Scala analysis: xen18-ayers-table-18
7 Iterated Subcontraries to the Harmonic Mean
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 433/348 378.335663 2: 17/12 603.000409 2nd septendecimal tritone 3: 689/444 760.733168 4: 5/3 884.358713 major sixth, BP sixth 5: 3373/1914 980.929786 6: 61/33 1063.611862 7: 8077/4191 1135.830022 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8382/8077 64.1700 1: 433/348 378.3357 2: 493/433 224.6647 3: 689/629 157.7328 4: 740/689 123.6255 5: 3373/3190 96.5711 6: 3538/3373 82.6821 7: 8077/7747 72.2182 8: 8382/8077 64.1700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 8382/8077 64.170 cents 1: 1 8077/7747 72.218 cents 1: 1 3538/3373 82.682 cents 1: 1 3373/3190 96.571 cents 1: 1 740/689 123.626 cents 1: 1 689/629 157.733 cents 1: 1 493/433 224.665 cents 1: 1 433/348 378.336 cents 2: 1 66/61 136.388 cents 2: 1 468466/428371 154.900 cents 2: 1 61/55 179.253 cents 2: 1 249602/219791 220.197 cents 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 19981/16021 382.398 cents 2: 1 604901/468466 442.506 cents 2: 1 17/12 603.000 cents 2nd septendecimal tritone 3: 1 3828/3373 219.070 cents 3: 1 8077/6985 251.471 cents 3: 1 9028/7579 302.879 cents 3: 1 6746/5423 377.929 cents 3: 1 580/433 506.023 cents 3: 1 4763/3538 514.724 cents 3: 1 23749/16154 667.170 cents 3: 1 689/444 760.733 cents 4: 1 6/5 315.641 cents minor third 4: 1 1195396/962533 375.097 cents 4: 1 244/187 460.611 cents 4: 1 4763/3373 597.406 cents 4: 1 6746/4763 602.594 cents 4: 1 187/122 739.389 cents 4: 1 962533/597698 824.903 cents 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 888/689 439.267 cents 5: 1 32308/23749 532.830 cents 5: 1 7076/4763 685.276 cents 5: 1 433/290 693.977 cents 5: 1 5423/3373 822.071 cents 5: 1 7579/4514 897.121 cents 5: 1 13970/8077 948.529 cents 5: 1 3373/1914 980.930 cents 6: 1 24/17 597.000 cents 1st septendecimal tritone 6: 1 936932/604901 757.494 cents 6: 1 32042/19981 817.602 cents 6: 1 17/10 918.642 cents septendecimal diminished seventh 6: 1 219791/124801 979.803 cents 6: 1 110/61 1020.747 cents 6: 1 428371/234233 1045.100 cents 6: 1 61/33 1063.612 cents 7: 1 696/433 821.664 cents 7: 1 866/493 975.335 cents 7: 1 1258/689 1042.267 cents 7: 1 689/370 1076.374 cents 7: 1 6380/3373 1103.429 cents 7: 1 3373/1769 1117.318 cents 7: 1 15494/8077 1127.782 cents 7: 1 8077/4191 1135.830 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 : 378.3 603.0 760.7 884.4 980.9 1063.6 1135.8 1200.0 378.3 : 224.7 382.4 506.0 602.6 685.3 757.5 821.7 1200.0 603.0 : 157.7 281.4 377.9 460.6 532.8 597.0 975.3 1200.0 760.7 : 123.6 220.2 302.9 375.1 439.3 817.6 1042.3 1200.0 884.4 : 96.6 179.3 251.5 315.6 694.0 918.6 1076.4 1200.0 980.9 : 82.7 154.9 219.1 597.4 822.1 979.8 1103.4 1200.0 1063.6: 72.2 136.4 514.7 739.4 897.1 1020.7 1117.3 1200.0 1135.8: 64.2 442.5 667.2 824.9 948.5 1045.1 1127.