Scala analysis: xen18-ayers-table-49
7 Iterated First Unnamed Means between 1/1 and 2/1
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 5/4 386.313714 major third 2: 4/3 498.044999 perfect fourth 3: 40/27 680.448711 grave fifth 4: 3/2 701.955001 perfect fifth 5: 9/5 1017.596288 just minor seventh, BP seventh 6: 15/8 1088.268715 classic major seventh 7: 255/128 1193.224124 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 256/255 6.7759 septendecimal kleisma 1: 5/4 386.3137 major third 2: 16/15 111.7313 minor diatonic semitone 3: 10/9 182.4037 minor whole tone 4: 81/80 21.5063 syntonic comma, Didymus comma 5: 6/5 315.6413 minor third 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 17/16 104.9554 17th harmonic 8: 256/255 6.7759 septendecimal kleisma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/255 6.776 cents septendecimal kleisma 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 17/16 104.955 cents 17th harmonic 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 1 6/5 315.641 cents minor third 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 425/384 175.628 cents 2: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 243/200 337.148 cents acute minor third 2: 1 5/4 386.314 cents major third 2: 1 64/51 393.090 cents 2: 1 4/3 498.045 cents perfect fourth 3: 1 10/9 182.404 cents minor whole tone 3: 1 6/5 315.641 cents minor third 3: 1 81/64 407.820 cents Pythagorean major third 3: 1 85/64 491.269 cents 3: 1 4/3 498.045 cents perfect fourth 3: 1 1024/765 504.821 cents 3: 1 27/20 519.551 cents acute fourth 3: 1 40/27 680.449 cents grave fifth 4: 1 4/3 498.045 cents perfect fourth 4: 1 1377/1024 512.775 cents 4: 1 25/18 568.717 cents classic augmented fourth 4: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 36/25 631.283 cents classic diminished fifth 4: 1 2048/1377 687.225 cents 4: 1 3/2 701.955 cents perfect fifth 5: 1 27/20 519.551 cents acute fourth 5: 1 40/27 680.449 cents grave fifth 5: 1 765/512 695.179 cents 5: 1 3/2 701.955 cents perfect fifth 5: 1 128/85 708.731 cents 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 3/2 701.955 cents perfect fifth 6: 1 51/32 806.910 cents 6: 1 8/5 813.686 cents minor sixth 6: 1 400/243 862.852 cents grave major sixth 6: 1 27/16 905.865 cents Pythagorean major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 1 768/425 1024.372 cents 6: 1 15/8 1088.269 cents classic major seventh 7: 1 8/5 813.686 cents minor sixth 7: 1 5/3 884.359 cents major sixth, BP sixth 7: 1 9/5 1017.596 cents just minor seventh, BP seventh 7: 1 15/8 1088.269 cents classic major seventh 7: 1 32/17 1095.045 cents 17th subharmonic 7: 1 48/25 1129.328 cents classic diminished octave 7: 1 160/81 1178.494 cents octave - syntonic comma 7: 1 255/128 1193.224 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 8.00000 = 8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 386.3 498.0 680.4 702.0 1017.6 1088.3 1193.2 1200.0 386.3 : 111.7 294.1 315.6 631.3 702.0 806.9 813.7 1200.0 498.0 : 182.4 203.9 519.6 590.2 695.2 702.0 1088.3 1200.0 680.4 : 21.5 337.1 407.8 512.8 519.6 905.9 1017.6 1200.0 702.0 : 315.6 386.3 491.3 498.0 884.4 996.1 1178.5 1200.0 1017.6: 70.7 175.6 182.4 568.7 680.4 862.9 884.4 1200.0 1088.3: 105.0 111.7 498.0 609.8 792.2 813.7 1129.3 1200.0 1193.2: 6.8 393.1 504.8 687.2 708.7 1024.4 1095.