Scala analysis: alafried
Fried alaska, with octave-fifth brats of 1 and 2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 98.868 cents 98.867788 2: 197.736 cents 197.735576 3: 299.074 cents 299.074366 4: 397.942 cents 397.942153 5: 496.810 cents 496.809941 6: 598.149 cents 598.148731 7: 697.017 cents 697.016520 8: 795.884 cents 795.884307 9: 897.223 cents 897.223099 10: 996.091 cents 996.090887 11: 1094.959 cents 1094.958674 12: 1196.297 cents 1196.297466
SHOW/INTERVAL
0: 101.3388 cents 101.3388 1: 98.8678 cents 98.8678 2: 98.8678 cents 98.8678 3: 101.3388 cents 101.3388 4: 98.8678 cents 98.8678 5: 98.8678 cents 98.8678 6: 101.3388 cents 101.3388 7: 98.8678 cents 98.8678 8: 98.8678 cents 98.8678 9: 101.3388 cents 101.3388 10: 98.8678 cents 98.8678 11: 98.8678 cents 98.8678 12: 101.3388 cents 101.3388
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 98.86779 cents 1: 4 101.33879 cents 2: 4 197.73558 cents 2: 8 200.20658 cents 3: 12 299.07437 cents 4: 8 397.94215 cents 4: 4 400.41315 cents 5: 4 496.80994 cents 5: 8 499.28094 cents 6: 12 598.14873 cents 7: 8 697.01652 cents 7: 4 699.48752 cents 8: 4 795.88431 cents 8: 8 798.35531 cents 9: 12 897.22310 cents 10: 8 996.09089 cents 10: 4 998.56189 cents 11: 4 1094.95867 cents 11: 8 1097.42968 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.72727 = 19/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 98.9 197.7 299.1 397.9 496.8 598.1 697.0 795.9 897.2 996.1 1095.0 1196.3 98.9 : 98.9 200.2 299.1 397.9 499.3 598.1 697.0 798.4 897.2 996.1 1097.4 1196.3 197.7 : 101.3 200.2 299.1 400.4 499.3 598.1 699.5 798.4 897.2 998.6 1097.4 1196.3 299.1 : 98.9 197.7 299.1 397.9 496.8 598.1 697.0 795.9 897.2 996.1 1095.0 1196.3 397.9 : 98.9 200.2 299.1 397.9 499.3 598.1 697.0 798.4 897.2 996.1 1097.4 1196.3 496.8 : 101.3 200.2 299.1 400.4 499.3 598.1 699.5 798.4 897.2 998.6 1097.4 1196.3 598.1 : 98.9 197.7 299.1 397.9 496.8 598.1 697.0 795.9 897.2 996.1 1095.0 1196.3 697.0 : 98.9 200.2 299.1 397.9 499.3 598.1 697.0 798.4 897.2 996.1 1097.4 1196.3 795.9 : 101.3 200.2 299.1 400.4 499.3 598.1 699.5 798.4 897.2 998.6 1097.4 1196.3 897.2 : 98.9 197.7 299.1 397.9 496.8 598.1 697.0 795.9 897.2 996.1 1095.0 1196.3 996.1 : 98.9 200.2 299.1 397.9 499.3 598.1 697.0 798.4 897.2 996.1 1097.4 1196.3 1095.0: 101.3 200.2 299.1 400.4 499.3 598.1 699.5 798.4 897.2 998.6 1097.4 1196.3 1196.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.8678 .. 101.3388 cents 2.47100 cents 98.86779 cents 2: 197.7356 .. 200.2066 cents 2.47100 cents 96.39679 cents 3: 299.0744 .. 299.0744 cents 1/1, 0.0000 cents 98.86779 cents 4: 397.9422 .. 400.4132 cents 2.47100 cents 98.86779 cents 5: 496.8099 .. 499.2809 cents 2.47100 cents 96.39679 cents 6: 598.1487 .. 598.1487 cents 1/1, 0.0000 cents 98.86779 cents 7: 697.0165 .. 699.4875 cents 2.47100 cents 98.86779 cents 8: 795.8843 .. 798.3553 cents 2.47100 cents 96.39678 cents 9: 897.2231 .. 897.2231 cents 1/1, 0.0000 cents 98.86779 cents 10: 996.0909 .. 998.5619 cents 2.47100 cents 98.86779 cents 11: 1094.9587 .. 