Scala analysis: golden-triforce
triforce[15]
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58.359 cents 58.359210 2: 152.786 cents 152.786400 3: 211.146 cents 211.145620 4: 305.573 cents 305.572810 5: 400.000 cents 400.000000 6: 458.359 cents 458.359210 7: 552.786 cents 552.786400 8: 611.146 cents 611.145620 9: 705.573 cents 705.572810 10: 800.000 cents 800.000000 11: 858.359 cents 858.359210 12: 952.786 cents 952.786400 13: 1011.146 cents 1011.145620 14: 1105.573 cents 1105.572810 15: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 94.4272 cents 94.4272 1: 58.3592 cents 58.3592 2: 94.4272 cents 94.4272 3: 58.3592 cents 58.3592 4: 94.4272 cents 94.4272 5: 94.4272 cents 94.4272 6: 58.3592 cents 58.3592 7: 94.4272 cents 94.4272 8: 58.3592 cents 58.3592 9: 94.4272 cents 94.4272 10: 94.4272 cents 94.4272 11: 58.3592 cents 58.3592 12: 94.4272 cents 94.4272 13: 58.3592 cents 58.3592 14: 94.4272 cents 94.4272 15: 94.4272 cents 94.4272
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 58.35921 cents 1: 9 94.42719 cents 2: 12 152.78640 cents 2: 3 188.85438 cents 3: 3 211.14562 cents 3: 12 247.21360 cents 4: 9 305.57281 cents 4: 6 341.64079 cents 5: 15 400.00000 cents 6: 6 458.35921 cents 6: 9 494.42719 cents 7: 12 552.78640 cents 7: 3 588.85438 cents 8: 3 611.14562 cents 8: 12 647.21360 cents 9: 9 705.57281 cents 9: 6 741.64079 cents 10: 15 800.00000 cents 11: 6 858.35921 cents 11: 9 894.42719 cents 12: 12 952.78640 cents 12: 3 988.85438 cents 13: 3 1011.14562 cents 13: 12 1047.21360 cents 14: 9 1105.57281 cents 14: 6 1141.64079 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.85714 = 13/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 58.4 152.8 211.1 305.6 400.0 458.4 552.8 611.1 705.6 800.0 858.4 952.8 1011.1 1105.6 1200.0 58.4 : 94.4 152.8 247.2 341.6 400.0 494.4 552.8 647.2 741.6 800.0 894.4 952.8 1047.2 1141.6 1200.0 152.8 : 58.4 152.8 247.2 305.6 400.0 458.4 552.8 647.2 705.6 800.0 858.4 952.8 1047.2 1105.6 1200.0 211.1 : 94.4 188.9 247.2 341.6 400.0 494.4 588.9 647.2 741.6 800.0 894.4 988.9 1047.2 1141.6 1200.0 305.6 : 94.4 152.8 247.2 305.6 400.0 494.4 552.8 647.2 705.6 800.0 894.4 952.8 1047.2 1105.6 1200.0 400.0 : 58.4 152.8 211.1 305.6 400.0 458.4 552.8 611.1 705.6 800.0 858.4 952.8 1011.1 1105.6 1200.0 458.4 : 94.4 152.8 247.2 341.6 400.0 494.4 552.8 647.2 741.6 800.0 894.4 952.8 1047.2 1141.6 1200.0 552.8 : 58.4 152.8 247.2 305.6 400.0 458.4 552.8 647.2 705.6 800.0 858.4 952.8 1047.2 1105.6 1200.0 611.1 : 94.4 188.9 247.2 341.6 400.0 494.4 588.9 647.2 741.6 800.0 894.4 988.9 1047.2 1141.6 1200.0 705.6 : 94.4 152.8 247.2 305.6 400.0 494.4 552.8 647.2 705.6 800.0 894.4 952.8 1047.2 1105.6 1200.0 800.0 : 58.4 152.8 211.1 305.6 400.0 458.4 552.8 611.1 705.6 800.0 858.4 952.8 1011.1 1105.6 1200.0 858.4 : 94.4 152.8 247.2 341.6 400.0 494.4 552.8 647.2 741.6 800.0 894.4 952.8 1047.2 1141.6 1200.0 952.8 : 58.4 152.8 247.2 305.6 400.0 458.4 552.8 647.2 705.6 800.0 858.4 952.8 1047.2 1105.6 1200.0 1011.1: 94.4 188.9 247.2 341.6 400.0 494.4 588.9 647.2 741.6 800.0 894.4 988.9 1047.2 1141.6 1200.0 1105.6: 94.4 152.8 247.2 305.6 400.0 494.4 552.8 647.2 705.6 800.0 894.4 952.8 1047.2 1105.