Scala analysis: xen15-chalmers-triadic-reversed-diamond-19-16
Triadic reversed diamond for M=19/16, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64/57 200.531983 2: 19/16 297.513016 19th harmonic 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 32/19 902.486984 19th subharmonic 6: 57/32 999.468017 undevicesimal minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 64/57 200.5320 1: 64/57 200.5320 2: 1083/1024 96.9810 3: 64/57 200.5320 4: 9/8 203.9100 major whole tone 5: 64/57 200.5320 6: 1083/1024 96.9810 7: 64/57 200.5320
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 1083/1024 96.981 cents 1: 4 64/57 200.532 cents 1: 1 9/8 203.910 cents major whole tone 2: 4 19/16 297.513 cents 19th harmonic 2: 1 4096/3249 401.064 cents 2: 2 24/19 404.442 cents smaller undevicesimal major third 3: 4 4/3 498.045 cents perfect fourth 3: 2 171/128 501.423 cents 3: 1 512/361 604.974 cents 4: 1 361/256 595.026 cents two (19th harmonic) 4: 2 256/171 698.577 cents 4: 4 3/2 701.955 cents perfect fifth 5: 2 19/12 795.558 cents undevicesimal minor sixth 5: 1 3249/2048 798.936 cents 5: 4 32/19 902.487 cents 19th subharmonic 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 57/32 999.468 cents undevicesimal minor seventh 6: 2 2048/1083 1103.019 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 : 200.5 297.5 498.0 702.0 902.5 999.5 1200.0 200.5 : 97.0 297.5 501.4 702.0 798.9 999.5 1200.0 297.5 : 200.5 404.4 605.0 702.0 902.5 1103.0 1200.0 498.0 : 203.9 404.4 501.4 702.0 902.5 999.5 1200.0 702.0 : 200.5 297.5 498.0 698.6 795.6 996.1 1200.0 902.5 : 97.0 297.5 498.0 595.0 795.6 999.5 1200.0 999.5 : 200.5 401.1 498.0 698.6 902.5 1103.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 96.9810 .. 203.9100 cents 384/361, 106.9290 cents 1083/1024, 96.9810 cents 2: 297.5130 .. 404.4420 cents 384/361, 106.9290 cents 19/18, 93.6030 cents 3: 498.0450 .. 604.9740 cents 384/361, 106.9290 cents 19/18, 93.6030 cents 4: 595.0260 .. 701.9550 cents 384/361, 106.9290 cents 130321/131072,-9.9479 cents 5: 795.5580 .. 902.4870 cents 384/361, 106.9290 cents 19/18, 93.6030 cents 6: 996.0900 .. 1103.0190 cents 384/361, 106.9290 cents 19/18, 93.6030 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1083/1024, 96.9810 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.767650 Largest / Average step : 1.189475 Largest / Smallest step : 2.102576 Median interval of one step : 64/57, 200.5320 cents, amount: 4 Most common interval of one step : 64/57, 200.5320 cents, amount: 4 Least squares average step : 171.47683 cents, oct.: 1200.33780 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : MSMLMSM Scale is a Constant Structure, by a margin of 9.94794 cents Scale diversity : 1.301376 Lumma stability : 0.473645 Lumma impropriety factor : 0.008290 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 : 513/512, 3.3780 cents Number of recognisable fifths : 6, average 700.8290 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best major thirds form a closed circle Best minor thirds form a closed circle Scale is a complete diamond : 1 3 57 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 : 19 Odd number limit : 3249 (O: 3249 U: 3249) Highest odd numerator or denominator: 57 Scale harmonicity : 0.011828 Average absolute harmonicity : 0.226592 Specific harmonicity : 0.063083 Fundamental : 1/1824, -10.8329 octaves, 0.1434 Hz. Guide tone : 3648, 11.8329 octaves, 954410.062 Hz. Exponens Consonantiae : 6.653952E+06, 22.66578 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 155.5, average 22.21429 Mersenne's string divisions : 19222665 Sum of van Prooijen's expressibility: 7.02350, average 1.00336 Sum of Tenney's harmonic distance : 14.24822, average 2.03546 Vogel's harmonic complexity : 27.57143 Wille's k value : 1624 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 138.87641, average 4.95987 Lattice compactness (without 2's) : 39.08641, average 1.39594 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 6 0.57143 24 1 3: -1 .. 