Scala analysis: 12_lumma_6thcomma2226_tuning_69860_70000
1/6-comma SSSSLLLSLLLS temperament.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 94.135 cents 94.135000 2: 196.090 cents 196.090000 3: 294.135 cents 294.135000 4: 392.180 cents 392.180000 5: 498.045 cents 498.045000 6: 592.180 cents 592.180000 7: 698.045 cents 698.045000 8: 796.090 cents 796.090000 9: 894.135 cents 894.135000 10: 996.090 cents 996.090000 11: 1090.225 cents 1090.225000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 109.7750 cents 109.7750 1: 94.1350 cents 94.1350 2: 101.9550 cents 101.9550 3: 98.0450 cents 98.0450 4: 98.0450 cents 98.0450 5: 105.8650 cents 105.8650 6: 94.1350 cents 94.1350 7: 105.8650 cents 105.8650 8: 98.0450 cents 98.0450 9: 98.0450 cents 98.0450 10: 101.9550 cents 101.9550 11: 94.1350 cents 94.1350 12: 109.7750 cents 109.7750
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 : 94.1 196.1 294.1 392.2 498.0 592.2 698.0 796.1 894.1 996.1 1090.2 1200.0 94.1 : 102.0 200.0 298.0 403.9 498.0 603.9 702.0 800.0 902.0 996.1 1105.9 1200.0 196.1 : 98.0 196.1 302.0 396.1 502.0 600.0 698.0 800.0 894.1 1003.9 1098.0 1200.0 294.1 : 98.0 203.9 298.0 403.9 502.0 600.0 702.0 796.1 905.9 1000.0 1102.0 1200.0 392.2 : 105.9 200.0 305.9 403.9 502.0 603.9 698.0 807.8 902.0 1003.9 1102.0 1200.0 498.0 : 94.1 200.0 298.0 396.1 498.0 592.2 702.0 796.1 898.0 996.1 1094.1 1200.0 592.2 : 105.9 203.9 302.0 403.9 498.0 607.8 702.0 803.9 902.0 1000.0 1105.9 1200.0 698.0 : 98.0 196.1 298.0 392.2 502.0 596.1 698.0 796.1 894.1 1000.0 1094.1 1200.0 796.1 : 98.0 200.0 294.1 403.9 498.0 600.0 698.0 796.1 902.0 996.1 1102.0 1200.0 894.1 : 102.0 196.1 305.9 400.0 502.0 600.0 698.0 803.9 898.0 1003.9 1102.0 1200.0 996.1 : 94.1 203.9 298.0 400.0 498.0 596.1 702.0 796.1 902.0 1000.0 1098.0 1200.0 1090.2: 109.8 203.9 305.9 403.9 502.0 607.8 702.0 807.8 905.9 1003.9 1105.9 1200.0 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 : 99.44057 cents, oct.: 1193.28683 cents Scale is strictly proper Step pattern alph. order: ABCCDADCCBAE Step pattern size order : ACBBDADBBCAE 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 : 1 = 8.3333% Limited transpositions with margin 15.6400 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: 5.5869 c. M:-9.7750 c. Twelve-tone Chromatic (1/11-comma) 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 5.0029 c. M: 11.1161 c. Schismic-12 54: 4 5 4 5 4 5 4 5 4 5 4 5 SP B ME SD: 5.9174 c. M: 9.1561 c. 55: 4 5 4 5 5 4 5 4 5 5 4 5 SP M ME SD: 5.4174 c. M: 10.6355 c. 