Scala analysis: 366_D1
Diatonic tetrachord 11/10 * 15/13 * 104/99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 33/26 412.745281 tridecimal major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 104/99 85.2997 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 15/13 247.7411 tridecimal 5/4-tone 3: 104/99 85.2997
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 104/99 85.300 cents 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 40/33 333.041 cents 2: 1 33/26 412.745 cents tridecimal major third 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 : 165.0 412.7 498.0 165.0: 247.7 333.0 498.0 412.7: 85.3 250.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.2997 .. 247.7411 cents 1485/1352, 162.4413 cents 104/99, 85.2997 cents 2: 250.3039 .. 412.7453 cents 1485/1352, 162.4413 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 104/99, 85.2997 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 1.946255 Largest / Average step : 1.492281 Largest / Smallest step : 2.904360 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 177.47356 cents, oct.: 532.42067 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1156-tone equal temperament with octave 4/3 degrees: 383 958 1156 Least number of segments generator : 579 of 249.453 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 677 of 291.675 cents and inv. generated superset size: 38 = 35 more = 1266.667% 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 : 1.075152 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.347684 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 : 99 (O: 33 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.018159 Average absolute harmonicity : 0.092034 Specific harmonicity : 0.086773 Fundamental : 1/390, -8.6073 octaves, 0.6708 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 5.148000E+04, 15.65172 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 43.5, average 14.50000 Mersenne's string divisions : 1239 Sum of van Prooijen's expressibility: 3.03703, average 1.01234 Sum of Tenney's harmonic distance : 6.05406, average 2.01802 Vogel's harmonic complexity : 23.33333 Wille's k value : 247 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.03725, average 2.50621 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 0.00000 4 3: -1 .. 1 0.00000 2 1 5: -1 .. 0 -0.33333 1 11: 0 .. 1 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: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 15 24 27| Scale is weakly epimorphic with val: <6 10 15 24 30| Scale is weakly epimorphic with val: <6 10 15 25 26| Scale is weakly epimorphic with val: <6 10 16 25 25| Scale is weakly epimorphic with val: <6 10 16 25 28| Scale is weakly epimorphic with val: <6 10 16 26 27| Scale is weakly epimorphic with val: <6 10 17 24 25| Scale is weakly epimorphic with val: <6 10 17 26 26| Scale is weakly epimorphic with val: <6 10 17 26 29| Scale is weakly epimorphic with val: <6 10 17 27 28| Scale is weakly epimorphic with val: <6 10 18 25 26| Scale is weakly epimorphic with val: <6 10 18 27 27| Scale is weakly epimorphic with val: <6 10 18 27 30| Scale is weakly epimorphic with val: <6 10 19 26 27| Scale is weakly epimorphic with val: <6 11 15 23 25| Scale is weakly epimorphic with val: <6 11 15 24 27| Scale is weakly epimorphic with val: <6 11 15 24 30| Scale is weakly epimorphic with val: <6 11 15 26 28| Scale is weakly epimorphic with val: <6 11 16 24 26| Scale is weakly epimorphic with val: <6 11 16 25 25| Scale is weakly epimorphic with val: <6 11 16 25 28| Scale is weakly epimorphic with val: <6 11 16 27 29| Scale is weakly epimorphic with val: <6 11 17 25 27| Scale is weakly epimorphic with val: <6 11 17 26 26| Scale is weakly epimorphic with val: <6 11 17 26 29| Scale is weakly epimorphic with val: <6 11 18 23 25| Scale is weakly epimorphic with val: <6 11 18 26 28| Scale is weakly epimorphic with val: <6 11 18 27 27| Scale is weakly epimorphic with val: <6 11 18 27 30| Scale is weakly epimorphic with val: <6 11 19 24 26| Scale is weakly epimorphic with val: <6 11 19 27 29| Scale is weakly epimorphic with val: <7 10 15 25 26| Scale is weakly epimorphic with val: <7 10 15 25 29| Scale is weakly epimorphic with val: <7 10 15 27 27| Scale is weakly epimorphic with val: <7 10 16 25 25| Scale is weakly epimorphic with val: <7 10 16 26 27| Scale is weakly epimorphic with val: <7 10 16 26 30| Scale is weakly epimorphic with val: <7 10 17 26 26| Scale is weakly epimorphic with val: <7 10 17 27 28| Scale is weakly epimorphic with val: <7 10 18 27 27| Scale is weakly epimorphic with val: <7 10 19 25 25| Scale is JI-epimorphic with val: <7 11 15 23 25| Scale is weakly epimorphic with val: <7 11 15 23 28| Scale is weakly epimorphic with val: <7 11 15 24 27| Scale is weakly epimorphic with val: <7 11 15 24 30| Scale is weakly epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 27 27| Scale is weakly epimorphic with val: <7 11 15 27 30| 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 25 25| Scale is weakly epimorphic with val: <7 11 16 25 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 25 27| = patent Scale is weakly epimorphic with val: <7 11 17 25 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 18 23 25| Scale is weakly epimorphic with val: <7 11 18 23 28| Scale is weakly epimorphic with val: <7 11 18 24 27| Scale is weakly epimorphic with val: <7 11 18 24 30| Scale is JI-epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 27 27| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 19 24 26| Scale is weakly epimorphic with val: <7 11 19 24 29| Scale is weakly epimorphic with val: <7 11 19 25 25| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is JI-epimorphic with val: <7 11 19 27 29| Scale is weakly epimorphic with val: <7 12 15 23 25| Scale is weakly epimorphic with val: <7 12 15 25 26| Scale is weakly epimorphic with val: <7 12 15 25 29| Scale is weakly epimorphic with val: <7 12 15 26 28| Scale is weakly epimorphic with val: <7 12 16 24 26| Scale is weakly epimorphic with val: <7 12 16 26 27| Scale is weakly epimorphic with val: <7 12 16 26 30| Scale is weakly epimorphic with val: <7 12 16 27 29| Scale is weakly epimorphic with val: <7 12 17 25 27| Scale is weakly epimorphic with val: <7 12 17 27 28| Scale is weakly epimorphic with val: <7 12 18 23 25| Scale is weakly epimorphic with val: <7 12 18 26 28| Scale is weakly epimorphic with val: <7 12 19 24 26| Scale is weakly epimorphic with val: <7 12 19 27 29| Scale is weakly epimorphic with val: <8 11 15 26 28| Scale is weakly epimorphic with val: <8 11 15 27 27| Scale is weakly epimorphic with val: <8 11 16 25 25| Scale is weakly epimorphic with val: <8 11 16 27 29| Scale is weakly epimorphic with val: <8 11 17 26 26| Scale is weakly epimorphic with val: <8 11 18 27 27| Scale is weakly epimorphic with val: <8 11 19 25 25| Scale is weakly epimorphic with val: <8 12 15 25 26| Scale is weakly epimorphic with val: <8 12 15 26 28| Scale is weakly epimorphic with val: <8 12 16 26 27| Scale is weakly epimorphic with val: <8 12 16 27 29| Scale is weakly epimorphic with val: <8 12 17 24 25| Scale is weakly epimorphic with