Scala analysis: xen09-chalmers-tritriadic-34-36-51
Tritriadic scale built from 34:36:51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 18/17 98.954592 Arabic lute index finger 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth 4: 24/17 596.999591 1st septendecimal tritone 5: 3/2 701.955001 perfect fifth 6: 27/17 800.909593 septendecimal minor sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 34/27 399.0904 septendecimal major third 1: 18/17 98.9546 Arabic lute index finger 2: 17/16 104.9554 17th harmonic 3: 32/27 294.1350 Pythagorean minor third 4: 18/17 98.9546 Arabic lute index finger 5: 17/16 104.9554 17th harmonic 6: 18/17 98.9546 Arabic lute index finger 7: 34/27 399.0904 septendecimal major third
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 : 99.0 203.9 498.0 597.0 702.0 800.9 1200.0 99.0 : 105.0 399.1 498.0 603.0 702.0 1101.0 1200.0 203.9 : 294.1 393.1 498.0 597.0 996.1 1095.0 1200.0 498.0 : 99.0 203.9 302.9 702.0 800.9 905.9 1200.0 597.0 : 105.0 203.9 603.0 702.0 806.9 1101.0 1200.0 702.0 : 99.0 498.0 597.0 702.0 996.1 1095.0 1200.0 800.9 : 399.1 498.0 603.0 897.1 996.1 1101.0 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 : 150.74386 cents, oct.: 1055.20703 cents Scale is not proper Step pattern alph. order: ABCABAD Step pattern size order : ABCABAD 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 98.955 701.955 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 4 Length of longest subharmonic part : 2 at degree 0 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: 27 Scale harmonicity : 0.021375 Average absolute harmonicity : 0.241232 Specific harmonicity : 0.101571 Fundamental : 1/408, -8.6724 octaves, 0.6412 Hz. Guide tone : 216, 7.7549 octaves, 56511.122 Hz. Exponens Consonantiae : 8.812800E+04, 16.42731 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 76.0, average 10.85714 Mersenne's string divisions : 3220140 Sum of van Prooijen's expressibility: 5.80075, average 0.82868 Sum of Tenney's harmonic distance : 11.77389, average 1.68198 Vogel's harmonic complexity : 19.57143 Wille's k value : 229 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 85.21215, average 3.04329 Lattice compactness (without 2's) : 49.62528, average 1.77233 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.42857 11 1 3: -1 .. 3 1.14286 10 3 17: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714 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: 1 0 2 0 1 1 2 N T3 SD: 49.0463 c. M: 82.7139 c. 10: 1 1 2 1 1 1 3 N T3 SD: 23.7056 c. M:-39.0904 c. 12: 1 1 3 1 1 1 4 N T3 SD: 2.1992 c. M: 3.9100 c. 82: 7 7 20 7 7 7 27 N T3 SD: 2.3390 c. M:-3.9685 c. 87: 7 8 21 7 8 7 29 N SD: 2.2412 c. M: 3.8961 c. 94: 8 8 23 8 8 8 31 N T3 SD: 2.0854 c. M:-3.3457 c. 99: 8 9 24 8 9 8 33 N SD: 1.7349 c. M: 3.0602 c. 106: 9 9 26 9 9 9 35 N T3 SD: 1.9210 c. M:-3.0004 c. 111: 9 10 27 9 10 9 37 N SD: 1.3476 c. M: 2.4050 c. 123: 10 11 30 10 11 10 41 N SD: 1.0489 c. M: 1.8776 c. 135: 11 12 33 11 12 11 45 N SD: 0.8217 c. M: 1.4440 c. 147: 12 13 36 12 13 12 49 N SD: 0.6581 c. M: 1.0812 c. 159: 13 14 39 13 14 13 53 N SD: 0.5556 c. M: 0.9096 c. 171: 14 15 42 14 15 14 57 N SD: 0.5113 c. M: 0.9096 c. 229: 19 20 56 19 20 19 76 N SD: 0.4674 c. M:-0.8371 c. 241: 20 21 59 20 21 20 80 N SD: 0.4321 c. M:-0.7502 c. 253: 21 22 62 21 22 21 84 N SD: 0.4262 c. M:-0.6714 c. 352: 29 31 86 29 31 29 117 N SD: 0.3448 c. M:-0.6355 c. 364: 30 32 89 30 32 30 121 N SD: 0.2619 c. M:-0.4856 c. 376: 31 33 92 31 33 31 125 N SD: 0.1850 c. M:-0.3453 c. 388: 32 34 95 32 34 32 129 N SD: 0.1146 c. M:-0.2137 c. 400: 33 35 98 33 35 33 133 N SD: 0.0565 c. M:-0.0904 c. 412: 34 36 101 34 36 34 137 N SD: 0.0508 c. M:-0.0878 c. 812: 67 71 199 67 71 67 270 N SD: 0.0427 c. M:-0.0756 c. 1224: 101 107 300 101 107 101 407 N SD: 0.0430 c. M:-0.0708 c. 1371: 113 120 336 113 120 113 456 N SD: 0.0354 c. M: 0.0630 c. 1383: 114 121 339 114 121 114 460 N SD: 0.0258 c. M: 0.0419 c. 1783: 147 156 437 147 156 147 593 N SD: 0.0157 c. M: 0.0282 c. 1795: 148 157 440 148 157 148 597 N SD: 0.0102 c. M: 0.0182 c. 2195: 181 192 538 181 192 181 730 N SD: 0.0046 c. M:-0.0080 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 x 5:6 S SD: 27.8164 cents 4 x x 5 x 6 x 8 S SD: 37.2438 cents 5 x 6 x 7 x 8:10 S SD: 28.3472 cents 6 x 7:8 x 9:10:12 S SD: 20.9073 cents 7 x 8:9:10 x 11:14 SD: 14.7870 cents 8 x 9 x 11:12:13:16 SD: 12.0936 cents 9 x 10:12:13 x 14:18 SD: 11.5372 cents 10 x 11:13:14:15:16:20 SD: 10.2848 cents 11:12 x 15:16 x 17:22 SD: 19.0688 cents 12:13:14:16:17:18:19:24 SD: 10.6888 cents 14:15:16:19:20:21:22:28 SD: 7.6412 cents 15:16:17:20:21:23:24:30 SD: 6.6201 cents 17:18:19:23:24:26:27:34 SD: 6.2233 cents 22:23:25:29:31:33:35:44 SD: 4.9433 cents 24:25:27:32:34:36:38:48 SD: 4.2004 cents 30:32:34:40:42:45:48:60 SD: 3.7786 cents 32:34:36:43:45:48:51:64 SD: 2.4721 cents 34:36:38:45:48:51:54:68 SD: 2.4416 cents 46:49:52:61:65:69:73:92 SD: 2.3546 cents 48:51:54:64:68:72:76:96 SD: 1.4333 cents 66:70:74:88:93:99:105:132 SD: 1.1233 cents 88:93:99:117:124:132:140:176 SD: 1.0525 cents 90:95:101:120:127:135:143:180 SD: 0.9908 cents 102:108:115:136:144:153:162:204 SD: 0.5382 cents 136:144:153:181:192:204:216:272 SD: 0.4550 cents 168:178:189:224:237:252:267:336 SD: 0.2956 cents 240:254:270:320:339:360:381:480 SD: 0.2069 cents 306:324:344:408:432:459:486:612 SD: 0.1797 cents 408:432:459:544:576:612:648:816 SD: 0.0000 cents