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.6359 c. M: 7.9812 c. 66: 5 6 5 6 5 6 5 6 5 6 5 6 SP B ME SD: 5.0141 c. M:-7.8200 c. 67: 5 6 5 6 6 5 6 5 6 6 5 6 SP M ME SD: 4.2352 c. M: 8.0303 c. 74: 6 6 6 6 7 5 7 6 6 6 6 7 SP D3 SD: 3.9563 c. M: 8.3962 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 2.9154 c. M:-6.5074 c. 79: 6 7 6 7 7 6 7 6 7 7 6 7 SP M ME SD: 3.6080 c. M:-6.4416 c. 86: 7 7 7 7 8 6 8 7 7 7 7 8 SP D3 SD: 2.9845 c. M: 6.1335 c. 87: 7 7 7 7 8 7 8 7 7 7 7 8 SP D3 SD: 3.3311 c. M: 5.9731 c. 89: 7 8 7 7 8 7 8 7 7 8 7 8 SP M ME SD: 2.6090 c. M:-6.1572 c. 90: 7 8 7 7 8 7 8 8 7 8 7 8 SP D3 SD: 3.6816 c. M: 5.5133 c. 91: 7 8 7 8 8 7 8 7 8 8 7 8 SP M ME SD: 3.3143 c. M:-6.1078 c. 98: 8 8 8 8 9 7 9 8 8 8 8 9 SP D3 SD: 2.3938 c. M: 4.4249 c. 101: 8 9 8 8 9 8 9 8 8 9 8 9 SP M ME SD: 2.5520 c. M:-5.8902 c. 102: 8 9 8 8 9 8 9 9 8 9 8 9 SP D3 SD: 3.2014 c. M: 3.9447 c. 105: 8 9 9 8 10 8 9 9 8 9 8 10 SP SD: 2.9898 c. M:-4.8121 c. 110: 9 9 9 9 10 8 10 9 9 9 9 10 SP D3 SD: 2.0964 c. M:-4.0468 c. 122: 10 10 10 10 11 9 11 10 10 10 10 11 SP D3 SD: 2.0130 c. M:-4.2257 c. 131: 10 11 11 11 11 11 11 11 11 11 10 12 SP D3 SD: 2.3959 c. M: 3.7236 c. 134: 11 11 11 11 12 10 12 11 11 11 11 12 SP D3 SD: 2.0632 c. M:-4.3725 c. 140: 11 12 11 12 12 11 12 12 11 12 11 13 SP D3 SD: 1.8891 c. M: 3.7593 c. 142: 11 12 12 11 13 11 13 11 12 12 11 13 SP D3 SD: 1.7749 c. M: 3.4476 c. 152: 12 13 12 13 13 12 13 13 12 13 12 14 SP D3 SD: 1.6384 c. M: 3.3082 c. 154: 12 13 13 12 14 12 14 12 13 13 12 14 SP D3 SD: 1.6140 c. M:-3.2537 c. 164: 13 14 13 14 14 13 14 14 13 14 13 15 SP D3 SD: 1.5314 c. M:-2.9420 c. 166: 13 14 14 13 15 13 15 13 14 14 13 15 SP D3 SD: 1.5828 c. M:-3.1598 c. 172: 13 15 14 14 15 14 15 14 14 15 13 16 SP SD: 1.6239 c. M: 3.4373 c. 175: 14 15 14 14 16 13 16 14 14 15 14 16 SP SD: 1.7983 c. M:-2.7671 c. 176: 14 15 14 15 15 14 15 15 14 15 14 16 SP D3 SD: 1.5365 c. M:-3.2745 c. 184: 14 16 15 15 16 15 16 15 15 16 14 17 SP SD: 1.3446 c. M: 2.8307 c. 192: 15 16 16 16 17 15 17 15 16 16 15 18 SP SD: 1.7529 c. M: 2.7250 c. 193: 15 16 16 16 17 15 17 16 16 16 15 18 SP SD: 1.5538 c. M: 3.3439 c. 195: 15 17 16 16 17 15 17 16 16 17 15 18 SP SD: 1.5185 c. M: 2.6604 c. 196: 15 17 16 16 17 16 17 16 16 17 15 18 SP SD: 1.1790 c. M: 2.2983 c. 200: 16 17 16 16 18 16 17 17 16 17 16 18 SP SD: 1.4781 c. M: 2.1800 c. 204: 16 17 17 17 18 16 18 16 17 17 16 19 SP SD: 1.6016 c. M: 1.9897 c. 205: 16 17 17 17 18 16 18 17 17 17 16 19 SP SD: 1.2696 c. M: 2.9193 c. 208: 16 18 17 17 18 17 18 17 17 18 16 19 SP SD: 1.1232 c. M:-2.0508 c. 217: 17 18 18 18 19 17 19 18 18 18 17 20 SP SD: 1.0763 c. M: 2.5416 c. 229: 18 19 19 19 20 18 20 19 19 19 18 21 SP SD: 0.9798 c. M: 2.2035 c. 241: 19 20 20 20 21 19 21 20 20 20 19 22 SP SD: 0.9743 c. M:-2.1306 c. 252: 20 21 21 20 23 19 23 20 21 21 20 23 SP SD: 1.2695 c. M:-1.9550 c. 253: 20 21 21 21 22 20 22 21 21 21 20 23 SP SD: 1.0375 c. M:-2.3077 c. 258: 20 22 21 21 23 20 23 21 21 22 20 24 SP SD: 1.0590 c. M: 1.8529 c. 270: 21 23 22 22 24 21 24 22 22 23 21 25 SP SD: 0.7637 c. M: 1.3361 c. 282: 22 24 23 23 25 22 25 23 23 24 22 26 SP SD: 0.4934 c. M: 0.8633 c. 294: 23 25 24 24 26 23 26 24 24 25 23 27 SP SD: 0.2452 c. M: 0.4291 c. 306: 24 26 25 25 27 24 27 25 25 26 24 28 SP SD: 0.0165 c. M: 0.0289 c. 2154: 169 183 176 176 190 169 190 176 176 183 169 197 SP SD: 0.0147 c. M:-0.0257 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: 3.2588 