Scala analysis: edo-15
15 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 80.000 cents 80.000000 2: 160.000 cents 160.000000 3: 240.000 cents 240.000000 4: 320.000 cents 320.000000 5: 400.000 cents 400.000000 6: 480.000 cents 480.000000 7: 560.000 cents 560.000000 8: 640.000 cents 640.000000 9: 720.000 cents 720.000000 10: 800.000 cents 800.000000 11: 880.000 cents 880.000000 12: 960.000 cents 960.000000 13: 1040.000 cents 1040.000000 14: 1120.000 cents 1120.000000 15: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 80.0000 cents 80.0000 1: 80.0000 cents 80.0000 2: 80.0000 cents 80.0000 3: 80.0000 cents 80.0000 4: 80.0000 cents 80.0000 5: 80.0000 cents 80.0000 6: 80.0000 cents 80.0000 7: 80.0000 cents 80.0000 8: 80.0000 cents 80.0000 9: 80.0000 cents 80.0000 10: 80.0000 cents 80.0000 11: 80.0000 cents 80.0000 12: 80.0000 cents 80.0000 13: 80.0000 cents 80.0000 14: 80.0000 cents 80.0000 15: 80.0000 cents 80.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 15 80.00000 cents 2: 15 160.00000 cents 3: 15 240.00000 cents 4: 15 320.00000 cents 5: 15 400.00000 cents 6: 15 480.00000 cents 7: 15 560.00000 cents 8: 15 640.00000 cents 9: 15 720.00000 cents 10: 15 800.00000 cents 11: 15 880.00000 cents 12: 15 960.00000 cents 13: 15 1040.00000 cents 14: 15 1120.00000 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 15 0.0 : 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 80.0 : 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 160.0 : 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 240.0 : 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 320.0 : 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 400.0 : 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 480.0 : 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 560.0 : 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 640.0 : 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 720.0 : 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 800.0 : 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 880.0 : 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 960.0 : 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 1040.0: 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 1120.0: 80.0 160.0 240.0 320.0 400.0 480.0 560.0 640.0 720.0 800.0 880.0 960.0 1040.0 1120.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.0000 .. 80.0000 cents 1/1, 0.0000 cents 80.00000 cents 2: 160.0000 .. 160.0000 cents 1/1, 0.0000 cents 80.00000 cents 3: 240.0000 .. 240.0000 cents 1/1, 0.0000 cents 80.00000 cents 4: 320.0000 .. 320.0000 cents 1/1, 0.0000 cents 80.00000 cents 5: 400.0000 .. 400.0000 cents 1/1, 0.0000 cents 80.00000 cents 6: 480.0000 .. 480.0000 cents 1/1, 0.0000 cents 80.00000 cents 7: 560.0000 .. 560.0000 cents 1/1, 0.0000 cents 80.00000 cents 8: 640.0000 .. 640.0000 cents 1/1, 0.0000 cents 80.00000 cents 9: 720.0000 .. 720.0000 cents 1/1, 0.0000 cents 80.00000 cents 10: 800.0000 .. 800.0000 cents 1/1, 0.0000 cents 80.00000 cents 11: 880.0000 .. 880.0000 cents 1/1, 0.0000 cents 80.00000 cents 12: 960.0000 .. 960.0000 cents 1/1, 0.0000 cents 80.00000 cents 13: 1040.0000 .. 1040.0000 cents 1/1, 0.0000 cents 80.00000 cents 14: 1120.0000 .. 1120.0000 cents 1/1, 0.0000 cents 80.00000 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 80.00000 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 80.00000 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 80.00000 cents, amount: 15 Most common interval of one step : 80.00000 cents, amount: 15 Least squares average step : 80.00000 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 80.00000 cents Ratio Whole / Half tone : infinite Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.066667 redundancy: 0.933333 Efficiency x scale size : 1.000000 Number of different interval sizes : 14 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 15, average 720.0000 cents Number of appreciable fifths : 0 Scale contains two identical disjunct heptachords Best minor thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
