Scala analysis: xen15-chalmers-triadic-reversed-diamond-21-16-tetrachord
Tetrachord 64/63 * 1323/1024 * 64/63 of triadic reversed diamond for M=21/16, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64/63 27.264092 septimal comma, Archytas' comma 2: 21/16 470.780907 narrow fourth 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/63 27.2641 septimal comma, Archytas' comma 1: 64/63 27.2641 septimal comma, Archytas' comma 2: 1323/1024 443.5168 3: 64/63 27.2641 septimal comma, Archytas' comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 1323/1024 443.517 cents 2: 1 4096/3969 54.528 cents two (septimal comma, Archytas' comma) 2: 2 21/16 470.781 cents narrow fourth 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 : 27.3 470.8 498.0 27.3 : 443.5 470.8 498.0 470.8: 27.3 54.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 443.5168 cents 83349/65536, 416.2527 cents 64/63, 27.2641 cents 2: 54.5282 .. 470.7809 cents 83349/65536, 416.2527 cents 4194304/5250987,-388.9886 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 1323/1024, 443.5168 cents Average / Smallest step : 6.089145 Largest / Average step : 2.671547 Largest / Smallest step : 16.267434 Median interval of one step : 64/63, 27.2641 cents, amount: 2 Most common interval of one step : 64/63, 27.2641 cents, amount: 2 Least squares average step : 175.92578 cents, oct.: 527.77734 cents Scale is not proper Scale has Myhill's property chromas: 83349/65536, 416.2527 cents and 5250987/4194304, 388.9886 cents, ratio: 1.070090 generators: 1 of 27.26409 cents and 2 of 470.78091 cents ET pair of linear temperament : 36&110 Scale is distributional even Scale is a mode of a 274-tone equal temperament with octave 4/3 degrees: 15 259 274 generators: 15 and 259 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 27.26409 cents Scale diversity : 0.095769 Lumma stability : 0.109484 Lumma impropriety factor : 0.781031 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 : 64/63, 27.2641 cents Most common intervals : 64/63, 27.2641 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 : 3969 (O: 1323 U: 3969) Highest odd numerator or denominator: 63 Scale harmonicity : 0.025926 Average absolute harmonicity : 0.106510 Specific harmonicity : 0.132911 Fundamental : 1/1008, -9.9773 octaves, 0.2595 Hz. Guide tone : 1344, 10.3923 octaves, 351624.760 Hz. Exponens Consonantiae : 1.354752E+06, 20.36960 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 85.5, average 28.50000 Mersenne's string divisions : 32893 Sum of van Prooijen's expressibility: 3.59868, average 1.19956 Sum of Tenney's harmonic distance : 7.21104, average 2.40368 Vogel's harmonic complexity : 16.33333 Wille's k value : 661 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 34.15774, average 5.69296 Lattice compactness (without 2's) : 11.90611, average 1.98435 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 6 1.33333 12 3: -2 .. 1 -0.66667 4 1 7: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 11 18| Scale is JI-epimorphic with val: <7 11 19| Scale is weakly epimorphic with val: <7 11 21| Scale is weakly epimorphic with val: <7 11 22|
