Scala analysis: xen15-chalmers-triadic-diamond-34-27
Triadic diamond for M=34/27, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/68 302.864594 Persian wosta 2: 34/27 399.090407 septendecimal major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 27/17 800.909593 septendecimal minor sixth 6: 136/81 897.135406 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 81/68 302.8646 Persian wosta 1: 81/68 302.8646 Persian wosta 2: 2312/2187 96.2258 3: 18/17 98.9546 Arabic lute index finger 4: 9/8 203.9100 major whole tone 5: 18/17 98.9546 Arabic lute index finger 6: 2312/2187 96.2258 7: 81/68 302.8646 Persian wosta
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 2312/2187 96.226 cents 1: 2 18/17 98.955 cents Arabic lute index finger 1: 1 9/8 203.910 cents major whole tone 1: 2 81/68 302.865 cents Persian wosta 2: 2 272/243 195.180 cents Persian whole tone 2: 2 81/68 302.865 cents Persian wosta 2: 2 34/27 399.090 cents septendecimal major third 2: 1 6561/4624 605.729 cents two (Persian wosta) 3: 2 34/27 399.090 cents septendecimal major third 3: 1 729/578 401.819 cents 3: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 4: 2 4/3 498.045 cents perfect fourth 4: 2 3/2 701.955 cents perfect fifth 4: 1 1156/729 798.181 cents two (septendecimal major third) 4: 2 27/17 800.910 cents septendecimal minor sixth 5: 1 9248/6561 594.271 cents 5: 2 27/17 800.910 cents septendecimal minor sixth 5: 2 136/81 897.135 cents 5: 2 243/136 1004.820 cents 6: 2 136/81 897.135 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 17/9 1101.045 cents septendecimal major seventh 6: 2 2187/1156 1103.774 cents 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 : 302.9 399.1 498.0 702.0 800.9 897.1 1200.0 302.9 : 96.2 195.2 399.1 498.0 594.3 897.1 1200.0 399.1 : 99.0 302.9 401.8 498.0 800.9 1103.8 1200.0 498.0 : 203.9 302.9 399.1 702.0 1004.8 1101.0 1200.0 702.0 : 99.0 195.2 498.0 800.9 897.1 996.1 1200.0 800.9 : 96.2 399.1 702.0 798.2 897.1 1101.0 1200.0 897.1 : 302.9 605.7 702.0 800.9 1004.8 1103.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 96.2258 .. 302.8646 cents 177147/157216, 206.6388 cents 2312/2187, 96.2258 cents 2: 195.1804 .. 605.7292 cents 1594323/1257728, 410.5488 cents 18496/19683,-107.6842 cents 3: 399.0904 .. 701.9550 cents 81/68, 302.8646 cents 157216/177147,-206.6388 cents 4: 498.0450 .. 800.9096 cents 81/68, 302.8646 cents 8/9,-203.9100 cents 5: 594.2708 .. 1004.8196 cents 1594323/1257728, 410.5488 cents 157216/177147,-206.6388 cents 6: 897.1354 .. 1103.7742 cents 177147/157216, 206.6388 cents 18496/19683,-107.6842 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 2312/2187, 96.2258 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 81/68, 302.8646 cents Average / Smallest step : 1.781524 Largest / Average step : 1.766710 Largest / Smallest step : 3.147436 Median interval of one step : 18/17, 98.9546 cents, amount: 2 Least squares average step : 165.64543 cents, oct.: 1159.51804 cents Scale is not proper Scale is a mode of a 2195-tone equal temperament with octave 2/1 degrees: 554 730 911 1284 1465 1641 2195 Least number of segments generator : 1098 of 600.273 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1252 of 684.465 cents and inv. generated superset size: 91 = 84 more = 1300.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCBA Step pattern size order : DABCBAD Scale is not a Constant Structure Scale diversity : 1.310194 Lumma stability : 0.160376 Lumma impropriety factor : 0.514323 Rothenberg efficiency : 0.506122 redundancy: 0.493878 Efficiency x scale size : 3.542857 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 : 19683/19652, 2.7288 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 17 27 81 Formal octave complements present : 7 = 100.0000% Scale is differentially coherent in interval classes 3 and 4 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 17 Odd number limit : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.011552 Average absolute harmonicity : 0.226432 Specific