Scala analysis: tet3a
Eight notes, two major one minor tetrad
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: 6/5 315.641287 minor third 3: 9/7 435.084095 septimal major third, BP third 4: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 5: 3/2 701.955001 perfect fifth 6: 8/5 813.686286 minor sixth 7: 12/7 933.129094 septimal major sixth 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 15/14 119.4428 major diatonic semitone 2: 28/25 196.1985 middle second 3: 15/14 119.4428 major diatonic semitone 4: 49/45 147.4281 BP minor semitone 5: 15/14 119.4428 major diatonic semitone 6: 16/15 111.7313 minor diatonic semitone 7: 15/14 119.4428 major diatonic semitone 8: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 4 15/14 119.443 cents major diatonic semitone 1: 1 49/45 147.428 cents BP minor semitone 1: 1 28/25 196.198 cents middle second 1: 1 7/6 266.871 cents septimal minor third 2: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 3: 1 60/49 350.617 cents smaller approximation to neutral third 3: 1 56/45 378.602 cents septimal narrow major third 3: 1 5/4 386.314 cents major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 1 98/75 463.069 cents 3: 1 4/3 498.045 cents perfect fourth 3: 1 75/56 505.757 cents marvelous fourth 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 2 4/3 498.045 cents perfect fourth 4: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 2 10/7 617.488 cents Euler's tritone 4: 2 3/2 701.955 cents perfect fifth 5: 1 10/7 617.488 cents Euler's tritone 5: 1 112/75 694.243 cents marvelous fifth 5: 1 3/2 701.955 cents perfect fifth 5: 1 75/49 736.931 cents BP fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 1 45/28 821.398 cents septimale wide minor sixth 5: 1 49/30 849.383 cents larger approximation to neutral sixth 6: 2 8/5 813.686 cents minor sixth 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 2 12/7 933.129 cents septimal major sixth 6: 2 7/4 968.826 cents harmonic seventh 7: 1 12/7 933.129 cents septimal major sixth 7: 1 25/14 1003.802 cents middle minor seventh 7: 1 90/49 1052.572 cents 7: 4 28/15 1080.557 cents grave major seventh 7: 1 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 5.42857 = 38/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 119.4 315.6 435.1 582.5 702.0 813.7 933.1 1200.0 119.4 : 196.2 315.6 463.1 582.5 694.2 813.7 1080.6 1200.0 315.6 : 119.4 266.9 386.3 498.0 617.5 884.4 1003.8 1200.0 435.1 : 147.4 266.9 378.6 498.0 764.9 884.4 1080.6 1200.0 582.5 : 119.4 231.2 350.6 617.5 736.9 933.1 1052.6 1200.0 702.0 : 111.7 231.2 498.0 617.5 813.7 933.1 1080.6 1200.0 813.7 : 119.4 386.3 505.8 702.0 821.4 968.8 1088.3 1200.0 933.1 : 266.9 386.3 582.5 702.0 849.4 968.8 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 266.8709 cents 35/32, 155.1396 cents 16/15, 111.7313 cents 2: 231.1741 .. 386.3137 cents 35/32, 155.1396 cents 48/49,-35.6968 cents 3: 350.6169 .. 582.5122 cents 343/300, 231.8953 cents 48/49,-35.6968 cents 4: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 20/21,-84.4672 cents 5: 617.4878 .. 849.3831 cents 343/300, 231.8953 cents 20/21,-84.4672 cents 6: 813.6863 .. 968.8259 cents 35/32, 155.1396 cents 48/49,-35.6968 cents 7: 933.1291 .. 1088.2687 cents 35/32, 155.1396 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.342507 Largest / Average step : 1.779139 Largest / Smallest step : 2.388507 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 : 141.71482 cents, oct.: 1133.71854 cents Scale is not proper Step pattern alph. order: ABACADAE Step pattern size order : BDBCBABE Scale is not a Constant Structure Scale diversity : 1.473897 Lumma stability : 0.186219 Lumma impropriety factor : 0.259768 Rothenberg efficiency : 0.378571 redundancy: 0.621429 Efficiency x scale size : 3.028571 Number of different interval sizes : 30 = 4.28571 / class Number of one step interval sizes : 5 Highest interval variety : 8 Mean interval variety : 5.42857 = 38/7 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 15/14, 119.4428 cents & inv., amount: 4 Most common triad is 0.0 119.443 1088.269 cents, amount: 1 Number of recognisable fifths : 4, average 700.0271 cents Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 1 = 12.5000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval class 4 Scale is differentially coherent in interval classes 5 and 6 combined Scale is differentially coherent in interval