Scala analysis: 12_lumma_5thcomma246
1/5-comma SLSSLLLSLLLS temperament.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99.609 cents 99.609000 2: 199.218 cents 199.218000 3: 298.827 cents 298.827000 4: 393.744 cents 393.744000 5: 502.737 cents 502.737000 6: 597.654 cents 597.654000 7: 697.263 cents 697.263000 8: 796.872 cents 796.872000 9: 896.481 cents 896.481000 10: 1000.782 cents 1000.782000 11: 1095.699 cents 1095.699000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 104.3010 cents 104.3010 1: 99.6090 cents 99.6090 2: 99.6090 cents 99.6090 3: 99.6090 cents 99.6090 4: 94.9170 cents 94.9170 5: 108.9930 cents 108.9930 6: 94.9170 cents 94.9170 7: 99.6090 cents 99.6090 8: 99.6090 cents 99.6090 9: 99.6090 cents 99.6090 10: 104.3010 cents 104.3010 11: 94.9170 cents 94.9170 12: 104.3010 cents 104.3010
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 : 99.6 199.2 298.8 393.7 502.7 597.7 697.3 796.9 896.5 1000.8 1095.7 1200.0 99.6 : 99.6 199.2 294.1 403.1 498.0 597.7 697.3 796.9 901.2 996.1 1100.4 1200.0 199.2 : 99.6 194.5 303.5 398.4 498.0 597.7 697.3 801.6 896.5 1000.8 1100.4 1200.0 298.8 : 94.9 203.9 298.8 398.4 498.0 597.7 702.0 796.9 901.2 1000.8 1100.4 1200.0 393.7 : 109.0 203.9 303.5 403.1 502.7 607.0 702.0 806.3 905.9 1005.5 1105.1 1200.0 502.7 : 94.9 194.5 294.1 393.7 498.0 593.0 697.3 796.9 896.5 996.1 1091.0 1200.0 597.7 : 99.6 199.2 298.8 403.1 498.0 602.3 702.0 801.6 901.2 996.1 1105.1 1200.0 697.3 : 99.6 199.2 303.5 398.4 502.7 602.3 702.0 801.6 896.5 1005.5 1100.4 1200.0 796.9 : 99.6 203.9 298.8 403.1 502.7 602.3 702.0 796.9 905.9 1000.8 1100.4 1200.0 896.5 : 104.3 199.2 303.5 403.1 502.7 602.3 697.3 806.3 901.2 1000.8 1100.4 1200.0 1000.8: 94.9 199.2 298.8 398.4 498.0 593.0 702.0 796.9 896.5 996.1 1095.7 1200.0 1095.7: 104.3 203.9 303.5 403.1 498.0 607.0 702.0 801.6 901.2 1000.8 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 : 99.77502 cents, oct.: 1197.30030 cents Scale is strictly proper Scale is a mode of a 2301-tone equal temperament with octave 2/1 degrees: 191 382 573 755 964 1146 1337 1528 1719 1919 2101 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: AAABCBAAADBD Step pattern size order : BBBADABBBCAC 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 : 5 = 41.6667% Limited transpositions with margin 9.3840 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 10-11 -- 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: 2.9303 c. M:-6.2560 c. Twelve-tone Chromatic (1/11-comma) 71: 6 6 6 5 7 5 6 6 6 6 6 6 SP D3 SD: 3.7956 c. M: 6.1047 c. 79: 7 6 7 6 7 6 7 6 7 7 6 7 SP D3 SD: 3.6795 c. M: 6.9986 c. 83: 7 7 7 6 8 6 7 7 7 7 7 7 SP D3 SD: 3.0983 c. M: 4.8829 c. 95: 8 8 8 7 9 7 8 8 8 8 8 8 SP D3 SD: 2.6232 c. M:-4.3309 c. 107: 9 9 9 8 10 8 9 9 9 9 9 9 SP D3 SD: 2.2998 c. M:-3.9767 c. 110: 9 9 9 9 10 9 9 9 9 10 8 10 SP D3 SD: 2.4467 c. M: 4.7899 c. 119: 10 10 10 9 11 9 10 10 10 10 10 10 SP D3 SD: 2.0836 c. M:-3.6940 c. 122: 10 10 10 10 11 10 10 10 10 11 9 11 SP D3 SD: 2.1058 c. M: 3.8957 c. 128: 11 10 11 10 12 10 10 11 11 11 10 11 SP D3 SD: 2.3922 c. M:-3.5190 c. 131: 11 11 11 10 12 10 11 11 11 11 11 11 SP D3 SD: 1.9443 c. M:-3.5376 c. 134: 11 11 11 11 12 11 11 11 11 12 10 12 SP D3 SD: 1.8587 c. M: 3.3046 c. 143: 12 12 12 11 13 11 12 12 12 12 12 12 SP D3 SD: 1.8599 c. M:-3.6017 c. 146: 12 12 12 12 13 12 12 12 12 13 11 13 SP D3 SD: 1.6854 c. M: 2.9366 c. 155: 13 13 13 12 14 12 13 13 13 13 13 13 SP D3 SD: 1.8143 c. M:-3.6558 c. 157: 13 13 13 12 15 12 13 13 13 14 12 14 SP SD: 1.8432 c. M: 3.9351 c. 158: 13 13 13 13 14 13 13 13 13 14 12 14 SP D3 SD: 1.5700 c. M: 2.6245 c. 169: 14 14 14 13 16 13 14 14 14 15 13 15 SP SD: 1.5043 c. M: 3.2115 c. 170: 14 14 14 14 15 14 14 14 14 15 13 15 SP D3 