Scala analysis: porc15
Pocupine[15] in 7-limit minimax tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60.839 cents 60.839199 2: 162.737 cents 162.737257 3: 223.576 cents 223.576457 4: 325.475 cents 325.474514 5: 386.314 cents 386.313714 6: 488.212 cents 488.211772 7: 549.051 cents 549.050971 8: 650.949 cents 650.949029 9: 711.788 cents 711.788228 10: 813.686 cents 813.686286 11: 874.525 cents 874.525486 12: 976.424 cents 976.423543
SHOW/INTERVAL
0: 101.8981 cents 101.8981 1: 60.8392 cents 60.8392 2: 101.8981 cents 101.8981 3: 60.8392 cents 60.8392 4: 101.8981 cents 101.8981 5: 60.8392 cents 60.8392 6: 101.8981 cents 101.8981 7: 60.8392 cents 60.8392 8: 101.8981 cents 101.8981 9: 60.8392 cents 60.8392 10: 101.8981 cents 101.8981 11: 60.8392 cents 60.8392 12: 101.8981 cents 101.8981
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 60.83920 cents 1: 6 101.89806 cents 2: 12 162.73726 cents 3: 6 223.57646 cents 3: 6 264.63532 cents 4: 12 325.47451 cents 5: 6 386.31371 cents 5: 6 427.37257 cents 6: 12 488.21177 cents 7: 6 549.05097 cents 7: 6 590.10983 cents 8: 12 650.94903 cents 9: 6 711.78823 cents 9: 6 752.84709 cents 10: 12 813.68629 cents 11: 6 874.52549 cents 11: 6 915.58434 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.54545 = 17/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 60.8 162.7 223.6 325.5 386.3 488.2 549.1 650.9 711.8 813.7 874.5 976.4 60.8 : 101.9 162.7 264.6 325.5 427.4 488.2 590.1 650.9 752.8 813.7 915.6 976.4 162.7: 60.8 162.7 223.6 325.5 386.3 488.2 549.1 650.9 711.8 813.7 874.5 976.4 223.6: 101.9 162.7 264.6 325.5 427.4 488.2 590.1 650.9 752.8 813.7 915.6 976.4 325.5: 60.8 162.7 223.6 325.5 386.3 488.2 549.1 650.9 711.8 813.7 874.5 976.4 386.3: 101.9 162.7 264.6 325.5 427.4 488.2 590.1 650.9 752.8 813.7 915.6 976.4 488.2: 60.8 162.7 223.6 325.5 386.3 488.2 549.1 650.9 711.8 813.7 874.5 976.4 549.1: 101.9 162.7 264.6 325.5 427.4 488.2 590.1 650.9 752.8 813.7 915.6 976.4 650.9: 60.8 162.7 223.6 325.5 386.3 488.2 549.1 650.9 711.8 813.7 874.5 976.4 711.8: 101.9 162.7 264.6 325.5 427.4 488.2 590.1 650.9 752.8 813.7 915.6 976.4 813.7: 60.8 162.7 223.6 325.5 386.3 488.2 549.1 650.9 711.8 813.7 874.5 976.4 874.5: 101.9 162.7 264.6 325.5 427.4 488.2 590.1 650.9 752.8 813.7 915.6 976.4 976.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 60.8392 .. 101.8981 cents 41.05886 cents 60.83920 cents 2: 162.7373 .. 162.7373 cents 1/1, 0.0000 cents 60.83920 cents 3: 223.5765 .. 264.6353 cents 41.05886 cents 60.83920 cents 4: 325.4745 .. 325.4745 cents 1/1, 0.0000 cents 60.83920 cents 5: 386.3137 .. 427.3726 cents 41.05886 cents 60.83920 cents 6: 488.2118 .. 488.2118 cents 1/1, 0.0000 cents 60.83920 cents 7: 549.0510 .. 590.1098 cents 41.05886 cents 60.83920 cents 8: 650.9490 .. 650.9490 cents 1/1, 0.0000 cents 60.83920 cents 9: 711.7882 .. 752.8471 cents 41.05886 cents 60.83920 cents 10: 813.6863 .. 813.6863 cents 1/1, 0.0000 cents 60.83920 cents 11: 874.5255 .. 