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.3592 .. 94.4272 cents 36.06798 cents 58.35921 cents 2: 152.7864 .. 188.8544 cents 36.06798 cents 58.35921 cents 3: 211.1456 .. 247.2136 cents 36.06798 cents 22.29124 cents 4: 305.5728 .. 341.6408 cents 36.06798 cents 58.35921 cents 5: 400.0000 .. 400.0000 cents 1/1, 0.0000 cents 58.35921 cents 6: 458.3592 .. 494.4272 cents 36.06798 cents 58.35921 cents 7: 552.7864 .. 588.8544 cents 36.06798 cents 58.35921 cents 8: 611.1456 .. 647.2136 cents 36.06798 cents 22.29124 cents 9: 705.5728 .. 741.6408 cents 36.06798 cents 58.35921 cents 10: 800.0000 .. 800.0000 cents 1/1, 0.0000 cents 58.35921 cents 11: 858.3592 .. 894.4272 cents 36.06798 cents 58.35921 cents 12: 952.7864 .. 988.8544 cents 36.06798 cents 58.35921 cents 13: 1011.1456 .. 1047.2136 cents 36.06798 cents 22.29124 cents 14: 1105.5728 .. 1141.6408 cents 36.06798 cents 58.35921 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 58.35921 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 94.42719 cents Average / Smallest step : 1.370820 Largest / Average step : 1.180340 Largest / Smallest step : 1.618034 Median interval of one step : 94.42719 cents, amount: 9 Most common interval of one step : 94.42719 cents, amount: 9 Least squares average step : 78.69108 cents, oct.: 1180.36622 cents Scale is strictly proper Scale has 3 repeating blocks of 5 notes Blocks have Myhill's property chromas: 36.06798 cents and 22.29123 cents, ratio: 1.618035 generators: 2 of 152.78640 cents and 247.21360 cents ET pair of linear temperament : 39&63 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1131-tone equal temperament with octave 1200.000 cents degrees: 55 144 199 288 377 432 521 576 665 754 809 898 953 1042 1131 Least number of segments generator : 566 of 600.531 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 610 of 647.215 cents and inv. generated superset size: 759 = 744 more = 5060.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABBABABBABABB Step pattern size order : SLSLLSLSLLSLSLL Scale is a Constant Structure, by a margin of 22.29124 cents Scale diversity : 1.186261 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.639320 Number of different interval sizes : 26 = 1.85714 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.85714 = 13/7 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 22.29124 cents Most common intervals : 400.00000 cents & inv., amount: 15 Most common triad is 0.0 400.000 800.000 cents, amount: 15 Number of recognisable fifths : 9, average 705.5728 cents Best minor thirds form a closed circle Formal octave complements present : 