Scala analysis: 12_lumma_6thcomma2226
1/6-comma SSSSLLLSLLLS temperament.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 98.045 cents 98.045000 2: 196.090 cents 196.090000 3: 298.045 cents 298.045000 4: 392.180 cents 392.180000 5: 501.955 cents 501.955000 6: 596.090 cents 596.090000 7: 698.045 cents 698.045000 8: 796.090 cents 796.090000 9: 894.135 cents 894.135000 10: 1000.000 cents 1000.000000 11: 1094.135 cents 1094.135000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 105.8650 cents 105.8650 1: 98.0450 cents 98.0450 2: 98.0450 cents 98.0450 3: 101.9550 cents 101.9550 4: 94.1350 cents 94.1350 5: 109.7750 cents 109.7750 6: 94.1350 cents 94.1350 7: 101.9550 cents 101.9550 8: 98.0450 cents 98.0450 9: 98.0450 cents 98.0450 10: 105.8650 cents 105.8650 11: 94.1350 cents 94.1350 12: 105.8650 cents 105.8650
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 94.13500 cents 1: 4 98.04500 cents 1: 2 101.95500 cents 1: 2 105.86500 cents 1: 1 109.77500 cents 2: 4 196.09000 cents 2: 4 200.00000 cents 2: 4 203.91000 cents 3: 2 294.13500 cents 3: 5 298.04500 cents 3: 2 301.95500 cents 3: 3 305.86500 cents 4: 2 392.18000 cents 4: 2 396.09000 cents 4: 2 400.00000 cents 4: 6 403.91000 cents 5: 6 498.04500 cents 5: 6 501.95500 cents 6: 2 592.18000 cents 6: 2 596.09000 cents 6: 4 600.00000 cents 6: 2 603.91000 cents 6: 2 607.82000 cents 7: 6 698.04500 cents 7: 6 701.95500 cents 8: 6 796.09000 cents 8: 2 800.00000 cents 8: 2 803.91000 cents 8: 2 807.82000 cents 9: 3 894.13500 cents 9: 2 898.04500 cents 9: 5 901.95500 cents 9: 2 905.86500 cents 10: 4 996.09000 cents 10: 4 1000.00000 cents 10: 4 1003.91000 cents 11: 1 1090.22500 cents 11: 2 1094.13500 cents 11: 2 1098.04500 cents 11: 4 1101.95500 cents 11: 3 1105.86500 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.72727 = 41/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 98.0 196.1 298.0 392.2 502.0 596.1 698.0 796.1 894.1 1000.0 1094.1 1200.0 98.0 : 98.0 200.0 294.1 403.9 498.0 600.0 698.0 796.1 902.0 996.1 1102.0 1200.0 196.1 : 102.0 196.1 305.9 400.0 502.0 600.0 698.0 803.9 898.0 1003.9 1102.0 1200.0 298.0 : 94.1 203.9 298.0 400.0 498.0 596.1 702.0 796.1 902.0 1000.0 1098.0 1200.0 392.2 : 109.8 203.9 305.9 403.9 502.0 607.8 702.0 807.8 905.9 1003.9 1105.9 1200.0 502.0 : 94.1 196.1 294.1 392.2 498.0 592.2 698.0 796.1 894.1 996.1 1090.2 1200.0 596.1 : 102.0 200.0 298.0 403.9 498.0 603.9 702.0 800.0 902.0 996.1 1105.9 1200.0 698.0 : 98.0 196.1 302.0 396.1 502.0 600.0 698.0 800.0 894.1 1003.9 1098.0 1200.0 796.1 : 98.0 203.9 298.0 403.9 502.0 600.0 702.0 796.1 905.9 1000.0 1102.0 1200.0 894.1 : 105.9 200.0 305.9 403.9 502.0 603.9 698.0 807.8 902.0 1003.9 1102.0 1200.0 1000.0: 94.1 200.0 298.0 396.1 498.0 592.2 702.0 796.1 898.0 996.1 1094.1 1200.0 1094.1: 105.9 203.9 302.0 403.9 498.0 607.8 702.0 803.9 902.0 1000.0 1105.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 94.1350 .. 109.7750 cents 15.64000 cents 94.13500 cents 2: 196.0900 .. 203.9100 cents 7.82000 cents 86.31500 cents 3: 294.1350 .. 305.8650 cents 11.73000 cents 90.22500 cents 4: 392.1800 .. 