Scala analysis: xen18-ayers-table-45
Complementary Ratios to 3 Fibonacci-Type Means for Lower Tetrachord Between 1/1 and 4/3
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6/5 315.641287 minor third 2: 26/21 369.746754 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 21/13 830.253246 6: 5/3 884.358713 major sixth, BP sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 6/5 315.6413 minor third 2: 65/63 54.1055 3: 14/13 128.2982 2/3-tone 4: 9/8 203.9100 major whole tone 5: 14/13 128.2982 2/3-tone 6: 65/63 54.1055 7: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 65/63 54.105 cents 1: 2 14/13 128.298 cents 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 6/5 315.641 cents minor third 2: 2 10/9 182.404 cents minor whole tone 2: 2 63/52 332.208 cents 2: 2 26/21 369.747 cents 2: 1 36/25 631.283 cents classic diminished fifth 3: 2 5/4 386.314 cents major third 3: 1 441/338 460.506 cents 3: 2 4/3 498.045 cents perfect fourth 3: 2 52/35 685.388 cents 4: 2 35/26 514.612 cents 4: 2 3/2 701.955 cents perfect fifth 4: 1 676/441 739.494 cents 4: 2 8/5 813.686 cents minor sixth 5: 1 25/18 568.717 cents classic augmented fourth 5: 2 21/13 830.253 cents 5: 2 104/63 867.792 cents 5: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 13/7 1071.702 cents 16/3-tone 6: 2 126/65 1145.895 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 : 315.6 369.7 498.0 702.0 830.3 884.4 1200.0 315.6 : 54.1 182.4 386.3 514.6 568.7 884.4 1200.0 369.7 : 128.3 332.2 460.5 514.6 830.3 1145.9 1200.0 498.0 : 203.9 332.2 386.3 702.0 1017.6 1071.7 1200.0 702.0 : 128.3 182.4 498.0 813.7 867.8 996.1 1200.0 830.3 : 54.1 369.7 685.4 739.5 867.8 1071.7 1200.0 884.4 : 315.6 631.3 685.4 813.7 1017.6 1145.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.1055 .. 315.6413 cents 378/325, 261.5358 cents 65/63, 54.1055 cents 2: 182.4037 .. 631.2826 cents 162/125, 448.8789 cents 25/27,-133.2376 cents 3: 386.3137 .. 685.3880 cents 208/175, 299.0743 cents 125/144,-244.9689 cents 4: 514.6120 .. 813.6863 cents 208/175, 299.0743 cents 1225/1352,-170.7761 cents 5: 568.7174 .. 1017.5963 cents 162/125, 448.8789 cents 125/144,-244.9689 cents 6: 884.3587 .. 1145.8945 cents 378/325, 261.5358 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 65/63, 54.1055 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 3.168415 Largest / Average step : 1.841241 Largest / Smallest step : 5.833815 Median interval of one step : 14/13, 128.2982 cents, amount: 2 Least squares average step : 165.81792 cents, oct.: 1160.72542 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DABCBAD Scale is a Constant Structure, by a margin of 16.56696 cents Scale diversity : 1.507185 Lumma stability : 0.090176 Lumma impropriety factor : 0.578206 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 24 = 4.00000 / 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 : 105/104, 16.5670 cents Number of recognisable fifths : 2, average 701.9550 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 100.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 13 Odd number limit : 441 (O: 441 U: 441) Highest odd numerator or denominator: 21 Scale harmonicity : 0.011626 Average absolute harmonicity : 0.250403 Specific harmonicity : 0.097896 Fundamental : 1/2730, -11.4147 octaves, 0.0958 Hz. Guide tone : 5460, 12.4147 octaves, 1428475.587 Hz. Exponens Consonantiae : 1.490580E+07, 23.82937 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 57.5, average 8.21429 Mersenne's string divisions : 7382760 Sum of van Prooijen's expressibility: 4.99662, average 0.71380 Sum of Tenney's harmonic distance : 9.98493, average 1.42642 Vogel's harmonic complexity : 29.57143 Wille's k value : 2047 Wilson's harmonic complexity : 56 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 60.71957, average 2.16856 Lattice compactness (without 2's) : 47.83273, average 1.70831 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 6 1 3: -1 .. 