Scala analysis: 12_lumma_6thcomma1335
1/6-comma SSSLSLLSLLLS 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: 396.090 cents 396.090000 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: 98.0450 cents 98.0450 5: 105.8650 cents 105.8650 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: 2 94.13500 cents 1: 5 98.04500 cents 1: 2 101.95500 cents 1: 3 105.86500 cents 2: 3 196.09000 cents 2: 6 200.00000 cents 2: 3 203.91000 cents 3: 1 294.13500 cents 3: 6 298.04500 cents 3: 3 301.95500 cents 3: 2 305.86500 cents 4: 1 392.18000 cents 4: 3 396.09000 cents 4: 3 400.00000 cents 4: 5 403.91000 cents 5: 6 498.04500 cents 5: 6 501.95500 cents 6: 1 592.18000 cents 6: 3 596.09000 cents 6: 4 600.00000 cents 6: 3 603.91000 cents 6: 1 607.82000 cents 7: 6 698.04500 cents 7: 6 701.95500 cents 8: 5 796.09000 cents 8: 3 800.00000 cents 8: 3 803.91000 cents 8: 1 807.82000 cents 9: 2 894.13500 cents 9: 3 898.04500 cents 9: 6 901.95500 cents 9: 1 905.86500 cents 10: 3 996.09000 cents 10: 6 1000.00000 cents 10: 3 1003.91000 cents 11: 3 1094.13500 cents 11: 2 1098.04500 cents 11: 5 1101.95500 cents 11: 2 1105.86500 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.54545 = 39/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 98.0 196.1 298.0 396.1 502.0 596.1 698.0 796.1 894.1 1000.0 1094.1 1200.0 98.0 : 98.0 200.0 298.0 403.9 498.0 600.0 698.0 796.1 902.0 996.1 1102.0 1200.0 196.1 : 102.0 200.0 305.9 400.0 502.0 600.0 698.0 803.9 898.0 1003.9 1102.0 1200.0 298.0 : 98.0 203.9 298.0 400.0 498.0 596.1 702.0 796.1 902.0 1000.0 1098.0 1200.0 396.1 : 105.9 200.0 302.0 400.0 498.0 603.9 698.0 803.9 902.0 1000.0 1102.0 1200.0 502.0 : 94.1 196.1 294.1 392.2 498.0 592.2 698.0 796.1 894.1 996.1 1094.1 1200.0 596.1 : 102.0 200.0 298.0 403.9 498.0 603.9 702.0 800.0 902.0 1000.0 1105.9 1200.0 698.0 : 98.0 196.1 302.0 396.1 502.0 600.0 698.0 800.0 898.0 1003.9 1098.0 1200.0 796.1 : 98.0 203.9 298.0 403.9 502.0 600.0 702.0 800.0 905.9 1000.0 1102.0 1200.0 894.1 : 105.9 200.0 305.9 403.9 502.0 603.9 702.0 807.8 902.0 1003.9 1102.0 1200.0 1000.0: 94.1 200.0 298.0 396.1 498.0 596.1 702.0 796.1 898.0 996.1 1094.1 1200.0 1094.1: 105.9 203.9 302.0 403.9 502.0 607.8 702.0 803.9 902.0 1000.0 1105.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 94.1350 .. 105.8650 cents 11.73000 cents 94.13500 cents 2: 196.0900 .. 203.9100 cents 7.82000 cents 90.22500 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: 1094.1350 .. 1105.8650 cents 11.73000 cents 90.22500 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 : 105.86500 cents Average / Smallest step : 1.062304 Largest / Average step : 1.058650 Largest / Smallest step : 1.124608 Median interval of one step : 98.04500 cents, amount: 5 Most common interval of one step : 98.04500 cents, amount: 5 Least squares average step : 99.68118 cents, oct.: 1196.17422 cents Scale is strictly proper Step pattern alph. order: AABACDBAACDC Step pattern size order : BBCBDACBBDAD Scale is a Constant Structure, by a margin of 86.31500 cents Scale diversity : 1.074914 