Scala analysis: xen15-chalmers-triadic-reversed-diamond-17-13
Triadic reversed diamond for M=17/13, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 52/51 33.617251 2: 17/13 464.427748 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 26/17 735.572252 6: 51/26 1166.382749 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 52/51 33.6173 1: 52/51 33.6173 2: 867/676 430.8105 3: 52/51 33.6173 4: 9/8 203.9100 major whole tone 5: 52/51 33.6173 6: 867/676 430.8105 7: 52/51 33.6173
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 52/51 33.617 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 867/676 430.810 cents 2: 1 2704/2601 67.235 cents 2: 2 39/34 237.527 cents 2: 4 17/13 464.428 cents 3: 1 338/289 271.145 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 153/104 668.338 cents 4: 2 208/153 531.662 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 289/169 928.855 cents 5: 4 26/17 735.572 cents 5: 2 68/39 962.473 cents 5: 1 2601/1352 1132.765 cents 6: 2 1352/867 769.190 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 51/26 1166.383 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 4 5 6 7 0.0 : 33.6 464.4 498.0 702.0 735.6 1166.4 1200.0 33.6 : 430.8 464.4 668.3 702.0 1132.8 1166.4 1200.0 464.4 : 33.6 237.5 271.1 702.0 735.6 769.2 1200.0 498.0 : 203.9 237.5 668.3 702.0 735.6 1166.4 1200.0 702.0 : 33.6 464.4 498.0 531.7 962.5 996.1 1200.0 735.6 : 430.8 464.4 498.0 928.9 962.5 1166.4 1200.0 1166.4: 33.6 67.2 498.0 531.7 735.6 769.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6173 .. 430.8105 cents 44217/35152, 397.1932 cents 52/51, 33.6173 cents 2: 67.2345 .. 464.4277 cents 44217/35152, 397.1932 cents 1827904/2255067,-363.5760 cents 3: 271.1445 .. 668.3377 cents 44217/35152, 397.1932 cents 4394/4913,-193.2832 cents 4: 531.6623 .. 928.8555 cents 44217/35152, 397.1932 cents 21632/23409,-136.6755 cents 5: 735.5723 .. 1132.7655 cents 44217/35152, 397.1932 cents 4394/4913,-193.2832 cents 6: 769.1895 .. 1166.3827 cents 44217/35152, 397.1932 cents 1827904/2255067,-363.5760 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 52/51, 33.6173 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 867/676, 430.8105 cents Average / Smallest step : 5.099423 Largest / Average step : 2.513061 Largest / Smallest step : 12.815161 Median interval of one step : 52/51, 33.6173 cents, amount: 4 Most common interval of one step : 52/51, 33.6173 cents, amount: 4 Least squares average step : 173.86133 cents, oct.: 1217.02928 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2142-tone equal temperament with octave 2/1 degrees: 60 829 889 1253 1313 2082 2142 Least number of segments generator : 1073 of 601.120 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1433 of 802.801 cents and inv. generated superset size: 71 = 64 more = 1014.286% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Scale is a Constant Structure, by a margin of 33.61725 cents Scale diversity : 1.264932 Lumma stability : 0.056029 Lumma impropriety factor : 0.775885 Rothenberg efficiency : 0.506122 redundancy: 0.493878 Efficiency x scale size : 3.542857 Number of different interval sizes : 18 = 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 : 52/51, 33.6173 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale is a complete diamond : 13 17 51 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 100.0000% Scale is differentially coherent in interval classes 3 and 4 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 17 Odd number limit : 2601 (O: 2601 U: 2601) Highest odd numerator or denominator: 51 Scale harmonicity : 0.008859 Average absolute harmonicity : 0.222907 Specific harmonicity : 0.047110 Fundamental : 1/1326, -10.3729 octaves, 0.1973 Hz. Guide tone : 2652, 11.3729 octaves, 693830.999 Hz. Exponens Consonantiae : 3.516552E+06, 21.74573 octaves Euler's gradus suavitatis : 64 Sum of Mann's harmonic distance : 134.0, average 19.14286 Mersenne's string divisions : 10230990 Sum of van Prooijen's expressibility: 6.83028, average 0.97575 Sum of Tenney's harmonic distance : 13.69429, average 1.95633 Vogel's harmonic complexity : 34.57143 Wille's k value : 1300 Wilson's harmonic complexity : 66 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 64.97815, average 2.32065 Lattice compactness (without 2's) : 47.53320, average 1.69761 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -1 .. 1 0.00000 4 2 13: -1 .. 1 0.00000 4 17: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 24 29| Scale is weakly epimorphic with val: <7 10 24 30| Scale is weakly epimorphic with val: <7 10 25 30| Scale is weakly epimorphic with val: <7 10 25 31| Scale is weakly epimorphic with val: <7 10 26 31| Scale is weakly epimorphic with val: <7 10 26 32| Scale is weakly epimorphic with val: <7 10 27 32| Scale is JI-epimorphic with val: <7 11 24 26| Scale is weakly epimorphic with val: <7 11 24 32| Scale is weakly epimorphic with val: <7 11 25 26| Scale is JI-epimorphic with val: <7 11 25 27| Scale is weakly epimorphic with val: <7 11 26 27| Scale is JI-epimorphic with val: <7 11 26 28| Scale is weakly epimorphic with val: <7 11 27 28| Scale is JI-epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <7 11 28 29| Scale is JI-epimorphic with val: <7 11 28 30| Scale is weakly epimorphic with val: <7 11 29 30| Scale is JI-epimorphic with val: <7 11 29 31| Scale is weakly epimorphic with val: <7 12 24 27| Scale is weakly epimorphic with val: <7 12 24 30| Scale is weakly epimorphic with val: <7 12 25 28| Scale is weakly epimorphic with val: <7 12 25 31| Scale is weakly epimorphic with val: <7 12 26 29| Scale is weakly epimorphic with val: <7 12 26 32| Scale is weakly epimorphic with val: <7 12 27 30| Scale is weakly epimorphic with val: <7 12 28 31| Scale is weakly epimorphic with val: <7 12 29 32|
FIT/MODE
7: 0 3 0 1 0 3 0 N T3 I SD: 33.2939 c. M:-49.8580 c. 8: 0 3 0 2 0 3 0 N T3 I SD: 32.2783 c. M:-48.0450 c. 10: 0 4 0 2 0 4 0 N T3 I SD: 22.0275 c. M:-33.6173 c. 21: 1 7 1 3 1 7 1 N T3 I SD: 15.7687 c. M:-23.5256 c. 24: 1 8 1 4 1 8 1 N T3 I SD: 11.7154 c. M:-16.3827 c. 26: 1 9 1 4 1 9 1 N T3 I SD: 8.5954 c. M:-12.5366 c. 29: 1 10 1 5 1 10 1 N T3 I SD: 6.5058 c. M:-9.2553 c. 31: 1 11 1 5 1 11 1 N T3 I SD: 3.8833 c. M: 5.1808 c. 34: 1 12 1 6 1 12 1 N T3 I SD: 3.7661 