1 0.00000 6 2 5: -1 .. 1 0.00000 2 2 7: -1 .. 1 0.00000 2 13: -1 .. 1 0.00000 2 2 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 15 18 27| Scale is weakly epimorphic with val: <7 10 15 18 29| Scale is weakly epimorphic with val: <7 10 15 19 28| Scale is weakly epimorphic with val: <7 10 15 20 24| Scale is weakly epimorphic with val: <7 10 15 20 29| Scale is weakly epimorphic with val: <7 10 15 21 25| Scale is weakly epimorphic with val: <7 10 15 22 24| Scale is weakly epimorphic with val: <7 10 15 22 26| Scale is weakly epimorphic with val: <7 10 16 18 26| Scale is weakly epimorphic with val: <7 10 16 19 24| Scale is weakly epimorphic with val: <7 10 16 19 27| Scale is weakly epimorphic with val: <7 10 16 20 25| Scale is weakly epimorphic with val: <7 10 16 20 28| Scale is weakly epimorphic with val: <7 10 16 21 26| Scale is weakly epimorphic with val: <7 10 16 21 29| Scale is weakly epimorphic with val: <7 10 16 22 27| Scale is weakly epimorphic with val: <7 10 18 18 26| Scale is weakly epimorphic with val: <7 10 18 19 24| Scale is weakly epimorphic with val: <7 10 18 19 27| Scale is weakly epimorphic with val: <7 10 18 20 25| Scale is weakly epimorphic with val: <7 10 18 20 28| Scale is weakly epimorphic with val: <7 10 18 21 26| Scale is weakly epimorphic with val: <7 10 18 21 29| Scale is weakly epimorphic with val: <7 10 18 22 27| Scale is weakly epimorphic with val: <7 11 16 18 28| Scale is weakly epimorphic with val: <7 11 16 19 24| Scale is weakly epimorphic with val: <7 11 16 19 29| Scale is weakly epimorphic with val: <7 11 16 20 25| Scale is weakly epimorphic with val: <7 11 16 21 24| Scale is weakly epimorphic with val: <7 11 16 21 26| Scale is weakly epimorphic with val: <7 11 16 22 25| Scale is weakly epimorphic with val: <7 11 16 22 27| Scale is JI-epimorphic with val: <7 11 17 18 24| Scale is weakly epimorphic with val: <7 11 17 18 27| Scale is JI-epimorphic with val: <7 11 17 19 25| Scale is weakly epimorphic with val: <7 11 17 19 28| Scale is JI-epimorphic with val: <7 11 17 20 26| Scale is weakly epimorphic with val: <7 11 17 20 29| Scale is JI-epimorphic with val: <7 11 17 21 27| Scale is weakly epimorphic with val: <7 11 17 22 24| Scale is JI-epimorphic with val: <7 11 17 22 28| Scale is weakly epimorphic with val: <7 12 15 18 24| Scale is weakly epimorphic with val: <7 12 15 18 29| Scale is weakly epimorphic with val: <7 12 15 19 25| Scale is weakly epimorphic with val: <7 12 15 20 24| Scale is weakly epimorphic with val: <7 12 15 20 26| Scale is weakly epimorphic with val: <7 12 15 21 25| Scale is weakly epimorphic with val: <7 12 15 21 27| Scale is weakly epimorphic with val: <7 12 15 22 26| Scale is weakly epimorphic with val: <7 12 15 22 28| Scale is weakly epimorphic with val: <7 12 16 18 24| Scale is weakly epimorphic with val: <7 12 16 18 29| Scale is weakly epimorphic with val: <7 12 16 19 25| Scale is weakly epimorphic with val: <7 12 16 20 24| Scale is weakly epimorphic with val: <7 12 16 20 26| Scale is weakly epimorphic with val: <7 12 16 21 25| Scale is weakly epimorphic with val: <7 12 16 21 27| Scale is weakly