Scala analysis: 382_D4
Diatonic tetrachord 72/67 * 67/62 * 31/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 72/67 124.602973 2: 36/31 258.874429 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 31/27 239.1706 1: 72/67 124.6030 2: 67/62 134.2715 3: 31/27 239.1706
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 72/67 124.603 cents 1: 1 67/62 134.271 cents 1: 1 31/27 239.171 cents 2: 1 36/31 258.874 cents 2: 1 248/201 363.774 cents 2: 1 67/54 373.442 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 : 124.6 258.9 498.0 124.6: 134.3 373.4 498.0 258.9: 239.2 363.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 124.6030 .. 239.1706 cents 2077/1944, 114.5676 cents 72/67, 124.6030 cents 2: 258.8744 .. 373.4420 cents 2077/1944, 114.5676 cents 972/961, 19.7039 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 72/67, 124.6030 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 31/27, 239.1706 cents Average / Smallest step : 1.332352 Largest / Average step : 1.440656 Largest / Smallest step : 1.919461 Median interval of one step : 67/62, 134.2715 cents, amount: 1 Least squares average step : 152.60620 cents, oct.: 457.81861 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1339-tone equal temperament with octave 4/3 degrees: 335 696 1339 Least number of segments generator : 670 of 249.208 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1154 of 429.234 cents and inv. generated superset size: 39 = 36 more = 1300.000% 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 19.70386 cents Scale diversity : 1.206383 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.539931 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 : 4489/4464, 9.6685 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 104.8991 cents: 2 -- Rational properties -- Prime limit : 67 Odd number limit : 201 (O: 67 U: 201) Highest odd numerator or denominator: 67 Scale harmonicity : 0.090909 Fundamental : 1/6231, -12.6052 octaves, 0.0420 Hz. Guide tone : 72, 6.1699 octaves, 18837.041 Hz. Exponens Consonantiae : 4.486320E+05, 18.77517 octaves Euler's gradus suavitatis : 106 Sum of Mann's harmonic distance : 106.5, average 35.50000 Mersenne's string divisions : 65191 Sum of van Prooijen's expressibility: 3.79456, average 1.26485 Sum of Tenney's harmonic distance : 7.81025, average 2.60342 Vogel's harmonic complexity : 73.66667 Wille's k value : 1038 Wilson's harmonic complexity : 107 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.83232, average 2.63872 Lattice compactness (without 2's) : 11.00000, average 1.83333 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 2 1.00000 5 1 31: -1 .. 0 -0.33333 1 1 67: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 11 34 45| Scale is weakly epimorphic with val: <7 11 35 44| Scale is weakly epimorphic with val: <7 11 37 45| Scale is weakly epimorphic with val: <7 11 38 44| Scale is weakly epimorphic with val: <7 12 35 44| Scale is weakly epimorphic with val: <8 11 34 43| Scale is weakly epimorphic with val: <8 11 35 45| Scale is weakly epimorphic with val: <8 11 37 43| Scale is weakly epimorphic with val: <8 12 35 45| Scale is weakly epimorphic with val: <8 12 37 43| Scale is weakly epimorphic with val: <8 12 38 45|
FIT/MODE
