Scala analysis: edo-14
14 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 85.714 cents 85.714286 2: 171.429 cents 171.428571 3: 257.143 cents 257.142857 4: 342.857 cents 342.857143 5: 428.571 cents 428.571429 6: 514.286 cents 514.285714 7: 600.000 cents 600.000000 8: 685.714 cents 685.714286 9: 771.429 cents 771.428571 10: 857.143 cents 857.142857 11: 942.857 cents 942.857143 12: 1028.571 cents 1028.571429 13: 1114.286 cents 1114.285714 14: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 85.7143 cents 85.7143 1: 85.7143 cents 85.7143 2: 85.7143 cents 85.7143 3: 85.7143 cents 85.7143 4: 85.7143 cents 85.7143 5: 85.7143 cents 85.7143 6: 85.7143 cents 85.7143 7: 85.7143 cents 85.7143 8: 85.7143 cents 85.7143 9: 85.7143 cents 85.7143 10: 85.7143 cents 85.7143 11: 85.7143 cents 85.7143 12: 85.7143 cents 85.7143 13: 85.7143 cents 85.7143 14: 85.7143 cents 85.7143
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 14 85.71429 cents 2: 14 171.42857 cents 3: 14 257.14286 cents 4: 14 342.85714 cents 5: 14 428.57143 cents 6: 14 514.28571 cents 7: 14 600.00000 cents 8: 14 685.71429 cents 9: 14 771.42857 cents 10: 14 857.14286 cents 11: 14 942.85714 cents 12: 14 1028.57143 cents 13: 14 1114.28571 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.0 : 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 85.7 : 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 171.4 : 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 257.1 : 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 342.9 : 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 428.6 : 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 514.3 : 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 600.0 : 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 685.7 : 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 771.4 : 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 857.1 : 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 942.9 : 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 1028.6: 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 1114.3: 85.7 171.4 257.1 342.9 428.6 514.3 600.0 685.7 771.4 857.1 942.9 1028.6 1114.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.7143 .. 85.7143 cents 1/1, 0.0000 cents 85.71429 cents 2: 171.4286 .. 171.4286 cents 1/1, 0.0000 cents 85.71428 cents 3: 257.1429 .. 257.1429 cents 1/1, 0.0000 cents 85.71429 cents 4: 342.8571 .. 342.8571 cents 1/1, 0.0000 cents 85.71429 cents 5: 428.5714 .. 428.5714 cents 1/1, 0.0000 cents 85.71429 cents 6: 514.2857 .. 514.2857 cents 1/1, 0.0000 cents 85.71428 cents 7: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 85.71429 cents 8: 685.7143 .. 685.7143 cents 1/1, 0.0000 cents 85.71429 cents 9: 771.4286 .. 771.4286 cents 1/1, 0.0000 cents 85.71428 cents 10: 857.1429 .. 857.1429 cents 1/1, 0.0000 cents 85.71429 cents 11: 942.8571 .. 942.8571 cents 1/1, 0.0000 cents 85.71429 cents 12: 1028.5714 .. 1028.5714 cents 1/1, 0.0000 cents 85.71429 cents 13: 1114.2857 .. 1114.2857 cents 1/1, 0.0000 cents 85.71428 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 85.71428 cents, class 1 Average step (divided formal octave): 85.7143 cents Largest one step interval : 85.71429 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 85.71429 cents, amount: 14 Most common interval of one step : 85.71429 cents, amount: 14 Least squares average step : 85.71429 cents, oct.: 1200.00000 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 85.71429 cents Ratio Whole / Half tone : 1.000000 ( 1 ) Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.071429 redundancy: 0.928571 Efficiency x scale size : 1.000000 Number of different interval sizes : 13 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 14, average 685.7143 cents Number of appreciable fifths : 0 Scale contains two identical disjunct heptachords Best major thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
