Scala analysis: ares12
Ares[12] (64/63&100/99) hobbit, POTE tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 98.862 cents 98.862420 2: 172.077 cents 172.077030 3: 318.236 cents 318.236120 4: 391.451 cents 391.450730 5: 490.313 cents 490.313150 6: 563.528 cents 563.527760 7: 709.687 cents 709.686850 8: 808.549 cents 808.549270 9: 881.764 cents 881.763880 10: 1027.923 cents 1027.922970 11: 1101.138 cents 1101.137580 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 98.8624 cents 98.8624 1: 98.8624 cents 98.8624 2: 73.2146 cents 73.2146 3: 146.1591 cents 146.1591 4: 73.2146 cents 73.2146 5: 98.8624 cents 98.8624 6: 73.2146 cents 73.2146 7: 146.1591 cents 146.1591 8: 98.8624 cents 98.8624 9: 73.2146 cents 73.2146 10: 146.1591 cents 146.1591 11: 73.2146 cents 73.2146 12: 98.8624 cents 98.8624
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 73.21461 cents 1: 4 98.86242 cents 1: 3 146.15909 cents 2: 5 172.07703 cents 2: 1 197.72484 cents 2: 5 219.37370 cents 2: 1 245.02151 cents 3: 1 245.29164 cents 3: 2 270.93945 cents 3: 2 292.58831 cents 3: 7 318.23612 cents 4: 1 344.15406 cents 4: 7 391.45073 cents 4: 3 417.09854 cents 4: 1 464.39521 cents 5: 1 464.66534 cents 5: 8 490.31315 cents 5: 3 537.60982 cents 6: 4 563.52776 cents 6: 2 589.17557 cents 6: 2 610.82443 cents 6: 4 636.47224 cents 7: 3 662.39018 cents 7: 8 709.68685 cents 7: 1 735.33466 cents 8: 1 735.60479 cents 8: 3 782.90146 cents 8: 7 808.54927 cents 8: 1 855.84594 cents 9: 7 881.76388 cents 9: 2 907.41169 cents 9: 2 929.06055 cents 9: 1 954.70836 cents 10: 1 954.97849 cents 10: 5 980.62630 cents 10: 1 1002.27516 cents 10: 5 1027.92297 cents 11: 3 1053.84091 cents 11: 4 1101.13758 cents 11: 5 1126.78539 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.63636 = 40/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 98.9 172.1 318.2 391.5 490.3 563.5 709.7 808.5 881.8 1027.9 1101.1 1200.0 98.9 : 73.2 219.4 292.6 391.5 464.7 610.8 709.7 782.9 929.1 1002.3 1101.1 1200.0 172.1 : 146.2 219.4 318.2 391.5 537.6 636.5 709.7 855.8 929.1 1027.9 1126.8 1200.0 318.2 : 73.2 172.1 245.3 391.5 490.3 563.5 709.7 782.9 881.8 980.6 1053.8 1200.0 391.5 : 98.9 172.1 318.2 417.1 490.3 636.5 709.7 808.5 907.4 980.6 1126.8 1200.0 490.3 : 73.2 219.4 318.2 391.5 537.6 610.8 709.7 808.5 881.8 1027.9 1101.1 1200.0 563.5 : 146.2 245.0 318.2 464.4 537.6 636.5 735.3 808.5 954.7 1027.9 1126.8 1200.0 709.7 : 98.9 172.1 318.2 391.5 490.3 589.2 662.4 808.5 881.8 980.6 1053.8 1200.0 808.5 : 73.2 219.4 292.6 391.5 490.3 563.5 709.7 782.9 881.8 955.0 1101.1 1200.0 881.8 : 146.2 219.4 318.2 417.1 490.3 636.5 709.7 808.5 881.8 1027.9 1126.8 1200.0 1027.9: 73.2 172.1 270.9 344.2 490.3 563.5 662.4 735.6 881.8 980.6 1053.8 1200.0 1101.1: 98.9 197.7 270.9 417.1 490.3 589.2 662.4 808.5 907.4 980.6 1126.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.2146 .. 146.1591 cents 72.94448 cents 73.21461 cents 2: 172.0770 .. 245.0215 cents 72.94448 cents 25.91794 cents 3: 245.2916 .. 318.2361 cents 72.94448 cents 0.27013 cents 4: 344.1541 .. 464.3952 cents 120.24115 cents 25.91794 cents 5: 464.6653 .. 537.6098 cents 72.94448 cents 0.27013 cents 6: 563.5278 .. 636.4722 cents 72.94448 cents 25.91794 cents 7: 662.3902 .. 735.3347 cents 72.94448 cents 25.91794 cents 8: 735.6048 .. 