1097.4297 cents 2.47100 cents 96.39678 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 98.86779 cents, class 1 Average step (divided formal octave): 99.6915 cents Largest one step interval : 101.33879 cents Average / Smallest step : 1.008331 Largest / Average step : 1.016524 Largest / Smallest step : 1.024993 Median interval of one step : 98.86779 cents, amount: 8 Most common interval of one step : 98.86779 cents, amount: 8 Least squares average step : 99.59768 cents, oct.: 1195.17221 cents Scale is strictly proper Scale is maximally even in 484-tone equal temperament Scale has 4 repeating blocks of 3 notes Blocks have Myhill's property chromas: 2.47100 cents and 96.39679 cents, ratio: 39.011213 generators: 1 of 98.86779 cents and 200.20658 cents ET pair of linear temperament : 484&43088 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 484-tone equal temperament with octave 1196.297 cents degrees: 40 80 121 161 201 242 282 322 363 403 443 484 Least number of segments generator : 243 of 600.620 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 323 of 798.356 cents and inv. generated superset size: 366 = 354 more = 3050.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAABAABAAB Step pattern size order : SSLSSLSSLSSL Scale is a Constant Structure, by a margin of 96.39678 cents Scale diversity : 1.015689 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.983476 Rothenberg efficiency (ambiguous key): 0.312963 redundancy: 0.687037 Efficiency x scale size : 3.755556 Number of different interval sizes : 19 = 1.72727 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.72727 = 19/11 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 2.47100 cents Most common triad is 0.0 299.074 598.149 cents, amount: 12 Number of recognisable fifths : 12, average 697.8402 cents Number of recognisable fourths : 12, average 498.4573 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 4 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 3 6 9 Limited inverse transpositions : 2 5 8 11 Inversional symmetry on degrees : 1 4 7 10 Inversional symmetry on intervals : 2-3 5-6 8-9 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 1.0634 c. M:-1.6473 c. Twelve-tone Chromatic (1/11-comma) 244: 20 20 21 20 20 21 20 20 21 20 20 21 SP B ME S SD: 1.0465 c. M: 1.6212 c. 256: 21 21 22 21 21 22 21 21 22 21 21 22 SP B ME S SD: 0.9476 c. M: 1.4680 c. 268: 22 22 23 22 22 23 22 22 23 22 22 23 SP B ME S SD: 0.8576 c. M: 1.3285 c. 280: 23 23 24 23 23 24 23 23 24 23 23 24 SP B ME S SD: 0.7752 c. M: 1.2010 c. 292: 24 24 25 24 24 25 24 24 25 24 24 25 SP B ME S SD: 0.6997 c. M: 1.0839 c. 304: 25 25 26 25 25 26 25 25 26 25 25 26 SP B ME S SD: 0.6301 c. M: 0.9761 c. 316: 26 26 27 26 26 27 26 26 27 26 26 27 SP B ME S SD: 0.5658 c. M: 0.8765 c. 328: 27 27 28 27 27 28 27 27 28 27 27 28 SP B ME S SD: 0.5062 c. M: 0.7842 c. 340: 28 28 29 28 28 29 28 28 29 28 28 29 SP B ME S SD: 0.4508 c. M: 0.6983 c. 352: 29 29 30 29 29 30 29 29 30 29 29 30 SP B ME S SD: 0.3992 c. M: 0.6184 c. 364: 30 30 31 30 30 31 30 30 31 30 30 31 SP B ME S SD: 0.3509 c. M: 0.5437 c. 376: 31 31 32 31 31 32 31 31 32 31 31 32 SP B ME S SD: 0.3058 c. M: 0.4738 c. 388: 32 32 33 32 32 33 32 32 33 32 32 33 SP B ME S SD: 0.2635 c. M: 0.4082 c. 400: 33 33 34 33 33 34 33 33 34 33 33 34 SP B ME S SD: 0.2237 c. M: 0.3465 c. 412: 34 34 35 34 34 35 34 34 35 34 34 35 SP B ME S SD: 0.1862 c. M: 0.2884 c. 424: 35 35 36 35 35 36 35 35 36 35 35 36 SP B ME S SD: 0.1508 c. M: 0.2336 c. 436: 36 36 37 36 36 37 36 36 37 36 36 37 SP B ME S SD: 0.1174 c. M: 0.1819 c. 448: 37 37 38 37 37 38 37 37 38 37 37 38 SP B ME S SD: 0.0858 c. M: 0.1329 c. 460: 38 38 39 38 38 39 38 38 39 38 38 39 SP B ME S SD: 0.0558 c. M: 0.0864 c. 472: 39 39 40 39 39 40 39 39 40 39 39 40 SP B ME S SD: 0.0273 c. M: 0.0424 c. 484: 40 40 41 40 40 41 40 40 41 40 40 41 SP B ME S SD: 0.0003 c. M: 0.0005 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 3.7025 cents 2 x x x x x x 3 x x x x 4 S SD: 3.0862 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.4812 