Scala analysis: xen18-ayers-table-62
7 Iterated Fourth 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: 256/255 6.775876 septendecimal kleisma 2: 16/15 111.731285 minor diatonic semitone 3: 10/9 182.403712 minor whole tone 4: 4/3 498.044999 perfect fourth 5: 27/20 519.551289 acute fourth 6: 3/2 701.955001 perfect fifth 7: 8/5 813.686286 minor sixth 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 5/4 386.3137 major third 1: 256/255 6.7759 septendecimal kleisma 2: 17/16 104.9554 17th harmonic 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 6/5 315.6413 minor third 5: 81/80 21.5063 syntonic comma, Didymus comma 6: 10/9 182.4037 minor whole tone 7: 16/15 111.7313 minor diatonic semitone 8: 5/4 386.3137 major third
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 : 6.8 111.7 182.4 498.0 519.6 702.0 813.7 1200.0 6.8 : 105.0 175.6 491.3 512.8 695.2 806.9 1193.2 1200.0 111.7 : 70.7 386.3 407.8 590.2 702.0 1088.3 1095.0 1200.0 182.4 : 315.6 337.1 519.6 631.3 1017.6 1024.4 1129.3 1200.0 498.0 : 21.5 203.9 315.6 702.0 708.7 813.7 884.4 1200.0 519.6 : 182.4 294.1 680.4 687.2 792.2 862.9 1178.5 1200.0 702.0 : 111.7 498.0 504.8 609.8 680.4 996.1 1017.6 1200.0 813.7 : 386.3 393.1 498.0 568.7 884.4 905.9 1088.3 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 : 121.93588 cents, oct.: 975.48706 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : ADCGBFEH 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 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 : 0.228828 Specific harmonicity : 0.115911 Fundamental : 1/3060, -11.5793 octaves, 0.0855 Hz. Guide tone : 34560, 15.0768 octaves, 9041779.537 Hz. Exponens Consonantiae : 1.057536E+08, 26.65613 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 318.0, average 39.75000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.62145, average 0.95268 Sum of Tenney's harmonic distance : 15.64205, average 1.95526 Vogel's harmonic complexity : 27.62500 Wille's k value : 2065 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: -2 .. 8 2.00000 22 1 3: -2 .. 3 -0.12500 9 2 5: -1 .. 1 -0.37500 5 4 17: -1 .. 0 -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: 0 0 1 2 0 1 1 3 N SD: 66.3101 c. M: 111.7313 c. 9: 0 1 0 3 0 1 1 3 N SD: 26.8985 c. M: 49.0704 c. 12: 0 1 1 3 0 2 1 4 N SD: 11.5671 c. M: 19.5513 c. 19: 0 2 1 5 0 3 2 6 N SD: 9.1598 c. M:-14.5845 c. 31: 0 3 2 8 0 5 3 10 N SD: 7.9865 c. M: 16.3255 c. 32: 0 3 2 8 1 5 3 10 N SD: 7.5213 c. M:-11.3137 c. 34: 0 3 2 9 1 5 3 11 N SD: 5.5576 c. M:-9.8605 c. 41: 0 4 2 11 1 6 4 13 N SD: 5.0988 c. M:-7.2780 c. 46: 0 4 3 12 1 7 4 15 N SD: 4.2073 c. M: 7.3835 c. 53: 0 5 3 14 1 8 5 17 N SD: 2.5775 c. M: 6.7759 c. 65: 0 6 4 17 1 10 6 21 N SD: 2.7587 c. M: 6.7759 c. 92: 1 8 5 24 2 