915.5843 cents 41.05886 cents 60.83920 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 60.83920 cents, class 1 Average step (divided formal octave): 81.3686 cents Largest one step interval : 101.89806 cents Average / Smallest step : 1.337438 Largest / Average step : 1.252302 Largest / Smallest step : 1.674875 Median interval of one step : 81.36863 cents, amount: 0 Least squares average step : 80.23161 cents, oct.: 962.77937 cents Scale is strictly proper Scale has 6 repeating blocks of 2 notes Blocks have Myhill's property chromas: 41.05886 cents and 19.78034 cents, ratio: 2.075741 generator: 1 of 60.83920 cents ET pair of linear temperament : 749&3052 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 642-tone equal temperament with octave 976.424 cents degrees: 40 107 147 214 254 321 361 428 468 535 575 642 Least number of segments generator : 323 of 491.254 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 361 of 549.048 cents and inv. generated superset size: 537 = 525 more = 4475.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABAB Step pattern size order : SLSLSLSLSLSL Scale is a Constant Structure, by a margin of 60.83920 cents Scale diversity : 1.077755 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.747698 Rothenberg efficiency (ambiguous key): 1.000000 redundancy: 0.000000 Efficiency x scale size : 12.000000 Number of different interval sizes : 17 = 1.54545 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.54545 = 17/11 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 41.05886 cents Scale is a chain of 6 triads 0.0 711.788 813.686 cents Most common triad is 0.0 162.737 325.475 cents, amount: 12 Number of recognisable fifths : 6, average 711.7882 cents Number of recognisable fourths : 12, average 488.2118 cents Scale contains two identical conjunct heptachords Best major thirds form a closed circle Formal octave complements present : 6 = 50.0000% 2/1 octave complements present : 9 = 75.0000% Limited transpositions : 2 4 6 8 10 Limited inverse transpositions : 1 3 5 7 9 11 Inversional symmetry on intervals : 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 14.5165 c. M:-20.5294 c. Twelve-tone Chromatic (1/11-comma) 16: 1 2 1 1 1 2 1 2 1 1 1 2 P B D3 SD: 16.6098 c. M:-20.5294 c. 18: 1 2 1 2 1 2 1 2 1 2 1 2 SP B ME SD: 4.6623 c. M: 6.5934 c. 30: 2 3 2 3 2 3 2 3 2 3 2 3 SP B ME SD: 3.0092 c. M:-4.2557 c. 48: 3 5 3 5 3 5 3 5 3 5 3 5 SP B DE SD: 0.1324 c. M:-0.1873 c. 354: 22 37 22 37 22 37 22 37 22 37 22 37 SP B DE SD: 0.1114 c. M: 0.1575 c. 402: 25 42 25 42 25 42 25 42 25 42 25 42 SP B DE SD: 0.0823 c. M: 0.1163 c. 450: 28 47 28 47 28 47 28 47 28 47 28 47 SP B DE SD: 0.0594 c. M: 0.0840 c. 498: 31 52 31 52 31 52 31 52 31 52 31 52 SP B DE SD: 0.0409 c. M: 0.0578 c. 546: 34 57 34 57 34 57 34 57 34 57 34 57 SP B DE SD: 0.0256 c. M: 0.0363 c. 594: 37 62 37 62 37 62 37 62 37 62 37 62 SP B DE SD: 0.0129 c. M: 0.0182 c. 642: 40 67 40 67 40 67 40 67 40 67 40 67 SP B DE SD: 0.0020 c. M: 0.0028 c. 1974: 123 206 123 206 123 206 123 206 123 206 123 206 SP B DE SD: 0.0013 c. M:-0.0018 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 223.5765 cents 2 x x x x x x x x 3 x x 4 S SD: 111.8963 cents 3 x x x x x 4 x x x x 5 x S SD: 6.9531 cents 4 x x x x 5 x x x 6 x x 7 S SD: 4.1421 cents 5 x x x 6 x x 7 x x 8 x 9 S SD: 13.4897 cents 6 x x 7 x x 8 x x 9 x 10:11 S SD: 17.3028 cents 7 x x 8 x 9 x x 10 x 11 x 12 S SD: 16.0043 