403.9100 cents 11.73000 cents 86.31500 cents 5: 498.0450 .. 501.9550 cents 3.91000 cents 94.13500 cents 6: 592.1800 .. 607.8200 cents 15.64000 cents 90.22500 cents 7: 698.0450 .. 701.9550 cents 3.91000 cents 90.22500 cents 8: 796.0900 .. 807.8200 cents 11.73000 cents 94.13500 cents 9: 894.1350 .. 905.8650 cents 11.73000 cents 86.31500 cents 10: 996.0900 .. 1003.9100 cents 7.82000 cents 90.22500 cents 11: 1090.2250 .. 1105.8650 cents 15.64000 cents 86.31500 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 94.13500 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 109.77500 cents Average / Smallest step : 1.062304 Largest / Average step : 1.097750 Largest / Smallest step : 1.166144 Median interval of one step : 98.04500 cents, amount: 4 Most common interval of one step : 98.04500 cents, amount: 4 Least squares average step : 99.65712 cents, oct.: 1195.88548 cents Scale is strictly proper Step pattern alph. order: AABCDCBAAECE Step pattern size order : BBCAEACBBDAD Scale is a Constant Structure, by a margin of 86.31500 cents Scale diversity : 1.080405 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.902250 Rothenberg efficiency : 0.312031 redundancy: 0.687969 Efficiency x scale size : 3.744372 Number of different interval sizes : 41 = 3.72727 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 3.72727 = 41/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 3.91000 cents 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 : 3 = 25.0000% Limited transpositions with margin 11.7300 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: 3.9906 c. M:-7.8200 c. Twelve-tone Chromatic (1/11-comma) 59: 5 5 5 4 6 4 5 5 5 5 5 5 SP D3 SD: 5.0910 c. M:-7.2998 c. 62: 5 5 5 5 6 5 5 5 5 6 4 6 SP D3 SD: 4.8308 c. M: 10.2640 c. 67: 5 6 6 5 6 5 6 5 6 6 5 6 SP M ME SD: 4.2967 c. M: 8.4928 c. Meantone Chromatic (4/25-comma) 71: 6 6 6 5 7 5 6 6 6 6 6 6 SP D3 SD: 4.2079 c. M:-6.7269 c. 74: 6 6 6 6 7 6 6 6 6 7 5 7 SP D3 SD: 3.6628 c. M: 7.6485 c. 76: 6 6 7 6 7 6 6 6 7 6 6 7 SP D3 SD: 4.3766 c. M: 6.6163 c. 77: 6 6 7 6 7 6 7 6 6 7 6 7 SP M ME SD: 4.1061 c. M: 9.0770 c. 79: 6 7 7 6 7 6 7 6 7 7 6 7 SP M ME SD: 3.5865 c. M: 6.9058 c. Meantone Chromatic (3/20-comma) 82: 7 6 7 7 7 7 7 6 7 7 7 7 SP B ME SD: 4.2486 c. M: 5.8461 c. 83: 7 7 7 6 8 6 7 7 7 7 7 7 SP D3 SD: 3.6719 c. M:-6.3196 c. 86: 7 7 7 7 8 7 7 7 7 8 6 8 SP D3 SD: 2.8910 c. M: 5.7629 c. 89: 7 7 8 7 8 7 8 7 7 8 7 8 SP M ME SD: 3.2257 c. M: 7.3260 c. 91: 7 8 8 7 8 7 8 7 8 8 7 8 SP M ME SD: 3.1519 c. M: 5.7373 c. Meantone Chromatic (1/7-comma), Romieu-12 94: 8 7 8 8 8 8 8 7 8 8 8 8 SP B ME SD: 3.7890 c. M: 4.6006 c. 95: 8 8 8 7 9 7 8 8 8 8 8 8 SP D3 SD: 3.3469 c. M:-6.0153 c. 98: 8 8 8 8 9 8 8 8 8 9 7 9 SP D3 SD: 2.3876 c. M: 4.3391 c. 101: 8 8 9 8 9 8 9 8 8 9 8 9 SP M ME SD: 2.6095 c. M: 5.9910 c. 102: 8 9 8 8 10 8 8 9 8 9 8 9 SP D3 SD: 3.2031 c. M: 3.9447 c. 103: 8 9 9 8 9 8 9 8 9 9 8 9 SP M ME SD: 2.8938 c. M:-4.8676 c. Meantone Chromatic (3/22-comma) 110: 9 9 9 9 10 9 9 9 9 10 8 10 SP D3 SD: 2.0784 c. M:-3.9100 c. 113: 9 9 10 9 10 9 10 9 9 10 9 10 SP M ME SD: 2.1873 