Scala analysis: valentine15
Valentine[15] in 46-et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 78.261 cents 78.260870 2: 156.522 cents 156.521739 3: 234.783 cents 234.782609 4: 313.043 cents 313.043478 5: 391.304 cents 391.304348 6: 469.565 cents 469.565217 7: 547.826 cents 547.826087 8: 626.087 cents 626.086957 9: 704.348 cents 704.347826 10: 782.609 cents 782.608696 11: 886.957 cents 886.956522 12: 965.217 cents 965.217391 13: 1043.478 cents 1043.478261 14: 1121.739 cents 1121.739130 15: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 78.2609 cents 78.2609 1: 78.2609 cents 78.2609 2: 78.2609 cents 78.2609 3: 78.2609 cents 78.2609 4: 78.2609 cents 78.2609 5: 78.2609 cents 78.2609 6: 78.2609 cents 78.2609 7: 78.2609 cents 78.2609 8: 78.2609 cents 78.2609 9: 78.2609 cents 78.2609 10: 78.2609 cents 78.2609 11: 104.3478 cents 104.3478 12: 78.2609 cents 78.2609 13: 78.2609 cents 78.2609 14: 78.2609 cents 78.2609 15: 78.2609 cents 78.2609
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 14 78.26087 cents 1: 1 104.34783 cents 2: 13 156.52174 cents 2: 2 182.60870 cents 3: 12 234.78261 cents 3: 3 260.86956 cents 4: 11 313.04348 cents 4: 4 339.13043 cents 5: 10 391.30435 cents 5: 5 417.39130 cents 6: 9 469.56522 cents 6: 6 495.65217 cents 7: 8 547.82609 cents 7: 7 573.91304 cents 8: 7 626.08696 cents 8: 8 652.17391 cents 9: 6 704.34783 cents 9: 9 730.43478 cents 10: 5 782.60870 cents 10: 10 808.69565 cents 11: 4 860.86957 cents 11: 11 886.95652 cents 12: 3 939.13044 cents 12: 12 965.21739 cents 13: 2 1017.39130 cents 13: 13 1043.47826 cents 14: 1 1095.65217 cents 14: 14 1121.73913 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 78.3 156.5 234.8 313.0 391.3 469.6 547.8 626.1 704.3 782.6 887.0 965.2 1043.5 1121.7 1200.0 78.3 : 78.3 156.5 234.8 313.0 391.3 469.6 547.8 626.1 704.3 808.7 887.0 965.2 1043.5 1121.7 1200.0 156.5 : 78.3 156.5 234.8 313.0 391.3 469.6 547.8 626.1 730.4 808.7 887.0 965.2 1043.5 1121.7 1200.0 234.8 : 78.3 156.5 234.8 313.0 391.3 469.6 547.8 652.2 730.4 808.7 887.0 965.2 1043.5 1121.7 1200.0 313.0 : 78.3 156.5 234.8 313.0 391.3 469.6 573.9 652.2 730.4 808.7 887.0 965.2 1043.5 1121.7 1200.0 391.3 : 78.3 156.5 234.8 313.0 391.3 495.7 573.9 652.2 730.4 808.7 887.0 965.2 1043.5 1121.7 1200.0 469.6 : 78.3 156.5 234.8 313.0 417.4 495.7 573.9 652.2 730.4 808.7 887.0 965.2 1043.5 1121.7 1200.0 547.8 : 78.3 156.5 234.8 339.1 417.4 495.7 573.9 652.2 730.4 808.7 887.0 965.2 1043.5 1121.7 1200.0 626.1 : 78.3 156.5 260.9 339.1 417.4 495.7 573.9 652.2 730.4 808.7 887.0 965.2 1043.5 1121.7 1200.0 704.3 : 78.3 182.6 260.9 339.1 417.4 495.7 573.9 652.2 730.4 808.7 887.0 965.2 1043.5 1121.7 1200.0 782.6 : 104.3 182.6 260.9 339.1 417.4 495.7 573.9 652.2 730.4 808.7 887.0 965.2 1043.5 1121.7 1200.0 887.0 : 78.3 156.5 234.8 313.0 391.3 469.6 547.8 626.1 704.3 782.6 860.9 939.1 1017.4 1095.7 1200.0 965.2 : 78.3 156.5 234.8 313.0 391.3 469.6 547.8 626.1 704.3 782.6 860.9 939.1 1017.4 1121.7 1200.0 1043.5: 78.3 156.5 234.8 313.0 391.3 469.6 547.8 626.1 704.3 782.6 860.9 939.1 1043.5 1121.7 1200.0 1121.7: 78.3 156.5 234.8 313.0 391.3 469.6 547.8 626.1 704.3 782.6 860.9 965.2 1043.5 1121.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 78.2609 .. 104.3478 cents 26.08696 cents 78.26087 cents 2: 156.5217 .. 182.6087 cents 26.08696 cents 52.17391 cents 3: 234.7826 .. 260.8696 cents 26.08696 cents 52.17391 cents 4: 313.0435 .. 