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.908767 Rothenberg efficiency : 0.326269 redundancy: 0.673731 Efficiency x scale size : 3.915224 Number of different interval sizes : 39 = 3.54545 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 3.54545 = 39/11 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 with margin 11.7300 cents: 1 2 3 4 5 6 7 8 9 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: 3.4789 c. M:-5.8650 c. Twelve-tone Chromatic (1/11-comma) 78: 6 7 6 7 7 6 6 7 6 7 6 7 SP D3 SD: 4.0773 c. M: 5.7373 c. 79: 6 7 7 6 7 6 7 6 7 7 6 7 SP M ME SD: 3.5129 c. M: 6.9058 c. Meantone Chromatic (3/20-comma) 86: 7 7 7 7 8 7 7 7 7 8 6 8 SP D3 SD: 3.2554 c. M: 5.7629 c. 90: 7 8 7 8 8 7 7 8 7 8 7 8 SP D3 SD: 3.5501 c. M: 4.7117 c. 91: 7 8 8 7 8 7 8 7 8 8 7 8 SP M ME SD: 2.9961 c. M: 5.7373 c. Meantone Chromatic (1/7-comma), Romieu-12 98: 8 8 8 8 9 8 8 8 8 9 7 9 SP D3 SD: 2.6830 c. M: 4.3391 c. 101: 8 8 9 8 9 8 9 8 8 9 8 9 SP M ME SD: 2.8547 c. M: 5.9910 c. 102: 8 9 8 9 9 8 8 9 8 9 8 9 SP D3 SD: 3.1996 c. M: 3.9274 c. 103: 8 9 9 8 9 8 9 8 9 9 8 9 SP M ME SD: 2.6614 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: 2.2885 c. M:-3.9100 c. 113: 9 9 10 9 10 9 10 9 9 10 9 10 SP M ME SD: 2.3614 c. M: 4.9396 c. 121: 10 10 10 10 11 9 10 10 10 11 9 11 SP SD: 2.2427 c. M:-3.8301 c. 122: 10 10 10 10 11 10 10 10 10 11 9 11 SP D3 SD: 2.0260 c. M:-3.9100 c. 125: 10 10 11 10 11 10 11 10 10 11 10 11 SP M ME SD: 2.0041 c. M: 4.0900 c. 133: 11 11 11 11 12 10 11 11 11 12 10 12 SP SD: 1.9080 c. M: 3.3082 c. 134: 11 11 11 11 12 11 11 11 11 12 10 12 SP D3 SD: 1.8627 c. M:-3.9100 c. 137: 11 11 12 11 12 11 12 11 11 12 11 12 SP M ME SD: 1.7548 c. M: 3.3893 c. 145: 12 12 12 12 13 11 12 12 12 13 11 13 SP SD: 1.6699 c. M:-2.8726 c. 149: 12 12 13 12 13 12 13 12 12 13 12 13 SP M ME SD: 1.5928 c. M: 2.8014 c. 157: 13 13 13 13 14 12 13 13 13 14 12 14 SP SD: 1.5121 c. M:-2.6361 c. 161: 13 13 14 13 14 13 14 13 13 14 13 14 SP M ME SD: 1.5002 c. M: 2.5761 c. 169: 14 14 14 14 15 13 14 14 14 15 13 15 SP SD: 1.4197 c. M:-2.7266 c. 173: 14 14 15 14 15 14 15 14 14 15 14 15 SP M ME SD: 1.4605 c. M: 2.5330 c. 181: 15 15 15 15 16 14 15 15 15 16 14 16 SP SD: 1.3786 c. M:-2.8050 c. 184: 15 15 16 15 16 14 16 15 15 16 15 16 SP D3 SD: 1.3430 c. M: 2.6117 c. 185: 15 15 16 15 16 15 16 15 15 16 15 16 SP M ME SD: 1.4587 c. M: 2.4955 c. 193: 16 16 16 16 17 15 16 16 16 17 15 17 SP SD: 1.3752 c. M:-2.8737 c. 196: 16 16 17 16 17 15 17 16 16 17 16 17 SP D3 SD: 1.2814 c. M: 2.2124 c. 205: 17 17 17 17 18 16 17 17 17 18 16 18 SP SD: 1.3978 c. M:-2.9344 c. 208: 17 17 18 17 18 16 18 17 17 18 17 18 SP D3 SD: 1.2590 c. M:-2.0188 c. 216: 18 17 19 17 19 17 19 17 18 19 17 19 SP T3 SD: 1.4807 c. M: 1.9550 c. 217: 18 18 18 18 19 17 18 18 18 19 17 19 SP SD: 1.4372 c. M:-2.9883 c. 220: 18 18 19 18 19 17 19 18 18 19 18 19 SP D3 SD: 1.2659 c. M:-2.2286 c. 222: 18 18 19 18 20 17 19 18 18 20 17 20 SP SD: 1.3305 c. M: 2.2431 c. 227: 19 18 19 19 20 18 19 19 18 20 18 20 SP SD: 1.2200 c. M:-2.3955 c. 234: 19 19 20 19 21 18 20 19 19 21 18 