Scala analysis: xen15-chalmers-triadic-reversed-diamond-56-45
Triadic reversed diamond for M=56/45, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 56/45 378.602191 septimal narrow major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 45/28 821.397809 septimale wide minor sixth 6: 28/15 1080.557192 grave major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 15/14 119.4428 major diatonic semitone 2: 784/675 259.1594 3: 15/14 119.4428 major diatonic semitone 4: 9/8 203.9100 major whole tone 5: 15/14 119.4428 major diatonic semitone 6: 784/675 259.1594 7: 15/14 119.4428 major diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 15/14 119.443 cents major diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 784/675 259.159 cents 2: 1 225/196 238.886 cents two (major diatonic semitone) 2: 2 135/112 323.353 cents septimal wide minor third 2: 4 56/45 378.602 cents septimal narrow major third 3: 1 2025/1568 442.796 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 2 10/7 617.488 cents Euler's tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 3136/2025 757.204 cents two (septimal narrow major third) 5: 4 45/28 821.398 cents septimale wide minor sixth 5: 2 224/135 876.647 cents narrow septimal major sixth 5: 1 392/225 961.114 cents 6: 2 675/392 940.841 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 28/15 1080.557 cents grave major seventh 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 : 119.4 378.6 498.0 702.0 821.4 1080.6 1200.0 119.4 : 259.2 378.6 582.5 702.0 961.1 1080.6 1200.0 378.6 : 119.4 323.4 442.8 702.0 821.4 940.8 1200.0 498.0 : 203.9 323.4 582.5 702.0 821.4 1080.6 1200.0 702.0 : 119.4 378.6 498.0 617.5 876.6 996.1 1200.0 821.4 : 259.2 378.6 498.0 757.2 876.6 1080.6 1200.0 1080.6: 119.4 238.9 498.0 617.5 821.4 940.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 119.4428 .. 259.1594 cents 10976/10125, 139.7166 cents 15/14, 119.4428 cents 2: 238.8856 .. 378.6022 cents 10976/10125, 139.7166 cents 151875/153664,-20.2738 cents 3: 442.7956 .. 582.5122 cents 10976/10125, 139.7166 cents 91125/87808, 64.1934 cents 4: 617.4878 .. 757.2044 cents 10976/10125, 139.7166 cents 50/49, 34.9756 cents 5: 821.3978 .. 961.1144 cents 10976/10125, 139.7166 cents 91125/87808, 64.1934 cents 6: 940.8406 .. 1080.5572 cents 10976/10125, 139.7166 cents 151875/153664,-20.2738 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 15/14, 119.4428 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 784/675, 259.1594 cents Average / Smallest step : 1.435236 Largest / Average step : 1.511763 Largest / Smallest step : 2.169736 Median interval of one step : 15/14, 119.4428 cents, amount: 4 Most common interval of one step : 15/14, 119.4428 cents, amount: 4 Least squares average step : 172.63525 cents, oct.: 1208.44672 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Scale is a Constant Structure, by a margin of 20.27377 cents Scale diversity : 1.423363 Lumma stability : 0.335207 Lumma impropriety factor : 0.033790 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 : 153664/151875, 20.2738 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Scale is a complete diamond : 7 15 45 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 : 7 Odd number limit : 2025 (O: 2025 U: 2025) Highest odd numerator or denominator: 45 Scale harmonicity : 0.020392 Average absolute harmonicity : 0.237797 Specific harmonicity : 0.110766 Fundamental : 1/1260, -10.2992 octaves, 0.2076 Hz. Guide tone : 2520, 11.2992 octaves, 659296.425 Hz. Exponens Consonantiae : 3.175200E+06, 21.59842 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 130.5, average 18.64286 Mersenne's string divisions : 965383755 Sum of van Prooijen's expressibility: 6.61285, average 0.94469 Sum of Tenney's harmonic distance : 13.60560, average 1.94366 Vogel's harmonic complexity : 20.57143 Wille's k value : 1012 Wilson's harmonic complexity : 36 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 5: -1 .. 