Scala analysis: nakika12
Nakika[12] (100/99&245/242) hobbit, 41et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 87.805 cents 87.804880 2: 175.610 cents 175.609760 3: 321.951 cents 321.951220 4: 409.756 cents 409.756100 5: 497.561 cents 497.560980 6: 585.366 cents 585.365850 7: 702.439 cents 702.439020 8: 790.244 cents 790.243900 9: 878.049 cents 878.048780 10: 1024.390 cents 1024.390240 11: 1112.195 cents 1112.195120 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 87.8049 cents 87.8049 1: 87.8049 cents 87.8049 2: 87.8049 cents 87.8049 3: 146.3415 cents 146.3415 4: 87.8049 cents 87.8049 5: 87.8049 cents 87.8049 6: 87.8049 cents 87.8049 7: 117.0732 cents 117.0732 8: 87.8049 cents 87.8049 9: 87.8049 cents 87.8049 10: 146.3415 cents 146.3415 11: 87.8049 cents 87.8049 12: 87.8049 cents 87.8049
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 87.80488 cents 1: 1 117.07317 cents 1: 2 146.34146 cents 2: 6 175.60976 cents 2: 2 204.87804 cents 2: 4 234.14634 cents 3: 3 263.41463 cents 3: 3 292.68292 cents 3: 6 321.95122 cents 4: 1 351.21952 cents 4: 3 380.48780 cents 4: 7 409.75610 cents 4: 1 439.02439 cents 5: 2 468.29268 cents 5: 7 497.56098 cents 5: 3 526.82926 cents 6: 1 556.09756 cents 6: 5 585.36585 cents 6: 5 614.63414 cents 6: 1 643.90244 cents 7: 3 673.17074 cents 7: 7 702.43902 cents 7: 2 731.70732 cents 8: 1 760.97561 cents 8: 7 790.24390 cents 8: 3 819.51220 cents 8: 1 848.78048 cents 9: 6 878.04878 cents 9: 3 907.31708 cents 9: 3 936.58536 cents 10: 4 965.85366 cents 10: 2 995.12196 cents 10: 6 1024.39024 cents 11: 2 1053.65854 cents 11: 1 1082.92683 cents 11: 9 1112.19512 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 87.8 175.6 322.0 409.8 497.6 585.4 702.4 790.2 878.0 1024.4 1112.2 1200.0 87.8 : 87.8 234.1 322.0 409.8 497.6 614.6 702.4 790.2 936.6 1024.4 1112.2 1200.0 175.6 : 146.3 234.1 322.0 409.8 526.8 614.6 702.4 848.8 936.6 1024.4 1112.2 1200.0 322.0 : 87.8 175.6 263.4 380.5 468.3 556.1 702.4 790.2 878.0 965.9 1053.7 1200.0 409.8 : 87.8 175.6 292.7 380.5 468.3 614.6 702.4 790.2 878.0 965.9 1112.2 1200.0 497.6 : 87.8 204.9 292.7 380.5 526.8 614.6 702.4 790.2 878.0 1024.4 1112.2 1200.0 585.4 : 117.1 204.9 292.7 439.0 526.8 614.6 702.4 790.2 936.6 1024.4 1112.2 1200.0 702.4 : 87.8 175.6 322.0 409.8 497.6 585.4 673.2 819.5 907.3 995.1 1082.9 1200.0 790.2 : 87.8 234.1 322.0 409.8 497.6 585.4 731.7 819.5 907.3 995.1 1112.2 1200.0 878.0 : 146.3 234.1 322.0 409.8 497.6 643.9 731.7 819.5 907.3 1024.4 1112.2 1200.0 1024.4: 87.8 175.6 263.4 351.2 497.6 585.4 673.2 761.0 878.0 965.9 1053.7 1200.0 1112.2: 87.8 175.6 263.4 409.8 497.6 585.4 673.2 790.2 878.0 965.9 1112.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 87.8049 .. 146.3415 cents 58.53658 cents 87.80488 cents 2: 175.6098 .. 234.1463 cents 58.53658 cents 29.26830 cents 3: 263.4146 .. 321.9512 cents 58.53659 cents 29.26829 cents 4: 351.2195 .. 439.0244 cents 87.80487 cents 29.26830 cents 5: 468.2927 .. 526.8293 cents 58.53658 cents 29.26829 cents 6: 556.0976 .. 643.9024 cents 87.80488 cents 29.26830 cents 7: 673.1707 .. 731.7073 cents 58.53658 cents 29.26830 cents 8: 760.9756 .. 848.7805 cents 87.80487 cents 29.26829 cents 9: 878.0488 .. 936.5854 cents 58.53658 cents 29.26830 cents 10: 965.8537 .. 1024.3902 cents 58.53658 cents 29.26830 cents 11: 1053.6585 .. 1112.1951 cents 58.53658 cents 29.26830 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 87.80487 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 146.34146 cents Average / Smallest step : 1.138889 Largest / Average step : 1.463415 Largest / Smallest step : 1.666667 Median interval of one step : 87.80488 cents, amount: 9 Most common interval of one step : 87.80488 cents, amount: 9 Least squares average step : 100.09756 cents, oct.: 1201.17073 cents Scale is strictly proper Scale is a mode of a 41-tone equal temperament with octave 1200.000 cents degrees: 3 6 11 14 17 20 24 27 30 35 38 41 Least number of segments generator : 21 of 614.634 cents and inv. number of contiguous generator circle segments: 2 Shortest superset generator : 24 of 702.439 cents and inv. generated superset size: 21 = 9 more = 175.