Scala analysis: xen09-chalmers-tritriadic-14-16-21
Tritriadic scale built from 14:16:21
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: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 32/21 729.219093 wide fifth 6: 12/7 933.129094 septimal major sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 9/8 203.9100 major whole tone 2: 64/63 27.2641 septimal comma, Archytas' comma 3: 7/6 266.8709 septimal minor third 4: 9/8 203.9100 major whole tone 5: 64/63 27.2641 septimal comma, Archytas' comma 6: 9/8 203.9100 major whole tone 7: 7/6 266.8709 septimal minor third
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 : 203.9 231.2 498.0 702.0 729.2 933.1 1200.0 203.9 : 27.3 294.1 498.0 525.3 729.2 996.1 1200.0 231.2 : 266.9 470.8 498.0 702.0 968.8 1172.7 1200.0 498.0 : 203.9 231.2 435.1 702.0 905.9 933.1 1200.0 702.0 : 27.3 231.2 498.0 702.0 729.2 996.1 1200.0 729.2 : 203.9 470.8 674.7 702.0 968.8 1172.7 1200.0 933.1 : 266.9 470.8 498.0 764.9 968.8 996.1 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 : 161.52202 cents, oct.: 1130.65416 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : MSLMSML 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 0.0 231.174 701.955 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: 21 Scale harmonicity : 0.038043 Average absolute harmonicity : 0.257837 Specific harmonicity : 0.195150 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 4.838400E+04, 15.56224 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 59.5, average 8.50000 Mersenne's string divisions : 1797495 Sum of van Prooijen's expressibility: 4.92090, average 0.70299 Sum of Tenney's harmonic distance : 10.51553, average 1.50222 Vogel's harmonic complexity : 12.14286 Wille's k value : 94 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 95.46537, average 3.40948 Lattice compactness (without 2's) : 41.76998, average 1.49178 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 1.28571 17 1 3: -1 .. 2 0.28571 6 3 7: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is JI-epimorphic with val: <7 11 19| Scale is weakly epimorphic with val: <7 12 22|
FIT/MODE
7: 1 0 2 1 0 1 2 N T3 SD: 42.7930 c. M: 75.9862 c. 10: 2 0 2 2 0 2 2 N M DE S SD: 20.1376 c. M:-36.0900 c. 12: 2 0 3 2 0 2 3 N T3 SD: 20.5150 c. M: 33.1291 c. 15: 3 0 3 3 0 3 3 N M DE S SD: 20.1376 c. M:-36.0900 c. 17: 3 0 4 3 0 3 4 N T3 SD: 13.3821 c. M: 23.3367 c. 22: 4 0 5 4 0 4 5 N T3 SD: 11.4253 c. M: 20.1282 c. 24: 4 1 5 4 1 4 5 N T3 SD: 12.5004 c. M:-20.7809 c. 26: 4 1 6 4 1 4 6 N T3 SD: 10.3168 c. M: 19.2946 c. 28: 5 0 7 4 1 5 6 N SD: 12.0443 c. M: 16.8884 c. 29: 5 1 6 5 1 5 6 N T3 SD: 11.3090 c. M:-18.5950 c. 31: 5 1 7 5 1 5 7 N T3 SD: 5.5838 c. M: 10.3616 c. 36: 6 1 8 6 1 6 8 N T3 SD: 2.5231 c. M:-4.1142 c. 41: 7 1 9 7 1 7 9 N T3 SD: 2.0134 c. M:-3.4563 c. 77: 13 2 17 13 2 13 17 N T3 SD: 1.8363 c. M:-3.2484 c. 89: 15 2 20 15 2 