1 0.00000 4 7: -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 15 19| Scale is weakly epimorphic with val: <7 10 15 20| Scale is weakly epimorphic with val: <7 10 16 20| Scale is weakly epimorphic with val: <7 10 16 21| Scale is weakly epimorphic with val: <7 10 17 21| Scale is weakly epimorphic with val: <7 10 17 22| Scale is weakly epimorphic with val: <7 10 18 22| Scale is JI-epimorphic with val: <7 11 15 18| Scale is weakly epimorphic with val: <7 11 16 18| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 17 19| Scale is JI-epimorphic with val: <7 11 17 20| Scale is weakly epimorphic with val: <7 11 18 20| Scale is JI-epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 12 15 21| Scale is weakly epimorphic with val: <7 12 16 18| Scale is weakly epimorphic with val: <7 12 16 22| Scale is weakly epimorphic with val: <7 12 17 19| Scale is weakly epimorphic with val: <7 12 18 20|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 34.8220 c. M: 51.9858 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 23.2752 c. M:-35.2883 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 13.8561 c. M: 18.6022 c. 19: 2 4 2 3 2 4 2 P T3 I SD: 5.3307 c. M:-7.2182 c. 29: 3 6 3 5 3 6 3 P T3 I SD: 4.2281 c. M: 6.1884 c. 41: 4 9 4 7 4 9 4 N T3 I SD: 1.6393 c. M:-2.3696 c. 60: 6 13 6 10 6 13 6 N T3 I SD: 1.3187 c. M:-1.9550 c. 70: 7 15 7 12 7 15 7 N T3 I SD: 0.9642 c. M: 1.4593 c. 111: 11 24 11 19 11 24 11 N T3 I SD: 0.5025 c. M:-0.7477 c. 130: 13 28 13 22 13 28 13 N T3 I SD: 0.3794 c. M:-0.5572 c. 171: 17 37 17 29 17 37 17 N T3 I SD: 0.2270 c. M: 0.3452 c. 241: 24 52 24 41 24 52 24 N T3 I SD: 0.1194 c. M: 0.1790 c. 412: 41 89 41 70 41 89 41 N T3 I SD: 0.0257 c. M: 0.0386 c. 1065: 106 230 106 181 106 230 106 N T3 I SD: 0.0111 c. M: 0.0168 c. 1477: 147 319 147 251 147 319 147 N T3 I SD: 0.0078 c. M:-0.0115 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: 20.9870 cents 4 x 5 x 6 x 7:8 S SD: 27.9993 cents 5 x 6:7 x 8:9:10 S SD: 24.5946 cents 6 x 7:8:9:10:11:12 S SD: 21.9981 cents 7:8:9 x x 11:13:14 SD: 26.2802 cents 8:9:10:11:12:13:15:16 SD: 14.6089 cents 9:10:11:12 x 14:17:18 SD: 15.4084 cents 10:11:12:13:15:16:19:20 SD: 13.5221 cents 12:13:15:16:18:19:22:24 SD: 6.4936 cents 16:17:20:21:24:26:30:32 SD: 5.4175 cents 24:26:30:32:36:39:45:48 SD: 4.1670 cents 28:30:35:37:42:45:52:56 SD: 2.7810 cents 30:32:37:40:45:48:56:60 SD: 2.7106 cents 40:43:50:53:60:64:75:80 SD: 2.5928 cents 42:45:52:56:63:68:78:84 SD: 2.5558 cents 44:47:55:59:66:71:82:88 SD: 2.2128 cents 54:58:67:72:81:87:101:108 SD: 1.2360 cents 66:71:82:88:99:106:123:132 SD: 1.1598 cents 82:88:102:109:123:132:153:164 SD: 0.9573 cents 102:109:127:136:153:164:190:204 SD: 0.8474 cents 110:118:137:147:165:177:205:220 SD: 0.8345 cents 114:122:142:152:171:183:213:228 SD: 0.5249 cents 156:167:194:208:234:251:291:312 SD: 0.4264 cents 168:180:209:224:252:270:314:336 SD: 0.3250 cents 180:193:224:240:270:289:336:360 SD: 0.3054 cents 270:289:336:360:405:434:504:540 SD: 0.2478 cents 306:328:381:408:459:492:571:612 SD: 0.2181 cents 336:360:418:448:504:540:627:672 SD: 0.1115 cents 450:482:560:600:675:723:840:900 SD: 0.1036 cents 504:540:627:672:756:810:941:1008 SD: 0.0948 cents