Scala analysis: xen15-chalmers-triadic-reversed-diamond-7-6-tetrachord
Tetrachord 8/7 * 49/48 * 8/7 of triadic reversed 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: 8/7 231.174094 septimal whole tone 2: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 8/7 231.1741 septimal whole tone 2: 49/48 35.6968 slendro diesis, septimal 1/6-tone 3: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 64/49 462.348 cents 2 septatones or septatonic major third Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 231.2 266.9 498.0 231.2: 35.7 266.9 498.0 266.9: 231.2 462.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 231.1741 cents 384/343, 195.4773 cents 49/48, 35.6968 cents 2: 266.8709 .. 462.3482 cents 384/343, 195.4773 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 4.650695 Largest / Average step : 1.392489 Largest / Smallest step : 6.476043 Median interval of one step : 8/7, 231.1741 cents, amount: 2 Most common interval of one step : 8/7, 231.1741 cents, amount: 2 Least squares average step : 161.36078 cents, oct.: 484.08234 cents Scale is strictly proper Scale has Myhill's property chromas: 384/343, 195.4773 cents and 18432/16807, 159.7805 cents, ratio: 1.223412 generators: 1 of 231.17409 cents and 2 of 266.87091 cents ET pair of linear temperament : 26&56 Scale is distributional even Scale is a mode of a 293-tone equal temperament with octave 4/3 degrees: 136 157 293 generators: 136 and 157 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : LSL Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 0.492957 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.215022 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 49/48, 35.6968 cents Most common intervals : 8/7, 231.1741 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 7 Scale harmonicity : 0.036713 Average absolute harmonicity : 0.120409 Specific harmonicity : 0.185226 Fundamental : 1/42, -5.3923 octaves, 6.2292 Hz. Guide tone : 56, 5.8074 octaves, 14651.032 Hz. Exponens Consonantiae : 2.352000E+03, 11.19967 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 17.5, average 5.83333 Mersenne's string divisions : 1365 Sum of van Prooijen's expressibility: 2.16732, average 0.72244 Sum of Tenney's harmonic distance : 4.45062, average 1.48354 Vogel's harmonic complexity : 10.33333 Wille's k value : 24 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 16.60730, average 2.76788 Lattice compactness (without 2's) : 8.06450, average 1.34408 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -1 .. 0 -0.66667 2 1 7: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <7 11 19| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 11 22|
FIT/MODE
3: 1 1 1 SP B ME I SD: 53.2022 c. M: 65.1591 c. 4: 2 0 2 P M DE I SD: 14.5732 c. M: 17.8484 c. 6: 3 0 3 P M DE I SD: 14.5732 c. M: 17.8484 c. 7: 3 1 3 SP M DE I SD: 14.4734 c. M: 17.7262 c. 9: 4 1 4 SP M DE I SD: 8.0186 c. M: 9.8208 c. 11: 5 1 5 SP M DE I SD: 3.9110 c. M: 4.7900 c. 13: 6 1 6 SP M DE I SD: 1.0673 c. M: 1.3072 c. 15: 7 1 7 SP M DE I SD: 1.0181 c. M: 1.2469 c. 28: 13 2 13 SP M DE I SD: 0.0499 c. M: 0.0611 c. 153: 71 11 71 SP M DE I SD: 0.0450 c. M: 0.0552 c. 181: 84 13 84 SP M DE I SD: 0.0304 c. M: 0.0372 c. 209: 97 15 97 SP M DE I SD: 0.0196 c. M: 0.0240 c. 237: 110 17 110 SP M DE I SD: 0.0114 c. M: 0.0140 c. 265: 123 19 123 SP M DE I SD: 0.0049 c. M: 0.0060 c. 293: 136 21 136 SP M DE I SD: 0.0003 c. M: 0.0004 c. 2316: 1075 166 1075 SP M DE I SD: 0.0003 c. M: 0.0004 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: 48.7680 cents 6 x 7:8 S SD: 0.0000 cents 7:8 x 9 S SD: 31.4805 cents 8:9 x 11 SD: 29.9221 cents 11 x 13:15 SD: 22.4315 cents 12 x 14:16 S SD: 0.0000 cents 13:15 x 17 SD: 18.7389 cents 14:16 x 19 SD: 15.3211 cents 18 x 21:24 S SD: 0.0000 cents 19 x 22:25 SD: 13.1959 cents 20:23 x 27 SD: 12.0299 cents 21:24:25:28 SD: 11.6585 cents 22:25:26:29 SD: 10.4765 cents 23:26:27:31 SD: 9.5639 cents 24:27:28:32 S SD: 9.0880 cents 25 x 29:33 SD: 10.0146 cents 26:30 x 35 SD: 11.7146 cents 27:31:32:36 SD: 9.4709 cents 28:32:33:37 SD: 7.8174 cents 29:33:34:39 SD: 6.2284 cents 30:34:35:40 SD: 4.8291 cents 32 x 37:43 SD: 10.2786 cents 33:38:39:44 SD: 8.6265 cents 34:39:40:45 SD: 6.7782 cents 35:40:41:47 SD: 4.7324 cents 36:41:42:48 SD: 2.0072 cents 42:48:49:56 S SD: 0.0000 cents