Scala analysis: 404_D6
Diatonic tetrachord 17/16 * 8/7 * 56/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/16 104.955410 17th harmonic 2: 17/14 336.129503 supraminor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 56/51 161.9155 1: 17/16 104.9554 17th harmonic 2: 8/7 231.1741 septimal whole tone 3: 56/51 161.9155
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 17/16 104.955 cents 17th harmonic 1: 1 56/51 161.915 cents 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 17/14 336.130 cents supraminor third 2: 1 64/51 393.090 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 : 105.0 336.1 498.0 105.0: 231.2 393.1 498.0 336.1: 161.9 266.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.9554 .. 231.1741 cents 128/119, 126.2187 cents 17/16, 104.9554 cents 2: 266.8709 .. 393.0896 cents 128/119, 126.2187 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 17/16, 104.9554 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.581767 Largest / Average step : 1.392489 Largest / Smallest step : 2.202593 Median interval of one step : 56/51, 161.9155 cents, amount: 1 Least squares average step : 162.23924 cents, oct.: 486.71773 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2107-tone equal temperament with octave 4/3 degrees: 444 1422 2107 Least number of segments generator : 1054 of 249.141 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1970 of 465.661 cents and inv. generated superset size: 40 = 37 more = 1333.333% 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 : 1.245877 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.493143 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 : 49/48, 35.6968 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 17 Odd number limit : 51 (O: 17 U: 51) Highest odd numerator or denominator: 17 Scale harmonicity : 0.020379 Average absolute harmonicity : 0.089249 Specific harmonicity : 0.089722 Fundamental : 1/336, -8.3923 octaves, 0.7786 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 2.284800E+04, 14.47978 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 35.5, average 11.83333 Mersenne's string divisions : 7161 Sum of van Prooijen's expressibility: 2.93802, average 0.97934 Sum of Tenney's harmonic distance : 5.89033, average 1.96344 Vogel's harmonic complexity : 21.00000 Wille's k value : 178 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 20.88202, average 3.48034 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.00000 7 3: -1 .. 0 -0.33333 1 1 7: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 2 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <6 10 19 28| Scale is weakly epimorphic with val: <6 10 20 27| Scale is weakly epimorphic with val: <6 10 22 31| Scale is weakly epimorphic with val: <6 11 19 27| Scale is weakly epimorphic with val: <6 11 20 29| Scale is weakly epimorphic with val: <6 11 22 27| Scale is weakly epimorphic with val: <7 10 19 31| Scale is weakly epimorphic with val: <7 10 20 30| Scale is weakly epimorphic with val: <7 10 22 31| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 19 33| Scale is JI-epimorphic with val: <7 11 20 29| Scale is weakly epimorphic with val: <7 11 20 32| Scale is weakly epimorphic with val: <7 11 22 27| Scale is weakly epimorphic with val: <7 11 22 30| Scale is weakly epimorphic with val: <7 11 22 33| Scale is weakly epimorphic with val: <7 12 19 29| Scale is weakly epimorphic with val: <7 12 20 31| Scale is weakly epimorphic with val: <7 12 22 32| Scale is weakly epimorphic with val: <8 11 19 30| Scale is weakly epimorphic with val: <8 11 22 33| Scale is weakly epimorphic with val: <8 12 20 31|
FIT/MODE
3: 1 1 1 SP B ME I SD: 35.3321 c. M:-61.0596 c. 4: 1 2 1 P M ME I SD: 24.3688 c. M:-37.4042 c. 5: 1 2 2 SP M ME S SD: 21.7567 c. M: 37.3025 c. 6: 1 3 2 P T3 SD: 12.8908 c. M: 21.9479 c. 9: 2 4 3 SP T3 SD: 4.0636 c. M:-5.7213 c. 15: 3 7 5 SP T3 SD: 3.8897 c. M: 5.3464 c. 19: 4 9 6 SP T3 SD: 2.6785 c. M:-4.6381 c. 24: 5 11 8 SP T3 SD: 2.4655 c. M: 4.0995 c. 28: 6 13 9 SP T3 SD: 1.4691 c. M:-1.8296 c. 34: 7 16 11 SP T3 SD: 1.4668 c. M: 2.4167 c. 43: 9 20 14 SP T3 SD: 0.4343 c. M: 0.7134 c. 71: 15 33 23 SP T3 SD: 0.3667 c. M:-0.5770 c. 95: 20 44 31 SP T3 SD: 0.3541 c. M: 0.6045 c. 114: 24 53 37 SP T3 SD: 0.1666 c. M:-0.2693 c. 166: 35 77 54 SP T3 SD: 0.0652 c. M: 0.0991 c. 280: 59 130 91 SP T3 SD: 0.0300 c. M:-0.0509 c. 446: 94 207 145 SP T3 SD: 0.0084 c. M:-0.0137 c. 726: 153 337 236 SP T3 SD: 0.0099 c. M:-0.0166 c. 1172: 247 544 381 SP T3 SD: 0.0067 c. M:-0.0084 c. 1618: 341 751 526 SP T3 SD: 0.0062 c. M:-0.0096 c. 1661: 350 771 540 SP T3 SD: 0.0054 c. M: 0.0091 c. 2107: 444 978 685 SP T3 SD: 0.0028 c. M: 0.0043 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: 50.1842 cents 5 x 6:7 S SD: 43.4582 cents 6 x 7:8 S SD: 34.6293 cents 7 x x 9 SD: 62.9609 cents 8:9:10:11 H SD: 41.0264 cents 9:10:11:12 H SD: 26.0884 cents 10:11:12:13 H SD: 25.7051 cents 11:12:13:15 SD: 25.3902 cents 12:13:15:16 SD: 20.1345 cents 13:14:16:17 S SD: 15.7053 cents 14:15:17:19 SD: 11.2981 cents 15:16:18:20 S SD: 7.1932 cents 18:19:22:24 SD: 5.3342 cents 32:34:39:43 SD: 4.9652 cents 33:35:40:44 SD: 1.4560 cents 93:99:113:124 SD: 1.1532 cents 111:118:135:148 SD: 0.9664 cents 126:134:153:168 SD: 0.5386 cents 144:153:175:192 SD: 0.4713 cents 159:169:193:212 SD: 0.3019 cents 177:188:215:236 SD: 0.2712 cents 303:322:368:404 SD: 0.1584 cents 336:357:408:448 SD: 0.0000 cents