Scala analysis: 12_lumma_5thcomma246_tuning_69860_70000
1/5-comma SLSSLLLSLLLS temperament.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 94.917 cents 94.917000 2: 194.526 cents 194.526000 3: 294.135 cents 294.135000 4: 393.744 cents 393.744000 5: 498.045 cents 498.045000 6: 592.962 cents 592.962000 7: 697.263 cents 697.263000 8: 796.872 cents 796.872000 9: 896.481 cents 896.481000 10: 996.090 cents 996.090000 11: 1091.007 cents 1091.007000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 108.9930 cents 108.9930 1: 94.9170 cents 94.9170 2: 99.6090 cents 99.6090 3: 99.6090 cents 99.6090 4: 99.6090 cents 99.6090 5: 104.3010 cents 104.3010 6: 94.9170 cents 94.9170 7: 104.3010 cents 104.3010 8: 99.6090 cents 99.6090 9: 99.6090 cents 99.6090 10: 99.6090 cents 99.6090 11: 94.9170 cents 94.9170 12: 108.9930 cents 108.9930
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 94.91700 cents 1: 6 99.60900 cents 1: 2 104.30100 cents 1: 1 108.99300 cents 2: 2 194.52600 cents 2: 6 199.21800 cents 2: 4 203.91000 cents 3: 2 294.13500 cents 3: 5 298.82700 cents 3: 5 303.51900 cents 4: 2 393.74400 cents 4: 4 398.43600 cents 4: 6 403.12800 cents 5: 7 498.04500 cents 5: 5 502.73700 cents 6: 2 592.96200 cents 6: 4 597.65400 cents 6: 4 602.34600 cents 6: 2 607.03800 cents 7: 5 697.26300 cents 7: 7 701.95500 cents 8: 6 796.87200 cents 8: 4 801.56400 cents 8: 2 806.25600 cents 9: 5 896.48100 cents 9: 5 901.17300 cents 9: 2 905.86500 cents 10: 4 996.09000 cents 10: 6 1000.78200 cents 10: 2 1005.47400 cents 11: 1 1091.00700 cents 11: 2 1095.69900 cents 11: 6 1100.39100 cents 11: 3 1105.08300 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 94.9 194.5 294.1 393.7 498.0 593.0 697.3 796.9 896.5 996.1 1091.0 1200.0 94.9 : 99.6 199.2 298.8 403.1 498.0 602.3 702.0 801.6 901.2 996.1 1105.1 1200.0 194.5 : 99.6 199.2 303.5 398.4 502.7 602.3 702.0 801.6 896.5 1005.5 1100.4 1200.0 294.1 : 99.6 203.9 298.8 403.1 502.7 602.3 702.0 796.9 905.9 1000.8 1100.4 1200.0 393.7 : 104.3 199.2 303.5 403.1 502.7 602.3 697.3 806.3 901.2 1000.8 1100.4 1200.0 498.0 : 94.9 199.2 298.8 398.4 498.0 593.0 702.0 796.9 896.5 996.1 1095.7 1200.0 593.0 : 104.3 203.9 303.5 403.1 498.0 607.0 702.0 801.6 901.2 1000.8 1105.1 1200.0 697.3 : 99.6 199.2 298.8 393.7 502.7 597.7 697.3 796.9 896.5 1000.8 1095.7 1200.0 796.9 : 99.6 199.2 294.1 403.1 498.0 597.7 697.3 796.9 901.2 996.1 1100.4 1200.0 896.5 : 99.6 194.5 303.5 398.4 498.0 597.7 697.3 801.6 896.5 1000.8 1100.4 1200.0 996.1 : 94.9 203.9 298.8 398.4 498.0 597.7 702.0 796.9 901.2 1000.8 1100.4 1200.0 1091.0: 109.0 203.9 303.5 403.1 502.7 607.0 702.0 806.3 905.9 1005.5 1105.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 94.9170 .. 108.9930 cents 14.07600 cents 94.91700 cents 2: 194.5260 .. 203.9100 cents 9.38400 cents 85.53300 cents 3: 294.1350 .. 303.5190 cents 9.38400 cents 90.22500 cents 4: 393.7440 .. 403.1280 cents 9.38400 cents 90.22500 cents 5: 498.0450 .. 502.7370 cents 4.69200 cents 94.91700 cents 6: 592.9620 .. 607.0380 cents 14.07600 cents 90.22500 cents 7: 697.2630 .. 701.9550 cents 4.69200 cents 90.22500 cents 8: 796.8720 .. 806.2560 cents 9.38400 cents 94.91700 cents 9: 896.4810 .. 905.8650 cents 9.38400 cents 90.22500 cents 10: 996.0900 .. 1005.4740 cents 9.38400 cents 90.22500 cents 11: 1091.0070 .. 