Scala analysis: 12_Sorgean_6th-comma
Sorgean 1/6-Pyth-comma temperament SSSSLSLLLSLL.
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: 298.045 cents 298.045000 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: 1094.135 cents 1094.135000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 105.8650 cents 105.8650 1: 94.1350 cents 94.1350 2: 101.9550 cents 101.9550 3: 101.9550 cents 101.9550 4: 94.1350 cents 94.1350 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: 98.0450 cents 98.0450 12: 105.8650 cents 105.8650
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 94.13500 cents 1: 3 98.04500 cents 1: 3 101.95500 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: 4 596.09000 cents 6: 2 600.00000 cents 6: 4 603.91000 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: 3 1098.04500 cents 11: 3 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: 3.54545 = 39/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 94.1 196.1 298.0 392.2 498.0 592.2 698.0 796.1 894.1 996.1 1094.1 1200.0 94.1 : 102.0 203.9 298.0 403.9 498.0 603.9 702.0 800.0 902.0 1000.0 1105.9 1200.0 196.1 : 102.0 196.1 302.0 396.1 502.0 600.0 698.0 800.0 898.0 1003.9 1098.0 1200.0 298.0 : 94.1 200.0 294.1 400.0 498.0 596.1 698.0 796.1 902.0 996.1 1098.0 1200.0 392.2 : 105.9 200.0 305.9 403.9 502.0 603.9 702.0 807.8 902.0 1003.9 1105.9 1200.0 498.0 : 94.1 200.0 298.0 396.1 498.0 596.1 702.0 796.1 898.0 1000.0 1094.1 1200.0 592.2 : 105.9 203.9 302.0 403.9 502.0 607.8 702.0 803.9 905.9 1000.0 1105.9 1200.0 698.0 : 98.0 196.1 298.0 396.1 502.0 596.1 698.0 800.0 894.1 1000.0 1094.1 1200.0 796.1 : 98.0 200.0 298.0 403.9 498.0 600.0 702.0 796.1 902.0 996.1 1102.0 1200.0 894.1 : 102.0 200.0 305.9 400.0 502.0 603.9 698.0 803.9 898.0 1003.9 1102.0 1200.0 996.1 : 98.0 203.9 298.0 400.0 502.0 596.1 702.0 796.1 902.0 1000.0 1098.0 1200.0 1094.1: 105.9 200.0 302.0 403.9 498.0 603.9 698.0 803.9 902.0 1000.0 1102.0 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 : 100.00000 cents, amount: 0 Least squares average step : 99.52478 cents, oct.: 1194.29742 cents Scale is strictly proper Step pattern alph. order: ABBACACDDBDC Step pattern size order : ACCADADBBCBD 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 : 0.324669 redundancy: 0.675331 Efficiency x scale size : 3.896032 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 : 1 = 8.3333% Limited transpositions with margin 15.6400 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: 4.8548 c. M:-7.8200 c. Twelve-tone Chromatic (1/11-comma) 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.9499 c. M: 7.9812 c. 73: 6 6 6 6 6 6 6 6 6 7 6 6 SP M ME SD: 5.0176 c. M: 7.6340 c. 75: 6 6 7 6 6 6 7 6 6 6 6 7 SP D3 SD: 4.3745 c. M:-7.8200 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 3.0526 c. M:-6.5074 c. 79: 6 7 7 6 7 6 7 6 7 7 6 7 SP M ME SD: 3.5011 c. M:-6.4416 c. Meantone Chromatic (3/20-comma) 86: 7 7 7 7 8 6 8 7 7 7 7 8 SP D3 SD: 3.6588 c. M: 6.1335 c. 87: 7 7 8 6 8 7 8 7 7 7 7 8 SP D3 SD: 3.6746 c. M: 5.9731 c. 89: 7 8 7 7 8 7 8 7 7 8 7 8 SP M ME SD: 2.5466 c. M:-6.1572 c. 93: 7 8 8 7 9 7 8 8 7 8 8 8 SP D3 SD: 3.1888 c. M:-5.1808 c. 98: 8 8 8 8 9 7 9 8 8 8 8 9 SP D3 SD: 2.9539 c. M: 4.4249 c. 101: 8 9 8 8 9 8 9 8 8 9 8 9 SP M ME SD: 2.3067 c. M:-5.8902 c. 110: 9 9 9 9 10 8 10 9 9 9 9 10 SP D3 SD: 2.4959 c. M:-4.0468 c. 113: 9 9 10 9 10 9 10 9 9 10 9 10 SP M ME SD: 2.0868 c. M: 