Scala analysis: 367_D1
Diatonic tetrachord 12/11 * 15/13 * 143/135
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 180/143 398.378111 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 143/135 99.6669 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 15/13 247.7411 tridecimal 5/4-tone 3: 143/135 99.6669
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 143/135 99.667 cents 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 180/143 398.378 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 : 150.6 398.4 498.0 150.6: 247.7 347.4 498.0 398.4: 99.7 250.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 99.6669 .. 247.7411 cents 2025/1859, 148.0742 cents 143/135, 99.6669 cents 2: 250.3039 .. 398.3781 cents 2025/1859, 148.0742 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 143/135, 99.6669 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 1.665699 Largest / Average step : 1.492281 Largest / Smallest step : 2.485691 Median interval of one step : 12/11, 150.6371 cents, amount: 1 Least squares average step : 174.39488 cents, oct.: 523.18463 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1749-tone equal temperament with octave 4/3 degrees: 529 1399 1749 Least number of segments generator : 875 of 249.165 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1574 of 448.212 cents and inv. generated superset size: 46 = 43 more = 1533.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.142102 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.405378 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 : 676/675, 2.5629 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle 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 : 13 Odd number limit : 143 (O: 143 U: 143) Highest odd numerator or denominator: 143 Scale harmonicity : 0.017626 Average absolute harmonicity : 0.092182 Specific harmonicity : 0.083745 Fundamental : 1/429, -8.7448 octaves, 0.6098 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 7.722000E+04, 16.23669 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 176.5, average 58.83333 Mersenne's string divisions : 52003 Sum of van Prooijen's expressibility: 3.67385, average 1.22462 Sum of Tenney's harmonic distance : 7.61036, average 2.53679 Vogel's harmonic complexity : 21.00000 Wille's k value : 71 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 15.43440, average 2.57240 Lattice compactness (without 2's) : 12.49219, average 2.08203 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.33333 1 11: -1 .. 0 -0.66667 2 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 11 18 24 25| Scale is weakly epimorphic with val: <6 11 19 24 26| Scale is weakly epimorphic with val: <7 10 19 25 25| Scale is weakly epimorphic with val: <7 11 15 23 27| Scale is weakly epimorphic with val: <7 11 15 23 30| Scale is JI-epimorphic with val: <7 11 15 24 25| Scale is weakly epimorphic with val: <7 11 15 24 28| Scale is weakly epimorphic with val: <7 11 15 26 27| Scale is weakly epimorphic with val: <7 11 15 26 30| Scale is weakly epimorphic with val: <7 11 15 27 28| Scale is weakly epimorphic with val: <7 11 16 23 25| Scale is weakly epimorphic with val: <7 11 16 23 28| Scale is JI-epimorphic with val: <7 11 16 24 26| Scale is weakly epimorphic with val: <7 11 16 24 29| Scale is weakly epimorphic with val: <7 11 16 26 28| Scale is weakly epimorphic with val: <7 11 16 27 29| Scale is weakly epimorphic with val: <7 11 17 23 26| Scale is weakly epimorphic with val: <7 11 17 23 29| Scale is JI-epimorphic with