1105.0830 cents 14.07600 cents 85.53300 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 94.91700 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 108.99300 cents Average / Smallest step : 1.053552 Largest / Average step : 1.089930 Largest / Smallest step : 1.148298 Median interval of one step : 99.60900 cents, amount: 6 Most common interval of one step : 99.60900 cents, amount: 6 Least squares average step : 99.50072 cents, oct.: 1194.00868 cents Scale is strictly proper Scale is a mode of a 2301-tone equal temperament with octave 2/1 degrees: 182 373 564 755 955 1137 1337 1528 1719 1910 2092 2301 Least number of segments generator : 1151 of 600.261 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2110 of 1100.391 cents and inv. generated superset size: 24 = 12 more = 200.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBBCACBBBAD Step pattern size order : ABBBCACBBBAD Scale is a Constant Structure, by a margin of 85.53300 cents Scale diversity : 1.073298 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.910070 Rothenberg efficiency : 0.353445 redundancy: 0.646555 Efficiency x scale size : 4.241342 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 4.69200 cents Most common intervals : 498.04500 cents & inv., amount: 7 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 2 different sizes of fifth Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 14.0760 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 5.0705 c. M:-8.9930 c. Twelve-tone Chromatic (1/11-comma) 65: 5 6 5 5 6 5 6 5 6 5 5 6 SP M ME SD: 4.2871 c. M:-8.5509 c. 66: 5 6 5 6 5 6 5 6 5 6 5 6 SP B ME SD: 4.9373 c. M: 7.1359 c. 67: 5 6 5 6 6 5 6 5 6 6 5 6 SP M ME SD: 4.4525 c. M: 8.8123 c. 74: 6 6 6 6 7 5 7 6 6 6 6 7 SP D3 SD: 4.3940 c. M: 9.1782 c. 75: 6 6 6 7 6 6 7 6 6 6 6 7 SP D3 SD: 3.7706 c. M:-6.7370 c. 77: 6 6 7 6 7 6 7 6 6 7 6 7 SP M ME SD: 3.7575 c. M: 8.1693 c. 79: 6 7 6 7 7 6 7 6 7 7 6 7 SP M ME SD: 3.7126 c. M: 6.9986 c. 86: 7 7 7 7 8 6 8 7 7 7 7 8 SP D3 SD: 3.3592 c. M: 6.9155 c. 87: 7 7 7 8 7 7 8 7 7 7 7 8 SP D3 SD: 3.2268 c. M:-6.2560 c. 89: 7 7 8 7 8 7 8 7 7 8 7 8 SP M ME SD: 3.0583 c. M: 6.5934 c. 91: 7 8 7 8 8 7 8 7 8 8 7 8 SP M ME SD: 3.3050 c. M:-6.1078 c. 97: 8 8 8 8 8 8 8 8 8 9 7 9 SP D3 SD: 3.7846 c. M:-5.9719 c. 98: 8 8 8 8 9 7 9 8 8 8 8 9 SP D3 SD: 2.6725 c. M: 5.2069 c. 101: 8 8 9 8 9 8 9 8 8 9 8 9 SP M ME SD: 2.6542 c. M: 5.3919 c. 107: 8 9 9 9 9 9 9 9 9 9 8 10 SP D3 SD: 2.7662 c. M: 5.1974 c. 110: 9 9 9 9 10 8 10 9 9 9 9 10 SP D3 SD: 2.2477 c. M: 3.8711 c. 119: 9 10 10 10 10 10 10 10 10 10 9 11 SP D3 SD: 2.2416 c. M: 4.1607 c. 122: 10 10 10 10 11 9 11 10 10 10 10 11 SP D3 SD: 2.0257 c. M:-3.5943 c. 131: 10 11 11 11 11 11 11 11 11 11 10 12 SP D3 SD: 1.9024 c. M: 3.3885 c. 134: 11 11 11 11 12 10 12 11 11 11 11 12 SP D3 SD: 1.9521 c. M:-3.5905 c. 143: 11 12 12 12 12 12 12 12 12 12 11 13 SP D3 SD: 1.7195 c. M: 2.9401 c. 146: 12 12 12 12 13 11 13 12 12 12 12 13 SP D3 SD: 1.9754 c. M:-3.7131 c. 152: 12 13 12 13 13 12 13 13 12 13 12 14 SP D3 SD: 1.9228 c. M: 4.3757 c. 154: 12 13 13 12 14 12 13 13 13 13 12 14 SP D3 S SD: 1.9211 c. M: 4.1336 c. 155: 12 13 13 13 13 13 13 13 13 13 12 14 SP D3 SD: 1.6603 c. M:-3.1670 c. 164: 13 14 13 14 14 13 14 14 14 13 13 15 SP D3 SD: 1.6466 c. M:-3.5190 c. 178: 14 15 15 14 16 14 15 15 15 15 14 16 SP D3 S SD: 1.5796 c. M: 2.8810 c. 187: 15 15 16 15 17 14 17 15 16 15 15 17 SP SD: 1.7572 c. M: 2.5877 c. 188: 15 15 16 16 16 15 16 16 15 16 15 17 SP D3 SD: 1.4859 c. M: 3.0366 c. 193: 15 16 16 16 17 15 17 16 16 16 15 18 SP SD: 1.6487 c. M: 2.9241 c. 198: 16 16 16 17 17 16 17 16 17 16 16 18 SP D3 SD: 1.5988 c. M: 3.2259 c. 199: 16 16 17 16 18 15 18 16 17 16 16 18 SP SD: 1.6130 c. M:-2.4575 c. 200: 16 16 17 17 17 16 17 17 16 17 16 18 SP D3 SD: 1.4071 c. M: 2.5260 c. 205: 16 17 17 17 18 16 18 17 17 17 16 19 SP SD: 