4.9396 c. 114: 9 10 9 9 10 9 10 10 9 10 9 10 SP D3 SD: 2.8052 c. M:-3.9100 c. 116: 9 10 10 9 10 9 10 10 9 10 10 10 SP D3 SD: 2.4836 c. M: 4.9416 c. 117: 9 10 10 9 11 9 10 10 9 10 10 10 SP D3 SD: 2.4183 c. M:-4.5191 c. 122: 10 10 10 10 11 9 11 10 10 10 10 11 SP D3 SD: 2.2258 c. M:-4.2257 c. 125: 10 10 11 10 11 10 11 10 10 11 10 11 SP M ME SD: 2.0033 c. M: 4.0900 c. 137: 11 11 12 11 12 11 12 11 11 12 11 12 SP M ME SD: 2.0201 c. M:-3.4404 c. 140: 11 12 12 11 12 11 12 12 11 12 12 12 SP D3 SD: 1.9501 c. M: 3.7593 c. 146: 11 13 12 12 13 11 13 12 12 12 12 13 SP D3 S SD: 1.9321 c. M: 3.7240 c. 152: 12 13 13 12 13 12 13 13 12 13 13 13 SP D3 SD: 1.8664 c. M: 3.3082 c. 158: 12 14 13 13 14 12 14 13 13 13 13 14 SP D3 S SD: 1.8368 c. M:-3.2208 c. 160: 13 13 14 12 14 13 14 13 13 14 13 14 SP D3 SD: 1.7643 c. M:-3.3650 c. 166: 13 14 14 13 15 13 15 13 14 14 13 15 SP D3 SD: 1.6470 c. M:-3.1598 c. 169: 13 14 15 13 15 13 15 14 14 14 14 15 SP SD: 1.9243 c. M: 4.3740 c. 170: 13 15 14 14 15 13 15 14 14 14 14 15 SP D3 S SD: 1.8194 c. M:-3.1315 c. 172: 13 15 15 13 15 14 15 14 14 15 14 15 SP D3 S SD: 1.6399 c. M: 3.4373 c. 174: 14 14 15 14 15 14 15 14 15 14 15 15 SP D3 SD: 2.0951 c. M: 2.9866 c. 177: 14 15 15 14 15 14 16 14 15 15 14 16 SP SD: 1.6667 c. M: 3.1297 c. 178: 14 15 15 14 16 14 16 14 15 15 14 16 SP D3 SD: 1.5393 c. M:-3.0786 c. 180: 14 15 16 14 16 14 16 14 15 15 15 16 SP T3 SD: 1.7994 c. M: 2.7567 c. 181: 14 15 16 14 16 14 16 15 15 15 15 16 SP SD: 1.5818 c. M: 3.8248 c. 184: 14 16 16 14 16 15 16 15 15 16 15 16 SP D3 S SD: 1.4774 c. M: 2.8307 c. 186: 15 15 16 15 16 15 16 15 16 15 16 16 SP D3 SD: 2.0179 c. M:-2.6392 c. 188: 15 16 16 14 17 15 16 16 15 16 15 17 SP SD: 1.7196 c. M: 2.8183 c. 189: 15 16 16 15 16 15 17 15 16 16 15 17 SP SD: 1.4992 c. M: 2.8069 c. 192: 15 16 17 15 17 15 17 15 16 16 16 17 SP T3 SD: 1.6650 c. M: 2.3400 c. 193: 15 16 17 15 17 15 17 16 16 16 16 17 SP SD: 1.3208 c. M: 3.3439 c. 196: 15 17 17 15 17 16 17 16 16 17 16 17 SP D3 S SD: 1.3974 c. M: 2.2983 c. 200: 16 17 17 15 18 16 17 17 16 17 16 18 SP SD: 1.6184 c. M: 2.1800 c. 201: 16 17 17 16 17 16 18 16 17 17 16 18 SP SD: 1.4101 c. M: 2.5226 c. 204: 16 17 18 16 18 16 18 16 17 17 17 18 SP T3 SD: 1.5981 c. M: 1.9724 c. 205: 16 17 18 16 18 16 18 17 17 17 17 18 SP SD: 1.1416 c. M: 2.9193 c. 217: 17 18 19 17 19 17 19 18 18 18 18 19 SP SD: 1.0443 c. M: 2.5416 c. 229: 18 19 20 18 20 18 20 19 19 19 19 20 SP SD: 1.0215 c. M: 2.2035 c. 246: 19 21 21 19 22 19 22 20 20 21 20 22 SP SD: 1.2020 c. M: 1.9361 c. 251: 20 21 21 20 22 20 22 21 20 21 21 22 SP SD: 1.1042 c. M:-2.3164 c. 258: 20 22 22 20 23 20 23 21 21 22 21 23 SP SD: 0.9203 c. M: 1.4823 c. 270: 21 23 23 21 24 21 24 22 22 23 22 24 SP SD: 0.6636 c. M: 1.0689 c. 282: 22 24 24 22 25 22 25 23 23 24 23 25 SP SD: 0.4288 c. M: 0.6906 c. 294: 23 25 25 23 26 23 26 24 24 25 24 26 SP SD: 0.2131 c. M: 0.3433 c. 306: 24 26 26 24 27 24 27 25 25 26 25 27 SP SD: 0.0144 c. M: 0.0231 c. 2154: 169 183 183 169 190 169 190 176 176 183 176 190 SP SD: 0.0128 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: 3.2588 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: 6.8564 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2605 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.9924 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.4160 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.0750 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0497 