harmonicity : 0.062612 Fundamental : 1/5508, -12.4273 octaves, 0.0475 Hz. Guide tone : 11016, 13.4273 octaves, 2882067.227 Hz. Exponens Consonantiae : 6.067613E+07, 25.85463 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 243.0, average 34.71429 Mersenne's string divisions : 1301726580 Sum of van Prooijen's expressibility: 7.63394, average 1.09056 Sum of Tenney's harmonic distance : 15.56604, average 2.22372 Vogel's harmonic complexity : 31.57143 Wille's k value : 3280 Wilson's harmonic complexity : 58 Rectangular lattice diameter : 10 Triangular lattice diameter : 8 Lattice compactness : 114.15290, average 4.07689 Lattice compactness (without 2's) : 95.51346, average 3.41120 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 10 1 3: -4 .. 4 0.00000 16 2 17: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 20 / 7 = 2.85714 Scale is weakly epimorphic with val: <7 10 31| Scale is weakly epimorphic with val: <7 10 32| Scale is weakly epimorphic with val: <7 11 31| Scale is weakly epimorphic with val: <7 11 32| Scale is weakly epimorphic with val: <7 12 26| Scale is weakly epimorphic with val: <7 12 30|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 37.8921 c. M: 56.2333 c. 8: 2 1 0 2 0 1 2 N I SD: 37.4483 c. M:-50.9096 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 27.0258 c. M: 36.1979 c. 12: 3 1 1 2 1 1 3 N I SD: 1.9165 c. M:-2.8646 c. Mela Yagapriya, Raga Kalahamsa 63: 16 5 5 11 5 5 16 N I SD: 1.8751 c. M: 2.8069 c. 75: 19 6 6 13 6 6 19 N I SD: 1.3415 c. M:-2.0450 c. 87: 22 7 7 15 7 7 22 N I SD: 0.9853 c. M: 1.4933 c. 99: 25 8 8 17 8 8 25 N I SD: 0.7580 c. M:-1.0753 c. 111: 28 9 9 19 9 9 28 N I SD: 0.6353 c. M:-0.9096 c. 123: 31 10 10 21 10 10 31 N I SD: 0.5959 c. M:-0.9096 c. 241: 61 19 20 41 20 19 61 N I SD: 0.6173 c. M:-0.8698 c. 253: 64 20 21 43 21 20 64 N I SD: 0.5158 c. M:-0.6927 c. 265: 67 21 22 45 22 21 67 N I SD: 0.4300 c. M: 0.5998 c. 277: 70 22 23 47 23 22 70 N I SD: 0.3609 c. M:-0.5345 c. 289: 73 23 24 49 24 23 73 N I SD: 0.3108 c. M:-0.4745 c. 301: 76 24 25 51 25 24 76 N I SD: 0.2818 c. M:-0.4193 c. 313: 79 25 26 53 26 25 79 N I SD: 0.2745 c. M:-0.3684 c. 376: 95 30 31 64 31 30 95 N I SD: 0.2141 c. M:-0.3269 c. 388: 98 31 32 66 32 31 98 N I SD: 0.1495 c. M:-0.2282 c. 400: 101 32 33 68 33 32 101 N I SD: 0.0903 c. M:-0.1354 c. 412: 104 33 34 70 34 33 104 N I SD: 0.0422 c. M: 0.0613 c. 836: 211 67 69 142 69 67 211 N I SD: 0.0337 c. M:-0.0473 c. 1347: 340 108 111 229 111 108 340 N I SD: 0.0327 c. M:-0.0495 c. 1359: 343 109 112 231 112 109 343 N I SD: 0.0223 c. M:-0.0318 c. 1771: 447 142 146 301 146 142 447 N I SD: 0.0143 c. M: 0.0213 c. 1783: 450 143 147 303 147 143 450 N I SD: 0.0081 c. M:-0.0122 c. 2195: 554 176 181 373 181 176 554 N I SD: 0.0038 c. M:-0.0056 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: 4.2589 cents 4 x 5 x 6 x 7:8 S SD: 18.2050 cents 5:6 x 7 x 8 x 10 S SD: 21.5946 cents 6:7 x 8:9 x 10:12 S SD: 7.6388 cents 7:8:9 x x 11:12:14 SD: 17.9664 cents 8 x 10:11:12:13 x 16 SD: 13.5216 cents 9:11 x 12 x 14:15:18 SD: 11.7352 cents 10:12 x 13:15:16:17:20 SD: 8.6765 cents 11:13:14:15 x 17:18:22 SD: 13.1847 cents 12:14:15:16:18:19:20:24 S SD: 5.8041 cents 20:24:25:27:30:32:34:40 SD: 5.3734 cents 22:26:28:29:33:35:37:44 SD: 4.3659 cents 26:31:33:35:39:41:44:52 SD: 4.0487 cents 27:32:34:36:41:43:45:54 SD: 3.8151 cents 30:36:38:40:45:48:50:60 S SD: 3.4783 cents 32:38:40:43:48:51:54:64 SD: 3.1481 cents 36:43:45:48:54:57:60:72 SD: 2.7761 cents 42:50:53:56:63:67:71:84 SD: 2.0752 cents 46:55:58:61:69:73:77:92 SD: 1.8391 cents 54:64:68:72:81:86:91:108 SD: 1.6847 cents 58:69:73:77:87:92:97:116 SD: 1.5183 cents 66:79:83:88:99:105:111:132 SD: 1.3758 cents 78:93:98:104:117:124:131:156 SD: 0.6549 cents 146:174:184:195:219:232:245:292 SD: 0.5186 cents 162:193:204:216:243:257:272:324 SD: 0.2854 cents 240:286:302:320:360:381:403:480 SD: 0.2389 cents 324:386:408:432:486:515:544:648 SD: 0.2014 cents 408:486:514:544:612:648:685:816 SD: 0.1078 cents 486:579:612:648:729:772:816:972 SD: 0.0533 cents