Scala analysis: 399_D6
Diatonic tetrachord 25/24 * 8/7 * 28/25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 25/21 301.846520 BP second, quasi-equal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 28/25 196.1985 middle second 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 8/7 231.1741 septimal whole tone 3: 28/25 196.1985 middle second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 28/25 196.198 cents middle second 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 32/25 427.373 cents classic diminished fourth 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 : 70.7 301.8 498.0 70.7 : 231.2 427.4 498.0 301.8: 196.2 266.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 231.1741 cents 192/175, 160.5017 cents 25/24, 70.6724 cents 2: 266.8709 .. 427.3726 cents 192/175, 160.5017 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.349077 Largest / Average step : 1.392489 Largest / Smallest step : 3.271065 Median interval of one step : 28/25, 196.1985 cents, amount: 1 Least squares average step : 154.89289 cents, oct.: 464.67867 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1353-tone equal temperament with octave 4/3 degrees: 192 820 1353 Least number of segments generator : 677 of 249.207 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 838 of 308.471 cents and inv. generated superset size: 42 = 39 more = 1400.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 0.933782 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.355473 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 : 50/49, 34.9756 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 25 (O: 25 U: 25) Highest odd numerator or denominator: 25 Scale harmonicity : 0.032518 Average absolute harmonicity : 0.102422 Specific harmonicity : 0.152298 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 100, 6.6439 octaves, 26162.557 Hz. Exponens Consonantiae : 1.680000E+04, 14.03617 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 51.0, average 17.00000 Mersenne's string divisions : 2254 Sum of van Prooijen's expressibility: 3.27300, average 1.09100 Sum of Tenney's harmonic distance : 6.57749, average 2.19250 Vogel's harmonic complexity : 14.00000 Wille's k value : 87 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 19.97466, average 3.32911 Lattice compactness (without 2's) : 10.92163, average 1.82027 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.33333 5 3: -1 ..-1 -1.00000 3 1 5: 0 .. 2 1.33333 4 1 7: -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 10 16 19| Scale is weakly epimorphic with val: <6 11 16 19| Scale is weakly epimorphic with val: <6 11 16 22| Scale is weakly epimorphic with val: <6 11 17 20| Scale is weakly epimorphic with val: <7 10 17 19| Scale is weakly epimorphic with val: <7 10 17 22| Scale is weakly epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 11 17 22| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 12 17 19| Scale is weakly epimorphic with val: <7 12 18 20| Scale is weakly epimorphic with val: <8 11 18 22| Scale is weakly epimorphic with val: <8 11 19 20|
FIT/MODE
3: 0 2 1 N G T3 SD: 44.3683 c. M: 70.6724 c. 4: 0 2 2 P M DE S SD: 50.9410 c. M: 70.6724 c. 5: 1 2 2 SP M ME S SD: 16.7972 c. M:-28.9366 c. 6: 1 3 2 P T3 SD: 18.8255 c. M:-30.1835 c. 7: 1 3 3 SP M DE S SD: 9.9627 c. M: 17.2494 c. 8: 1 4 3 P T3 SD: 7.2983 c. M:-9.4316 c. 13: 2 6 5 SP T3 SD: 4.3572 c. M:-5.9499 c. 15: 2 7 6 SP T3 SD: 3.0177 c. M: 4.2664 c. 20: 3 9 8 SP T3 SD: 2.9094 c. M:-4.0343 c. 28: 4 13 11 SP T3 SD: 0.4150 c. M:-0.5379 c. 71: 10 33 28 SP T3 SD: 0.3274 c. M: 0.5252 c. 99: 14 46 39 SP T3 SD: 0.1396 c. M: 0.2418 c. 127: 18 59 50 SP T3 SD: 0.0833 c. M:-0.1178 c. 282: 40 131 111 SP T3 SD: 0.0935 c. M:-0.1595 c. 345: 49 160 136 SP T3 SD: 0.0850 c. M: 0.1323 c. 373: 53 173 147 SP T3 SD: 0.0726 c. M:-0.0954 c. 401: 57 186 158 SP T3 SD: 0.0739 c. M:-0.1220 c. 416: 59 193 164 SP T3 SD: 0.0870 c. M: 0.1462 c. 429: 61 199 169 SP T3 SD: 0.0838 c. M:-0.1452 c. 444: 63 206 175 SP T3 SD: 0.0595 c. M: 0.1030 c. 472: 67 219 186 SP T3 SD: 0.0401 c. M: 0.0650 c. 500: 71 232 197 SP T3 SD: 0.0340 c. M:-0.0500 c. 571: 81 265 225 SP T3 SD: 0.0335 c. M: 0.0539 c. 599: 85 278 236 SP T3 SD: 0.0152 c. M: 0.0263 c. 627: 89 291 247 SP T3 SD: 0.0133 c. M:-0.0230 c. 726: 103 337 286 SP T3 SD: 0.0076 c. M: 0.0132 c. 1325: 188 615 522 SP T3 SD: 0.0081 c. M: 0.0125 c. 1353: 192 628 533 SP T3 SD: 0.0022 c. M:-0.0036 c. 2079: 295 965 819 SP T3 SD: 0.0014 c. M: 0.0023 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: 84.4672 cents 5 x 6:7 S SD: 42.7931 cents 6 x 7:8 S SD: 17.4878 cents 7 x 8:9 S SD: 47.3251 cents 8 x 10:11 S SD: 49.9317 cents 9:10:11:12 H SD: 40.2212 cents 10:11:12:13 H SD: 34.9761 cents 11:12:13:15 SD: 29.9401 cents 12:13:14:16 S SD: 25.4596 cents 14:15:17:19 SD: 22.3428 cents 15:16:18:20 S SD: 14.4381 cents 17:18:20:23 SD: 14.3698 cents 18:19:21:24 SD: 13.9408 cents 19:20:23:25 SD: 13.7053 cents 20:21:24:27 S SD: 9.6788 cents 21:22:25:28 SD: 3.2882 cents 47:49:56:63 SD: 3.1392 cents 48:50:57:64 SD: 1.4445 cents 69:72:82:92 SD: 1.4193 cents 99:103:118:132 SD: 0.9892 cents 120:125:143:160 SD: 0.5768 cents 147:153:175:196 SD: 0.4713 cents 168:175:200:224 SD: 0.0000 cents