c. M:-5.6042 c. 36: 1 13 1 6 1 13 1 N T3 I SD: 1.5960 c. M:-2.2389 c. 70: 2 25 2 12 2 25 2 N T3 I SD: 1.0320 c. M: 1.5706 c. 106: 3 38 3 18 3 38 3 N T3 I SD: 0.2392 c. M:-0.3450 c. 248: 7 89 7 42 7 89 7 N T3 I SD: 0.2325 c. M:-0.3421 c. 323: 9 116 9 55 9 116 9 N T3 I SD: 0.1499 c. M:-0.2122 c. 359: 10 129 10 61 10 129 10 N T3 I SD: 0.1464 c. M:-0.1962 c. 429: 12 154 12 73 12 154 12 N T3 I SD: 0.0948 c. M: 0.1429 c. 465: 13 167 13 79 13 167 13 N T3 I SD: 0.0608 c. M:-0.0884 c. 571: 16 205 16 97 16 205 16 N T3 I SD: 0.0193 c. M:-0.0286 c. 1571: 44 564 44 267 44 564 44 N T3 I SD: 0.0120 c. M: 0.0183 c. 2142: 60 769 60 364 60 769 60 N T3 I SD: 0.0038 c. M:-0.0058 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 49.5955 cents 4 x 5 x 6 x x 8 S SD: 26.0380 cents 5 x x 7 x 8 x 10 SD: 38.3500 cents 6 x x 8:9 x x 12 S SD: 0.0000 cents 7:8:9 x x 11 x 14 SD: 51.2904 cents 8:9:10:11:12 x x 16 S SD: 38.9561 cents 9:10 x 12 x 14 x 18 SD: 37.9131 cents 10:11:13 x 15 x x 20 SD: 32.9458 cents 11:12:14:15 x 17 x 22 SD: 26.6346 cents 12:13 x 16:18 x x 24 SD: 26.2389 cents 13:14:17 x x 20 x 26 SD: 23.8076 cents 14:15:18:19:21 x 27:28 SD: 16.6892 cents 15:16 x 20 x 23:29:30 SD: 16.4319 cents 16:17:21 x 24 x 31:32 SD: 14.9468 cents 17:18:22:23 x 26:33:34 SD: 12.4281 cents 18:19 x 24:27:28:35:36 SD: 11.4127 cents 19:20:25 x x 29:37:38 SD: 11.5400 cents 20:21:26:27:30:31:39:40 SD: 8.7979 cents 21:22:27:28 x 32:41:42 SD: 9.3816 cents 22:23:29 x 33:34:43:44 SD: 8.2229 cents 23:24:30:31 x 35:45:46 SD: 7.5838 cents 24:25:31:32:36:37:47:48 SD: 6.4329 cents 25:26:33 x x 38:49:50 SD: 7.8851 cents 26:27:34:35:39:40:51:52 SD: 5.3164 cents 27:28:35:36 x 41:53:54 SD: 5.8817 cents 28:29 x 37:42:43:55:56 SD: 5.3590 cents 29:30:38:39 x 44:57:58 SD: 5.4403 cents 30:31:39:40:45:46:59:60 SD: 3.7261 cents 31:32 x 41 x 47:61:62 SD: 6.0337 cents 32:33:42:43:48:49:63:64 SD: 3.6503 cents 33:34:43:44 x 50:65:66 SD: 4.3437 cents 34:35:44:45:51:52:67:68 SD: 4.1096 cents 36:37:47:48:54:55:71:72 SD: 2.4360 cents 42:43:55:56:63:64:82:84 SD: 1.8214 cents 48:49:63:64:72:73:94:96 SD: 1.7352 cents 58:59:76:77:87:89:114:116 SD: 1.6261 cents 62:63:81:83:93:95:122:124 SD: 1.6067 cents 72:73:94:96:108:110:141:144 SD: 1.5272 cents 84:86:110:112:126:128:165:168 SD: 1.4484 cents 87:89:114:116:131:133:171:174 SD: 1.4419 cents 88:90:115:117:132:135:173:176 SD: 1.4025 cents 90:92:118:120:135:138:177:180 SD: 1.2791 cents 94:96:123:125:141:144:184:188 SD: 1.0255 cents 98:100:128:131:147:150:192:196 SD: 0.8055 cents 100:102:131:133:150:153:196:200 SD: 0.7932 cents 102:104:133:136:153:156:200:204 SD: 0.7205 cents 104:106:136:139:156:159:204:208 SD: 0.6077 cents 108:110:141:144:162:165:212:216 SD: 0.5793 cents 150:153:196:200:225:229:294:300 SD: 0.5308 cents 156:159:204:208:234:239:306:312 SD: 0.4362 cents 162:165:212:216:243:248:318:324 SD: 0.4353 cents 198:202:259:264:297:303:388:396 SD: 0.3271 cents 204:208:267:272:306:312:400:408 SD: 0.2340 cents 306:312:400:408:459:468:600:612 SD: 0.1345 cents 312:318:408:416:468:477:612:624 SD: 0.1294 cents 468:477:612:624:702:716:918:936 SD: 0.1224 cents 510:520:667:680:765:780:1000:1020 SD: 0.0993 cents