Scala analysis: xen15-chalmers-triadic-reversed-diamond-9-7-tetrachord
Tetrachord 28/27 * 243/196 * 28/27 of triadic reversed diamond for M=9/7, 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: 9/7 435.084095 septimal major third, BP third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 243/196 372.1232 3: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 243/196 372.123 cents 2: 1 784/729 125.922 cents two (Archytas' 1/3-tone) 2: 2 9/7 435.084 cents septimal major third, BP 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 : 63.0 435.1 498.0 63.0 : 372.1 435.1 498.0 435.1: 63.0 125.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 372.1232 cents 6561/5488, 309.1623 cents 28/27, 62.9609 cents 2: 125.9218 .. 435.0841 cents 6561/5488, 309.1623 cents 153664/177147,-246.2014 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 : 243/196, 372.1232 cents Average / Smallest step : 2.636795 Largest / Average step : 2.241503 Largest / Smallest step : 5.910385 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Most common interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 173.37601 cents, oct.: 520.12802 cents Scale is not proper Scale has Myhill's property chromas: 6561/5488, 309.1623 cents and 177147/153664, 246.2014 cents, ratio: 1.255729 generators: 1 of 62.96090 cents and 2 of 435.08410 cents ET pair of linear temperament : 174&1060 Scale is distributional even Scale is a mode of a 356-tone equal temperament with octave 4/3 degrees: 45 311 356 generators: 45 and 311 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Scale is a Constant Structure, by a margin of 62.96090 cents Scale diversity : 0.626253 Lumma stability : 0.252832 Lumma impropriety factor : 0.494336 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 : 28/27, 62.9609 cents Most common intervals : 28/27, 62.9609 cents & inv., amount: 2 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 : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 7 Odd number limit : 729 (O: 243 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.027851 Average absolute harmonicity : 0.109202 Specific harmonicity : 0.142372 Fundamental : 1/189, -7.5622 octaves, 1.3843 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 4.762800E+04, 15.53952 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 39.0, average 13.00000 Mersenne's string divisions : 6160 Sum of van Prooijen's expressibility: 2.86273, average 0.95424 Sum of Tenney's harmonic distance : 5.75704, average 1.91901 Vogel's harmonic complexity : 15.33333 Wille's k value : 121 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 19.93608, average 3.32268 Lattice compactness (without 2's) : 17.18186, average 2.86364 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -3 .. 2 -0.66667 6 1 7: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 18| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 11 21|
FIT/MODE
3: 0 3 0 N M DE I SD: 51.4074 c. M: 62.9609 c. 4: 0 3 1 N G T3 SD: 50.8348 c. M: 62.9609 c. 5: 1 3 1 N M DE I SD: 29.9230 c. M: 36.6481 c. 6: 1 4 1 N M DE I SD: 16.3680 c. M: 20.0466 c. 7: 1 5 1 N M DE I SD: 6.6858 c. M: 8.1884 c. 8: 1 6 1 N M DE I SD: 0.5759 c. M: 0.7053 c. 47: 6 35 6 N M DE I SD: 0.5057 c. M: 0.6193 c. 55: 7 41 7 N M DE I SD: 0.3484 c. M: 0.4266 c. 63: 8 47 8 N M DE I SD: 0.2310 c. M: 0.2829 c. 71: 9 53 9 N M DE I SD: 0.1401 c. M: 0.1716 c. 79: 10 59 10 N M DE I SD: 0.0676 c. M: 0.0828 c. 87: 11 65 11 N M DE I SD: 0.0084 c. M: 0.0103 c. 356: 45 266 45 N M DE I SD: 0.0047 c. M: 0.0058 c. 443: 56 331 56 N M DE I SD: 0.0021 c. M: 0.0026 c. 530: 67 396 67 N M DE I SD: 0.0004 c. M: 0.0005 c. 1147: 145 857 145 N M DE I SD: 0.0003 c. M: 0.0003 c. 1677: 212 1253 212 N M DE I SD: 0.0001 c. M: 0.0001 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: 48.7704 cents 5 x 6:7 S SD: 73.1459 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 84.1066 cents 8:9:10:11 H SD: 52.7923 cents 9:10 x 12 S SD: 59.7214 cents 10:11:13 x SD: 51.9105 cents 11:12:14:15 S SD: 32.5059 cents 12:13:15:16 SD: 29.9920 cents 13:14:17 x SD: 35.8121 cents 14:15:18:19 S SD: 21.4195 cents 15:16:19:20 SD: 18.3976 cents 16:17 x 21 SD: 25.0343 cents 17:18:22:23 SD: 15.1347 cents 18:19:23:24 SD: 10.8210 cents 21:22:27:28 SD: 5.8587 cents 24:25:31:32 SD: 3.7030 cents 49:51:63:65 SD: 3.6221 cents 52:54:67:69 SD: 3.1431 cents 53:55:68:71 SD: 2.9988 cents 56:58:72:75 SD: 2.6739 cents 57:59:73:76 SD: 2.5021 cents 60:62:77:80 SD: 2.3253 cents 77:80:99:103 SD: 2.1548 cents 78:81:100:104 SD: 1.8271 cents 81:84:104:108 SD: 0.7921 cents 84:87:108:112 SD: 0.7365 cents 105:109:135:140 SD: 0.5886 cents 165:171:212:220 SD: 0.5400 cents 186:193:239:248 SD: 0.4789 cents 189:196:243:252 SD: 0.0000 cents