15 20 N T3 SD: 1.5612 c. M: 2.7920 c. 94: 16 2 21 16 2 16 21 N T3 SD: 0.9265 c. M: 1.5595 c. 130: 22 3 29 22 3 22 29 N T3 SD: 0.5182 c. M: 0.8331 c. 135: 23 3 30 23 3 23 30 N T3 SD: 0.2886 c. M:-0.5344 c. 265: 45 6 59 45 6 45 59 N T3 SD: 0.1677 c. M: 0.2989 c. 306: 52 7 68 52 7 52 68 N T3 SD: 0.1301 c. M:-0.2042 c. 400: 68 9 89 68 9 68 89 N T3 SD: 0.1237 c. M: 0.2191 c. 441: 75 10 98 75 10 75 98 N T3 SD: 0.1201 c. M:-0.2042 c. 571: 97 13 127 97 13 97 127 N T3 SD: 0.0305 c. M: 0.0571 c. 706: 120 16 157 120 16 120 157 N T3 SD: 0.0311 c. M:-0.0560 c. 1277: 217 29 284 217 29 217 284 N T3 SD: 0.0056 c. M: 0.0100 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 x 5:6 S SD: 16.2568 cents 4 x x 5:6 x 7:8 S SD: 29.3238 cents 5 x 6:7 x 8:9:10 S SD: 33.7869 cents 6 x 7:8:9 x 10:12 S SD: 12.0877 cents 7 x 8:9 x 11:12:14 SD: 16.4949 cents 8:9 x 11:12 x 14:16 SD: 12.8254 cents 9:10 x 12 x 14:15:18 S SD: 12.8302 cents 10:11 x 13:15 x 17:20 SD: 12.0743 cents 11:12:13:15 x 17:19:22 SD: 15.3540 cents 12 x 14:16:18 x 21:24 S SD: 10.0966 cents 13 x 15:17 x 20:22:26 SD: 9.3340 cents 14 x 16:19:21 x 24:28 SD: 6.1284 cents 15:17 x 20 x 23:26:30 SD: 5.0815 cents 16:18 x 21:24 x 27:32 SD: 7.7114 cents 17:19 x 23 x 26:29:34 SD: 5.9343 cents 18:20:21:24:27 x 31:36 SD: 7.0725 cents 19:21:22:25 x 29:33:38 SD: 8.3286 cents 20 x 23:27:30 x 34:40 SD: 5.6170 cents 21 x 24:28 x 32:36:42 S SD: 0.0000 cents 22 x 25:29:33:34:38:44 SD: 5.9061 cents 23:26 x 31 x 35:39:46 SD: 5.5980 cents 24:27 x 32:36:37:41:48 SD: 3.5083 cents 25:28:29:33 x 38:43:50 SD: 5.4736 cents 26:29:30:35:39:40:45:52 SD: 5.1877 cents 27:30:31:36 x 41:46:54 SD: 4.3386 cents 28 x 32:37:42:43:48:56 SD: 3.4262 cents 29 x 33:39 x 44:50:58 SD: 4.1527 cents 30:34 x 40:45:46:51:60 SD: 3.6874 cents 31:35 x 41 x 47:53:62 SD: 3.6503 cents 33:37:38:44 x 50:57:66 SD: 3.6242 cents 34:38:39:45:51:52:58:68 SD: 3.0143 cents 35:39:40:47 x 53:60:70 SD: 3.8877 cents 36 x 41:48:54:55:62:72 SD: 1.8294 cents 37 x 42:49 x 56:63:74 SD: 4.6949 cents 38:43 x 51:57:58:65:76 SD: 2.6527 cents 39:44:45:52 x 59:67:78 SD: 3.6109 cents 40:45:46:53:60:61:69:80 SD: 2.6815 cents 41:46:47:55 x 62:70:82 SD: 3.2736 cents 42:47:48:56:63:64:72:84 SD: 1.3120 cents 44 x 50:59:66:67:75:88 SD: 2.8497 cents 45:51 x 60:68:69:77:90 SD: 3.5478 cents 46:52:53:61:69:70:79:92 SD: 2.7537 cents 48:54:55:64:72:73:82:96 SD: 1.1779 cents 52 x 59:69:78:79:89:104 SD: 2.6950 cents 54:61:62:72:81:82:93:108 SD: 2.0932 cents 56:63:64:75:84:85:96:112 SD: 1.4665 cents 63:71:72:84:95:96:108:126 SD: 1.3760 cents 78:88:89:104:117:119:134:156 SD: 1.0096 cents 90:101:103:120:135:137:154:180 SD: 0.8765 cents 105:118:120:140:158:160:180:210 SD: 0.8265 cents 112:126:128:149:168:171:192:224 SD: 0.7337 cents 120:135:137:160:180:183:206:240 SD: 0.4707 cents 126:142:144:168:189:192:216:252 SD: 0.4358 cents 168:189:192:224:252:256:288:336 S SD: 0.0000 cents