Scala analysis: zeta12
12 equal zeta tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99.807 cents 99.807000 2: 199.614 cents 199.614000 3: 299.422 cents 299.422000 4: 399.229 cents 399.229000 5: 499.036 cents 499.036000 6: 598.843 cents 598.843000 7: 698.650 cents 698.650000 8: 798.457 cents 798.457000 9: 898.265 cents 898.265000 10: 998.072 cents 998.072000 11: 1097.879 cents 1097.879000 12: 1197.686 cents 1197.686000
SHOW/INTERVAL
0: 99.8070 cents 99.8070 1: 99.8070 cents 99.8070 2: 99.8070 cents 99.8070 3: 99.8080 cents 99.8080 4: 99.8070 cents 99.8070 5: 99.8070 cents 99.8070 6: 99.8070 cents 99.8070 7: 99.8070 cents 99.8070 8: 99.8070 cents 99.8070 9: 99.8080 cents 99.8080 10: 99.8070 cents 99.8070 11: 99.8070 cents 99.8070 12: 99.8070 cents 99.8070
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 99.80700 cents 1: 2 99.80800 cents 2: 8 199.61400 cents 2: 4 199.61500 cents 3: 6 299.42100 cents 3: 6 299.42200 cents 4: 4 399.22800 cents 4: 8 399.22900 cents 5: 2 499.03500 cents 5: 10 499.03600 cents 6: 12 598.84300 cents 7: 10 698.65000 cents 7: 2 698.65100 cents 8: 8 798.45700 cents 8: 4 798.45800 cents 9: 6 898.26400 cents 9: 6 898.26500 cents 10: 4 998.07100 cents 10: 8 998.07200 cents 11: 2 1097.87800 cents 11: 10 1097.87900 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.90909 = 21/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 99.8 199.6 299.4 399.2 499.0 598.8 698.7 798.5 898.3 998.1 1097.9 1197.7 99.8 : 99.8 199.6 299.4 399.2 499.0 598.8 698.7 798.5 898.3 998.1 1097.9 1197.7 199.6 : 99.8 199.6 299.4 399.2 499.0 598.8 698.7 798.5 898.3 998.1 1097.9 1197.7 299.4 : 99.8 199.6 299.4 399.2 499.0 598.8 698.6 798.5 898.3 998.1 1097.9 1197.7 399.2 : 99.8 199.6 299.4 399.2 499.0 598.8 698.7 798.5 898.3 998.1 1097.9 1197.7 499.0 : 99.8 199.6 299.4 399.2 499.0 598.8 698.6 798.5 898.3 998.1 1097.9 1197.7 598.8 : 99.8 199.6 299.4 399.2 499.0 598.8 698.6 798.5 898.3 998.1 1097.9 1197.7 698.7 : 99.8 199.6 299.4 399.2 499.0 598.8 698.6 798.5 898.3 998.1 1097.9 1197.7 798.5 : 99.8 199.6 299.4 399.2 499.0 598.8 698.7 798.5 898.3 998.1 1097.9 1197.7 898.3 : 99.8 199.6 299.4 399.2 499.0 598.8 698.7 798.5 898.3 998.1 1097.9 1197.7 998.1 : 99.8 199.6 299.4 399.2 499.0 598.8 698.7 798.5 898.3 998.1 1097.9 1197.7 1097.9: 99.8 199.6 299.4 399.2 499.0 598.8 698.7 798.5 898.3 998.1 1097.9 1197.7 1197.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 99.8070 .. 99.8080 cents 0.00100 cents 99.80700 cents 2: 199.6140 .. 199.6150 cents 0.00100 cents 99.80600 cents 3: 299.4210 .. 299.4220 cents 0.00100 cents 99.80600 cents 4: 399.2280 .. 399.2290 cents 0.00100 cents 99.80600 cents 5: 499.0350 .. 499.0360 cents 0.00100 cents 99.80600 cents 6: 598.8430 .. 598.8430 cents 1/1, 0.0000 cents 99.80700 cents 7: 698.6500 .. 698.6510 cents 0.00100 cents 99.80700 cents 8: 798.4570 .. 798.4580 cents 0.00100 cents 99.80600 cents 9: 898.2640 .. 898.2650 cents 0.00100 cents 99.80600 cents 10: 998.0710 .. 998.0720 cents 0.00100 cents 99.80600 cents 11: 1097.8780 .. 1097.8790 cents 0.00100 cents 99.80600 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 99.80700 cents, class 1 Average step (divided formal octave): 99.8072 cents Largest one step interval : 99.80800 cents Average / Smallest step : 1.000002 Largest / Average step : 1.000008 Largest / Smallest step : 1.000010 Median interval of one step : 99.80700 cents, amount: 10 Most common interval of one step : 99.80700 cents, amount: 10 Least squares average step : 99.80718 cents, oct.: 1197.68616 cents Scale is strictly proper Scale has 2 repeating blocks of 6 notes Blocks have Myhill's property chromas: 0.00100 cents and 99.80600 cents, ratio: 99805.999989 generators: 1 of 99.80700 cents and 5 of 499.03600 cents ET pair of linear temperament : 1197686&1197686 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 12-tone equal temperament with octave 1197.686 cents degrees: 1 2 3 4 5 6 7 8 9 10 11 12 Least number of segments generator : 7 of 698.650 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 7 of 698.650 cents and inv. generated superset size: 12 = 0 more = 100.000% Number of contiguous 1-step segments: 1 Step pattern alph. order: AABAAAAABAAA Step pattern size order : SSLSSSSSLSSS Interval vector is [ 2 4 6 8 10 6 ] Scale is a Constant Structure, by a margin of 99.80600 cents Scale diversity : 1.001544 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.999992 Rothenberg efficiency (ambiguous key): 0.505556 redundancy: 0.494444 Efficiency x scale size : 6.066667 Number of different interval sizes : 21 = 1.90909 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.90909 = 21/11 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 0.00100 cents Most common intervals : 598.84300 cents & inv., amount: 12 Number of recognisable fifths : 12, average 698.6502 cents Number of recognisable fourths : 12, average 499.0358 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 10 = 83.3333% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions : 1 2 3 4 5 6 7 8 9 10 11 Inversional symmetry on degrees : 0 1 2 3 4 5 6 7 8 9 10 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: 0.0003 c. M: 0.0005 c. Twelve-tone Chromatic (1/11-comma)
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 2.3140 cents 2 x x x x x x 3 x x x x 4 S SD: 2.0173 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.7108 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.0561 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.7772 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 10.0333 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.8874 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.9946 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.1380 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0418 cents 11 x 12:13:14:15:16 x 17:18:20:21:22 S SD: 11.2641 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.1856 cents 13:14:15 x 16:17:18:19:21:22:23:25:26 SD: 9.6854 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.1909 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.8905 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.0744 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.9879 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.6292 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.2746 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.6416 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1815 cents 46:49:52:55:58:61:65:69:73:77:82:87:92 SD: 1.9680 cents 48:51:54:57:60:64:68:72:76:81:85:91:96 SD: 1.8323 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.6451 cents 51:54:57:61:64:68:72:76:81:86:91:96:102 SD: 1.5533 cents 63:67:71:75:79:84:89:94:100:106:112:119:126 SD: 1.2485 cents 65:69:73:77:82:87:92:97:103:109:116:123:130 SD: 1.2099 cents 68:72:76:81:86:91:96:102:108:114:121:128:136 SD: 1.1573 cents 80:85:90:95:101:107:113:120:127:134:142:151:160 SD: 1.0538 cents 84:89:94:100:106:112:119:126:133:141:150:158:168 SD: 0.9767 cents 90:95:101:107:113:120:127:135:143:151:160:170:180 SD: 0.9126 cents 96:102:108:114:121:128:136:144:152:161:171:181:192 SD: 0.8553 cents 99:105:111:118:125:132:140:148:157:166:176:187:198 SD: 0.7769 cents 116:123:130:138:146:155:164:174:184:195:206:219:232 SD: 0.6232 cents 123:130:138:146:155:164:174:184:195:207:219:232:246 SD: 0.5597 cents 131:139:147:156:165:175:185:196:208:220:233:247:262 SD: 0.5003 cents 147:156:165:175:185:196:208:220:233:247:262:277:294 SD: 0.4990 cents 155:164:174:184:195:207:219:232:246:260:276:292:310 SD: 0.4928 cents 165:175:185:196:208:220:233:247:262:277:294:311:330 SD: 0.4560 cents 201:213:226:239:253:268:284:301:319:338:358:379:401 SD: 0.3999 cents 203:215:228:241:256:271:287:304:322:341:361:383:405 SD: 0.3976 cents 213:226:239:253:268:284:301:319:338:358:379:402:425 SD: 0.3846 cents 237:251:266:282:298:316:335:355:376:398:422:447:473 SD: 0.3285 cents 254:269:285:302:320:339:359:380:403:427:452:479:507 SD: 0.2006 cents 350:371:393:416:441:467:495:524:555:588:623:660:699 SD: 0.1838 cents 401:425:450:477:505:535:567:600:636:674:714:756:801 SD: 0.1787 cents 435:461:488:517:548:580:615:651:690:731:774:820:869 SD: 0.1633 cents 440:466:494:523:554:587:622:659:698:739:783:830:879 SD: 0.1464 cents 491:520:551:584:618:655:694:735:779:825:874:926:981 SD: 0.1443 cents 509:539:571:605:641:679:719:762:807:855:906:960:1017 SD: 0.1405 cents