. M: 0.2315 c. 251: 26 27 198 N T3 SD: 0.1321 c. M:-0.2095 c. 261: 27 28 206 N T3 SD: 0.0927 c. M: 0.1606 c. 280: 29 30 221 N T3 SD: 0.0576 c. M: 0.0992 c. 299: 31 32 236 N T3 SD: 0.0280 c. M: 0.0457 c. 318: 33 34 251 N T3 SD: 0.0124 c. M: 0.0214 c. 617: 64 66 487 N T3 SD: 0.0165 c. M: 0.0214 c. 935: 97 100 738 N T3 SD: 0.0138 c. M: 0.0197 c. 1243: 129 133 981 N T3 SD: 0.0134 c. M:-0.0227 c. 1253: 130 134 989 N T3 SD: 0.0129 c. M: 0.0202 c. 1523: 158 163 1202 N T3 SD: 0.0126 c. M:-0.0166 c. 1542: 160 165 1217 N T3 SD: 0.0092 c. M:-0.0152 c. 1561: 162 167 1232 N T3 SD: 0.0083 c. M:-0.0137 c. 1580: 164 169 1247 N T3 SD: 0.0105 c. M:-0.0133 c. 1841: 191 197 1453 N T3 SD: 0.0087 c. M: 0.0113 c. 1860: 193 199 1468 N T3 SD: 0.0056 c. M:-0.0089 c. 1879: 195 201 1483 N T3 SD: 0.0050 c. M:-0.0078 c. 2178: 226 233 1719 N T3 SD: 0.0031 c. M:-0.0045 c. 2197: 228 235 1734 N T3 SD: 0.0029 c. M:-0.0036 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: 80.9577 cents 7 x 8:9 S SD: 70.5252 cents 8 x 9:11 SD: 56.1917 cents 9 x 10:12 S SD: 38.7242 cents 10 x 11:13 SD: 37.1720 cents 11 x 12:15 S SD: 30.0020 cents 12 x 13:16 SD: 16.8086 cents 13 x 14:17 SD: 20.4634 cents 14 x 15:19 SD: 16.9472 cents 15 x 16:20 S SD: 3.3879 cents 16 x 17:21 SD: 13.6320 cents 17 x 18:23 SD: 12.9883 cents 18 x 19:24 SD: 5.6762 cents 19 x 20:25 S SD: 14.0249 cents 20 x 21:27 SD: 14.8517 cents 21 x 22:28 SD: 12.2092 cents 22:23 x 29 SD: 16.0487 cents 23:24 x 31 SD: 14.4414 cents 24:25:26:32 SD: 12.8700 cents 25:26:27:33 SD: 12.3182 cents 26:27:28:35 S SD: 10.5715 cents 27:28:29:36 SD: 7.2955 cents 29:30:31:39 SD: 6.5002 cents 30:31:32:40 S SD: 2.8238 cents 33:34:35:44 SD: 1.0296 cents 63:65:67:84 SD: 0.9708 cents 96:99:102:128 SD: 0.5302 cents 129:133:137:172 SD: 0.4743 cents 270:278:287:360 SD: 0.4534 cents 303:312:322:404 SD: 0.3544 cents 333:343:354:444 SD: 0.3419 cents 336:346:357:448 SD: 0.3032 cents 366:377:389:488 SD: 0.2319 cents 399:411:424:532 SD: 0.1534 cents 432:445:459:576 SD: 0.1179 cents 495:510:526:660 SD: 0.0686 cents 528:544:561:704 SD: 0.0000 cents