FIT/MODE
3: 0 3 0 N M DE I SD: 22.2610 c. M:-27.2641 c. 4: 0 4 0 N M DE I SD: 22.2610 c. M:-27.2641 c. 5: 0 5 0 N M DE I SD: 22.2610 c. M: 27.2641 c. 8: 0 7 1 N G T3 SD: 25.6108 c. M: 34.9915 c. 9: 0 8 1 N G T3 SD: 22.5942 c. M: 28.0742 c. 10: 0 9 1 N G T3 SD: 20.4238 c. M: 27.2641 c. 11: 0 10 1 N G T3 SD: 18.8661 c. M: 27.2641 c. 12: 0 11 1 N G T3 SD: 17.7586 c. M: 27.2641 c. 13: 1 11 1 N M DE I SD: 9.0199 c. M: 11.0471 c. 14: 1 12 1 N M DE I SD: 6.7855 c. M:-8.3106 c. 15: 1 13 1 N M DE I SD: 4.8491 c. M: 5.9389 c. 16: 1 14 1 N M DE I SD: 3.1547 c. M: 3.8637 c. 17: 1 15 1 N M DE I SD: 1.6597 c. M: 2.0327 c. 18: 1 16 1 N M DE I SD: 0.3307 c. M:-0.4051 c. 37: 2 33 2 N M DE I SD: 0.2798 c. M:-0.3427 c. 55: 3 49 3 N M DE I SD: 0.0800 c. M: 0.0980 c. 73: 4 65 4 N M DE I SD: 0.0213 c. M: 0.0260 c. 201: 11 179 11 N M DE I SD: 0.0064 c. M:-0.0079 c. 274: 15 244 15 N M DE I SD: 0.0009 c. M:-0.0011 c. 1023: 56 911 56 N M DE I SD: 0.0005 c. M: 0.0006 c. 1297: 71 1155 71 N M DE I SD: 0.0002 c. M:-0.0003 c. 1571: 86 1399 86 N M DE I SD: 0.0000 c. M: 0.0000 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 x 7 SD: 84.4672 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 103.5055 cents 8:9 x 11 SD: 92.2521 cents 9:10 x 12 S SD: 77.5698 cents 10:11:13 x SD: 69.3664 cents 11:12:14:15 S SD: 46.6340 cents 12:13 x 16 SD: 55.6543 cents 13:14:17 x SD: 50.6169 cents 14:15:18:19 S SD: 34.4966 cents 15:16 x 20 S SD: 42.2336 cents 16:17:21 x SD: 38.8457 cents 17:18:22:23 SD: 26.6136 cents 18:19 x 24 SD: 33.1695 cents 19:20:25 x S SD: 30.8445 cents 20:21:26:27 SD: 21.1060 cents 21:22 x 28 SD: 26.6365 cents 22:23:29 x SD: 25.1259 cents 23:24:30:31 S SD: 17.0657 cents 24:25 x 32 SD: 21.7042 cents 25:26:33 x SD: 20.9082 cents 26:27:34:35 SD: 14.0016 cents 27:28:35:36 S SD: 13.8916 cents 28:29:37 x SD: 17.7423 cents 29:30:38:39 SD: 11.6267 cents 30:31:39:40 SD: 11.2787 cents 31:32:41 x SD: 15.3522 cents 32:33:42:43 SD: 9.7637 cents 33:34:43:44 SD: 9.1495 cents 34:35 x 45 SD: 13.1204 cents 35:36:46:47 SD: 8.2992 cents 36:37:47:48 SD: 7.3875 cents 37:38 x 49 SD: 11.1261 cents 38:39:50:51 SD: 7.1581 cents 39:40:51:52 SD: 5.9145 cents 40:41 x 53 SD: 9.4550 cents 41:42:54:55 SD: 6.2889 cents 42:43:55:56 SD: 4.6781 cents 45:46:59:60 SD: 3.6471 cents 48:49:63:64 SD: 2.8109 cents 51:52:67:68 SD: 2.1851 cents 54:55:71:72 SD: 1.8129 cents 57:58:75:76 SD: 1.7280 cents 112:114:147:149 SD: 1.7120 cents 115:117:151:153 SD: 1.5418 cents 118:120:155:157 SD: 1.4450 cents 121:123:159:161 SD: 1.4237 cents 122:124:160:163 SD: 1.2985 cents 125:127:164:167 SD: 1.1760 cents 128:130:168:171 SD: 1.1348 cents 129:131:169:172 SD: 1.0865 cents 132:134:173:176 SD: 0.9287 cents 135:137:177:180 SD: 0.8573 cents 180:183:236:240 SD: 0.7592 cents 183:186:240:244 SD: 0.5389 cents 186:189:244:248 SD: 0.3294 cents 189:192:248:252 SD: 0.1454 cents 192:195:252:256 SD: 0.1409 cents 381:387:500:508 SD: 0.1012 cents