Scala analysis: xen15-chalmers-triadic-reversed-diamond-33-26
Triadic reversed diamond for M=33/26, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 104/99 85.299718 2: 33/26 412.745281 tridecimal major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 52/33 787.254719 tridecimal minor sixth 6: 99/52 1114.700282 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 104/99 85.2997 1: 104/99 85.2997 2: 3267/2704 327.4456 3: 104/99 85.2997 4: 9/8 203.9100 major whole tone 5: 104/99 85.2997 6: 3267/2704 327.4456 7: 104/99 85.2997
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 104/99 85.300 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 3267/2704 327.446 cents 2: 1 10816/9801 170.599 cents 2: 2 13/11 289.210 cents tridecimal minor third 2: 4 33/26 412.745 cents tridecimal major third 3: 1 1352/1089 374.509 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 297/208 616.655 cents 4: 2 416/297 583.345 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 1089/676 825.491 cents two (tridecimal major third) 5: 4 52/33 787.255 cents tridecimal minor sixth 5: 2 22/13 910.790 cents tridecimal major sixth 5: 1 9801/5408 1029.401 cents 6: 2 5408/3267 872.554 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 99/52 1114.700 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 : 85.3 412.7 498.0 702.0 787.3 1114.7 1200.0 85.3 : 327.4 412.7 616.7 702.0 1029.4 1114.7 1200.0 412.7 : 85.3 289.2 374.5 702.0 787.3 872.6 1200.0 498.0 : 203.9 289.2 616.7 702.0 787.3 1114.7 1200.0 702.0 : 85.3 412.7 498.0 583.3 910.8 996.1 1200.0 787.3 : 327.4 412.7 498.0 825.5 910.8 1114.7 1200.0 1114.7: 85.3 170.6 498.0 583.3 787.3 872.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.2997 .. 327.4456 cents 323433/281216, 242.1458 cents 104/99, 85.2997 cents 2: 170.5994 .. 412.7453 cents 323433/281216, 242.1458 cents 29246464/32019867,-156.8461 cents 3: 374.5094 .. 616.6553 cents 323433/281216, 242.1458 cents 35152/35937,-38.2358 cents 4: 583.3447 .. 825.4906 cents 323433/281216, 242.1458 cents 86528/88209,-33.3106 cents 5: 787.2547 .. 1029.4006 cents 323433/281216, 242.1458 cents 35152/35937,-38.2358 cents 6: 872.5544 .. 1114.7003 cents 323433/281216, 242.1458 cents 29246464/32019867,-156.8461 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 104/99, 85.2997 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 3267/2704, 327.4456 cents Average / Smallest step : 2.009720 Largest / Average step : 1.910099 Largest / Smallest step : 3.838765 Median interval of one step : 104/99, 85.2997 cents, amount: 4 Most common interval of one step : 104/99, 85.2997 cents, amount: 4 Least squares average step : 173.12300 cents, oct.: 1211.86103 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1224-tone equal temperament with octave 2/1 degrees: 87 421 508 716 803 1137 1224 Least number of segments generator : 613 of 600.980 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1045 of 1024.510 cents and inv. generated superset size: 51 = 44 more = 728.571% 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 33.31057 cents Scale diversity : 1.446003 Lumma stability : 0.142166 Lumma impropriety factor : 0.352895 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 : 88209/86528, 33.3106 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 33 99 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 : 13 Odd number limit : 9801 (O: 9801 U: 9801) Highest odd numerator or denominator: 99 Scale harmonicity : 0.010380 Average absolute harmonicity : 0.224783 Specific harmonicity : 0.055876 Fundamental : 1/5148, -12.3298 octaves, 0.0508 Hz. Guide tone : 10296, 13.3298 octaves, 2693696.820 Hz. Exponens Consonantiae : 5.300381E+07, 25.65959 octaves Euler's gradus suavitatis : 58 Sum of Mann's harmonic distance : 256.5, average 36.64286 Mersenne's string divisions : 461174385 Sum of van Prooijen's expressibility: 7.98254, average 1.14036 Sum of Tenney's harmonic distance : 16.05067, average 2.29295 Vogel's harmonic complexity : 32.57143 Wille's k value : 4900 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 86.13497, average 3.07625 Lattice compactness (without 2's) : 59.16021, average 2.11286 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 12 1 3: -2 .. 