c. M: 4.9396 c. 122: 10 10 10 10 11 10 10 10 10 11 9 11 SP D3 SD: 1.9114 c. M:-3.9100 c. 125: 10 10 11 10 11 10 11 10 10 11 10 11 SP M ME SD: 1.9151 c. M: 4.0900 c. 134: 11 11 11 11 12 11 11 11 11 12 10 12 SP D3 SD: 1.8442 c. M:-3.9100 c. 137: 11 11 12 11 12 11 12 11 11 12 11 12 SP M ME SD: 1.7596 c. M: 3.3893 c. 145: 12 12 12 11 14 11 12 12 12 13 11 13 SP SD: 1.8813 c. M: 3.2145 c. 146: 12 12 12 12 13 12 12 12 12 13 11 13 SP D3 SD: 1.8424 c. M:-3.9100 c. 149: 12 12 13 12 13 12 13 12 12 13 12 13 SP M ME SD: 1.6912 c. M: 2.8014 c. 157: 13 13 13 12 15 12 13 13 13 14 12 14 SP SD: 1.6125 c. M:-2.6361 c. 158: 13 13 13 13 14 13 13 13 13 14 12 14 SP D3 SD: 1.8799 c. M:-3.9100 c. 160: 13 13 14 12 15 12 14 13 13 14 13 14 SP SD: 1.6932 c. M: 3.5900 c. 161: 13 13 14 13 14 13 14 13 13 14 13 14 SP M ME SD: 1.6836 c. M:-2.8511 c. 169: 14 14 14 13 16 13 14 14 14 15 13 15 SP SD: 1.4294 c. M:-2.7266 c. 172: 14 14 15 13 16 13 15 14 14 15 14 15 SP SD: 1.4449 c. M: 3.0667 c. 181: 15 15 15 14 17 14 15 15 15 16 14 16 SP SD: 1.3215 c. M:-2.8050 c. 184: 15 15 16 14 17 14 16 15 15 16 15 16 SP SD: 1.2714 c. M: 2.6117 c. 192: 16 15 17 15 17 15 17 15 16 17 15 17 SP T3 SD: 1.6950 c. M: 2.3400 c. 193: 16 16 16 15 18 15 16 16 16 17 15 17 SP SD: 1.2760 c. M:-2.8737 c. 196: 16 16 17 15 18 15 17 16 16 17 16 17 SP SD: 1.1665 c. M: 2.2124 c. 200: 16 17 17 15 19 15 17 17 16 18 15 18 SP SD: 1.8565 c. M: 2.1800 c. 201: 16 17 17 16 18 16 17 16 17 18 15 18 SP SD: 1.5751 c. M:-2.9851 c. 204: 17 16 18 16 18 16 18 16 17 18 16 18 SP T3 SD: 1.5998 c. M: 1.9724 c. 205: 17 17 17 16 19 16 17 17 17 18 16 18 SP SD: 1.2783 c. M:-2.9344 c. 208: 17 17 18 16 19 16 18 17 17 18 17 18 SP SD: 1.1214 c. M:-2.0188 c. 217: 18 18 18 17 20 17 18 18 18 19 17 19 SP SD: 1.3138 c. M:-2.9883 c. 220: 18 18 19 17 20 17 19 18 18 19 18 19 SP SD: 1.1238 c. M:-2.2286 c. 234: 19 19 20 18 22 18 20 19 19 21 18 21 SP SD: 1.2433 c. M: 2.4364 c. 239: 20 19 20 19 22 19 20 20 19 21 19 21 SP SD: 1.2019 c. M:-2.3734 c. 244: 20 20 21 19 22 19 21 20 20 21 19 22 SP SD: 1.1744 c. M: 2.3317 c. 246: 20 20 21 19 23 19 21 20 20 22 19 22 SP SD: 0.9880 c. M: 1.9361 c. 247: 20 20 21 20 22 20 21 20 20 22 19 22 SP SD: 1.2145 c. M: 1.7580 c. 251: 21 20 21 20 23 20 21 21 20 22 20 22 SP SD: 1.1909 c. M:-2.3534 c. 256: 21 21 22 20 23 20 22 21 21 22 20 23 SP SD: 1.1621 c. M:-1.9550 c. 258: 21 21 22 20 24 20 22 21 21 23 20 23 SP SD: 0.7564 c. M: 1.4823 c. 270: 22 22 23 21 25 21 23 22 22 24 21 24 SP SD: 0.5455 c. M: 1.0689 c. 282: 23 23 24 22 26 22 24 23 23 25 22 25 SP SD: 0.3524 c. M: 0.6906 c. 294: 24 24 25 23 27 23 25 24 24 26 23 26 SP SD: 0.1752 c. M: 0.3433 c. 306: 25 25 26 24 28 24 26 25 25 27 24 27 SP SD: 0.0118 c. M: 0.0231 c. 2154: 176 176 183 169 197 169 183 176 176 190 169 190 SP SD: 0.0105 c. M:-0.0206 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: 1.9550 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.5097 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.9903 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.6731 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2834 