3 = 20.0000% Limited transpositions : 5 10 Limited inverse transpositions : 3 8 13 Inversional symmetry on degrees : 4 9 14 Inversional symmetry on intervals : 1-2 6-7 11-12 -- 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: 17.6696 c. M:-28.8544 c. 18: 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 P B ME S SD: 16.3848 c. M:-27.7605 c. 21: 1 2 1 1 2 1 2 1 1 2 1 2 1 1 2 P B ME S SD: 14.4709 c. M: 19.8585 c. 24: 1 2 1 2 2 1 2 1 2 2 1 2 1 2 2 P B ME S SD: 6.8253 c. M: 11.1456 c. Triforce-15 39: 2 3 2 3 3 2 3 2 3 3 2 3 2 3 3 SP B ME S SD: 2.5958 c. M:-4.2390 c. Triforce-15 63: 3 5 3 5 5 3 5 3 5 5 3 5 3 5 5 SP B DE S SD: 0.9932 c. M: 1.6218 c. Triforce-15 102: 5 8 5 8 8 5 8 5 8 8 5 8 5 8 8 SP B DE S SD: 0.3791 c. M:-0.6191 c. 165: 8 13 8 13 13 8 13 8 13 13 8 13 8 13 13 SP B DE S SD: 0.1448 c. M: 0.2365 c. 267: 13 21 13 21 21 13 21 13 21 21 13 21 13 21 21 SP B DE S SD: 0.0553 c. M:-0.0903 c. 432: 21 34 21 34 34 21 34 21 34 34 21 34 21 34 34 SP B DE S SD: 0.0211 c. M: 0.0345 c. 699: 34 55 34 55 55 34 55 34 55 55 34 55 34 55 55 SP B DE S SD: 0.0081 c. M:-0.0132 c. 1131: 55 89 55 89 89 55 89 55 89 89 55 89 55 89 89 SP B DE S SD: 0.0031 c. M: 0.0050 c. 1830: 89 144 89 144 144 89 144 89 144 144 89 144 89 144 144 SP B DE S SD: 0.0012 c. M:-0.0019 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: 1.8089 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 15.8147 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 5.3483 cents 5 x x x 6 x x x 7 x 8 x x 9 x 10 S SD: 6.7828 cents 6 x x x 7 x 8 x x 9 x 10 x 11 x 12 S SD: 12.0444 cents 7 x x 8 x x 9 x 10 x 11 x 12 x 13:14 S SD: 7.5907 cents 8 x x 9 x 10 x 11 x 12 x 13:14 x 15:16 S SD: 4.2011 cents 9 x x 10:11 x 12 x 13 x 14:15 x 16:17:18 S SD: 9.2657 cents 10 x 11 x 12 x 13 x 14:15:16 x 17:18:19:20 S SD: 5.0272 cents 11 x 12 x 13:14 x 15:16 x 17:18:19:20:21:22 S SD: 6.5723 cents 12 x 13 x 14:15:16 x 17:18:19:20:21:22:23:24 S SD: 6.6591 cents 13 x 14:15 x 16:17:18:19:20 x 21 x 23:25:26 SD: 8.8561 cents 14 x 15:16:17 x 18:19:20:21:22:23:24:25:27:28 SD: 5.6320 cents 15 x 16:17:18:19:20 x 21:23:24:25:26:27:28:30 SD: 6.4425 cents 16:17 x 18:19:20:21:22:23:24:25:26:28:29:30:32 S SD: 5.0012 cents 17:18 x 19:20:21:22:23:24:26:27:28:29:30:32:34 S SD: 6.2147 cents 18:19 x 20:21:23 x 25:26:27:29:30:31:32:34:36 SD: 6.3401 cents 19:20:21 x 23:24:25:26:27:29:30:31:33:34:36:38 SD: 4.1109 cents 20:21:22:23:24:25:26 x 28:30:32:33:35:36:38:40 SD: 4.2325 cents 22:23:24:25:26:28:29:30:31:33:35:36:38:39:42:44 SD: 3.4481 cents 24:25:26:27:29:30:31:33:34:36:38:39:42:43:45:48 SD: 3.1912 cents 26:27:28:29:31:33:34:36:37:39:41:43:45:47:49:52 SD: 3.0006 cents 30:31:33:34:36:38:39:41:43:45:48:49:52:54:57:60 SD: 2.1410 cents 42:43:46:47:50:53:55:58:60:63:67:69:73:75:80:84 SD: 2.1396 cents 45:47:49:51:54:57:59:62:64:68:71:74:78:81:85:90 SD: 2.0171 cents 46:48:50:52:55:58:60:63:65:69:73:76:80:82:87:92 SD: 1.9151 