2 0.00000 8 2 11: -1 .. 1 0.00000 4 13: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 22 26| Scale is weakly epimorphic with val: <7 10 22 27| Scale is weakly epimorphic with val: <7 10 23 27| Scale is weakly epimorphic with val: <7 10 23 28| Scale is weakly epimorphic with val: <7 10 24 28| Scale is weakly epimorphic with val: <7 10 24 29| Scale is weakly epimorphic with val: <7 10 25 29| Scale is JI-epimorphic with val: <7 11 22 24| Scale is weakly epimorphic with val: <7 11 22 25| Scale is JI-epimorphic with val: <7 11 23 25| Scale is weakly epimorphic with val: <7 11 23 26| Scale is JI-epimorphic with val: <7 11 24 26| = patent Scale is weakly epimorphic with val: <7 11 24 27| Scale is JI-epimorphic with val: <7 11 25 27| Scale is weakly epimorphic with val: <7 11 25 28| Scale is JI-epimorphic with val: <7 11 26 28| Scale is weakly epimorphic with val: <7 11 26 29| Scale is weakly epimorphic with val: <7 12 22 24| Scale is weakly epimorphic with val: <7 12 22 28| Scale is weakly epimorphic with val: <7 12 23 25| Scale is weakly epimorphic with val: <7 12 23 29| Scale is weakly epimorphic with val: <7 12 24 26| Scale is weakly epimorphic with val: <7 12 25 27| Scale is weakly epimorphic with val: <7 12 26 28|
FIT/MODE
7: 0 2 1 1 0 2 1 N T3 SD: 65.9183 c. M: 101.5404 c. 8: 0 2 1 1 1 2 1 N D3 SD: 73.9350 c. M: 112.7453 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 32.5793 c. M: 48.0336 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 10.4521 c. M: 14.7003 c. Double Harmonic Major, Major Gipsy, Bhairav That, Mela Mayamalavagaula, Raga Paraj, Kalingada, Gaulipantu, Lalitapancamam, Gandhakriya, Kalingda, Manjiri, Chromatic 2nd Byzantine Liturgical, Hitzazkiar: Greece, Maqam Zengule, Hijaz Kar, Suzidil 17: 1 5 1 3 1 5 1 N T3 I SD: 9.9735 c. M: 14.7115 c. 26: 2 7 2 4 2 7 2 N T3 I SD: 6.5279 c. M:-9.6473 c. 29: 2 8 2 5 2 8 2 N T3 I SD: 1.6720 c. M: 2.5411 c. 70: 5 19 5 12 5 19 5 N T3 I SD: 0.8815 c. M:-1.3167 c. 99: 7 27 7 17 7 27 7 N T3 I SD: 0.7070 c. M:-1.0753 c. 154: 11 42 11 26 11 42 11 N T3 I SD: 0.4346 c. M:-0.6563 c. 183: 13 50 13 31 13 50 13 N T3 I SD: 0.2613 c. M:-0.3695 c. 253: 18 69 18 43 18 69 18 N T3 I SD: 0.0668 c. M:-0.0971 c. 689: 49 188 49 117 49 188 49 N T3 I SD: 0.0450 c. M:-0.0682 c. 718: 51 196 51 122 51 196 51 N T3 I SD: 0.0496 c. M:-0.0681 c. 942: 67 257 67 160 67 257 67 N T3 I SD: 0.0361 c. M: 0.0506 c. 971: 69 265 69 165 69 265 69 N T3 I SD: 0.0196 c. M: 0.0268 c. 1224: 87 334 87 208 87 334 87 N T3 I SD: 0.0043 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: 32.3680 cents 4 x 5 x 6 x x 8 S SD: 8.8105 cents 5 x 6:7 x 8 x 10 S SD: 32.8467 cents 6 x x 8:9 x 11:12 SD: 16.3343 cents 7:8:9 x x 11:13:14 SD: 30.7571 cents 8:9:10:11:12:13:15:16 SD: 20.7717 cents 9:10:11:12 x 14:17:18 SD: 19.9886 cents 10:11:13 x 15:16:19:20 SD: 15.6199 cents 11:12:14:15 x 17:21:22 SD: 13.9026 cents 12:13:15:16:18:19:23:24 SD: 8.7372 cents 13:14 x 17 x 20:25:26 SD: 14.1441 cents 14:15:18:19:21:22:27:28 SD: 7.9865 cents 16:17:20:21:24:25:30:32 SD: 7.4791 cents 18:19:23:24:27:28:34:36 SD: 4.2605 cents 22:23:28:29:33:35:42:44 SD: 3.9921 cents 33:35:42:44:50:52:63:66 SD: 3.5645 cents 36:38:46:48:54:57:69:72 SD: 2.8852 cents 38:40:48:51:57:60:72:76 SD: 2.4381 cents 40:42:51:53:60:63:76:80 SD: 1.9852 cents 42:44:53:56:63:66:80:84 SD: 1.7291 cents 60:63:76:80:90:95:114:120 SD: 1.3862 cents 78:82:99:104:117:123:149:156 SD: 0.8706 cents 96:101:122:128:144:151:183:192 SD: 0.7293 cents 120:126:152:160:180:189:228:240 SD: 0.7270 cents 134:141:170:179:201:211:255:268 SD: 0.6598 cents 138:145:175:184:207:217:263:276 SD: 0.6180 cents 144:151:183:192:216:227:274:288 SD: 0.5707 cents 156:164:198:208:234:246:297:312 SD: 0.2586 cents 294:309:373:392:441:463:560:588 SD: 0.2459 cents 342:359:434:456:513:539:651:684 SD: 0.2021 cents 372:391:472:496:558:586:708:744 SD: 0.1921 cents 394:414:500:525:591:621:750:788 SD: 0.1866 cents 420:441:533:560:630:662:800:840 SD: 0.1849 cents 438:460:556:584:657:690:834:876 SD: 0.1041 cents 594:624:754:792:891:936:1131:1188 SD: 0.0357 cents