21 SP SD: 1.0839 c. M: 1.8273 c. 246: 20 20 21 20 22 19 21 20 20 22 19 22 SP SD: 0.8613 c. M: 1.4521 c. 258: 21 21 22 21 23 20 22 21 21 23 20 23 SP SD: 0.6595 c. M: 1.1117 c. 270: 22 22 23 22 24 21 23 22 22 24 21 24 SP SD: 0.4755 c. M: 0.8017 c. 282: 23 23 24 23 25 22 24 23 23 25 22 25 SP SD: 0.3072 c. M: 0.5180 c. 294: 24 24 25 24 26 23 25 24 24 26 23 26 SP SD: 0.1527 c. M: 0.2574 c. 306: 25 25 26 25 27 24 26 25 25 27 24 27 SP SD: 0.0103 c. M: 0.0174 c. 2154: 176 176 183 176 190 169 183 176 176 190 169 190 SP SD: 0.0091 c. M:-0.0154 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: 8.2261 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: 10.5153 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.9770 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.1236 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: 10.7974 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.3583 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.7976 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.3377 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.8718 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.2827 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.8014 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.1897 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.8574 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1004 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.0938 cents 48:51:54:57:60:64:68:72:76:80:86:90:96 SD: 1.8723 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.5654 cents 58:61:65:69:73:78:82:87:92:97:103:109:116 SD: 1.5207 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.4954 cents 65:69:73:77:82:87:92:97:103:109:116:122:130 SD: 1.1752 cents 68:72:76:81:85:91:96:102:108:114:121:128:136 SD: 1.1297 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 1.0056 cents 86:91:96:102:108:115:121:129:136:144:153:162:172 SD: 0.8544 cents 101:107:113:120:127:135:143:151:160:169:180:190:202 SD: 0.6123 cents 117:124:131:139:147:156:165:175:185:196:208:220:234 SD: 0.5898 cents 133:141:149:158:167:178:188:199:211:223:237:250:266 SD: 0.5349 cents 151:160:169:179:190:202:213:226:239:253:269:284:302 SD: 0.4330 cents 175:185:196:208:220:234:247:262:277:293:312:329:350 SD: 0.3053 cents 241:255:270:286:303:322:340:361:382:404:429:453:482 SD: 0.2994 cents 256:271:287:304:322:342:361:383:405:429:456:482:512 SD: 0.2958 cents 260:275:291:309:327:347:367:389:412:436:463:489:520 SD: 0.2889 cents 276:292:309:328:347:369:389:413:437:463:492:519:552 SD: 0.2584 cents 292:309:327:347:367:390:412:437:462:489:520:549:584 SD: 0.2516 cents 324:343:363:385:407:433:457:485:513:543:577:610:648 SD: 0.2038 cents 377:399:422:448:474:504:532:564:597:632:672:709:754 SD: 0.1528 cents 467:494:523:555:587:624:659:699:740:783:832:879:934 SD: 0.1459 cents 532:563:596:632:669:711:751:796:843:892:948:1001:1064 SD: 0.1360 cents 533:564:597:633:670:712:752:798:844:893:950:1003:1066 SD: 0.1240 cents 550:582:616:653:691:735:776:823:871:922:980:1035:1100 SD: 0.1219 cents