val: <8 12 17 27 28| Scale is weakly epimorphic with val: <8 12 18 25 26| Scale is weakly epimorphic with val: <8 12 19 26 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 46.6046 c. M: 80.7153 c. 4: 1 2 1 P M ME I SD: 32.5434 c. M: 40.4930 c. 5: 2 2 1 SP M ME S SD: 21.4113 c. M:-34.2138 c. 6: 2 3 1 P T3 SD: 1.4464 c. M:-2.2922 c. 52: 17 26 9 P T3 SD: 1.3627 c. M: 2.1818 c. 57: 19 28 10 SP T3 SD: 1.3334 c. M: 2.0766 c. 58: 19 29 10 P T3 SD: 1.1185 c. M: 1.8516 c. 63: 21 31 11 SP T3 SD: 1.1223 c. M: 1.6605 c. 64: 21 32 11 P T3 SD: 0.9305 c. M: 1.5832 c. 69: 23 34 12 SP T3 SD: 0.9584 c. M: 1.3168 c. 70: 23 35 12 P T3 SD: 0.7870 c. M: 1.3609 c. 75: 25 37 13 SP T3 SD: 0.8324 c. M: 1.0281 c. 76: 25 38 13 P T3 SD: 0.6805 c. M: 1.1736 c. 81: 27 40 14 SP T3 SD: 0.7379 c. M:-1.0108 c. 82: 27 41 14 P T3 SD: 0.6054 c. M: 1.0138 c. 88: 29 44 15 P T3 SD: 0.5572 c. M: 0.8758 c. 94: 31 47 16 P T3 SD: 0.5315 c. M: 0.7553 c. 100: 33 50 17 P T3 SD: 0.5232 c. M: 0.6494 c. 105: 35 52 18 SP T3 SD: 0.5854 c. M:-1.0108 c. 106: 35 53 18 P T3 SD: 0.5278 c. M:-0.7260 c. 111: 37 55 19 SP T3 SD: 0.5842 c. M:-1.0108 c. 112: 37 56 19 P T3 SD: 0.5411 c. M:-0.8099 c. 117: 39 58 20 SP T3 SD: 0.5912 c. M:-1.0108 c. 118: 39 59 20 P T3 SD: 0.5600 c. M:-0.8853 c. 123: 41 61 21 SP T3 SD: 0.6037 c. M:-1.0108 c. 124: 41 62 21 P T3 SD: 0.5821 c. M:-0.9534 c. 127: 42 63 22 SP T3 SD: 0.5888 c. M: 0.9758 c. 133: 44 66 23 SP T3 SD: 0.4975 c. M: 0.8284 c. 139: 46 69 24 SP T3 SD: 0.4143 c. M: 0.6937 c. 145: 48 72 25 SP T3 SD: 0.3381 c. M: 0.5701 c. 151: 50 75 26 SP T3 SD: 0.2684 c. M: 0.4564 c. 157: 52 78 27 SP T3 SD: 0.2046 c. M: 0.3513 c. 163: 54 81 28 SP T3 SD: 0.1467 c. M: 0.2540 c. 169: 56 84 29 SP T3 SD: 0.0959 c. M: 0.1636 c. 175: 58 87 30 SP T3 SD: 0.0582 c. M: 0.0794 c. 181: 60 90 31 SP T3 SD: 0.0540 c. M:-0.0936 c. 356: 118 177 61 SP T3 SD: 0.0505 c. M:-0.0781 c. 531: 176 264 91 SP T3 SD: 0.0519 c. M:-0.0728 c. 537: 178 267 92 SP T3 SD: 0.0505 c. M:-0.0833 c. 607: 201 302 104 SP T3 SD: 0.0516 c. M: 0.0832 c. 613: 203 305 105 SP T3 SD: 0.0423 c. M: 0.0725 c. 619: 205 308 106 SP T3 SD: 0.0365 c. M: 0.0620 c. 625: 207 311 107 SP T3 SD: 0.0359 c. M: 0.0517 c. 782: 259 389 134 SP T3 SD: 0.0384 c. M: 0.0507 c. 788: 261 392 135 SP T3 SD: 0.0286 c. M: 0.0426 c. 794: 263 395 136 SP T3 SD: 0.0205 c. M: 0.0347 c. 800: 265 398 137 SP T3 SD: 0.0164 c. M: 0.0268 c. 806: 267 401 138 SP T3 SD: 0.0189 c. M:-0.0265 c. 969: 321 482 166 SP T3 SD: 0.0155 c. M: 0.0207 c. 975: 323 485 167 SP T3 SD: 0.0073 c. M: 0.0109 c. 981: 325 488 168 SP T3 SD: 0.0051 c. M:-0.0076 c. 1156: 383 575 198 SP T3 SD: 0.0045 c. M: 0.0056 c. 1956: 648 973 335 SP T3 SD: 0.0045 c. M: 0.0077 c. 2131: 706 1060 365 SP T3 SD: 0.0036 c. M: 0.0060 c. 2137: 708 1063 366 SP T3 SD: 0.0006 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: 26.4316 cents 5 x 6:7 S SD: 64.3504 cents 6:7 x 8 S SD: 50.9333 cents 7:8:9 x S SD: 34.9195 cents 8:9:10:11 H SD: 23.6885 cents 9:10:11:12 H SD: 22.5381 cents 10:11:13 x SD: 20.7343 cents 11:12:14:15 S SD: 13.9155 cents 12:13:15:16 SD: 12.4600 cents 13:14 x 17 SD: 24.8870 cents 14:15:18:19 S SD: 19.7591 cents 15:17:19:20 SD: 17.2670 cents 17:19:22:23 SD: 16.7600 cents 18:20:23:24 SD: 6.9741 cents 29:32:37:39 SD: 6.0698 cents 30:33:38:40 SD: 1.1670 cents 108:119:137:144 SD: 1.0233 cents 111:122:141:148 SD: 0.6684 cents 141:155:179:188 SD: 0.3923 cents 171:188:217:228 SD: 0.3235 cents 219:241:278:292 SD: 0.2525 cents 249:274:316:332 SD: 0.2221 cents 330:363:419:440 SD: 0.2119 cents 360:396:457:480 SD: 0.0971 cents 390:429:495:520 SD: 0.0000 cents