14 8 30 N SD: 3.7501 c. M:-6.2676 c. 94: 1 8 5 25 2 14 9 30 N SD: 3.2683 c. M:-5.9901 c. 96: 1 8 6 25 2 14 9 31 N SD: 3.5012 c. M:-5.7241 c. 97: 1 8 6 25 2 15 9 31 N SD: 2.9545 c. M:-5.5953 c. 99: 1 8 6 26 2 15 9 32 N SD: 2.3294 c. M:-5.3453 c. 106: 1 9 6 28 2 16 10 34 N SD: 1.8672 c. M:-4.5449 c. 111: 1 9 7 29 2 17 10 36 N SD: 2.2666 c. M:-4.0349 c. 116: 1 10 7 30 2 18 11 37 N SD: 2.5954 c. M:-3.8032 c. 118: 1 10 7 31 2 18 11 38 N SD: 1.2712 c. M:-3.3936 c. 127: 1 11 7 34 2 19 12 41 N SD: 2.0736 c. M: 2.8762 c. 130: 1 11 8 34 2 20 12 42 N SD: 1.6201 c. M: 2.6282 c. 150: 1 13 9 39 3 23 14 48 N SD: 1.5016 c. M:-2.3137 c. 152: 1 13 9 40 3 23 14 49 N SD: 0.9242 c. M:-1.5013 c. 159: 1 14 9 42 3 24 15 51 N SD: 0.9894 c. M:-1.4763 c. 164: 1 14 10 43 3 25 15 53 N SD: 0.9461 c. M: 1.9752 c. 171: 1 15 10 45 3 26 16 55 N SD: 0.2804 c. M:-0.5494 c. 388: 2 34 23 102 7 59 36 125 N SD: 0.2764 c. M: 0.5903 c. 494: 3 43 29 130 9 75 46 159 N SD: 0.2256 c. M:-0.5116 c. 506: 3 44 30 133 9 77 47 163 N SD: 0.2015 c. M:-0.3387 c. 559: 3 49 33 147 10 85 52 180 N SD: 0.1318 c. M: 0.3358 c. 677: 4 59 40 178 12 103 63 218 N SD: 0.1511 c. M:-0.3142 c. 718: 4 63 42 189 13 109 67 231 N SD: 0.1701 c. M:-0.2464 c. 730: 4 64 43 192 13 111 68 235 N SD: 0.0861 c. M: 0.2005 c. 882: 5 77 52 232 16 134 82 284 N SD: 0.1056 c. M:-0.1766 c. 901: 5 79 53 237 16 137 84 290 N SD: 0.0933 c. M:-0.1444 c. 1053: 6 92 62 277 19 160 98 339 N SD: 0.0565 c. M:-0.1068 c. 1224: 7 107 72 322 22 186 114 394 N SD: 0.0448 c. M:-0.0869 c. 1612: 9 141 95 424 29 245 150 519 N SD: 0.0461 c. M: 0.0761 c. 1783: 10 156 105 469 32 271 166 574 N SD: 0.0194 c. M: 0.0456 c. 1954: 11 171 115 514 35 297 182 629 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 x x 3 x 4 S SD: 0.0000 cents 3 x x x 4 x x 5:6 S SD: 23.5575 cents 4 x x x 5 x 6 x 8 S SD: 37.2438 cents 5 x x 6 x 7 x 8:10 S SD: 36.8412 cents 6 x x 7:8 x 9:10:12 S SD: 22.0266 cents 7 x x 8:9 x x 11:14 SD: 21.3830 cents 8 x x 9 x 11:12:13:16 SD: 9.3640 cents 9 x x 10:12 x x 14:18 SD: 12.1926 cents 10 x x 11:13:14:15:16:20 SD: 13.1106 cents 11 x x 12 x 15:17:18:22 SD: 14.8278 cents 12 x 13 x 16 x 18:19:24 SD: 6.4779 cents 13 x 14 x 17:18:20:21:26 SD: 12.3843 cents 14 x 15:16 x 19:21:22:28 SD: 9.8525 cents 15 x 16:17:20 x 23:24:30 SD: 8.5362 cents 16 x 17:18:21:22:24:26:32 SD: 7.8002 cents 17 x 18:19 x 23:26:27:34 SD: 6.6121 cents 18 x 19:20:24 x 27:29:36 SD: 3.6216 cents 19 x 20:21:25:26:29:30:38 SD: 7.9770 cents 20 x 21:22 x 27:30:32:40 SD: 5.3905 cents 21 x 22:23:28 x 32:34:42 SD: 8.7507 cents 22 x 23:24:29:30:33:35:44 SD: 7.8376 cents 23 x 25:26 x 31:35:37:46 SD: 8.6145 cents 24 x 26:27:32 x 36:38:48 SD: 6.4799 cents 25 x 27:28:33:34:38:40:50 SD: 5.7934 cents 26 x 28:29 x 35:39:42:52 SD: 