epimorphic with val: <7 12 16 22 26| Scale is weakly epimorphic with val: <7 12 16 22 28| Scale is weakly epimorphic with val: <7 12 18 18 26| Scale is weakly epimorphic with val: <7 12 18 18 27| Scale is weakly epimorphic with val: <7 12 18 19 27| Scale is weakly epimorphic with val: <7 12 18 19 28| Scale is weakly epimorphic with val: <7 12 18 20 28| Scale is weakly epimorphic with val: <7 12 18 20 29| Scale is weakly epimorphic with val: <7 12 18 21 29| Scale is weakly epimorphic with val: <7 12 18 22 24|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 22.2166 c. M: 27.2159 c. 12: 3 1 1 2 1 1 3 N I SD: 18.2344 c. M: 30.2532 c. Mela Yagapriya, Raga Kalahamsa 16: 4 1 2 2 2 1 4 N I SD: 16.8931 c. M:-26.9550 c. 19: 5 1 2 3 2 1 5 N I SD: 6.2513 c. M: 9.2006 c. 39: 10 2 4 7 4 2 10 N I SD: 5.2473 c. M: 7.9490 c. 46: 12 2 5 8 5 2 12 N I SD: 3.0701 c. M: 4.5294 c. 65: 17 3 7 11 7 3 17 N I SD: 1.0229 c. M:-1.7951 c. 133: 35 6 14 23 14 6 35 N I SD: 0.9724 c. M: 1.8044 c. 140: 37 6 15 24 15 6 37 N I SD: 1.1276 c. M: 1.5016 c. 152: 40 7 16 26 16 7 40 N I SD: 0.7901 c. M: 1.3059 c. 159: 42 7 17 27 17 7 42 N I SD: 0.7179 c. M:-1.3398 c. 178: 47 8 19 30 19 8 47 N I SD: 0.9626 c. M:-1.2126 c. 198: 52 9 21 34 21 9 52 N I SD: 0.6321 c. M:-1.0753 c. 205: 54 9 22 35 22 9 54 N I SD: 0.6270 c. M: 0.9663 c. 217: 57 10 23 37 23 10 57 N I SD: 0.5037 c. M: 0.7602 c. 224: 59 10 24 38 24 10 59 N I SD: 0.2532 c. M: 0.4301 c. 289: 76 13 31 49 31 13 76 N I SD: 0.1640 c. M:-0.2249 c. 513: 135 23 55 87 55 23 135 N I SD: 0.1573 c. M:-0.2006 c. 646: 170 29 69 110 69 29 170 N I SD: 0.1460 c. M:-0.2122 c. 665: 175 30 71 113 71 30 175 N I SD: 0.1238 c. M:-0.1781 c. 711: 187 32 76 121 76 32 187 N I SD: 0.1080 c. M:-0.1547 c. 730: 192 33 78 124 78 33 192 N I SD: 0.0666 c. M: 0.1163 c. 954: 251 43 102 162 102 43 251 N I SD: 0.0666 c. M:-0.0820 c. 1019: 268 46 109 173 109 46 268 N I SD: 0.0544 c. M:-0.0904 c. 1376: 362 62 147 234 147 62 362 N I SD: 0.0534 c. M:-0.0799 c. 1441: 379 65 154 245 154 65 379 N I SD: 0.0340 c. M: 0.0575 c. 1665: 438 75 178 283 178 75 438 N I SD: 0.0251 c. M:-0.0344 c. 2395: 630 108 256 407 256 108 630 N I SD: 0.0158 c. M: 0.0236 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: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 21.5191 cents 5:6 x 7 x 8 x 10 S SD: 21.5191 cents 6:7 x 8:9 x 10:12 S SD: 9.7541 cents 7:8 x 9 x 11:12:14 SD: 25.1065 cents 8 x 10:11:12:13 x 16 SD: 11.3455 cents 9 x 11:12:14 x 15:18 SD: 13.3613 cents 10:12 x 13:15:16:17:20 SD: 9.6766 cents 11:13:14:15:17:18 x 22 SD: 14.5903 cents 12:14:15:16:18:19:20:24 S SD: 8.8718 cents 13 x 16:17:20:21:22:26 SD: 10.3487 cents 14:17 x 19:21 x 23:28 SD: 8.8977 cents 15:18:19:20:23:24:25:30 SD: 8.1846 cents 16:19:20:21:24:26:27:32 SD: 6.2507 cents 18 x 22:24:27:29:30:36 SD: 3.8008 cents 23:28 x 31:35:37:38:46 SD: 7.2103 cents 24:29:30:32:36:39:40:48 SD: 3.2688 cents 30:36:37:40:45:48:50:60 SD: 2.5514 cents 42:50:52:56:63:68:70:84 SD: 2.0488 cents 50:60:62:67:75:81:83:100 SD: 1.7739 cents 54:65:67:72:81:87:90:108 SD: 1.1352 cents 60:72:74:80:90:97:100:120 SD: 0.9730 cents 84:101:104:112:126:136:140:168 SD: 0.7444 cents 96:115:119:128:144:155:160:192 SD: 0.5367 cents 114:137:141:152:171:184:190:228 SD: 0.4858 cents 156:187:193:208:234:252:260:312 SD: 0.3215 cents 180:216:223:240:270:291:300:360 SD: 0.2522 cents 210:252:260:280:315:339:350:420 SD: 0.1683 cents 294:353:364:392:441:475:490:588 SD: 0.1458 cents 390:468:483:520:585:630:650:780 SD: 0.0732 cents 450:540:557:600:675:727:750:900 SD: 0.0686 cents