339.1304 cents 26.08696 cents 52.17391 cents 5: 391.3043 .. 417.3913 cents 26.08696 cents 52.17391 cents 6: 469.5652 .. 495.6522 cents 26.08696 cents 52.17391 cents 7: 547.8261 .. 573.9130 cents 26.08696 cents 52.17391 cents 8: 626.0870 .. 652.1739 cents 26.08696 cents 52.17391 cents 9: 704.3478 .. 730.4348 cents 26.08696 cents 52.17391 cents 10: 782.6087 .. 808.6957 cents 26.08696 cents 52.17391 cents 11: 860.8696 .. 886.9565 cents 26.08696 cents 52.17391 cents 12: 939.1304 .. 965.2174 cents 26.08696 cents 52.17391 cents 13: 1017.3913 .. 1043.4783 cents 26.08696 cents 52.17391 cents 14: 1095.6522 .. 1121.7391 cents 26.08696 cents 52.17391 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 78.26087 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 104.34783 cents Average / Smallest step : 1.022222 Largest / Average step : 1.304348 Largest / Smallest step : 1.333333 Median interval of one step : 78.26087 cents, amount: 14 Most common interval of one step : 78.26087 cents, amount: 14 Least squares average step : 79.62833 cents, oct.: 1194.42496 cents Scale is strictly proper Scale has Myhill's property chromas: 26.08696 cents and 52.17391 cents, ratio: 2.000000 generators: 1 of 78.26087 cents and 14 of 1121.73913 cents Scale is maximally even in 46-tone equal temperament ET pair of linear temperament : 15&46 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 46-tone equal temperament with octave 1200.000 cents degrees: 3 6 9 12 15 18 21 24 27 30 34 37 40 43 46 generators: 3 and 43 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAAAAAAAABAAAA Step pattern size order : SSSSSSSSSSLSSSS Interval vector is [ 0 0 14 1 0 13 2 0 12 3 0 11 4 0 10 5 0 9 6 0 8 7 0 ] Scale is a Constant Structure, by a margin of 52.17391 cents Scale diversity : 1.191435 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.695652 Rothenberg efficiency : 0.711111 redundancy: 0.288889 Efficiency x scale size : 10.666667 Number of different interval sizes : 28 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 26.08696 cents Most common intervals : 78.26087 cents & inv., amount: 14 Scale is a chain of 7 triads 0.0 547.826 1121.739 cents Number of recognisable fifths : 6, average 704.3478 cents Best minor thirds form a closed circle Formal octave complements present : 9 = 60.0000% Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 Inversional symmetry on intervals : 10-11 -- 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: 9.1477 c. M:-17.3913 c. 31: 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 SP M ME S SD: 4.4263 c. M: 8.4151 c. 46: 3 3 3 3 3 3 3 3 3 3 4 3 3 3 3 SP M ME S 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: 1.1964 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 9.5327 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 1.6518 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 10.6688 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 7.2416 cents 7 x x 8 x x 9 x 10 x 11 x 12:13 x 14 S SD: 7.9567 cents 8 x x 9 x 10 x 11 x 12 x 13:14 x 15:16 S SD: 8.1824 cents 9 x 10 x 11 x 12 x 13 x 14:15:16 x 17:18 S SD: 7.4319 cents 10 x 11 x 12 x 13:14 x 15:16:17 x 18:19:20 S SD: 6.5375 cents 11 x 12 x 13:14 x 15:16 x 17:18:19:20:21:22 S SD: 6.0147 cents 12 x 13:14 x 15:16 x 17:18:19:20:21:22:23:24 S SD: 4.5412 cents 13 x 14:15 x 16:17:18:19 x 20:22:23:24:25:26 S SD: 6.4882 cents 14 x 15:16:17 x 