855.8459 cents 120.24115 cents 0.27013 cents 9: 881.7639 .. 954.7084 cents 72.94448 cents 25.91794 cents 10: 954.9785 .. 1027.9230 cents 72.94448 cents 0.27013 cents 11: 1053.8409 .. 1126.7854 cents 72.94448 cents 25.91794 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 73.21461 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 146.15909 cents Average / Smallest step : 1.365848 Largest / Average step : 1.461591 Largest / Smallest step : 1.996310 Median interval of one step : 98.86242 cents, amount: 4 Most common interval of one step : 73.21461 cents, amount: 5 Least squares average step : 99.93858 cents, oct.: 1199.26302 cents Scale is strictly proper Step pattern alph. order: ABCBABCABCBA Step pattern size order : MSLSMSLMSLSM Scale is a Constant Structure, by a margin of 0.27013 cents Scale diversity : 1.390130 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.252514 Rothenberg efficiency : 0.364902 redundancy: 0.635098 Efficiency x scale size : 4.378824 Number of different interval sizes : 40 = 3.63636 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.63636 = 40/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 0.27013 cents Most common intervals : 490.31315 cents & inv., amount: 8 Most common triad is 0.0 490.313 709.687 cents, amount: 5 Number of recognisable fifths : 8, average 709.6869 cents Scale contains two identical disjunct hexachords Formal octave complements present : 11 = 91.6667% -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.0073 c. M:-36.4722 c. Twelve-tone Chromatic (1/11-comma) 15: 1 1 2 1 1 1 2 1 1 2 1 1 P D3 SD: 10.7271 c. M: 18.8624 c. 22: 2 1 3 1 2 1 3 2 1 3 1 2 N SD: 9.2555 c. M: 18.0732 c. 27: 2 2 3 2 2 2 3 2 2 3 2 2 SP D3 SD: 7.7394 c. M:-14.2500 c. 34: 3 2 4 2 3 2 4 3 2 4 2 3 P SD: 3.9673 c. M: 7.0199 c. 49: 4 3 6 3 4 3 6 4 3 6 3 4 P SD: 0.5330 c. M: 0.9032 c. 181: 15 11 22 11 15 11 22 15 11 22 11 15 P SD: 0.3170 c. M: 0.5851 c. 230: 19 14 28 14 19 14 28 19 14 28 14 19 P SD: 0.1410 c. M: 0.2680 c. 279: 23 17 34 17 23 17 34 23 17 34 17 23 P SD: 0.0476 c. M: 0.0869 c. 886: 73 54 108 54 73 54 108 73 54 108 54 73 P SD: 0.0464 c. M: 0.0966 c. 1165: 96 71 142 71 96 71 142 96 71 142 71 96 P SD: 0.0448 c. M: 0.0943 c. 1444: 119 88 176 88 119 88 176 119 88 176 88 119 P SD: 0.0445 c. M: 0.0929 c. 1723: 142 105 210 105 142 105 210 142 105 210 105 142 P SD: 0.0445 c. M: 0.0919 c. 2183: 180 133 266 133 180 133 266 180 133 266 133 180 P SD: 0.0532 c. M: 0.0840 c. 2210: 182 135 269 135 182 135 269 182 135 269 135 182 SP SD: 0.0450 c. M:-0.0921 c. 2281: 188 139 278 139 188 139 278 188 139 278 139 188 P SD: 0.0447 c. M: 0.0907 c. 2308: 190 141 281 141 190 141 281 190 141 281 141 190 SP SD: 0.0486 c. M:-0.0771 c. 2379: 196 145 290 145 196 145 290 196 145 290 145 196 P SD: 0.0475 c. M: 0.0977 c. 2391: 197 146 291 146 197 146 291 197 146 291 146 197 SP SD: 0.0433 c. M:-0.0858 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 3.8659 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.7186 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 14.9554 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 4.4729 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.4639 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 15.9667 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.6252 