14: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x 3 x x x x x 4 S SD: 8.1204 cents 3 x x x x x 4 x x x 5 x x x 6 S SD: 10.5644 cents 4 x x x x 5 x x 6 x x 7 x x 8 S SD: 13.0476 cents 5 x x x 6 x x 7 x 8 x x 9 x 10 S SD: 10.8677 cents 6 x x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 7.0615 cents 7 x x 8 x 9 x 10 x 11 x 12 x 13:14 S SD: 7.8935 cents 8 x 9 x x 10:11 x 12 x 13:14 x 15:16 S SD: 9.7654 cents 9 x 10 x 11 x 12:13 x 14:15 x 16:17:18 S SD: 6.8125 cents 10 x 11 x 12:13 x 14:15:16 x 17:18:19:20 S SD: 6.7165 cents 11 x 12:13 x 14:15 x 16:17:18:19:20:21:22 S SD: 5.6660 cents 12 x 13:14 x 15:16:17:18:19:20:21:22:23:24 S SD: 6.4929 cents 13:14 x 15:16:17 x 18:19:20:21:22:24:25:26 S SD: 8.0947 cents 14:15 x 16:17:18:19:20:21:22:23:24:25:27:28 SD: 4.8834 cents 15:16 x 17:18:19:20:21:22:23:25:26:27:29:30 SD: 6.5173 cents 16:17:18:19 x 21:22:23:24:25:26:28:29:30:32 SD: 7.2573 cents 17:18:19:20:21:22:23:24:25:27:28:29:31:32:34 SD: 4.6390 cents 18:19:20:21:22:23:24:25:27:28:30:31:33:34:36 SD: 4.0504 cents 19:20:21:22:23:24:26:27:28:30:31:33:34:36:38 SD: 3.9099 cents 25:26:28:29:30:32:34:35:37:39:41:43:45:48:50 SD: 3.7244 cents 26:27:29:30:32:33:35:37:39:41:43:45:47:49:52 SD: 3.6141 cents 27:28:30:31:33:35:36:38:40:42:44:47:49:51:54 SD: 3.5125 cents 29:30:32:34:35:37:39:41:43:45:48:50:53:55:58 SD: 3.2330 cents 31:33:34:36:38:40:42:44:46:48:51:53:56:59:62 SD: 2.7999 cents 32:34:35:37:39:41:43:45:48:50:53:55:58:61:64 SD: 2.6155 cents 36:38:40:42:44:46:48:51:53:56:59:62:65:69:72 SD: 2.3408 cents 37:39:41:43:45:47:50:52:55:58:61:64:67:70:74 SD: 1.9283 cents 50:53:55:58:61:64:67:71:74:78:82:86:91:95:100 SD: 1.6384 cents 55:58:61:64:67:70:74:78:82:86:90:95:100:105:110 SD: 1.4528 cents 58:61:64:67:71:74:78:82:86:91:95:100:105:110:116 SD: 1.2206 cents 64:67:71:74:78:82:86:91:95:100:105:110:116:122:128 SD: 1.1923 cents 75:79:83:87:91:96:101:106:111:117:123:129:136:143:150 SD: 0.9664 cents 86:90:95:100:105:110:116:122:128:134:141:148:156:164:172 SD: 0.9313 cents 95:100:105:110:116:122:128:134:141:148:156:164:172:181:190 SD: 0.7416 cents 113:119:125:131:138:145:152:160:168:176:185:195:205:215:226 SD: 0.6981 cents 118:124:130:137:144:151:159:167:175:184:194:203:214:225:236 SD: 0.6567 cents 132:139:146:153:161:169:178:187:196:206:217:228:239:251:264 SD: 0.6256 cents 133:140:147:154:162:170:179:188:198:208:218:229:241:253:266 SD: 0.5819 cents 136:143:150:158:166:174:183:192:202:212:223:234:246:259:272 SD: 0.5405 cents 142:149:157:165:173:182:191:201:211:222:233:245:257:270:284 SD: 0.4362 cents 164:172:181:190:200:210:221:232:244:256:269:283:297:312:328 SD: 0.3976 cents 193:203:213:224:235:247:260:273:287:301:317:333:350:367:386 SD: 0.3969 cents 196:206:216:227:239:251:264:277:291:306:322:338:355:373:392 SD: 0.3964 cents 200:210:221:232:244:256:269:283:297:312:328:345:362:381:400 SD: 0.3096 cents 232:244:256:269:283:297:312:328:345:362:381:400:420:442:464 SD: 0.3066 cents 237:249:262:275:289:304:319:335:352:370:389:409:429:451:474 SD: 0.3062 cents 239:251:264:277:291:306:322:338:355:373:392:412:433:455:478 SD: 0.2667 cents 278:292:307:323:339:356:374:393:413:434:456:479:504:529:556 SD: 0.2515 cents 292:307:322:339:356:374:393:413:434:456:479:503:529:556:584 SD: 0.2224 cents 319:335:352:370:389:409:429:451:474:498:523:550:578:607:638 SD: 0.2218 cents 338:355:373:392:412:433:455:478:502:528:555:583:612:643:676 SD: 0.1957 cents 356:374:393:413:434:456:479:503:529:556:584:614:645:678:712 SD: 0.1581 cents 413:434:456:479:503:529:556:584:614:645:678:712:748:786:826 SD: 0.1580 cents 451:474:498:523:550:578:607:638:670:704:740:777:817:858:902 SD: 0.1578 cents 474:498:523:550:578:607:638:670:704:740:778:817:859:902:948 SD: 0.1571 cents 488:513:539:566:595:625:657:690:725:762:801:841:884:929:976 SD: 0.1227 cents 529:556:584:614:645:678:712:748:786:826:868:912:958:1007:1058 SD: 0.1146 cents