cents 8 x x 9 x 10 x 11 x 12:13 x 14 S SD: 5.9320 cents 9 x 10 x 11 x 12 x 13 x 14:15:16 S SD: 9.0711 cents 10 x 11 x 12 x 13:14 x 15:16:17:18 S SD: 9.7752 cents 11 x 12 x 13:14 x 15:16:17 x 18:19 S SD: 9.4641 cents 12 x 13:14 x 15:16 x 17:18:19:20:21 S SD: 8.1905 cents 13 x 14:15 x 16:17:18:19:20:21:22:23 S SD: 7.8560 cents 14 x 15:16:17:18 x 19:20:21:22:23:25 SD: 8.9472 cents 15:16 x 17:18:19:20:21:22:23:24:25:26 S SD: 7.1000 cents 16:17 x 18:19:20:21:22:23:24:26:27:28 S SD: 6.9205 cents 17:18:19 x x 21 x 23:25:26:27:28:30 SD: 7.5306 cents 18:19:20 x 22:23:24:25:26:27:29:30:32 SD: 6.2995 cents 19:20:21:22:23:24:25:26:28:29:30:31:33 SD: 5.8207 cents 20:21:22:23:24:25 x 27:29:30:32:33:35 SD: 4.2045 cents 24:25:26:27:29:30:32:33:35:36:38:40:42 SD: 3.4946 cents 28:29:31:32:34:35:37:38:41:42:45:46:49 SD: 3.0360 cents 29:30:32:33:35:36:38:40:42:44:46:48:51 SD: 2.7658 cents 37:38:41:42:45:46:49:51:54:56:59:61:65 SD: 2.5436 cents 43:45:47:49:52:54:57:59:63:65:69:71:76 SD: 2.2920 cents 48:50:53:55:58:60:64:66:70:72:77:80:84 SD: 2.2104 cents 49:51:54:56:59:61:65:67:71:74:78:81:86 SD: 1.8006 cents 52:54:57:59:63:65:69:71:76:78:83:86:91 SD: 1.7178 cents 53:55:58:60:64:66:70:73:77:80:85:88:93 SD: 1.4508 cents 59:61:65:67:71:74:78:81:86:89:94:98:104 SD: 1.2498 cents 73:76:80:83:88:91:97:100:106:110:117:121:128 SD: 1.2233 cents 79:82:87:90:95:99:105:108:115:119:126:131:139 SD: 1.2183 cents 80:83:88:91:97:100:106:110:117:121:128:133:141 SD: 1.2085 cents 81:84:89:92:98:101:107:111:118:122:130:134:142 SD: 1.0856 cents 83:86:91:94:100:104:110:114:121:125:133:138:146 SD: 1.0406 cents 88:91:97:100:106:110:117:121:128:133:141:146:155 SD: 0.9338 cents 107:111:118:122:129:134:142:147:156:161:171:177:188 SD: 0.9092 cents 108:112:119:123:130:135:143:148:157:163:173:179:190 SD: 0.7886 cents 110:114:121:125:133:138:146:151:160:166:176:182:193 SD: 0.7835 cents 116:120:127:132:140:145:154:159:169:175:186:192:204 SD: 0.7196 cents 120:124:132:137:145:150:159:165:175:181:192:199:211 SD: 0.7113 cents 131:136:144:149:158:164:174:180:191:198:210:217:230 SD: 0.6822 cents 132:137:145:150:159:165:175:181:192:199:211:219:232 SD: 0.5747 cents 140:145:154:159:169:175:186:192:204:211:224:232:246 SD: 0.5121 cents 160:166:176:182:193:200:212:220:233:241:256:265:281 SD: 0.4622 cents 169:175:186:192:204:211:224:232:246:255:270:280:297 SD: 0.4593 cents 175:181:192:199:211:219:232:240:255:264:280:290:308 SD: 0.4536 cents 193:200:212:220:233:241:256:265:281:291:309:320:339 SD: 0.3656 cents 224:232:246:255:270:280:297:308:326:338:358:371:394 SD: 0.3611 cents 252:261:277:287:304:315:334:346:367:380:403:418:443 SD: 0.2368 cents 313:324:344:356:378:391:415:430:456:472:501:519:550 SD: 0.2316 cents 335:347:368:381:404:419:444:460:488:505:536:555:589 SD: 0.2001 cents 368:381:404:419:444:460:488:505:536:555:589:610:647 SD: 0.1998 cents 397:411:436:452:479:496:526:545:578:599:635:658:698 SD: 0.1961 cents 445:461:489:506:537:556:590:611:648:671:712:737:782 SD: 0.1761 cents 479:496:526:545:578:599:635:658:698:723:766:794:842 SD: 0.1754 cents 507:525:557:577:612:634:672:696:738:765:811:840:891 SD: 0.1438 cents 528:547:580:601:637:660:700:725:769:797:845:875:928 SD: 0.1229 cents