val: <7 11 17 24 27| Scale is weakly epimorphic with val: <7 11 17 24 30| Scale is weakly epimorphic with val: <7 11 17 26 26| Scale is weakly epimorphic with val: <7 11 17 26 29| Scale is weakly epimorphic with val: <7 11 17 27 27| Scale is weakly epimorphic with val: <7 11 17 27 30| Scale is weakly epimorphic with val: <7 11 18 23 27| Scale is weakly epimorphic with val: <7 11 18 23 30| Scale is weakly epimorphic with val: <7 11 18 24 25| Scale is JI-epimorphic with val: <7 11 18 24 28| Scale is weakly epimorphic with val: <7 11 18 26 27| Scale is weakly epimorphic with val: <7 11 18 26 30| Scale is weakly epimorphic with val: <7 11 18 27 28| Scale is weakly epimorphic with val: <7 11 19 23 25| Scale is weakly epimorphic with val: <7 11 19 23 28| Scale is weakly epimorphic with val: <7 11 19 24 26| Scale is JI-epimorphic with val: <7 11 19 24 29| Scale is weakly epimorphic with val: <7 11 19 26 28| Scale is weakly epimorphic with val: <7 11 19 27 29| Scale is weakly epimorphic with val: <7 12 15 23 26| Scale is weakly epimorphic with val: <7 12 15 23 29| Scale is weakly epimorphic with val: <7 12 15 25 25| Scale is weakly epimorphic with val: <7 12 16 23 27| Scale is weakly epimorphic with val: <7 12 16 23 30| Scale is weakly epimorphic with val: <7 12 16 25 26| Scale is weakly epimorphic with val: <7 12 17 23 25| Scale is weakly epimorphic with val: <7 12 17 23 28| Scale is weakly epimorphic with val: <7 12 17 25 27| Scale is weakly epimorphic with val: <7 12 18 23 26| Scale is weakly epimorphic with val: <7 12 18 23 29| Scale is weakly epimorphic with val: <7 12 18 25 28| Scale is weakly epimorphic with val: <7 12 19 23 27| Scale is weakly epimorphic with val: <7 12 19 23 30| Scale is weakly epimorphic with val: <7 12 19 25 29| Scale is weakly epimorphic with val: <8 11 15 23 27| Scale is weakly epimorphic with val: <8 11 15 24 25| Scale is weakly epimorphic with val: <8 11 15 24 28| Scale is weakly epimorphic with val: <8 11 16 23 28| Scale is weakly epimorphic with val: <8 11 16 24 26| Scale is weakly epimorphic with val: <8 11 16 24 29| Scale is weakly epimorphic with val: <8 11 17 23 29| Scale is weakly epimorphic with val: <8 11 17 24 27| Scale is weakly epimorphic with val: <8 11 17 24 30| Scale is weakly epimorphic with val: <8 11 17 26 26| Scale is weakly epimorphic with val: <8 11 18 23 30| Scale is weakly epimorphic with val: <8 11 18 24 25| Scale is weakly epimorphic with val: <8 11 18 24 28| Scale is weakly epimorphic with val: <8 11 18 26 27| Scale is weakly epimorphic with val: <8 11 19 24 26| Scale is weakly epimorphic with val: <8 11 19 24 29| Scale is weakly epimorphic with val: <8 11 19 26 28| Scale is weakly epimorphic with val: <8 12 15 23 29| Scale is weakly epimorphic with val: <8 12 15 25 25| Scale is weakly epimorphic with val: <8 12 15 25 28| Scale is weakly epimorphic with val: <8 12 15 26 26| Scale is weakly epimorphic with val: <8 12 16 23 30| Scale is weakly epimorphic with val: <8 12 16 25 26| Scale is weakly epimorphic with val: <8 12 16 25 29| Scale is weakly epimorphic with val: <8 12 16 26 27| Scale is weakly epimorphic with val: <8 12 17 25 27| Scale is weakly epimorphic with val: <8 12 17 25 30| Scale is weakly epimorphic with val: <8 12 17 26 28| Scale is weakly epimorphic with val: <8 12 18 25 25| Scale is weakly epimorphic with val: <8 12 18 25 28| Scale is weakly epimorphic with val: <8 12 18 26 29| Scale is weakly epimorphic with val: <8 12 19 25 26| Scale is weakly epimorphic with val: <8 12 19 25 29| Scale is weakly epimorphic with val: <8 12 19 26 30|
