Scala analysis: xen09-chalmers-tritriadic-16-21-24
Tritriadic scale built from 16:21:24
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 21/16 470.780907 narrow fourth 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 7/4 968.825906 harmonic seventh 6: 63/32 1172.735908 octave - septimal comma 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 64/63 27.2641 septimal comma, Archytas' comma 1: 9/8 203.9100 major whole tone 2: 7/6 266.8709 septimal minor third 3: 64/63 27.2641 septimal comma, Archytas' comma 4: 9/8 203.9100 major whole tone 5: 7/6 266.8709 septimal minor third 6: 9/8 203.9100 major whole tone 7: 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: 3 9/8 203.910 cents major whole tone 1: 2 7/6 266.871 cents septimal minor third 2: 3 8/7 231.174 cents septimal whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 21/16 470.781 cents narrow fourth 3: 1 9/7 435.084 cents septimal major third, BP third 3: 5 4/3 498.045 cents perfect fourth 3: 1 189/128 674.691 cents 4: 1 256/189 525.309 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 3 32/21 729.219 cents wide fifth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 3 7/4 968.826 cents harmonic seventh 6: 2 12/7 933.129 cents septimal major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 63/32 1172.736 cents octave - septimal comma 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 : 203.9 470.8 498.0 702.0 968.8 1172.7 1200.0 203.9 : 266.9 294.1 498.0 764.9 968.8 996.1 1200.0 470.8 : 27.3 231.2 498.0 702.0 729.2 933.1 1200.0 498.0 : 203.9 470.8 674.7 702.0 905.9 1172.7 1200.0 702.0 : 266.9 470.8 498.0 702.0 968.8 996.1 1200.0 968.8 : 203.9 231.2 435.1 702.0 729.2 933.1 1200.0 1172.7: 27.3 231.2 498.0 525.3 729.2 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 266.8709 cents 147/128, 239.6068 cents 64/63, 27.2641 cents 2: 231.1741 .. 470.7809 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 3: 435.0841 .. 674.6909 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 4: 525.3091 .. 764.9159 cents 147/128, 239.6068 cents 32768/35721,-149.3818 cents 5: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 6: 933.1291 .. 1172.7359 cents 147/128, 239.6068 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 6.287705 Largest / Average step : 1.556747 Largest / Smallest step : 9.788366 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 183.77123 cents, oct.: 1286.39859 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : MLSMLMS Scale is a Constant Structure, by a margin of 27.26409 cents Scale diversity : 1.208955 Lumma stability : 0.045440 Lumma impropriety factor : 0.243474 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 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 : 64/63, 27.2641 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 470.781 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 7 Odd number limit : 189 (O: 189 U: 189) Highest odd numerator or denominator: 63 Scale harmonicity : 0.039548 Average absolute harmonicity : 0.256556 Specific harmonicity : 0.192992 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 2.419200E+04, 14.56224 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 87.5, average 12.50000 Mersenne's string divisions : 13803405 Sum of van Prooijen's expressibility: 5.87514, average 0.83931 Sum of Tenney's harmonic distance : 11.29368, average 1.61338 Vogel's harmonic complexity : 11.42857 Wille's k value : 94 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 95.90563, average 3.42520 Lattice compactness (without 2's) : 42.59183, average 1.52114 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.71429 18 1 3: -1 .. 