cents 9 x 10:11 x 12 x x 14:15:16:17:18 S SD: 7.8475 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 5.8089 cents 11 x 12:13:14 x 15:17 x 18:20:21:22 SD: 8.5027 cents 12 x 13:14:15:16:17:18:19:20:22:23:24 S SD: 7.4602 cents 13:14 x x 16:17:18:20:21:22:24:25:26 S SD: 8.5189 cents 14:15 x 17:18 x 19:21:22:23:25:26:28 SD: 8.0911 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.5162 cents 16:17:18:19:20:21:22:24:26:27:29:30:32 SD: 5.1831 cents 18:19:20:22:23:24:25:27:29:30:33:34:36 SD: 4.5449 cents 19:20:21:23:24:25:26:29:30:32:34:36:38 SD: 4.3891 cents 20:21:22:24:25:27:28:30:32:33:36:38:40 SD: 3.7443 cents 27:29:30:32:34:36:37:41:43:45:49:51:54 SD: 3.6907 cents 28:30:31:34:35:37:39:42:45:47:51:53:56 SD: 3.2422 cents 30:32:33:36:38:40:42:45:48:50:54:57:60 SD: 2.9580 cents 31:33:34:37:39:41:43:47:49:52:56:59:62 SD: 2.8949 cents 34:36:38:41:43:45:47:51:54:57:62:64:68 SD: 2.8653 cents 35:37:39:42:44:46:48:53:56:58:63:66:70 SD: 2.7822 cents 36:38:40:43:45:48:50:54:57:60:65:68:72 SD: 2.0760 cents 39:41:43:47:49:52:54:59:62:65:71:74:78 SD: 1.8529 cents 47:50:52:56:59:62:65:71:75:78:85:89:94 SD: 1.8474 cents 49:52:54:59:61:65:68:74:78:82:89:93:98 SD: 1.7179 cents 54:57:60:65:68:72:75:81:86:90:98:102:108 SD: 1.6175 cents 55:58:61:66:69:73:76:83:88:92:100:104:110 SD: 1.4105 cents 65:69:72:78:81:86:90:98:104:108:118:123:130 SD: 1.3370 cents 67:71:74:81:84:89:93:101:107:112:121:127:134 SD: 1.3127 cents 75:79:83:90:94:100:104:113:120:125:136:142:150 SD: 1.2315 cents 79:84:87:95:99:105:109:119:126:131:143:149:158 SD: 1.0936 cents 83:88:92:100:104:110:115:125:132:138:150:157:166 SD: 0.9145 cents 89:94:98:107:112:118:123:134:142:148:161:168:178 SD: 0.8821 cents 99:105:109:119:124:131:137:149:158:165:179:187:198 SD: 0.7917 cents 104:110:115:125:130:138:144:157:166:173:188:196:208 SD: 0.7031 cents 122:129:135:147:153:162:169:184:195:203:221:230:244 SD: 0.6627 cents 134:142:148:161:168:178:186:202:214:223:243:253:268 SD: 0.4784 cents 153:162:169:184:192:203:212:231:244:255:277:289:306 SD: 0.4217 cents 190:201:210:228:238:252:263:286:303:316:344:359:380 SD: 0.3660 cents 208:220:230:250:261:276:288:313:332:346:377:393:416 SD: 0.3624 cents 223:236:246:268:280:296:309:336:356:371:404:421:446 SD: 0.3422 cents 237:251:262:285:297:315:328:357:378:394:429:448:474 SD: 0.3292 cents 239:253:264:287:300:317:331:360:381:398:433:451:478 SD: 0.3269 cents 257:272:284:309:322:341:356:387:410:428:465:485:514 SD: 0.2779 cents 268:284:296:322:336:356:371:404:428:446:485:506:536 SD: 0.2701 cents 288:305:318:346:361:382:399:434:459:479:522:544:576 SD: 0.2622 cents 306:324:338:368:384:406:424:461:488:509:554:578:612 SD: 0.2202 cents 327:346:361:393:410:434:453:493:522:544:592:618:654 SD: 0.2067 cents 343:363:379:412:430:455:475:517:547:571:621:648:686 SD: 0.1742 cents 422:447:466:507:529:560:584:636:673:702:764:797:844 SD: 0.1584 cents 440:466:486:529:552:584:609:663:702:732:797:831:880 SD: 0.1565 cents 476:504:526:572:597:632:659:717:759:792:862:899:952 SD: 0.1337 cents 497:526:549:597:623:660:688:749:793:827:900:939:994 SD: 0.1333 cents 544:576:601:654:682:722:753:820:868:905:985:1028:1088 SD: 0.1321 cents 556:589:614:668:697:738:770:838:887:925:1007:1050:1112 SD: 0.1255 cents 575:609:635:691:721:763:796:866:917:957:1041:1086:1150 SD: 0.1191 cents