Scala analysis: xen09-chalmers-tritriadic-12-17-18
Tritriadic scale built from 12:17:18
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/16 104.955410 17th harmonic 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth 4: 17/12 603.000409 2nd septendecimal tritone 5: 3/2 701.955001 perfect fifth 6: 17/9 1101.045408 septendecimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 18/17 98.9546 Arabic lute index finger 1: 17/16 104.9554 17th harmonic 2: 18/17 98.9546 Arabic lute index finger 3: 32/27 294.1350 Pythagorean minor third 4: 17/16 104.9554 17th harmonic 5: 18/17 98.9546 Arabic lute index finger 6: 34/27 399.0904 septendecimal major third 7: 18/17 98.9546 Arabic lute index finger
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 18/17 98.955 cents Arabic lute index finger 1: 2 17/16 104.955 cents 17th harmonic 1: 1 32/27 294.135 cents Pythagorean minor third 1: 1 34/27 399.090 cents septendecimal major third 2: 3 9/8 203.910 cents major whole tone 2: 1 64/51 393.090 cents 2: 1 34/27 399.090 cents septendecimal major third 2: 2 4/3 498.045 cents perfect fourth 3: 1 81/68 302.865 cents Persian wosta 3: 3 4/3 498.045 cents perfect fourth 3: 1 24/17 597.000 cents 1st septendecimal tritone 3: 2 17/12 603.000 cents 2nd septendecimal tritone 4: 2 24/17 597.000 cents 1st septendecimal tritone 4: 1 17/12 603.000 cents 2nd septendecimal tritone 4: 3 3/2 701.955 cents perfect fifth 4: 1 136/81 897.135 cents 5: 2 3/2 701.955 cents perfect fifth 5: 1 27/17 800.910 cents septendecimal minor sixth 5: 1 51/32 806.910 cents 5: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/17 800.910 cents septendecimal minor sixth 6: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 32/17 1095.045 cents 17th subharmonic 6: 3 17/9 1101.045 cents septendecimal major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 105.0 203.9 498.0 603.0 702.0 1101.0 1200.0 105.0 : 99.0 393.1 498.0 597.0 996.1 1095.0 1200.0 203.9 : 294.1 399.1 498.0 897.1 996.1 1101.0 1200.0 498.0 : 105.0 203.9 603.0 702.0 806.9 905.9 1200.0 603.0 : 99.0 498.0 597.0 702.0 800.9 1095.0 1200.0 702.0 : 399.1 498.0 603.0 702.0 996.1 1101.0 1200.0 1101.0: 99.0 203.9 302.9 597.0 702.0 800.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.9546 .. 399.0904 cents 289/243, 300.1358 cents 18/17, 98.9546 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 243/272,-195.1804 cents 3: 302.8646 .. 603.0004 cents 289/243, 300.1358 cents 243/272,-195.1804 cents 4: 596.9996 .. 897.1354 cents 289/243, 300.1358 cents 288/289,-6.0008 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 243/272,-195.1804 cents 6: 800.9096 .. 1101.0454 cents 289/243, 300.1358 cents 243/272,-195.1804 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 18/17, 98.9546 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 34/27, 399.0904 cents Average / Smallest step : 1.732396 Largest / Average step : 2.328027 Largest / Smallest step : 4.033066 Median interval of one step : 17/16, 104.9554 cents, amount: 2 Most common interval of one step : 18/17, 98.9546 cents, amount: 3 Least squares average step : 163.82114 cents, oct.: 1146.74797 cents Scale is not proper Step pattern alph. order: ABCABDB Step pattern size order : BACBADA Scale is not a Constant Structure Scale diversity : 1.315987 Lumma stability : 0.164924 Lumma impropriety factor : 0.495226 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 : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 289/288, 6.0008 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 603.000 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 6 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 