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 6.7759 .. 386.3137 cents 1275/1024, 379.5378 cents 256/255, 6.7759 cents 2: 111.7313 .. 498.0450 cents 5/4, 386.3137 cents 64/75,-274.5824 cents 3: 182.4037 .. 680.4487 cents 4/3, 498.0450 cents 5/6,-315.6413 cents 4: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 9/10,-182.4037 cents 5: 519.5513 .. 1017.5963 cents 4/3, 498.0450 cents 9/10,-182.4037 cents 6: 701.9550 .. 1088.2687 cents 5/4, 386.3137 cents 5/6,-315.6413 cents 7: 813.6863 .. 1193.2241 cents 1275/1024, 379.5378 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 256/255, 6.7759 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 22.137360 Largest / Average step : 2.575425 Largest / Smallest step : 57.013105 Median interval of one step : 108.34335 cents, amount: 0 Least squares average step : 175.49869 cents, oct.: 1403.98951 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : HEFBGCDA Scale is not a Constant Structure Scale diversity : 1.520779 Lumma stability : 0.011293 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.312500 redundancy: 0.687500 Efficiency x scale size : 2.500000 Number of different interval sizes : 42 = 6.00000 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 8.00000 = 8 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 256/255, 6.7759 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 3 Most common triad is 0.0 498.045 1193.224 cents, amount: 1 Number of recognisable fifths : 6, average 699.4999 cents Number of appreciable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 37.5000% Scale is differentially coherent in interval class 1 -- Rational properties -- Prime limit : 17 Odd number limit : 1377 (O: 1377 U: 1377) Highest odd numerator or denominator: 255 Scale harmonicity : 0.015094 Average absolute harmonicity : 0.231660 Specific harmonicity : 0.115911 Fundamental : 1/17280, -14.0768 octaves, 0.0151 Hz. Guide tone : 6120, 12.5793 octaves, 1601148.460 Hz. Exponens Consonantiae : 1.057536E+08, 26.65613 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 255.5, average 31.93750 Mersenne's string divisions : 371827890 Sum of van Prooijen's expressibility: 7.62145, average 0.95268 Sum of Tenney's harmonic distance : 14.73896, average 1.84237 Vogel's harmonic complexity : 24.50000 Wille's k value : 17212 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 151.27238, average 4.20201 Lattice compactness (without 2's) : 73.38955, average 2.03860 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -7 .. 3 -0.87500 19 1 3: -3 .. 2 0.12500 9 2 5: -1 .. 1 0.37500 5 4 17: 0 .. 1 0.12500 1 1 Average exponent except 2's : 5 / 8 = 0.62500 Average absolute exponent except 2's: 15 / 8 = 1.87500
