Scala analysis: xen15-chalmers-triadic-diamond-7-6-tetrachord
Upper tetrachord 28/27 * 54/49 * 7/6 of triadic diamond for M=7/6, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 54/49 168.2132 Zalzal's mujannab 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 54/49 168.213 cents Zalzal's mujannab 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 98/81 329.832 cents 2: 1 9/7 435.084 cents septimal major third, BP 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 : 63.0 231.2 498.0 63.0 : 168.2 435.1 498.0 231.2: 266.9 329.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 266.8709 cents 9/8, 203.9100 cents 28/27, 62.9609 cents 2: 231.1741 .. 435.0841 cents 9/8, 203.9100 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.636795 Largest / Average step : 1.607511 Largest / Smallest step : 4.238677 Median interval of one step : 54/49, 168.2132 cents, amount: 1 Least squares average step : 144.24601 cents, oct.: 432.73802 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2191-tone equal temperament with octave 4/3 degrees: 277 1017 2191 Least number of segments generator : 1096 of 249.136 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1327 of 301.646 cents and inv. generated superset size: 25 = 22 more = 833.333% 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 35.69681 cents Scale diversity : 0.948681 Lumma stability : 0.252832 Lumma impropriety factor : 0.071674 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 minor thirds form a closed circle Steps are strictly increasing 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 : 81 (O: 49 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.031674 Average absolute harmonicity : 0.112950 Specific harmonicity : 0.164303 Fundamental : 1/189, -7.5622 octaves, 1.3843 Hz. Guide tone : 56, 5.8074 octaves, 14651.032 Hz. Exponens Consonantiae : 1.058400E+04, 13.36960 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 38.5, average 12.83333 Mersenne's string divisions : 1155 Sum of van Prooijen's expressibility: 2.75358, average 0.91786 Sum of Tenney's harmonic distance : 5.70589, average 1.90196 Vogel's harmonic complexity : 14.33333 Wille's k value : 31 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.84978, average 2.80830 Lattice compactness (without 2's) : 12.41811, average 2.06969 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -3 .. 0 -1.33333 4 1 7: -1 .. 1 0.00000 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 18| Scale is weakly epimorphic with val: <7 10 19| Scale is weakly epimorphic with val: <8 11 20| Scale is weakly epimorphic with val: <8 11 21|
FIT/MODE
3: 0 1 2 N G T3 SD: 52.3125 c. M: 65.1591 c. 4: 1 1 2 P M ME S SD: 37.0000 c. M:-61.5503 c. 5: 0 2 3 N G T3 SD: 40.7646 c. M: 62.9609 c. 6: 1 2 3 P T3 SD: 15.4966 c. M:-20.0466 c. 7: 1 2 4 N T3 SD: 11.2734 c. M: 17.7262 c. 8: 1 3 4 P T3 SD: 10.3128 c. M:-17.8484 c. 9: 1 3 5 N T3 SD: 7.1775 c. M: 9.8208 c. 15: 2 5 8 N T3 SD: 2.1153 c. M:-3.4451 c. 24: 3 8 13 N T3 SD: 1.7251 c. M: 2.9035 c. 32: 4 11 17 N T3 SD: 1.3804 c. M:-2.2845 c. 39: 5 13 21 N T3 SD: 0.9133 c. M: 1.3072 c. 56: 7 19 30 N T3 SD: 0.4087 c. M: 0.7053 c. 71: 9 24 38 N T3 SD: 0.2054 c. M:-0.3116 c. 127: 16 43 68 N T3 SD: 0.1700 c. M: 0.2151 c. 166: 21 56 89 N T3 SD: 0.0922 c. M: 0.1532 c. 222: 28 75 119 N T3 SD: 0.1011 c. M: 0.1444 c. 237: 30 80 127 N T3 SD: 0.0485 c. M:-0.0828 c. 293: 37 99 157 N T3 SD: 0.0392 c. M: 0.0678 c. 364: 46 123 195 N T3 SD: 0.0373 c. M:-0.0611 c. 459: 58 155 246 N T3 SD: 0.0355 c. M: 0.0552 c. 530: 67 179 284 N T3 SD: 0.0035 c. M: 0.0060 c. 2191: 277 740 1174 N T3 SD: 0.0038 c. M:-0.0051 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: 59.7273 cents 6 x 7:8 S SD: 17.8484 cents 7 x 8:9 S SD: 31.4805 cents 8 x 9:11 SD: 29.9221 cents 9 x 10:12 S SD: 24.3852 cents 10 x 11:13 SD: 39.6850 cents 11 x 13:15 SD: 34.9349 cents 12:13:14:16 S SD: 27.8715 cents 13:14:15:17 SD: 25.1077 cents 14:15:16:19 SD: 21.4195 cents 15:16:17:20 SD: 16.9589 cents 18:19:21:24 SD: 15.6816 cents 19:20:22:25 SD: 13.7666 cents 20:21:23:27 SD: 10.7569 cents 21:22:24:28 S SD: 5.8587 cents 27:28:31:36 SD: 2.6655 cents 57:59:65:76 SD: 1.6685 cents 78:81:89:104 SD: 1.2182 cents 84:87:96:112 SD: 0.7365 cents 105:109:120:140 SD: 0.5886 cents 162:168:185:216 SD: 0.4454 cents 189:196:216:252 SD: 0.0000 cents