FIT/MODE
3: 1 1 1 SP B ME I SD: 39.3216 c. M: 66.3481 c. 4: 1 2 1 P M ME I SD: 20.8151 c. M: 26.1258 c. 6: 2 3 1 P T3 SD: 13.0896 c. M:-16.6594 c. 9: 3 4 2 SP T3 SD: 10.9193 c. M:-15.3779 c. 10: 3 5 2 P T3 SD: 0.7072 c. M: 1.2236 c. 79: 24 39 16 SP T3 SD: 0.7944 c. M: 1.2030 c. 86: 26 43 17 P T3 SD: 0.7031 c. M:-1.2161 c. 89: 27 44 18 SP T3 SD: 0.6667 c. M: 1.0613 c. 96: 29 48 19 P T3 SD: 0.6415 c. M:-1.0955 c. 99: 30 49 20 SP T3 SD: 0.5718 c. M: 0.9483 c. 109: 33 54 22 SP T3 SD: 0.5014 c. M: 0.8560 c. 115: 35 57 23 SP T3 SD: 0.5448 c. M:-0.9419 c. 119: 36 59 24 SP T3 SD: 0.4502 c. M: 0.7792 c. 125: 38 62 25 SP T3 SD: 0.4450 c. M:-0.7686 c. 129: 39 64 26 SP T3 SD: 0.4141 c. M: 0.7143 c. 135: 41 67 27 SP T3 SD: 0.3601 c. M:-0.6211 c. 145: 44 72 29 SP T3 SD: 0.2871 c. M:-0.4938 c. 155: 47 77 31 SP T3 SD: 0.2237 c. M:-0.3830 c. 165: 50 82 33 SP T3 SD: 0.1683 c. M:-0.2857 c. 175: 53 87 35 SP T3 SD: 0.1199 c. M:-0.1994 c. 185: 56 92 37 SP T3 SD: 0.0782 c. M:-0.1225 c. 195: 59 97 39 SP T3 SD: 0.0455 c. M:-0.0579 c. 205: 62 102 41 SP T3 SD: 0.0338 c. M:-0.0579 c. 400: 121 199 80 SP T3 SD: 0.0357 c. M:-0.0579 c. 595: 180 296 119 SP T3 SD: 0.0382 c. M:-0.0579 c. 605: 183 301 121 SP T3 SD: 0.0340 c. M:-0.0579 c. 810: 245 403 162 SP T3 SD: 0.0336 c. M:-0.0579 c. 899: 272 447 180 SP T3 SD: 0.0423 c. M: 0.0529 c. 909: 275 452 182 SP T3 SD: 0.0366 c. M: 0.0517 c. 919: 278 457 184 SP T3 SD: 0.0320 c. M: 0.0505 c. 929: 281 462 186 SP T3 SD: 0.0290 c. M: 0.0493 c. 939: 284 467 188 SP T3 SD: 0.0279 c. M: 0.0482 c. 949: 287 472 190 SP T3 SD: 0.0288 c. M: 0.0471 c. 959: 290 477 192 SP T3 SD: 0.0314 c. M: 0.0460 c. 969: 293 482 194 SP T3 SD: 0.0353 c. M: 0.0449 c. 1005: 304 500 201 SP T3 SD: 0.0346 c. M:-0.0579 c. 1015: 307 505 203 SP T3 SD: 0.0335 c. M:-0.0579 c. 1104: 334 549 221 SP T3 SD: 0.0295 c. M:-0.0396 c. 1114: 337 554 223 SP T3 SD: 0.0244 c. M: 0.0315 c. 1124: 340 559 225 SP T3 SD: 0.0203 c. M: 0.0307 c. 1134: 343 564 227 SP T3 SD: 0.0177 c. M: 0.0300 c. 1144: 346 569 229 SP T3 SD: 0.0171 c. M: 0.0292 c. 1154: 349 574 231 SP T3 SD: 0.0186 c. M: 0.0284 c. 1164: 352 579 233 SP T3 SD: 0.0217 c. M: 0.0277 c. 1309: 396 651 262 SP T3 SD: 0.0213 c. M:-0.0320 c. 1319: 399 656 264 SP T3 SD: 0.0165 c. M:-0.0225 c. 1329: 402 661 266 SP T3 SD: 0.0124 c. M: 0.0171 c. 1339: 405 666 268 SP T3 SD: 0.0098 c. M: 0.0165 c. 1349: 408 671 270 SP T3 SD: 0.0097 c. M: 0.0160 c. 1359: 411 676 272 SP T3 SD: 0.0121 c. M: 0.0154 c. 1524: 461 758 305 SP T3 SD: 0.0114 c. M:-0.0183 c. 1534: 464 763 307 SP T3 SD: 0.0072 c. M:-0.0102 c. 1544: 467 768 309 SP T3 SD: 0.0040 c. M: 0.0066 c. 1554: 470 773 311 SP T3 SD: 0.0049 c. M: 0.0062 c. 1739: 526 865 348 SP T3 SD: 0.0046 c. M:-0.0079 c. 1749: 529 870 350 SP T3 SD: 0.0008 c. M:-0.0009 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 5 x S SD: 12.0644 cents 5 x 6:7 S SD: 59.1187 cents 6:7 x 8 S SD: 58.1169 cents 7:8:9 x S SD: 44.2537 cents 8:9:10:11 H SD: 25.4331 cents 9:10:11:12 H SD: 20.0197 cents 10:11 x 13 SD: 23.0628 cents 11:12:14:15 S SD: 14.4515 cents 12:13:15:16 SD: 5.6872 cents 31:34:39:41 SD: 5.6129 cents 34:37:43:45 SD: 5.2522 cents 35:38:44:47 SD: 4.9995 cents 42:46:53:56 SD: 2.7058 cents 54:59:68:72 SD: 0.9210 cents 66:72:83:88 SD: 0.5346 cents 120:131:151:160 SD: 0.4421 cents 186:203:234:248 SD: 0.4039 cents 243:265:306:324 SD: 0.3091 cents 297:324:374:396 SD: 0.2374 cents 309:337:389:412 SD: 0.1718 cents 363:396:457:484 SD: 0.0971 cents 429:468:540:572 SD: 0.0000 cents