FIT/MODE
8: 2 1 1 0 2 1 0 1 N T3 SD: 88.3401 c. M: 143.2241 c. 9: 3 1 1 0 3 0 1 0 N SD: 26.8985 c. M:-49.0704 c. 12: 4 1 2 0 3 1 1 0 N SD: 11.5671 c. M:-19.5513 c. 19: 6 2 3 0 5 1 2 0 N SD: 9.1598 c. M: 14.5845 c. 31: 10 3 5 0 8 2 3 0 N SD: 7.9865 c. M:-16.3255 c. 32: 10 3 5 1 8 2 3 0 N SD: 7.5213 c. M: 11.3137 c. 34: 11 3 5 1 9 2 3 0 N SD: 5.5576 c. M: 9.8605 c. 41: 13 4 6 1 11 2 4 0 N SD: 5.0988 c. M: 7.2780 c. 46: 15 4 7 1 12 3 4 0 N SD: 4.2073 c. M:-7.3835 c. 53: 17 5 8 1 14 3 5 0 N SD: 2.5775 c. M:-6.7759 c. 65: 21 6 10 1 17 4 6 0 N SD: 2.7587 c. M:-6.7759 c. 91: 29 9 14 1 24 6 7 1 N SD: 4.2785 c. M: 6.4109 c. 93: 30 9 14 1 25 5 8 1 N SD: 3.9684 c. M: 6.1274 c. 94: 30 9 14 2 25 5 8 1 N SD: 3.2683 c. M: 5.9901 c. 96: 31 9 14 2 25 6 8 1 N SD: 3.5012 c. M: 5.7241 c. 97: 31 9 15 2 25 6 8 1 N SD: 2.9545 c. M: 5.5953 c. 99: 32 9 15 2 26 6 8 1 N SD: 2.3294 c. M: 5.3453 c. 105: 34 10 16 1 28 6 9 1 N SD: 3.6660 c. M:-5.2656 c. 106: 34 10 16 2 28 6 9 1 N SD: 1.8672 c. M: 4.5449 c. 110: 35 11 16 2 29 7 9 1 N SD: 3.5131 c. M: 4.4955 c. 111: 36 10 17 2 29 7 9 1 N SD: 2.2666 c. M: 4.0349 c. 116: 37 11 18 2 30 7 10 1 N SD: 2.5954 c. M: 3.8032 c. 118: 38 11 18 2 31 7 10 1 N SD: 1.2712 c. M: 3.3936 c. 127: 41 12 19 2 34 7 11 1 N SD: 2.0736 c. M:-2.8762 c. 130: 42 12 20 2 34 8 11 1 N SD: 1.6201 c. M:-2.6282 c. 150: 48 14 23 3 39 9 13 1 N SD: 1.5016 c. M: 2.3137 c. 152: 49 14 23 3 40 9 13 1 N SD: 0.9242 c. M: 1.5013 c. 159: 51 15 24 3 42 9 14 1 N SD: 0.9894 c. M: 1.4763 c. 164: 53 15 25 3 43 10 14 1 N SD: 0.9461 c. M:-1.9752 c. 171: 55 16 26 3 45 10 15 1 N SD: 0.2804 c. M: 0.5494 c. 388: 125 36 59 7 102 23 34 2 N SD: 0.2764 c. M:-0.5903 c. 494: 159 46 75 9 130 29 43 3 N SD: 0.2256 c. M: 0.5116 c. 506: 163 47 77 9 133 30 44 3 N SD: 0.2015 c. M: 0.3387 c. 559: 180 52 85 10 147 33 49 3 N SD: 0.1318 c. M:-0.3358 c. 677: 218 63 103 12 178 40 59 4 N SD: 0.1511 c. M: 0.3142 c. 718: 231 67 109 13 189 42 63 4 N SD: 0.1701 c. M: 0.2464 c. 730: 235 68 111 13 192 43 64 4 N SD: 0.0861 c. M:-0.2005 c. 882: 284 82 134 16 232 52 77 5 N SD: 0.1056 c. M: 0.1766 c. 901: 290 84 137 16 237 53 79 5 N SD: 0.0933 c. M: 0.1444 c. 1053: 339 98 160 19 277 62 92 6 N SD: 0.0565 c. M: 0.1068 c. 1224: 394 114 186 22 322 72 107 7 N SD: 0.0448 c. M: 0.0869 c. 1612: 519 150 245 29 424 95 141 9 N SD: 0.0461 c. M:-0.0761 c. 1783: 574 166 271 32 469 105 156 10 N SD: 0.0194 c. M:-0.0456 c. 1954: 629 182 297 35 514 115 171 11 N SD: 0.0197 c. M: 0.0394 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 0.0000 cents 3 x 4 x x 5 x x 6 S SD: 44.4125 cents 4:5 x x 6:7 x x 8 S SD: 12.1926 cents 5:6:7 x 8:9 x x 10 S SD: 31.3772 cents 6 x 8 x 9:11 x x 12 SD: 7.9417 cents 7:9 x 10:11 x 13 x 14 SD: 22.8939 cents 8:10:11 x 12:14:15 x 16 S SD: 12.0376 