17 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 17 Scale harmonicity : 0.021375 Average absolute harmonicity : 0.241897 Specific harmonicity : 0.101571 Fundamental : 1/144, -7.1699 octaves, 1.8168 Hz. Guide tone : 612, 9.2574 octaves, 160114.846 Hz. Exponens Consonantiae : 8.812800E+04, 16.42731 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 60.0, average 8.57143 Mersenne's string divisions : 14804790 Sum of van Prooijen's expressibility: 5.59983, average 0.79998 Sum of Tenney's harmonic distance : 10.94459, average 1.56351 Vogel's harmonic complexity : 15.85714 Wille's k value : 76 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 89.35377, average 3.19121 Lattice compactness (without 2's) : 47.46300, average 1.69511 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.00000 13 1 3: -2 .. 2 -0.14286 7 3 17: 0 .. 1 0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 10 29| Scale is weakly epimorphic with val: <7 11 27| Scale is weakly epimorphic with val: <7 12 32|
FIT/MODE
7: 0 1 2 0 1 2 1 N T3 SD: 60.6170 c. M: 104.9554 c. 8: 0 1 2 1 0 3 1 N SD: 64.6305 c. M: 104.9554 c. 9: 0 1 2 1 1 3 1 N SD: 68.5463 c. M: 104.9554 c. 10: 1 1 2 1 1 3 1 N T3 SD: 19.3907 c. M:-36.0900 c. 12: 1 1 3 1 1 4 1 N T3 SD: 2.8681 c. M: 4.9554 c. 58: 5 5 14 5 5 19 5 N T3 SD: 2.5311 c. M: 4.4937 c. 70: 6 6 17 6 6 23 6 N T3 SD: 2.1882 c. M: 3.9026 c. 82: 7 7 20 7 7 27 7 N T3 SD: 2.0312 c. M: 3.4844 c. 94: 8 8 23 8 8 31 8 N T3 SD: 1.9729 c. M: 3.1731 c. 106: 9 9 26 9 9 35 9 N T3 SD: 1.9656 c. M: 3.0686 c. 111: 10 9 27 10 9 37 9 N SD: 1.7657 c. M:-3.1527 c. 123: 11 10 30 11 10 41 10 N SD: 1.3337 c. M:-2.3617 c. 135: 12 11 33 12 11 45 11 N SD: 0.9876 c. M:-1.7113 c. 147: 13 12 36 13 12 49 12 N SD: 0.7137 c. M:-1.1670 c. 159: 14 13 39 14 13 53 13 N SD: 0.5114 c. M:-0.8414 c. 171: 15 14 42 15 14 57 14 N SD: 0.3959 c. M:-0.7090 c. 183: 16 15 45 16 15 61 15 N SD: 0.3835 c. M: 0.6313 c. 229: 20 19 56 20 19 76 19 N SD: 0.3487 c. M: 0.6087 c. 241: 21 20 59 21 20 80 20 N SD: 0.3580 c. M: 0.6305 c. 364: 32 30 89 32 30 121 30 N SD: 0.3240 c. M:-0.5391 c. 376: 33 31 92 33 31 125 31 N SD: 0.2230 c. M:-0.3637 c. 388: 34 32 95 34 32 129 32 N SD: 0.1293 c. M:-0.2137 c. 400: 35 33 98 35 33 133 33 N SD: 0.0481 c. M:-0.0900 c. 812: 71 67 199 71 67 270 67 N SD: 0.0336 c. M: 0.0602 c. 1212: 106 100 297 106 100 403 100 N SD: 0.0334 c. M: 0.0553 c. 1383: 121 114 339 121 114 460 114 N SD: 0.0241 c. M:-0.0392 c. 1395: 122 115 342 122 115 464 115 N SD: 0.0219 c. M: 0.0390 c. 1783: 156 147 437 156 147 593 147 N SD: 0.0203 c. M:-0.0362 c. 1795: 157 148 440 157 148 597 148 N SD: 0.0076 c. M:-0.0131 c. 2195: 192 181 538 192 181 730 181 N SD: 0.0060 c. M:-0.0104 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 60.8012 cents 4 x x 5 x 6 x 8 S SD: 37.2438 cents 5 x 6 x 7:8:9:10 S SD: 35.9729 cents 6 x 7:8 x 9:11:12 SD: 16.2913 cents 7 x 8:9:10:11:13:14 SD: 18.4576 cents 8 x 9 x 11:12:15:16 SD: 10.6477 cents 9 x 10:12:13:14:17:18 SD: 12.4239 cents 10 x 11:13:14:15:19:20 SD: 10.4850 cents 11:12 x 15:16:17:21:22 SD: 15.5435 cents 12:13:14:16:17:18:23:24 SD: 10.8166 cents 14:15:16:19:20:21:26:28 SD: 7.7763 cents 15:16:17:20:21:23:28:30 SD: 7.1379 cents 16:17:18:21:23:24:30:32 SD: 5.6158 cents 24:26:27:32:34:36:45:48 SD: 5.1376 cents 26:28:29:35:37:39:49:52 SD: 4.7738 cents 30:32:34:40:43:45:57:60 SD: 3.8393 cents 32:34:36:43:45:48:60:64 SD: 3.2198 cents 34:36:38:45:48:51:64:68 SD: 2.8577 cents 46:49:52:61:65:69:87:92 SD: 2.0340 cents 48:51:54:64:68:72:91:96 SD: 0.9076 cents 96:102:108:128:136:144:181:192 SD: 0.4550 cents 144:153:162:192:204:216:272:288 SD: 0.0000 cents