15: 1 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 x 2 S SD: 0.0000 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 9.0225 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 6.1880 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 6.0768 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 6.9715 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 6.4117 cents 7 x x 8 x 9 x x 10 x 11 x 12:13 x 14 S SD: 8.8631 cents 8 x x 9 x 10 x 11 x 12 x 13:14 x 15:16 S SD: 8.4165 cents 9 x 10 x 11 x 12 x 13 x 14:15:16 x 17:18 S SD: 7.4551 cents 10 x 11 x 12 x 13:14 x 15:16:17 x 18:19:20 S SD: 6.1654 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 5.7836 cents 12 x 13:14 x 15:16 x 17:18:19:20:21:22:23:24 S SD: 5.0228 cents 13 x 14:15:16 x 17:18:19:20:21:22:23:24:25:26 S SD: 6.4675 cents 14:15 x 16:17:18 x 19:20:21:22:23:24:26:27:28 S SD: 6.7429 cents 15:16 x 17:18:19:20:21:22:23:24:25:26:27:29:30 SD: 4.8660 cents 16:17 x 18:19:20:21:22:23:24:25:27:28:29:31:32 SD: 5.2844 cents 17:18:19 x 20:21:22:23:25:26:27:28:30:31:32:34 SD: 6.7736 cents 18:19:20:21:22:23:24:25:26:27:29:30:31:33:34:36 SD: 4.7015 cents 19:20:21:22:23:24:25:26:28:29:30:32:33:35:36:38 SD: 3.7255 cents 20:21:22:23:24:25:26:28:29:30:32:33:35:36:38:40 SD: 3.5137 cents 24:25:26:28:29:30:32:33:35:36:38:40:42:44:46:48 SD: 3.4372 cents 27:28:30:31:32:34:36:37:39:41:43:45:47:49:52:54 SD: 3.2348 cents 29:30:32:33:35:37:38:40:42:44:46:48:50:53:55:58 SD: 2.9808 cents 31:32:34:36:37:39:41:43:45:47:49:52:54:57:59:62 SD: 2.8286 cents 34:36:37:39:41:43:45:47:49:52:54:57:59:62:65:68 SD: 2.2929 cents 39:41:43:45:47:49:51:54:56:59:62:65:68:71:74:78 SD: 1.9232 cents 41:43:45:47:49:52:54:57:59:62:65:68:71:75:78:82 SD: 1.7607 cents 50:52:55:57:60:63:66:69:72:76:79:83:87:91:95:100 SD: 1.6748 cents 53:56:58:61:64:67:70:73:77:80:84:88:92:97:101:106 SD: 1.5809 cents 54:57:59:62:65:68:71:75:78:82:86:90:94:98:103:108 SD: 1.4770 cents 60:63:66:69:72:76:79:83:87:91:95:100:104:109:115:120 SD: 1.2691 cents 62:65:68:71:75:78:82:86:90:94:98:103:108:113:118:124 SD: 1.1673 cents 73:76:80:84:88:92:96:101:106:111:116:121:127:133:139:146 SD: 1.1354 cents 78:82:86:90:94:98:103:108:113:118:124:130:136:142:149:156 SD: 1.1237 cents 80:84:88:92:96:101:106:111:116:121:127:133:139:146:153:160 SD: 1.0036 cents 81:85:89:93:97:102:107:112:117:123:129:135:141:148:155:162 SD: 0.9140 cents 85:89:93:98:102:107:112:117:123:129:135:141:148:155:162:170 SD: 0.8570 cents 89:93:98:102:107:112:117:123:129:135:141:148:155:162:170:178 SD: 0.8267 cents 100:105:110:115:120:126:132:138:145:152:159:166:174:182:191:200 SD: 0.7752 cents 103:108:113:118:124:130:136:142:149:156:164:171:179:188:197:206 SD: 0.7020 cents 107:112:117:123:129:135:141:148:155:162:170:178:186:195:204:214 SD: 0.6137 cents 123:129:135:141:148:155:162:170:178:186:195:204:214:224:235:246 SD: 0.5796 cents 128:134:140:147:154:161:169:177:185:194:203:213:223:233:244:256 SD: 0.5399 cents 134:140:147:154:161:169:177:185:194:203:213:223:233:244:256:268 SD: 0.4875 cents 143:150:157:164:172:180:189:198:207:217:227:238:249:261:273:286 SD: 0.4776 cents 147:154:161:169:177:185:194:203:213:223:233:244:256:268:281:294 SD: 0.4211 cents 186:195:204:214:224:234:245:257:269:282:295:309:324:339:355:372 SD: 0.4104 cents 188:197:206:216:226:237:248:260:272:285:298:313:327:343:359:376 SD: 0.3368 cents 228:239:250:262:274:287:301:315:330:346:362:379:397:416:435:456 SD: 0.2847 cents 235:246:258:270:283:296:310:325:340:356:373:391:409:429:449:470 SD: 0.2764 cents 257:269:282:295:309:324:339:355:372:390:408:427:447:469:491:514 SD: 0.2760 cents 270:283:296:310:325:340:356:373:391:409:429:449:470:492:516:540 SD: 0.2611 cents 281:294:308:323:338:354:371:388:407:426:446:467:489:512:537:562 SD: 0.2588 cents 291:305:319:334:350:367:384:402:421:441:462:484:507:531:556:582 SD: 0.2400 cents 301:315:330:346:362:379:397:416:436:456:478:500:524:549:575:602 SD: 0.2283 cents 320:335:351:368:385:403:422:442:463:485:508:532:557:584:611:640 SD: 0.2035 cents 335:351:367:385:403:422:442:463:485:508:532:557:583:611:640:670 SD: 0.1947 cents 364:381:399:418:438:459:480:503:527:552:578:605:634:664:695:728 SD: 0.1942 cents 385:403:422:442:463:485:508:532:557:584:611:640:670:702:735:770 SD: 0.1745 cents 403:422:442:463:485:508:532:557:583:611:640:670:702:735:770:806 SD: 0.1480 cents 463:485:508:532:557:583:611:640:670:702:735:770:806:844:884:926 SD: 0.1199 cents 566:593:621:650:681:713:747:782:819:858:898:941:985:1032:1081:1132 SD: 0.1160 cents