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.0402 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.2887 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.3731 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.8427 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.3875 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.1279 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.2604 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.2155 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.4455 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.2612 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.8444 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.1146 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 5.0831 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 5.0025 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 3.9796 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.5384 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.4600 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.9395 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1963 cents 39:41:44:46:49:52:55:58:62:65:69:73:78 SD: 2.1375 cents 48:51:54:57:60:64:68:72:76:80:85:90:96 S SD: 1.8672 cents 49:52:55:58:61:65:69:73:78:82:87:92:98 SD: 1.8522 cents 50:53:56:59:63:67:70:75:79:84:89:94:100 SD: 1.6554 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.3953 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.3346 cents 66:70:74:78:83:88:93:99:105:111:117:124:132 SD: 1.3119 cents 71:75:80:84:89:95:100:106:112:119:126:133:142 SD: 1.3119 cents 72:76:81:85:90:96:101:108:114:121:128:135:144 SD: 1.2392 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 1.0701 cents 75:79:84:89:94:100:106:112:119:126:133:141:150 SD: 0.9693 cents 86:91:96:102:108:115:121:129:136:144:153:161:172 SD: 0.9384 cents 90:95:101:107:113:120:127:135:143:151:160:169:180 SD: 0.8766 cents 91:96:102:108:114:121:128:136:144:153:162:171:182 SD: 0.7716 cents 108:114:121:128:135:144:152:162:171:181:192:203:216 SD: 0.6258 cents 123:130:138:146:154:164:173:184:195:206:219:231:246 SD: 0.5563 cents 145:153:162:172:182:193:204:217:230:243:258:272:290 SD: 0.5480 cents 157:166:176:186:197:209:221:235:249:263:279:295:314 SD: 0.4343 cents 177:187:198:210:222:236:249:265:280:297:315:332:354 SD: 0.4042 cents 201:212:225:238:252:268:283:301:318:337:357:377:402 SD: 0.3419 cents 216:228:242:256:271:288:304:323:342:362:384:405:432 SD: 0.2288 cents 302:319:338:358:379:403:425:452:478:506:537:567:604 SD: 0.2250 cents 318:336:356:377:399:424:448:476:504:533:565:597:636 SD: 0.2129 cents 324:342:363:384:406:432:456:485:513:543:576:608:648 SD: 0.1728 cents 432:456:484:512:542:576:608:647:684:724:768:811:864 SD: 0.1489 cents 507:535:568:601:636:676:714:759:803:850:901:952:1014 SD: 0.1471 cents 519:548:581:615:651:692:731:777:822:870:923:974:1038 SD: 0.1229 cents 594:627:665:704:745:792:836:889:941:996:1056:1115:1188 SD: 0.1045 cents