class 6 -- Rational properties -- Prime limit : 7 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 15 Scale harmonicity : 0.023417 Average absolute harmonicity : 0.214802 Specific harmonicity : 0.143491 Fundamental : 1/70, -6.1293 octaves, 3.7375 Hz. Guide tone : 2520, 11.2992 octaves, 659296.425 Hz. Exponens Consonantiae : 1.764000E+05, 17.42849 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 54.0, average 6.75000 Mersenne's string divisions : 18910320 Sum of van Prooijen's expressibility: 5.69559, average 0.71195 Sum of Tenney's harmonic distance : 11.74827, average 1.46853 Vogel's harmonic complexity : 12.87500 Wille's k value : 52 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 85.52205, average 2.37561 Lattice compactness (without 2's) : 55.68749, average 1.54687 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 0.62500 9 1 3: 0 .. 2 0.75000 6 1 5: -1 .. 1 -0.25000 4 2 7: -1 .. 1 -0.25000 4 4 Average exponent except 2's : 2 / 8 = 0.25000 Average absolute exponent except 2's: 14 / 8 = 1.75000 Scale is weakly epimorphic with val: <8 13 17 20| Scale is weakly epimorphic with val: <8 14 19 21| Scale is weakly epimorphic with val: <8 14 21 23|
FIT/MODE
8: 1 1 1 1 1 0 1 2 N T3 SD: 33.8535 c. M: 63.6863 c. 9: 1 1 1 1 1 1 1 2 P M ME SD: 30.9708 c. M: 49.1789 c. 10: 1 2 1 1 1 1 1 2 N D3 SD: 27.4576 c. M:-44.9159 c. 12: 1 2 1 2 1 1 1 3 N SD: 20.7607 c. M: 35.0841 c. 16: 2 2 2 2 1 2 1 4 N SD: 21.3858 c. M: 33.1291 c. 18: 2 3 2 2 2 1 2 4 N SD: 19.3041 c. M:-31.5826 c. 19: 2 3 2 2 2 2 2 4 N SD: 8.6908 c. M:-14.2393 c. 22: 2 4 2 3 2 2 2 5 N SD: 9.0508 c. M:-17.4878 c. 27: 3 4 3 3 3 2 3 6 N SD: 8.6219 c. M:-13.8905 c. 31: 3 5 3 4 3 3 3 7 N SD: 4.7480 c. M: 9.2776 c. 41: 4 7 4 5 4 4 4 9 N SD: 3.7951 c. M:-6.3099 c. 50: 5 8 5 6 5 5 5 11 N SD: 3.7840 c. M: 6.5122 c. 53: 5 9 5 7 5 5 5 12 N SD: 3.9994 c. M: 6.2353 c. 58: 6 9 6 7 6 5 6 13 N SD: 3.7654 c. M: 6.7897 c. 68: 7 11 7 8 7 6 7 15 N SD: 3.1951 c. M:-6.0924 c. 72: 7 12 7 9 7 7 7 16 N SD: 1.7764 c. M:-2.9804 c. Three Tetrads 99: 10 16 10 12 10 9 10 22 N SD: 1.0687 c. M:-1.7693 c. 130: 13 21 13 16 13 12 13 29 N SD: 1.0466 c. M: 1.7951 c. 140: 14 23 14 17 14 13 14 31 N SD: 1.0859 c. M:-2.0588 c. 152: 15 25 15 19 15 14 15 34 N SD: 0.9908 c. M:-1.6983 c. 171: 17 28 17 21 17 16 17 38 N SD: 0.1766 c. M:-0.3488 c. 441: 44 72 44 54 44 41 44 98 N SD: 0.1805 c. M:-0.2901 c. 593: 59 97 59 73 59 55 59 132 N SD: 0.1738 c. M:-0.2871 c. 612: 61 100 61 75 61 57 61 136 N SD: 0.1332 c. M:-0.2100 c. 764: 76 125 76 94 76 71 76 170 N SD: 0.1115 c. M:-0.2103 c. 783: 78 128 78 96 78 73 78 174 N SD: 0.1197 c. M:-0.2042 c. 935: 93 153 93 115 93 87 93 208 N SD: 0.0808 c. M:-0.1616 c. 1106: 110 181 110 136 110 103 110 246 N SD: 0.0700 c. M:-0.1280 c. 1205: 120 197 120 148 120 112 120 268 N SD: 0.0707 c. M:-0.1197 c. 1236: 123 202 123 152 123 115 123 275 N SD: 0.0815 c. M: 0.1326 c. 1277: 127 209 127 157 127 119 127 284 N SD: 0.0705 c. M:-0.1033 c. 1376: 137 225 137 169 137 128 137 306 N SD: 0.0520 c. M:-0.0903 c. 1547: 154 253 154 190 154 144 154 344 N SD: 0.0448 c. M:-0.0807 c. 1718: 171 281 171 211 171 160 171 382 N SD: 0.0463 c. M:-0.0747 c. 1848: 184 302 184 227 184 172 184 411 N SD: 0.0348 c. M: 0.0569 c. 2019: 201 330 201 248 201 188 201 449 N SD: 0.0257 c. M: 0.0456 c. 2190: 218 358 218 269 218 204 218 487 N SD: 0.0253 c. M: 0.0464 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x x x 5:6 S SD: 26.5469 cents 4 x x 5 x 6 x 7:8 S SD: 15.1096 cents 5 x 6 x 7 x 8:9:10 S SD: 16.8934 cents 6 x 7:8 x 9 x 10:12 S SD: 18.6774 cents 7 x 8:9:10 x 11:12:14 S SD: 16.0996 cents 8:9 x 10:11:12:13:14:16 S SD: 15.9598 cents 9:10:11:12:13 x 14:15:18 S SD: 18.4179 cents 10:11:12:13:14:15:16:17:20 SD: 6.4368 cents 14:15:17:18:20:21:22:24:28 SD: 6.3935 cents 15:16:18:19:21:23:24:26:30 SD: 6.3010 cents 18:19:22:23:25:27:29:31:36 SD: 5.8490 cents 20:21:24:26:28:30:32:34:40 SD: 5.3020 cents 24:26:29:31:34:36:38:41:48 SD: 4.6065 cents 25:27:30:32:35:38:40:43:50 SD: 3.5549 cents 28:30:34:36:39:42:45:48:56 SD: 2.9518 cents 38:41:46:49:53:57:61:65:76 SD: 2.7671 cents 40:43:48:51:56:60:64:69:80 SD: 2.3698 cents 42:45:50:54:59:63:67:72:84 SD: 1.9823 cents 45:48:54:58:63:68:72:77:90 SD: 1.9813 cents 55:59:66:71:77:83:88:94:110 SD: 1.7237 cents 56:60:67:72:78:84:90:96:112 SD: 1.6033 cents 60:64:72:77:84:90:96:103:120 SD: 1.0864 cents 70:75:84:90:98:105:112:120:140 SD: 0.0000 cents