4.1416 cents 27 x 29:30:36 x 41:43:54 SD: 4.2795 cents 28 x 30:31:37:38:42:45:56 SD: 3.1359 cents 29:30:31:32 x 39:44:46:58 SD: 8.4672 cents 30:31:32:33:40:41:45:48:60 SD: 7.1295 cents 32:33:34:36 x 43:48:51:64 SD: 7.5334 cents 33:34:35:37:44:45:50:53:66 SD: 6.8553 cents 34:35:36:38:45:46:51:54:68 SD: 6.2391 cents 35:36:37:39 x 47:53:56:70 SD: 6.9732 cents 36:37:38:40:48:49:54:58:72 SD: 6.0294 cents 38:39:41:42 x 51:57:61:76 SD: 6.5003 cents 39:40:42:43:52:53:59:62:78 SD: 5.9933 cents 40:41:43:44:53:54:60:64:80 SD: 5.4430 cents 41:42:44:46:55 x 62:66:82 SD: 6.4401 cents 42:43:45:47:56:57:63:67:84 SD: 4.8003 cents 44:45:47:49:59 x 66:70:88 SD: 5.0454 cents 45:46:48:50:60:61:68:72:90 SD: 4.3155 cents 46:47:49:51:61:62:69:74:92 SD: 4.2060 cents 47:48:50:52:63 x 71:75:94 SD: 4.9724 cents 48:49:51:53:64:65:72:77:96 SD: 4.0483 cents 54:55:58:60:72:73:81:86:108 SD: 3.6191 cents 57:58:61:63:76:77:86:91:114 SD: 3.4862 cents 60:61:64:67:80:81:90:96:120 SD: 2.9356 cents 63:64:67:70:84:85:95:101:126 SD: 2.9119 cents 70:71:75:78:93:95:105:112:140 SD: 2.8555 cents 71:72:76:79:95:96:107:114:142 SD: 2.7788 cents 72:73:77:80:96:97:108:115:144 SD: 2.2864 cents 78:79:83:87:104:105:117:125:156 SD: 2.2605 cents 80:81:85:89:107:108:120:128:160 SD: 2.1533 cents 88:89:94:98:117:119:132:141:176 SD: 1.8698 cents 90:91:96:100:120:122:135:144:180 SD: 1.7817 cents 92:93:98:102:123:124:138:147:184 SD: 1.7576 cents 100:101:107:111:133:135:150:160:200 SD: 1.5820 cents 102:103:109:113:136:138:153:163:204 SD: 1.5668 cents 105:106:112:117:140:142:158:168:210 SD: 1.5644 cents 106:107:113:118:141:143:159:170:212 SD: 1.4597 cents 108:109:115:120:144:146:162:173:216 SD: 1.2684 cents 117:118:125:130:156:158:176:187:234 SD: 1.2437 cents 118:119:126:131:157:159:177:189:236 SD: 1.2143 cents 120:121:128:133:160:162:180:192:240 SD: 1.0926 cents 132:133:141:147:176:178:198:211:264 SD: 1.0271 cents 134:135:143:149:179:181:201:214:268 SD: 0.9783 cents 135:136:144:150:180:182:203:216:270 SD: 0.9673 cents 146:147:156:162:195:197:219:234:292 SD: 0.9531 cents 150:151:160:167:200:203:225:240:300 SD: 0.9061 cents 152:153:162:169:203:205:228:243:304 SD: 0.7628 cents 162:163:173:180:216:219:243:259:324 SD: 0.6431 cents 178:179:190:198:237:240:267:285:356 SD: 0.6358 cents 180:181:192:200:240:243:270:288:360 SD: 0.3519 cents 240:241:256:267:320:324:360:384:480 SD: 0.2754 cents 252:253:269:280:336:340:378:403:504 SD: 0.2318 cents 288:289:307:320:384:389:432:461:576 SD: 0.2246 cents 432:434:461:480:576:583:648:691:864 SD: 0.2038 cents 468:470:499:520:624:632:702:749:936 SD: 0.1460 cents 480:482:512:533:640:648:720:768:960 SD: 0.1452 cents 522:524:557:580:696:705:783:835:1044 SD: 0.1326 cents 540:542:576:600:720:729:810:864:1080 SD: 0.0470 cents