1.2554 c. M: 2.2265 c. 217: 17 18 18 18 19 17 19 18 18 18 17 20 SP SD: 0.9055 c. M: 1.6061 c. 229: 18 19 19 19 20 18 20 19 19 19 18 21 SP SD: 0.5924 c. M: 1.0507 c. 241: 19 20 20 20 21 19 21 20 20 20 19 22 SP SD: 0.3104 c. M: 0.5506 c. 253: 20 21 21 21 22 20 22 21 21 21 20 23 SP SD: 0.0552 c. M: 0.0979 c. 771: 61 64 64 64 67 61 67 64 64 64 61 70 SP SD: 0.0246 c. M:-0.0436 c. 1024: 81 85 85 85 89 81 89 85 85 85 81 93 SP SD: 0.0049 c. M:-0.0086 c. 2301: 182 191 191 191 200 182 200 191 191 191 182 209 SP SD: 0.0017 c. M: 0.0031 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: 2.3460 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.0408 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.1613 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.2580 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.5741 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.6677 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.4374 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.2167 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0926 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.1839 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.4064 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.2407 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.8888 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.1084 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 5.0652 cents 17:18:19:20:21:23:24:25:27:29:30:32:34 SD: 4.9169 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.0000 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.6656 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.3478 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.9175 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1638 cents 48:51:54:57:60:64:68:72:76:81:85:90:96 SD: 1.9029 cents 49:52:55:58:62:65:69:73:78:82:87:92:98 SD: 1.8772 cents 50:53:56:59:63:67:70:75:79:84:89:94:100 SD: 1.6198 cents 54:57:60:64:68:72:76:81:86:91:96:101:108 SD: 1.6169 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.4305 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.3625 cents 66:70:74:78:83:88:93:99:105:111:117:124:132 SD: 1.1861 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 1.1670 cents 75:79:84:89:94:100:106:112:119:126:133:141:150 SD: 0.8944 cents 90:95:101:107:113:120:127:135:143:151:160:169:180 SD: 0.8838 cents 91:96:102:108:114:121:128:136:144:153:162:171:182 SD: 0.7705 cents 103:109:115:122:129:137:145:154:163:173:183:193:206 SD: 0.7594 cents 108:114:121:128:136:144:152:162:171:181:192:203:216 SD: 0.6951 cents 125:132:140:148:157:167:176:187:198:210:222:235:250 SD: 0.4475 cents 161:170:180:191:202:215:227:241:255:270:286:302:322 SD: 0.4282 cents 193:204:216:229:242:257:272:289:306:324:343:362:386 SD: 0.4123 cents 195:206:218:231:245:260:275:292:309:327:347:366:390 SD: 0.3606 cents 211:223:236:250:265:281:297:316:334:354:375:396:422 SD: 0.3355 cents 228:241:255:270:286:304:321:341:361:383:405:428:456 SD: 0.2982 cents 252:266:282:299:316:336:355:377:399:423:448:473:504 SD: 0.2883 cents 270:285:302:320:339:360:380:404:428:453:480:507:540 SD: 0.1861 cents 387:409:433:459:486:516:545:579:613:650:688:727:774 SD: 0.1849 cents 395:417:442:468:496:527:556:591:626:663:702:742:790 SD: 0.1820 cents 411:434:460:487:516:548:579:615:651:690:731:772:822 SD: 0.1330 cents 563:595:630:667:707:751:793:842:892:945:1001:1057:1126 SD: 0.1318 cents 573:605:641:679:719:764:807:857:908:962:1019:1076:1146 SD: 0.1268 cents 588:621:658:697:738:784:828:880:932:987:1045:1104:1176 SD: 0.1156 cents