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.1441 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.4207 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.5332 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.7764 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.0723 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 5.0666 cents 19:20:21:23:24:25:27:28:30:32:34:36:38 SD: 5.0342 cents 20:21:22:24:25:27:28:30:32:34:36:38:40 SD: 5.0270 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.1224 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.6940 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.4053 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.9155 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.2268 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.0232 cents 48:51:54:57:60:64:68:72:76:80:85:90:96 S SD: 1.9030 cents 50:53:56:59:63:67:70:75:79:84:89:94:100 SD: 1.7946 cents 51:54:57:61:64:68:72:76:81:85:91:96:102 SD: 1.7026 cents 52:55:58:62:65:69:73:78:82:87:92:98:104 SD: 1.6438 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.3022 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.2970 cents 68:72:76:81:85:91:96:102:108:114:121:128:136 SD: 1.1754 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 0.9886 cents 75:79:84:89:94:100:106:112:119:126:133:141:150 SD: 0.9435 cents 86:91:96:102:108:115:121:129:136:144:153:162:172 SD: 0.8952 cents 90:95:101:107:113:120:127:135:143:151:160:169:180 SD: 0.8090 cents 91:96:102:108:114:121:128:136:144:153:162:171:182 SD: 0.7606 cents 108:114:121:128:135:144:152:162:171:181:192:203:216 SD: 0.6916 cents 111:117:124:132:139:148:156:166:176:186:197:209:222 SD: 0.6683 cents 123:130:138:146:154:164:173:184:195:206:219:231:246 SD: 0.5763 cents 127:134:142:151:159:169:179:190:201:213:226:239:254 SD: 0.5517 cents 149:157:167:177:187:199:210:223:236:250:265:280:298 SD: 0.4986 cents 159:168:178:189:199:212:224:238:252:267:283:299:318 SD: 0.4935 cents 161:170:180:191:202:215:227:241:255:270:286:303:322 SD: 0.4647 cents 176:186:197:209:221:235:248:263:279:295:313:331:352 SD: 0.4257 cents 177:187:198:210:222:236:249:265:280:297:315:333:354 SD: 0.3977 cents 192:203:215:228:241:256:270:287:304:322:341:361:384 SD: 0.3822 cents 201:212:225:239:252:268:283:301:318:337:357:378:402 SD: 0.3314 cents 216:228:242:257:271:288:304:323:342:362:384:406:432 SD: 0.3154 cents 228:241:255:271:286:304:321:341:361:382:405:429:456 SD: 0.3148 cents 235:248:263:279:295:313:331:352:372:394:418:442:470 SD: 0.3086 cents 252:266:282:299:316:336:355:377:399:422:448:474:504 SD: 0.2725 cents 284:300:318:337:356:379:400:425:450:476:505:534:568 SD: 0.2579 cents 302:319:338:359:379:403:425:452:478:506:537:568:604 SD: 0.2493 cents 318:336:356:378:399:424:448:476:504:533:565:598:636 SD: 0.2394 cents 324:342:363:385:406:432:456:485:513:543:576:610:648 SD: 0.2026 cents 373:394:418:443:468:497:525:558:591:625:663:702:746 SD: 0.1942 cents 377:398:422:448:473:503:531:564:597:632:670:709:754 SD: 0.1861 cents 432:456:484:513:542:576:608:647:684:724:768:813:864 SD: 0.1609 cents 468:494:524:556:587:624:659:700:741:784:832:880:936 SD: 0.1606 cents 483:510:541:574:606:644:680:723:765:810:859:909:966 SD: 0.1390 cents 500:528:560:594:627:667:704:748:792:838:889:941:1000 SD: 0.1160 cents 574:606:643:682:720:765:808:859:909:962:1020:1080:1148 SD: 0.1094 cents