cents 9:11:12:13:14:16:17 x 18 SD: 12.7972 cents 10 x 13 x 15:18:19 x 20 SD: 9.8934 cents 11:14:15:16:17:20:21 x 22 SD: 12.3245 cents 12:15:16 x 18:22:23 x 24 SD: 8.2613 cents 13:16:17:19:20:23:24 x 26 SD: 11.0044 cents 14:18:19 x 21:25:26 x 28 SD: 10.2500 cents 15:19:20:22:23:27:28 x 30 SD: 6.9044 cents 16:20:21 x 24:29:30 x 32 SD: 4.9634 cents 17:21:23:25:26:31:32 x 34 SD: 7.6975 cents 18:23:24 x 27:32:34 x 36 SD: 7.5895 cents 19:24:25:28:29:34:36 x 38 SD: 6.8157 cents 20:25:27 x 30:36:38 x 40 SD: 5.2396 cents 21:26:28:31:32:38:39 x 42 SD: 5.3721 cents 22:28:29 x 33:40:41 x 44 SD: 7.0278 cents 23:29:31:34:35:41:43 x 46 SD: 5.5649 cents 24:30:32 x 36:43:45 x 48 SD: 1.3389 cents 25:31:33:37:38:45:47 x 50 SD: 4.6207 cents 26:33:35 x 39:47:49 x 52 SD: 5.5428 cents 27:34:36:40:41:49:51 x 54 SD: 4.4701 cents 28:35:37:41:42:50:53 x 56 SD: 4.7578 cents 29:36:39:43:44:52:54 x 58 SD: 4.3934 cents 30:38:40:44:45:54:56 x 60 SD: 4.2571 cents 31:39:41:46:47:56:58 x 62 SD: 3.8422 cents 32:40:43:47:48:58:60 x 64 SD: 3.3452 cents 33:41:44:49:50:59:62 x 66 SD: 3.4345 cents 34:43:45:50:51:61:64 x 68 SD: 4.0771 cents 35:44:47:52:53:63:66 x 70 SD: 3.6144 cents 36:45:48:53:54:65:68 x 72 SD: 2.5133 cents 37:46:49:55:56:67:69 x 74 SD: 3.7702 cents 38:48:51:56:57:68:71 x 76 SD: 3.7283 cents 39:49:52:58:59:70:73 x 78 SD: 2.7585 cents 40:50:53:59:60:72:75 x 80 SD: 1.8922 cents 41:51:55:61:62:74:77 x 82 SD: 3.0745 cents 42:53:56:62:63:76:79 x 84 SD: 2.9320 cents 43:54:57:64:65:77:81 x 86 SD: 3.3646 cents 44:55:59:65:66:79:83 x 88 SD: 2.2545 cents 45:56:60:67:68:81:84 x 90 SD: 2.6982 cents 46:58:61:68:69:83:86 x 92 SD: 2.7501 cents 47:59:63:70:71:85:88 x 94 SD: 3.0141 cents 48:60:64:71:72:86:90 x 96 SD: 1.2111 cents 49:61:65:73:74:88:92 x 98 SD: 2.7891 cents 50:63:67:74:75:90:94 x 100 SD: 2.4290 cents 51:64:68:76:77:92:96 x 102 SD: 2.6199 cents 52:65:69:77:78:94:98 x 104 SD: 2.0365 cents 53:66:71:79:80:95:99 x 106 SD: 2.9788 cents 54:68:72:80:81:97:101 x 108 SD: 1.9912 cents 55:69:73:81:83:99:103 x 110 SD: 2.5587 cents 56:70:75:83:84:101:105 x 112 SD: 1.2108 cents 57:71:76:84:86:103:107 x 114 SD: 2.3555 cents 58:73:77:86:87:104:109 x 116 SD: 2.3022 cents 59:74:79:87:89:106:111 x 118 SD: 2.4471 cents 60:75:80:89:90:108:113 x 120 SD: 1.1394 cents 61:76:81:90:92:110:114 x 122 SD: 2.3242 cents 62:78:83:92:93:112:116 x 124 SD: 2.1784 cents 63:79:84:93:95:113:118 x 126 SD: 1.9832 cents 64:80:85:95:96:115:120 x 128 SD: 1.1639 cents 72:90:96:107:108:130:135:143:144 SD: 1.1566 cents 88:110:117:130:132:158:165:175:176 SD: 1.0984 cents 96:120:128:142:144:173:180:191:192 SD: 0.5072 cents 120:150:160:178:180:216:225:239:240 SD: 0.2762 cents 216:270:288:320:324:389:405:430:432 SD: 0.1926 cents 264:330:352:391:396:475:495:526:528 SD: 0.1129 cents 384:480:512:569:576:691:720:765:768 SD: 0.0756 cents 480:600:640:711:720:864:900:956:960 SD: 0.0659 cents 600:750:800:889:900:1080:1125:1195:1200 SD: 0.0627 cents