cents 47:49:51:53:56:59:61:65:67:71:75:77:81:84:89:94 SD: 1.9070 cents 50:52:55:56:60:63:65:69:71:75:79:82:87:90:95:100 SD: 1.9033 cents 52:54:57:59:62:66:68:72:74:78:83:85:90:93:98:104 SD: 1.7891 cents 53:55:58:60:63:67:69:73:75:80:84:87:92:95:100:106 SD: 1.2355 cents 56:58:61:63:67:71:73:77:80:84:89:92:97:100:106:112 SD: 1.2322 cents 63:65:69:71:75:79:82:87:90:95:100:103:109:113:119:126 SD: 1.2244 cents 76:79:83:86:91:96:99:105:108:114:121:125:132:136:144:152 SD: 1.0928 cents 77:80:84:87:92:97:100:106:110:116:122:126:134:138:146:154 SD: 1.0588 cents 78:81:85:88:93:98:102:107:111:117:124:128:135:140:148:156 SD: 0.9539 cents 83:86:91:94:99:105:108:114:118:125:132:136:144:149:157:166 SD: 0.9057 cents 85:88:93:96:101:107:111:117:121:128:135:140:147:152:161:170 SD: 0.8473 cents 87:90:95:98:104:110:113:120:124:131:138:143:151:156:165:174 SD: 0.8213 cents 108:112:118:122:129:136:141:149:154:162:171:177:187:194:205:216 SD: 0.7819 cents 109:113:119:123:130:137:142:150:155:164:173:179:189:195:206:218 SD: 0.5763 cents 139:144:152:157:166:175:181:191:198:209:221:228:241:249:263:278 SD: 0.4397 cents 165:171:180:186:197:208:215:227:235:248:262:271:286:296:312:330 SD: 0.4385 cents 177:183:193:200:211:223:231:244:252:266:281:291:307:317:335:354 SD: 0.4191 cents 199:206:217:225:237:251:259:274:283:299:316:327:345:357:377:398 SD: 0.4046 cents 207:214:226:234:247:261:270:285:295:311:329:340:359:371:392:414 SD: 0.2921 cents 238:246:260:269:284:300:310:328:339:358:378:391:413:427:451:476 SD: 0.2860 cents 260:269:284:294:310:328:339:358:370:391:413:427:451:466:492:520 SD: 0.2721 cents 284:294:310:321:339:358:370:391:404:427:451:466:492:509:538:568 SD: 0.2393 cents 293:303:320:331:350:369:382:403:417:440:465:481:508:525:555:586 SD: 0.2319 cents 300:310:328:339:358:378:391:413:427:451:476:493:520:538:568:600 SD: 0.2106 cents 316:327:345:357:377:398:412:435:450:475:502:519:548:567:598:632 SD: 0.1932 cents 346:358:378:391:413:436:451:476:492:520:549:568:600:620:655:692 SD: 0.1900 cents 369:382:403:417:440:465:481:508:525:555:586:606:640:662:699:738 SD: 0.1879 cents 378:391:413:427:451:476:493:520:538:568:600:621:655:678:716:756 SD: 0.1715 cents 435:450:475:491:519:548:567:599:619:654:691:714:754:780:824:870 SD: 0.1689 cents 439:454:480:496:524:553:572:604:625:660:697:721:761:787:831:878 SD: 0.1653 cents 446:461:487:504:532:562:581:614:635:670:708:732:773:800:845:892 SD: 0.1556 cents 455:471:497:514:543:573:593:626:648:684:722:747:789:816:862:910 SD: 0.1525 cents 465:481:508:525:555:586:606:640:662:699:738:763:806:834:881:930 SD: 0.1360 cents 508:525:555:574:606:640:662:699:723:764:806:834:881:911:962:1016 SD: 0.1339 cents 519:537:567:586:619:654:676:714:739:780:824:852:900:931:983:1038 SD: 0.1297 cents 553:572:604:625:660:697:721:761:787:831:878:908:959:992:1047:1106 SD: 0.1208 cents 555:574:606:627:662:699:723:764:790:834:881:911:962:995:1051:1110 SD: 0.1037 cents