18:19:20:21:22:23:24:26:27:28 S SD: 6.1407 cents 15:16 x 17:18:19:20:21:22:23:24:25:26:27:29:30 SD: 6.6323 cents 16:17 x 18:19:20:21:22:23:24:25:27:28:29:31:32 SD: 4.0166 cents 17:18:19 x 20:21:22:23:24:26:27:28:30:31:33:34 SD: 6.4891 cents 18:19:20:21:22:23:24:25:26:27:28:30:31:33:34:36 SD: 5.5522 cents 19:20:21:22:23:24:25:26:27:29:30:32:33:35:36:38 SD: 3.7766 cents 20:21:22:23:24:25:26:27:29:30:31:33:35:37:38:40 SD: 3.7050 cents 21:22:23:24:25:26:28:29:30:32:33:35:37:38:40:42 SD: 3.5242 cents 28:29:31:32:34:35:37:38:40:42:44:47:49:51:54:56 SD: 3.1620 cents 30:31:33:34:36:38:39:41:43:45:47:50:52:55:57:60 SD: 2.8582 cents 32:33:35:37:38:40:42:44:46:48:50:53:56:58:61:64 SD: 2.7498 cents 35:37:38:40:42:44:46:48:50:53:55:58:61:64:67:70 SD: 2.1359 cents 40:42:44:46:48:50:52:55:57:60:63:67:70:73:76:80 SD: 1.8780 cents 42:44:46:48:50:53:55:58:60:63:66:70:73:77:80:84 SD: 1.6728 cents 46:48:50:53:55:58:60:63:66:69:72:77:80:84:88:92 SD: 1.6714 cents 51:53:56:58:61:64:67:70:73:77:80:85:89:93:97:102 SD: 1.5572 cents 60:63:66:69:72:75:79:82:86:90:94:100:105:110:115:120 SD: 1.3434 cents 62:65:68:71:74:78:81:85:89:93:97:103:108:113:119:124 SD: 1.2918 cents 64:67:70:73:77:80:84:88:92:96:101:107:112:117:122:128 SD: 1.0526 cents 82:86:90:94:98:103:108:113:118:123:129:137:143:150:157:164 SD: 0.9999 cents 83:87:91:95:99:104:109:114:119:125:130:139:145:152:159:166 SD: 0.9699 cents 86:90:94:98:103:108:113:118:123:129:135:144:150:157:164:172 SD: 0.9612 cents 87:91:95:100:104:109:114:119:125:131:137:145:152:159:166:174 SD: 0.8403 cents 91:95:100:104:109:114:119:125:131:137:143:152:159:166:174:182 SD: 0.8211 cents 102:107:112:117:122:128:134:140:146:153:160:170:178:186:195:204 SD: 0.7929 cents 103:108:113:118:123:129:135:141:148:155:162:172:180:188:197:206 SD: 0.6855 cents 110:115:120:126:132:138:144:151:158:165:173:184:192:201:210:220 SD: 0.6102 cents 115:120:126:132:138:144:151:158:165:173:181:192:201:210:220:230 SD: 0.5873 cents 126:132:138:144:151:158:165:173:181:189:198:210:220:230:241:252 SD: 0.4474 cents 145:152:159:166:174:182:190:199:208:218:228:242:253:265:277:290 SD: 0.4446 cents 151:158:165:173:181:189:198:207:217:227:237:252:264:276:289:302 SD: 0.4166 cents 170:178:186:195:204:213:223:233:244:255:267:284:297:311:325:340 SD: 0.4022 cents 177:185:194:203:212:222:232:243:254:266:278:295:309:323:338:354 SD: 0.3927 cents 193:202:211:221:231:242:253:265:277:290:303:322:337:353:369:386 SD: 0.2869 cents 221:231:242:253:265:277:290:303:317:332:347:369:386:404:422:442 SD: 0.2821 cents 241:252:264:276:289:302:316:331:346:362:379:402:421:440:461:482 SD: 0.2470 cents 283:296:310:324:339:355:371:388:406:425:445:472:494:517:541:566 SD: 0.2293 cents 296:310:324:339:355:371:388:406:425:445:465:494:517:541:566:592 SD: 0.2191 cents 308:322:337:353:369:386:404:423:442:463:484:514:538:563:589:616 SD: 0.2115 cents 347:363:380:397:416:435:455:476:498:521:545:579:606:634:663:694 SD: 0.1903 cents 392:410:429:449:470:491:514:538:563:589:616:654:685:716:749:784 SD: 0.1855 cents 394:412:431:451:472:494:517:541:566:592:619:658:688:720:753:788 SD: 0.1841 cents 411:430:450:471:492:515:539:564:590:617:646:686:718:751:786:822 SD: 0.1728 cents 414:433:453:474:496:519:543:568:594:622:651:691:723:756:791:828 SD: 0.1528 cents 434:454:475:497:520:544:569:596:623:652:682:724:758:793:830:868 SD: 0.1359 cents 516:540:565:591:618:647:677:708:741:775:811:861:901:943:986:1032 SD: 0.1124 cents