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAACAABAA Step pattern size order : SSLSSSMSSLSS Interval vector is [ 0 0 9 1 2 6 2 4 3 3 6 1 3 7 1 2 7 3 1 5 ] Scale is a Constant Structure, by a margin of 29.26829 cents Scale diversity : 1.391140 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.390244 Rothenberg efficiency : 0.416997 redundancy: 0.583003 Efficiency x scale size : 5.003968 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 29.26828 cents Most common intervals : 87.80488 cents & inv., amount: 9 Most common triad is 0.0 87.805 1112.195 cents, amount: 5 Number of recognisable fifths : 7, average 702.4390 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle 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: 15.4578 c. M: 24.3902 c. Twelve-tone Chromatic (1/11-comma) 14: 1 1 2 1 1 1 1 1 1 2 1 1 P D3 I SD: 14.1405 c. M: 20.9059 c. 15: 1 1 2 1 1 1 2 1 1 2 1 1 P D3 SD: 13.1255 c. M: 25.3658 c. 26: 2 2 3 2 2 2 2 2 2 3 2 2 SP D3 I SD: 7.5724 c. M:-14.6342 c. 27: 2 2 3 2 2 2 3 2 2 3 2 2 SP D3 SD: 7.3321 c. M: 10.8401 c. 29: 2 2 4 2 2 2 3 2 2 4 2 2 P SD: 6.3964 c. M: 10.0925 c. 41: 3 3 5 3 3 3 4 3 3 5 3 3 SP SD: 0.0000 c. M: 0.0000 c. Nakika
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: 0.2420 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.1095 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 15.0772 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 5.0741 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.1349 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 13.9199 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 10.8812 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.7998 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.5453 cents 11 x 12:13:14:15 x x 17:18:20:21:22 SD: 8.2107 cents 12 x 13:14:15:16:17:18:19:20:22:23:24 S SD: 7.1338 cents 13:14 x 16 x 17:18:20:21:22:23:25:26 SD: 10.4495 cents 14:15:16:17:18:19:20:21:22:23:25:27:28 SD: 7.6281 cents 15:16:17:18:19:20:21:23:24:25:27:29:30 SD: 6.0108 cents 18:19:20:22:23:24:25:27:28:30:33:34:36 SD: 4.2883 cents 20:21:22:24:25:27:28:30:32:33:36:38:40 SD: 3.6559 cents 30:32:33:36:38:40:42:45:47:50:54:57:60 SD: 2.6217 cents 36:38:40:43:46:48:50:54:57:60:65:68:72 SD: 2.5968 cents 38:40:42:46:48:51:53:57:60:63:69:72:76 SD: 1.7712 cents 54:57:60:65:68:72:76:81:85:90:98:103:108 SD: 1.6358 cents 57:60:63:69:72:76:80:86:90:95:103:108:114 SD: 1.3965 cents 64:67:71:77:81:85:90:96:101:106:116:122:128 SD: 1.2612 cents 72:76:80:87:91:96:101:108:114:120:130:137:144 SD: 1.1899 cents 74:78:82:89:94:99:104:111:117:123:134:141:148 SD: 0.9665 cents 92:97:102:111:117:123:129:138:145:153:166:175:184 SD: 0.9224 cents 93:98:103:112:118:124:130:140:147:154:168:177:186 SD: 0.8838 cents 94:99:104:113:119:125:132:141:148:156:170:179:188 SD: 0.6996 cents 102:107:113:123:129:136:143:153:161:169:184:194:204 SD: 0.6869 cents 112:118:124:135:142:149:157:168:177:186:202:213:224 SD: 0.5142 cents 132:139:146:159:167:176:185:198:208:219:239:251:264 SD: 0.4934 cents 150:158:166:181:190:200:210:225:237:249:271:285:300 SD: 0.4457 cents 171:180:189:206:217:228:240:257:270:284:309:325:342 SD: 0.4179 cents 176:185:195:212:223:235:247:264:278:292:318:335:352 SD: 0.4148 cents 206:217:228:248:261:275:289:309:325:342:372:392:412 SD: 0.3558 cents 214:225:237:258:271:285:300:321:338:355:387:407:428 SD: 0.3298 cents 244:257:270:294:309:325:342:366:385:405:441:464:488 SD: 0.2599 cents 270:284:299:325:342:360:379:405:426:448:488:513:540 SD: 0.2555 cents 289:304:320:348:366:385:405:434:456:480:522:549:578 SD: 0.2504 cents 327:344:362:394:414:436:459:491:516:543:591:622:654 SD: 0.2431 cents 328:345:363:395:416:437:460:492:518:545:593:624:656 SD: 0.2353 cents 348:366:385:419:441:464:488:522:549:578:629:662:696 SD: 0.1655 cents 363:382:402:437:460:484:509:545:573:603:656:690:726 SD: 0.1645 cents 442:465:489:532:560:589:620:663:698:734:799:840:884 SD: 0.1596 cents 460:484:509:554:583:613:645:690:726:764:831:875:920 SD: 0.1260 cents 498:524:551:600:631:664:698:747:786:827:900:947:996 SD: 0.1252 cents 562:591:622:677:712:749:788:843:887:933:1016:1068:1124 SD: 0.1251 cents 577:607:639:695:731:769:809:866:911:958:1043:1097:1154 SD: 0.1240 cents