1 0.00000 4 2 19: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is weakly epimorphic with val: <7 10 27| Scale is weakly epimorphic with val: <7 10 33| Scale is weakly epimorphic with val: <7 11 29| Scale is JI-epimorphic with val: <7 11 30| = patent Scale is weakly epimorphic with val: <7 12 27| Scale is weakly epimorphic with val: <7 12 31|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 30.0802 c. M: 45.3441 c. Lebeng 12: 2 1 2 2 2 1 2 P M ME I SD: 1.7147 c. M:-2.4870 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 77: 13 6 13 13 13 6 13 N M DE I SD: 1.3817 c. M:-2.0654 c. 89: 15 7 15 15 15 7 15 N M DE I SD: 1.1230 c. M:-1.7152 c. 101: 17 8 17 17 17 8 17 N M DE I SD: 0.9654 c. M:-1.4482 c. 113: 19 9 19 19 19 9 19 N M DE I SD: 0.8792 c. M:-1.2379 c. 125: 21 10 21 21 21 10 21 N M DE I SD: 0.8421 c. M:-1.1550 c. 137: 23 11 23 23 23 11 23 N M DE I SD: 0.8367 c. M:-1.2251 c. 186: 31 15 31 32 31 15 31 N T3 I SD: 0.8356 c. M:-1.2708 c. 198: 33 16 33 34 33 16 33 N T3 I SD: 0.7040 c. M:-1.0753 c. 210: 35 17 35 36 35 17 35 N T3 I SD: 0.5937 c. M:-0.9021 c. 222: 37 18 37 38 37 18 37 N T3 I SD: 0.5039 c. M:-0.7477 c. 234: 39 19 39 40 39 19 39 N T3 I SD: 0.4342 c. M:-0.6091 c. 246: 41 20 41 42 41 20 41 N T3 I SD: 0.3853 c. M:-0.5320 c. 258: 43 21 43 44 43 21 43 N T3 I SD: 0.3571 c. M:-0.5320 c. 270: 45 22 45 46 45 22 45 N T3 I SD: 0.3483 c. M:-0.5320 c. 282: 47 23 47 48 47 23 47 N T3 I SD: 0.3553 c. M:-0.5320 c. 299: 50 24 50 51 50 24 50 N T3 I SD: 0.3551 c. M: 0.5230 c. 311: 52 25 52 53 52 25 52 N T3 I SD: 0.2754 c. M:-0.4069 c. 323: 54 26 54 55 54 26 54 N T3 I SD: 0.2016 c. M:-0.2994 c. 335: 56 27 56 57 56 27 56 N T3 I SD: 0.1333 c. M:-0.1996 c. 347: 58 28 58 59 58 28 58 N T3 I SD: 0.0702 c. M:-0.1067 c. 359: 60 29 60 61 60 29 60 N T3 I SD: 0.0174 c. M:-0.0251 c. 1448: 242 117 242 246 242 117 242 N T3 I SD: 0.0158 c. M:-0.0213 c. 1807: 302 146 302 307 302 146 302 N T3 I SD: 0.0151 c. M:-0.0214 c. 2166: 362 175 362 368 362 175 362 N T3 I SD: 0.0149 c. M:-0.0220 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: 6.0428 cents 4 x 5 x 6 x 7:8 S SD: 23.4847 cents 5 x 6:7 x 8:9:10 S SD: 25.0420 cents 6 x 7:8:9:10:11:12 S SD: 10.2158 cents 7:8 x 9:11:12 x 14 SD: 22.2065 cents 8:9:10:11:12:13:14:16 S SD: 17.7930 cents 9:10:11:12:14:15:16:18 S SD: 12.0562 cents 10:11:12:13:15:17:18:20 SD: 9.1491 cents 13:15 x 17:20:22:23:26 SD: 12.3449 cents 14:16:17:19:21:24:25:28 SD: 9.3969 cents 15:17:18:20:23:25:27:30 SD: 7.4158 cents 16:18:19:21:24:27:29:32 SD: 5.8427 cents 18:20:21:24:27:30:32:36 S SD: 5.7279 cents 22:25:26:29:33:37:39:44 SD: 4.4427 cents 26:29:31:35:39:44:46:52 SD: 3.6744 cents 32:36:38:43:48:54:57:64 SD: 2.0421 cents 42:47:50:56:63:71:75:84 SD: 1.5159 cents 64:72:76:85:96:108:114:128 SD: 1.1844 cents 90:101:107:120:135:152:160:180 SD: 0.8965 cents 96:108:114:128:144:162:171:192 SD: 0.6825 cents 132:148:157:176:198:222:235:264 SD: 0.6479 cents 138:155:164:184:207:232:246:276 SD: 0.5285 cents 156:175:185:208:234:263:278:312 SD: 0.4847 cents 180:202:214:240:270:303:321:360 SD: 0.4476 cents 186:209:221:248:279:313:331:372 SD: 0.3901 cents 228:256:271:304:342:384:406:456 SD: 0.2406 cents 294:330:349:392:441:495:524:588 SD: 0.2051 cents 342:384:406:456:513:576:609:684 SD: 0.1077 cents 522:586:620:696:783:879:930:1044 SD: 0.0944 cents 570:640:677:760:855:960:1015:1140 SD: 0.0888 cents