2 0.71429 7 3 7: 0 .. 1 0.42857 3 3 Average exponent except 2's : 8 / 7 = 1.14286 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is JI-epimorphic with val: <7 11 19| Scale is weakly epimorphic with val: <7 12 22|
FIT/MODE
7: 1 2 0 1 2 1 0 N T3 SD: 33.3554 c. M:-59.7455 c. 10: 2 2 0 2 2 2 0 N M DE S SD: 20.2130 c. M:-36.0900 c. 12: 2 3 0 2 3 2 0 N T3 SD: 19.2422 c. M:-31.1741 c. 16: 3 3 1 2 4 3 0 N SD: 21.0822 c. M:-27.2641 c. 17: 3 4 0 3 4 3 0 N T3 SD: 15.8439 c. M:-27.2641 c. 22: 4 5 0 4 5 4 0 N T3 SD: 15.2259 c. M:-27.2641 c. 24: 4 5 1 4 5 4 1 N T3 SD: 13.7639 c. M: 22.7359 c. 26: 4 6 1 4 6 4 1 N T3 SD: 11.9573 c. M: 19.2946 c. 29: 5 6 1 5 6 5 1 N T3 SD: 10.3421 c. M: 17.1018 c. 31: 5 7 1 5 7 5 1 N T3 SD: 6.8917 c. M: 11.4456 c. 36: 6 8 1 6 8 6 1 N T3 SD: 3.4092 c. M: 6.0692 c. 41: 7 9 1 7 9 7 1 N T3 SD: 1.7091 c. M: 2.9722 c. 89: 15 20 2 15 20 15 2 N T3 SD: 1.1561 c. M:-1.9606 c. 94: 16 21 2 16 21 16 2 N T3 SD: 1.0375 c. M:-1.7322 c. 130: 22 29 3 22 29 22 3 N T3 SD: 0.4454 c. M: 0.8331 c. 135: 23 30 3 23 30 23 3 N T3 SD: 0.3582 c. M:-0.5974 c. 265: 45 59 6 45 59 45 6 N T3 SD: 0.1290 c. M:-0.2307 c. 306: 52 68 7 52 68 52 7 N T3 SD: 0.1263 c. M: 0.1985 c. 441: 75 98 10 75 98 75 10 N T3 SD: 0.0942 c. M:-0.1716 c. 571: 97 127 13 97 127 97 13 N T3 SD: 0.0356 c. M: 0.0571 c. 1012: 172 225 23 172 225 172 23 N T3 SD: 0.0300 c. M: 0.0512 c. 1277: 217 284 29 217 284 217 29 N T3 SD: 0.0072 c. M:-0.0127 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: 28.1557 cents 4 x 5 x 6:7 x 8 S SD: 21.1168 cents 5:6 x 7:8:9 x 10 S SD: 37.1381 cents 6:7 x 8:9:11 x 12 SD: 20.4453 cents 7:8:9 x 11:12 x 14 SD: 19.7768 cents 8:9 x 11:12:14 x 16 SD: 10.6546 cents 9:10 x 12:14:16 x 18 S SD: 14.3804 cents 10:11:13 x 15:18 x 20 SD: 12.9100 cents 11:12:14:15:17:19 x 22 SD: 16.9746 cents 12:14 x 16:18:21 x 24 S SD: 12.5922 cents 13:15:17 x 20:23 x 26 SD: 13.0241 cents 14:16:18:19:21:25 x 28 SD: 10.7753 cents 15:17 x 20:23:26 x 30 SD: 8.6846 cents 16:18:21 x 24:28 x 32 S SD: 0.0000 cents 18:20 x 24:27:32:35:36 SD: 6.8076 cents 19:21:25 x 29:33:37:38 SD: 8.1520 cents 20:23:26:27:30:35:39:40 SD: 7.0845 cents 21:24 x 28:32:37:41:42 SD: 7.1363 cents 22:25:29 x 33:39:43:44 SD: 5.3094 cents 24:27 x 32:36:42:47:48 SD: 1.5307 cents 25:28:33 x 38:44:49:50 SD: 4.8286 cents 26:29:34:35:39:46:51:52 SD: 4.3660 cents 28:32:37 x 42:49:55:56 SD: 4.9904 cents 29:33:38:39:44:51:57:58 SD: 4.7215 cents 30:34:39:40:45:53:59:60 SD: 3.8075 cents 31:35:41 x 47:54:61:62 SD: 4.1546 cents 32:36:42:43:48:56:63:64 SD: 1.9247 cents 34:38 x 45:51:60:67:68 SD: 3.7439 cents 36:41:47:48:54:63:71:72 SD: 3.3347 cents 37:42 x 49:56:65:73:74 SD: 4.3404 cents 38:43:50:51:57:67:75:76 SD: 2.9847 cents 39:44:51:52:59:68:77:78 SD: 2.6586 cents 40:45 x 53:60:70:79:80 SD: 2.0271 cents 48:54:63:64:72:84:95:96 SD: 1.3051 cents 64:72:84:85:96:112:126:128 SD: 0.9680 cents 96:108:126:128:144:168:189:192 S SD: 0.0000 cents