SD: 1.4996 c. M: 2.3564 c. 181: 15 15 15 14 17 14 15 15 15 16 14 16 SP SD: 1.2102 c. M: 2.5838 c. 182: 15 15 15 15 16 15 15 15 15 16 14 16 SP D3 SD: 1.4632 c. M:-2.3460 c. 193: 16 16 16 15 18 15 16 16 16 17 15 17 SP SD: 0.9528 c. M: 2.0342 c. 205: 17 17 17 16 19 16 17 17 17 18 16 18 SP SD: 0.7255 c. M: 1.5489 c. 217: 18 18 18 17 20 17 18 18 18 19 17 19 SP SD: 0.5233 c. M: 1.1173 c. 229: 19 19 19 18 21 18 19 19 19 20 18 20 SP SD: 0.3424 c. M: 0.7309 c. 241: 20 20 20 19 22 19 20 20 20 21 19 21 SP SD: 0.1794 c. M: 0.3830 c. 253: 21 21 21 20 23 20 21 21 21 22 20 22 SP SD: 0.0319 c. M: 0.0681 c. 771: 64 64 64 61 70 61 64 64 64 67 61 67 SP SD: 0.0142 c. M:-0.0303 c. 1024: 85 85 85 81 93 81 85 85 85 89 81 89 SP SD: 0.0028 c. M:-0.0060 c. 2301: 191 191 191 182 209 182 191 191 191 200 182 200 SP SD: 0.0010 c. M: 0.0021 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: 4.3329 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.2856 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.5649 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.6598 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.3503 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.0385 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.0036 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.3184 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.9904 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.2817 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 9.6552 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.3308 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.8151 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.3865 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.8164 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.2593 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.7568 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 1.8775 cents 48:51:54:57:60:64:68:72:76:81:86:90:96 SD: 1.6713 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.6031 cents 51:54:57:61:64:68:72:76:81:86:91:96:102 SD: 1.4949 cents 63:67:71:75:79:84:89:94:100:106:112:119:126 SD: 1.2960 cents 65:69:73:77:82:87:92:97:103:109:116:122:130 SD: 1.1593 cents 68:72:76:81:85:91:96:102:108:114:121:128:136 SD: 1.0920 cents 83:88:93:99:104:111:117:124:132:139:148:156:166 SD: 0.9887 cents 89:94:100:106:112:119:126:133:141:149:159:168:178 SD: 0.9697 cents 97:103:109:115:122:130:137:145:154:163:173:183:194 SD: 0.8327 cents 101:107:113:120:127:135:143:151:160:170:180:190:202 SD: 0.7432 cents 106:112:119:126:133:142:150:159:168:178:189:200:212 SD: 0.7408 cents 121:128:136:144:152:162:171:181:192:203:216:228:242 SD: 0.5463 cents 133:141:149:158:167:178:188:199:211:223:237:250:266 SD: 0.4748 cents 165:175:185:196:207:221:233:247:261:277:294:311:330 SD: 0.4716 cents 180:191:202:214:226:241:254:269:285:302:321:339:360 SD: 0.4109 cents 187:198:210:222:235:250:264:280:296:314:333:352:374 SD: 0.3731 cents 223:236:250:265:280:298:315:334:353:374:398:420:446 SD: 0.3586 cents 238:252:267:283:299:318:336:356:377:399:424:448:476 SD: 0.2681 cents 255:270:286:303:320:341:360:381:404:428:455:480:510 SD: 0.2576 cents 270:286:303:321:339:361:381:404:428:453:481:508:540 SD: 0.2241 cents 286:303:321:340:359:382:404:428:453:480:510:539:572 SD: 0.2224 cents 318:337:357:378:399:425:449:476:504:534:567:599:636 SD: 0.2031 cents 371:393:416:441:466:496:524:555:588:623:661:699:742 SD: 0.1830 cents 419:444:470:498:526:560:592:627:664:703:747:789:838 SD: 0.1259 cents 541:573:607:643:679:723:764:809:857:908:964:1019:1082 SD: 0.1193 cents 573:607:643:681:719:766:809:857:908:962:1021:1079:1146 SD: 0.1189 cents 575:609:645:683:722:769:812:860:911:965:1025:1083:1150 SD: 0.1068 cents