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 64.1700 .. 378.3357 cents 3497341/2916936, 314.1657 cents 8382/8077, 64.1700 cents 2: 136.3881 .. 603.0004 cents 1037/792, 466.6123 cents 22968/26413,-241.9475 cents 3: 219.0702 .. 760.7332 cents 2323997/1699632, 541.6630 cents 45936/57341,-383.9302 cents 4: 315.6413 .. 884.3587 cents 25/18, 568.7174 cents 2664/3445,-445.0919 cents 5: 439.2668 .. 980.9298 cents 2323997/1699632, 541.6630 cents 2664/3445,-445.0919 cents 6: 596.9996 .. 1063.6119 cents 1037/792, 466.6123 cents 45936/57341,-383.9302 cents 7: 821.6643 .. 1135.8300 cents 3497341/2916936, 314.1657 cents 22968/26413,-241.9475 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 8382/8077, 64.1700 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 433/348, 378.3357 cents Average / Smallest step : 2.337542 Largest / Average step : 2.522238 Largest / Smallest step : 5.895836 Median interval of one step : 110.09831 cents, amount: 0 Least squares average step : 177.65246 cents, oct.: 1421.21965 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : HGFEDCBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.40629 cents Scale diversity : 1.640315 Lumma stability : 0.106950 Lumma impropriety factor : 0.772686 Rothenberg efficiency : 0.250000 redundancy: 0.750000 Efficiency x scale size : 2.000000 Number of different interval sizes : 56 = 8.00000 / 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 : 80971/80952, 0.4063 cents Number of recognisable fifths : 1, average 693.9769 cents Steps are strictly decreasing Formal octave complements present : 1 = 12.5000% -- Rational properties -- Prime limit : 3373 Odd number limit : 962533 (O: 962533 U: 962533) Highest odd numerator or denominator: 8077 Harmonicity values : limit above prime count Fundamental : 1/17987772, -24.1005 octaves, 0.0000 Hz. Guide tone : too high to compute Sum of Mann's harmonic distance : 9801.5, average 1225.18750 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 16.62472, average 2.07809 Sum of Tenney's harmonic distance : 32.09379, average 4.01172 Vogel's harmonic complexity : 697.87500 Wille's k value : 13956728 Lattice compactness : 71.74200, average 1.99283 Lattice compactness (without 2's) : 48.42981, average 1.34527 Number of different primes : 15 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.75000 8 1 3: -1 .. 0 -0.87500 7 5: 0 .. 1 0.12500 1 1 11: -1 .. 0 -0.37500 3 13: 0 .. 1 0.12500 1 17: 0 .. 1 0.12500 1 1 29: -1 .. 0 -0.25000 2 37: -1 .. 0 -0.12500 1 41: 0 .. 1 0.12500 1 53: 0 .. 1 0.12500 1 1 61: 0 .. 1 0.12500 1 1 127: -1 .. 0 -0.12500 1 197: 0 .. 1 0.12500 1 1 433: 0 .. 1 0.12500 1 1 3373: 0 .. 1 0.12500 1 1 Average exponent except 2's :-5 / 8 =-0.62500 Average absolute exponent except 2's: 23 / 8 = 2.87500
FIT/MODE