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.5693 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.2445 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.6049 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.9947 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.0015 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.0338 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0319 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.2029 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.2353 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 9.6550 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.3557 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.9249 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.7432 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.0046 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.9426 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.7436 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.2361 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.4450 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.3311 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.2617 cents 46:49:52:55:58:61:65:69:73:77:82:87:92 SD: 2.1675 cents 48:51:54:57:60:64:68:72:76:81:85:90:96 SD: 1.7509 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.6850 cents 51:54:57:61:64:68:72:76:81:86:91:96:102 SD: 1.5523 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.3987 cents 65:69:73:77:82:87:92:97:103:109:116:122:130 SD: 1.3416 cents 68:72:76:81:86:91:96:102:108:114:121:128:136 SD: 1.3113 cents 69:73:77:82:87:92:97:103:109:116:123:130:138 SD: 1.2389 cents 75:79:84:89:94:100:106:112:119:126:133:141:150 SD: 1.1704 cents 81:86:91:96:102:108:114:121:128:136:144:152:162 SD: 1.0777 cents 84:89:94:100:106:112:119:126:133:141:149:158:168 SD: 0.9171 cents 85:90:95:101:107:113:120:127:135:143:151:160:170 SD: 0.8289 cents 116:123:130:138:146:155:164:174:184:195:206:218:232 SD: 0.8193 cents 117:124:131:139:147:156:165:175:185:196:208:220:234 SD: 0.6774 cents 139:147:156:165:175:185:196:208:220:233:247:262:277 SD: 0.5925 cents 159:168:178:189:200:212:225:238:252:267:283:299:317 SD: 0.5411 cents 165:175:185:196:208:220:233:247:261:277:293:311:329 SD: 0.5218 cents 171:181:192:203:215:228:242:256:271:287:304:322:341 SD: 0.4766 cents 175:185:196:208:220:233:247:262:277:294:311:329:349 SD: 0.4337 cents 189:200:212:225:238:252:267:283:299:317:336:356:377 SD: 0.4181 cents 190:201:213:226:239:253:268:284:301:319:338:358:379 SD: 0.3681 cents 206:218:231:245:259:274:291:308:326:346:366:388:411 SD: 0.3574 cents 238:252:267:283:300:317:336:356:377:400:423:448:475 SD: 0.3246 cents 240:254:269:285:302:320:339:359:380:403:427:452:479 SD: 0.2290 cents 271:287:304:322:341:361:383:405:429:455:482:510:541 SD: 0.2073 cents 414:438:464:492:521:552:585:619:656:695:736:779:826 SD: 0.1986 cents 424:449:475:504:534:565:599:634:671:712:754:798:846 SD: 0.1943 cents 430:455:482:511:541:573:607:643:681:722:764:809:858 SD: 0.1874 cents 440:466:493:523:554:586:622:658:697:739:782:828:878 SD: 0.1806 cents 445:471:499:529:560:593:629:666:705:747:791:838:888 SD: 0.1713 cents 446:472:500:530:561:594:630:667:706:749:793:839:890 SD: 0.1598 cents 511:541:573:607:643:681:722:764:809:858:908:962:1020 SD: 0.1502 cents 514:544:576:611:647:685:726:769:814:863:914:967:1026 SD: 0.1319 cents 526:557:590:625:662:701:743:787:833:883:935:990:1050 SD: 0.1281 cents 545:577:611:648:686:726:770:815:863:915:969:1026:1088 SD: 0.0956 cents