3: 1 1 1 SP B ME I SD: 48.5342 c. M:-73.1556 c. 4: 1 1 2 P M ME S SD: 5.6883 c. M: 9.8519 c. 13: 3 4 6 SP T3 SD: 7.7472 c. M: 9.6695 c. 15: 4 4 7 SP M DE S SD: 6.1358 c. M:-8.2090 c. 17: 4 5 8 SP T3 SD: 5.0991 c. M: 7.4159 c. 19: 5 5 9 SP M DE S SD: 4.1770 c. M:-6.4615 c. 21: 5 6 10 SP T3 SD: 3.6640 c. M: 6.0208 c. 23: 6 6 11 SP M DE S SD: 3.1237 c. M:-5.3218 c. 25: 6 7 12 SP T3 SD: 2.9291 c. M: 5.0722 c. 27: 7 7 13 SP M DE S SD: 2.6346 c. M:-4.5198 c. 29: 7 8 14 SP T3 SD: 2.6350 c. M: 4.3852 c. 31: 8 8 15 SP M DE S SD: 2.4975 c. M:-3.9248 c. 33: 8 9 16 SP T3 SD: 2.5983 c. M: 3.8648 c. 35: 9 9 17 SP M DE S SD: 2.5497 c. M:-3.4657 c. 36: 9 10 17 SP T3 SD: 2.3000 c. M:-3.9827 c. 37: 9 10 18 SP T3 SD: 2.6891 c. M: 3.4569 c. 39: 10 10 19 SP M DE S SD: 2.6854 c. M: 3.4667 c. 40: 10 11 19 SP T3 SD: 1.5016 c. M:-2.5992 c. 44: 11 12 21 SP T3 SD: 0.8488 c. M:-1.4673 c. 48: 12 13 23 SP T3 SD: 0.3071 c. M:-0.5240 c. 52: 13 14 25 SP T3 SD: 0.1669 c. M: 0.2741 c. 100: 25 27 48 SP T3 SD: 0.0822 c. M:-0.1090 c. 152: 38 41 73 SP T3 SD: 0.0545 c. M: 0.0917 c. 356: 89 96 171 SP T3 SD: 0.0629 c. M: 0.0917 c. 404: 101 109 194 SP T3 SD: 0.0533 c. M: 0.0917 c. 508: 127 137 244 SP T3 SD: 0.0597 c. M: 0.0917 c. 556: 139 150 267 SP T3 SD: 0.0530 c. M: 0.0917 c. 679: 170 183 326 SP T3 SD: 0.0604 c. M:-0.0917 c. 683: 171 184 328 SP T3 SD: 0.0525 c. M:-0.0906 c. 687: 172 185 330 SP T3 SD: 0.0639 c. M:-0.0895 c. 708: 177 191 340 SP T3 SD: 0.0530 c. M: 0.0917 c. 727: 182 196 349 SP T3 SD: 0.0658 c. M:-0.0816 c. 731: 183 197 351 SP T3 SD: 0.0480 c. M:-0.0786 c. 735: 184 198 353 SP T3 SD: 0.0474 c. M:-0.0777 c. 779: 195 210 374 SP T3 SD: 0.0516 c. M:-0.0681 c. 783: 196 211 376 SP T3 SD: 0.0391 c. M:-0.0673 c. 787: 197 212 378 SP T3 SD: 0.0457 c. M:-0.0665 c. 831: 208 224 399 SP T3 SD: 0.0398 c. M:-0.0581 c. 835: 209 225 401 SP T3 SD: 0.0337 c. M:-0.0574 c. 839: 210 226 403 SP T3 SD: 0.0465 c. M: 0.0572 c. 883: 221 238 424 SP T3 SD: 0.0304 c. M:-0.0493 c. 887: 222 239 426 SP T3 SD: 0.0318 c. M:-0.0487 c. 931: 233 251 447 SP T3 SD: 0.0355 c. M:-0.0448 c. 935: 234 252 449 SP T3 SD: 0.0240 c. M:-0.0414 c. 939: 235 253 451 SP T3 SD: 0.0328 c. M:-0.0409 c. 983: 246 265 472 SP T3 SD: 0.0258 c. M:-0.0349 c. 987: 247 266 474 SP T3 SD: 0.0211 c. M:-0.0344 c. 1035: 259 279 497 SP T3 SD: 0.0181 c. M:-0.0286 c. 1039: 260 280 499 SP T3 SD: 0.0218 c. M:-0.0281 c. 1087: 272 293 522 SP T3 SD: 0.0132 c. M:-0.0228 c. 1135: 284 306 545 SP T3 SD: 0.0161 c. M:-0.0212 c. 1139: 285 307 547 SP T3 SD: 0.0128 c. M:-0.0176 c. 1187: 297 320 570 SP T3 SD: 0.0090 c. M:-0.0132 c. 1239: 310 334 595 SP T3 SD: 0.0055 c. M:-0.0088 c. 1339: 335 361 643 SP T3 SD: 0.0029 c. M:-0.0048 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 6:7 S SD: 50.8851 cents 6 x 7:8 S SD: 3.9982 cents 7 x 8:9 S SD: 34.3925 cents 8 x 9:11 SD: 38.2724 cents 9:10 x 12 S SD: 28.9004 cents 10:11:12:13 H SD: 27.4386 cents 11:12:13:15 SD: 18.5941 cents 12:13:14:16 S SD: 5.3655 cents 30:32:35:40 SD: 5.0511 cents 38:41:44:51 SD: 4.7473 cents 39:42:45:52 SD: 3.9102 cents 42:45:49:56 SD: 3.1723 cents 51:55:59:68 SD: 3.0031 cents 54:58:63:72 SD: 2.6820 cents 67:72:78:89 SD: 2.5903 cents 68:73:79:91 SD: 2.2109 cents 69:74:80:92 SD: 1.4889 cents 81:87:94:108 SD: 0.4949 cents 93:100:108:124 SD: 0.3446 cents 174:187:202:232 SD: 0.1900 cents 390:419:453:520 SD: 0.1895 cents 441:474:512:588 SD: 0.1818 cents 471:506:547:628 SD: 0.1736 cents 483:519:561:644 SD: 0.1113 cents 564:606:655:752 SD: 0.0899 cents 576:619:669:768 SD: 0.0846 cents