8: 3 1 1 1 1 0 1 0 N SD: 42.6884 c. M:-71.6643 c. 10: 3 2 1 1 1 1 0 1 N SD: 31.2164 c. M: 55.8300 c. 12: 4 2 2 1 1 1 0 1 N SD: 25.5843 c. M:-39.2668 c. 14: 4 3 2 1 1 1 1 1 N SD: 25.6523 c. M: 38.0726 c. 16: 5 3 2 2 1 1 1 1 N SD: 9.4718 c. M:-15.6413 c. 28: 9 5 4 3 2 2 2 1 N SD: 10.9585 c. M:-21.3128 c. 32: 10 6 4 3 3 2 2 2 N SD: 10.9022 c. M: 21.8587 c. 34: 11 6 5 3 3 2 2 2 N SD: 7.7151 c. M:-15.7374 c. 35: 11 7 4 4 3 2 2 2 N SD: 7.8367 c. M:-14.1424 c. 38: 12 7 5 4 3 3 2 2 N SD: 3.9348 c. M:-10.0723 c. 50: 16 9 7 5 4 3 3 3 N SD: 5.4294 c. M: 7.8300 c. 54: 17 10 7 6 4 4 3 3 N SD: 3.2044 c. M: 5.1776 c. 60: 19 11 8 6 5 4 4 3 N SD: 2.7975 c. M: 4.3587 c. 76: 24 14 10 8 6 5 5 4 N SD: 2.6243 c. M: 5.7171 c. 88: 28 16 12 9 7 6 5 5 N SD: 2.5116 c. M: 4.0118 c. 95: 30 18 12 10 8 6 6 5 N SD: 2.3926 c. M:-4.3334 c. 98: 31 18 13 10 8 7 6 5 N SD: 2.0539 c. M: 3.0004 c. 99: 31 19 13 10 8 7 6 5 N SD: 2.4368 c. M:-3.5639 c. 114: 36 21 15 12 9 8 7 6 N SD: 1.6814 c. M: 3.0004 c. 115: 36 22 15 12 9 8 7 6 N SD: 1.6904 c. M: 2.6835 c. 133: 42 25 17 14 11 9 8 7 N SD: 1.5515 c. M: 2.8384 c. 169: 53 32 22 18 13 12 10 9 N SD: 1.5390 c. M:-3.2153 c. 175: 55 33 23 18 14 12 11 9 N SD: 1.0337 c. M:-2.4557 c. 185: 58 35 24 19 15 13 11 10 N SD: 1.3848 c. M: 2.1966 c. 187: 59 35 25 19 15 13 11 10 N SD: 1.2959 c. M:-2.9032 c. 191: 60 36 25 20 15 13 12 10 N SD: 1.1337 c. M: 1.8318 c. 203: 64 38 27 21 16 14 12 11 N SD: 1.1102 c. M:-2.3408 c. 213: 67 40 28 22 17 15 13 11 N SD: 0.9669 c. M:-2.1981 c. 229: 72 43 30 24 18 16 14 12 N SD: 0.8864 c. M:-1.2879 c. 235: 74 44 31 24 19 16 14 13 N SD: 1.0425 c. M: 2.2130 c. 247: 78 46 33 25 20 17 15 13 N SD: 0.8770 c. M:-2.0199 c. 263: 83 49 35 27 21 18 16 14 N SD: 0.6320 c. M:-1.2440 c. 301: 95 56 40 31 24 21 18 16 N SD: 0.6200 c. M: 1.0071 c. 334: 105 63 44 34 27 23 20 18 N SD: 0.6108 c. M: 1.0902 c. 372: 117 70 49 38 30 26 22 20 N SD: 0.5542 c. M: 0.9163 c. 380: 120 71 50 39 31 26 23 20 N SD: 0.6410 c. M:-1.1755 c. 388: 122 73 51 40 31 27 23 21 N SD: 0.5060 c. M: 1.0161 c. 396: 125 74 52 41 32 27 24 21 N SD: 0.4382 c. M:-0.8884 c. 448: 141 84 59 46 36 31 27 24 N SD: 0.3725 c. M: 0.6571 c. 521: 164 98 68 54 42 36 31 28 N SD: 0.4218 c. M: 0.6564 c. 543: 171 102 71 56 44 37 33 29 N SD: 0.3839 c. M: 0.6284 c. 555: 175 104 73 57 45 38 33 30 N SD: 0.3831 c. M: 0.6949 c. 581: 183 109 76 60 47 40 35 31 N SD: 0.3089 c. M: 0.6643 c. 615: 194 115 81 63 50 42 37 33 N SD: 0.2926 c. M:-0.5336 c. 653: 206 122 86 67 53 45 39 35 N SD: 0.2825 c. M: 0.4383 c. 669: 211 125 88 69 54 46 40 36 N SD: 0.2179 c. M: 0.4040 c. 746: 235 140 98 77 60 51 45 40 N SD: 0.2580 c. M:-0.3598 c. 768: 242 144 101 79 62 53 46 41 N SD: 0.2289 c. M:-0.4506 c. 784: 247 147 103 81 63 54 47 42 N SD: 0.1834 c. M:-0.3352 c. 844: 266 158 111 87 68 58 51 45 N SD: 0.1159 c. M:-0.1889 c. 1513: 477 283 199 156 122 104 91 81 N SD: 0.1124 c. M: 0.2245 c. 1628: 513 305 214 168 131 112 98 87 N SD: 0.1104 c. M: 0.2030 c. 1741: 549 326 229 179 140 