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.8216 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.9236 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.8411 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.2566 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.8817 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.3184 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.6826 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.4877 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.9553 cents 20:21:22:24:25:27:28:30:32:34:36:38:40 SD: 4.9406 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.4284 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.7451 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.2316 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.8887 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 1.9967 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 1.9898 cents 48:51:54:57:60:64:68:72:76:80:86:90:96 SD: 1.7552 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.6658 cents 51:54:57:61:64:68:72:76:81:85:91:96:102 SD: 1.5669 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.4594 cents 65:69:73:77:82:87:92:97:103:109:116:122:130 SD: 1.3491 cents 68:72:76:81:85:91:96:102:108:114:121:128:136 SD: 0.9227 cents 83:88:93:99:104:111:117:124:131:139:148:156:166 SD: 0.9200 cents 86:91:96:102:108:115:121:129:136:144:153:162:172 SD: 0.8611 cents 101:107:113:120:127:135:143:151:160:169:180:190:202 SD: 0.7120 cents 117:124:131:139:147:156:165:175:185:196:208:220:234 SD: 0.6356 cents 133:141:149:158:167:178:188:199:211:223:237:250:266 SD: 0.5334 cents 149:158:167:177:187:199:210:223:236:250:265:280:298 SD: 0.5110 cents 151:160:169:179:189:202:213:226:239:253:269:284:302 SD: 0.5073 cents 161:170:180:191:202:215:227:241:255:270:287:303:322 SD: 0.4884 cents 169:179:189:201:212:226:238:253:268:283:301:318:338 SD: 0.4843 cents 170:180:190:202:213:227:240:254:269:285:303:320:340 SD: 0.4694 cents 175:185:196:208:219:234:247:262:277:293:312:329:350 SD: 0.4452 cents 185:196:207:220:232:247:261:277:293:310:330:348:370 SD: 0.3454 cents 224:237:251:266:281:299:316:335:355:375:399:421:448 SD: 0.3315 cents 240:254:269:285:301:321:339:359:380:402:428:452:480 SD: 0.3299 cents 241:255:270:286:302:322:340:361:382:404:429:453:482 SD: 0.3258 cents 243:257:272:289:305:325:343:364:385:407:433:457:486 SD: 0.3226 cents 244:258:273:290:306:326:344:365:386:409:435:459:488 SD: 0.3106 cents 256:271:287:304:321:342:361:383:405:429:456:482:512 SD: 0.2862 cents 260:275:291:309:326:347:367:389:412:436:463:489:520 SD: 0.2839 cents 276:292:309:328:346:369:389:413:437:463:492:519:552 SD: 0.2674 cents 294:311:329:349:369:393:415:440:466:493:524:553:588 SD: 0.2443 cents 324:343:363:385:406:433:457:485:513:543:577:610:648 SD: 0.2201 cents 358:379:401:425:449:478:505:536:567:600:638:674:716 SD: 0.2061 cents 377:399:422:448:473:504:532:564:597:632:672:709:754 SD: 0.1576 cents 499:528:559:593:626:667:704:747:790:836:889:939:998 SD: 0.1374 cents 550:582:616:653:690:735:776:823:871:922:980:1035:1100 SD: 0.0966 cents