120 105 93 N SD: 0.1031 c. M:-0.2088 c. 1779: 561 333 234 183 143 123 107 95 N SD: 0.0993 c. M: 0.1541 c. 1795: 566 336 236 185 144 124 108 96 N SD: 0.0842 c. M: 0.2056 c. 1874: 591 351 246 193 151 129 113 100 N SD: 0.0987 c. M:-0.2013 c. 1890: 596 354 248 195 152 130 114 101 N SD: 0.0935 c. M:-0.1742 c. 1928: 608 361 253 199 155 133 116 103 N SD: 0.0870 c. M: 0.1523 c. 2147: 677 402 282 221 173 148 129 115 N SD: 0.0742 c. M: 0.1482 c. 2316: 730 434 304 239 186 160 139 124 N SD: 0.0959 c. M:-0.1187 c. 2322: 732 435 305 239 187 160 140 124 N SD: 0.0697 c. M: 0.1210 c. 2376: 749 445 312 245 191 164 143 127 N SD: 0.0674 c. M: 0.1271 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x x 4 S SD: 29.3891 cents 3 x 4 x 5 x x x 6 S SD: 34.9851 cents 4:5 x 6 x 7 x x 8 S SD: 15.1349 cents 5:6:7:8 x 9 x x 10 S SD: 18.4378 cents 6:7 x 9:10 x 11 x 12 SD: 25.3632 cents 7:9:10:11 x 12:13 x 14 SD: 13.1804 cents 8:10:11:12:13:14:15 x 16 S SD: 13.4508 cents 9:11:13:14:15:16 x 17:18 SD: 8.5044 cents 10:12:14:16:17:18 x 19:20 S SD: 14.4849 cents 11:14:16:17:18:19:20:21:22 SD: 10.4388 cents 12:15:17:19:20:21:22:23:24 SD: 5.1787 cents 20:25:28:31:33:35:37:39:40 SD: 4.5969 cents 21:26:30:33:35:37:39:40:42 SD: 4.3922 cents 24:30:34:37:40:42:44:46:48 SD: 3.1433 cents 29:36:41:45:48:51:54:56:58 SD: 2.3626 cents 33:41:47:51:55:58:61:64:66 SD: 2.0999 cents 41:51:58:64:68:72:76:79:82 SD: 1.9475 cents 45:56:64:70:75:79:83:87:90 SD: 1.5392 cents 53:66:75:82:88:93:98:102:106 SD: 1.4628 cents 58:72:82:90:97:102:107:112:116 SD: 1.2518 cents 67:83:95:104:112:118:124:129:134 SD: 1.2199 cents 72:90:102:112:120:127:133:139:144 SD: 1.2118 cents 81:101:115:126:135:143:150:156:162 SD: 1.0173 cents 87:108:123:135:145:153:161:168:174 SD: 0.9424 cents 93:116:132:144:155:164:172:179:186 SD: 0.8888 cents 94:117:133:146:157:166:174:181:188 SD: 0.8118 cents 98:122:139:152:163:173:181:189:196 SD: 0.6935 cents 111:138:157:172:185:196:205:214:222 SD: 0.6887 cents 118:147:167:183:197:208:218:227:236 SD: 0.6627 cents 123:153:174:191:205:217:227:237:246 SD: 0.5483 cents 127:158:180:197:212:224:235:245:254 SD: 0.5138 cents 139:173:197:216:232:245:257:268:278 SD: 0.4604 cents 147:183:208:228:245:259:272:283:294 SD: 0.4411 cents 156:194:221:242:260:275:288:301:312 SD: 0.4025 cents 180:224:255:279:300:317:333:347:360 SD: 0.3466 cents 192:239:272:298:320:338:355:370:384 SD: 0.2568 cents 290:361:411:450:483:511:536:559:580 SD: 0.2074 cents 303:377:429:470:505:534:560:584:606 SD: 0.1606 cents 357:444:506:554:595:629:660:688:714 SD: 0.1543 cents 384:478:544:596:640:677:710:740:768 SD: 0.1482 cents 442:550:626:686:737:779:817:852:884 SD: 0.1284 cents 480:597:680:745:800:846:887:925:960 SD: 0.1209 cents 540:672:765:838:900:952:998:1041:1080 SD: 0.1168 cents 573:713:812:889:955:1010:1059:1104:1146 SD: 0.1163 cents 593:738:840:920:988:1045:1096:1143:1186 SD: 0.1113 cents