Scala analysis: kb2_118
118 equal version of Kirnberger 2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 91.525 cents 91.525424 2: 203.390 cents 203.389831 3: 294.915 cents 294.915254 4: 386.441 cents 386.440678 5: 498.305 cents 498.305085 6: 589.831 cents 589.830509 7: 701.695 cents 701.694915 8: 793.220 cents 793.220339 9: 894.915 cents 894.915254 10: 996.610 cents 996.610170 11: 1088.136 cents 1088.135593 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 111.8644 cents 111.8644 1: 91.5254 cents 91.5254 2: 111.8644 cents 111.8644 3: 91.5254 cents 91.5254 4: 91.5254 cents 91.5254 5: 111.8644 cents 111.8644 6: 91.5254 cents 91.5254 7: 111.8644 cents 111.8644 8: 91.5254 cents 91.5254 9: 101.6949 cents 101.6949 10: 101.6949 cents 101.6949 11: 91.5254 cents 91.5254 12: 111.8644 cents 111.8644
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 91.52542 cents 1: 2 101.69491 cents 1: 4 111.86441 cents 2: 1 183.05085 cents 2: 2 193.22034 cents 2: 9 203.38983 cents 3: 8 294.91525 cents 3: 2 305.08474 cents 3: 2 315.25424 cents 4: 3 386.44068 cents 4: 2 396.61017 cents 4: 7 406.77966 cents 5: 10 498.30508 cents 5: 2 508.47458 cents 6: 5 589.83051 cents 6: 2 600.00000 cents 6: 5 610.16949 cents 7: 2 691.52542 cents 7: 10 701.69491 cents 8: 7 793.22034 cents 8: 2 803.38983 cents 8: 3 813.55932 cents 9: 2 884.74576 cents 9: 2 894.91525 cents 9: 8 905.08475 cents 10: 9 996.61017 cents 10: 2 1006.77966 cents 10: 1 1016.94915 cents 11: 4 1088.13559 cents 11: 2 1098.30508 cents 11: 6 1108.47458 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.81818 = 31/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 91.5 203.4 294.9 386.4 498.3 589.8 701.7 793.2 894.9 996.6 1088.1 1200.0 91.5 : 111.9 203.4 294.9 406.8 498.3 610.2 701.7 803.4 905.1 996.6 1108.5 1200.0 203.4 : 91.5 183.1 294.9 386.4 498.3 589.8 691.5 793.2 884.7 996.6 1088.1 1200.0 294.9 : 91.5 203.4 294.9 406.8 498.3 600.0 701.7 793.2 905.1 996.6 1108.5 1200.0 386.4 : 111.9 203.4 315.3 406.8 508.5 610.2 701.7 813.6 905.1 1016.9 1108.5 1200.0 498.3 : 91.5 203.4 294.9 396.6 498.3 589.8 701.7 793.2 905.1 996.6 1088.1 1200.0 589.8 : 111.9 203.4 305.1 406.8 498.3 610.2 701.7 813.6 905.1 996.6 1108.5 1200.0 701.7 : 91.5 193.2 294.9 386.4 498.3 589.8 701.7 793.2 884.7 996.6 1088.1 1200.0 793.2 : 101.7 203.4 294.9 406.8 498.3 610.2 701.7 793.2 905.1 996.6 1108.5 1200.0 894.9 : 101.7 193.2 305.1 396.6 508.5 600.0 691.5 803.4 894.9 1006.8 1098.3 1200.0 996.6 : 91.5 203.4 294.9 406.8 498.3 589.8 701.7 793.2 905.1 996.6 1098.3 1200.0 1088.1: 111.9 203.4 315.3 406.8 498.3 610.2 701.7 813.6 905.1 1006.8 1108.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 91.5254 .. 111.8644 cents 20.33898 cents 91.52542 cents 2: 183.0508 .. 203.3898 cents 20.33898 cents 71.18644 cents 3: 294.9153 .. 315.2542 cents 20.33898 cents 91.52542 cents 4: 386.4407 .. 406.7797 cents 20.33898 cents 71.18644 cents 5: 498.3051 .. 508.4746 cents 10.16949 cents 91.52542 cents 6: 589.8305 .. 610.1695 cents 20.33898 cents 81.35593 cents 7: 691.5254 .. 701.6949 cents 10.16949 cents 81.35593 cents 8: 793.2203 .. 813.5593 cents 20.33898 cents 91.52542 cents 9: 884.7458 .. 905.0847 cents 20.33898 cents 71.18644 cents 10: 996.6102 .. 1016.9492 cents 20.33898 cents 91.52542 cents 11: 1088.1356 .. 1108.4746 cents 20.33898 cents 71.18644 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 91.52542 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 111.86441 cents Average / Smallest step : 1.092593 Largest / Average step : 1.118644 Largest / Smallest step : 1.222222 Median interval of one step : 96.61017 cents, amount: 0 Most common interval of one step : 91.52542 cents, amount: 6 Least squares average step : 99.39505 cents, oct.: 1192.74055 cents Scale is strictly proper Scale is 3-distributional even Scale is a mode of a 118-tone equal temperament with octave 2/1 degrees: 9 20 29 38 49 58 69 78 88 98 107 118 Least number of segments generator : 63 of 640.678 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 69 of 701.695 cents and inv. generated superset size: 65 = 53 more = 541.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABABACCAB Step pattern size order : SLSSLSLSMMSL Interval vector is [ 0 0 0 0 0 0 0 0 6 2 4 0 0 0 0 0 0 1 2 9 0 0 0 0 0 0 0 0 8 2 2 0 0 0 0 0 0 3 2 7 0 0 0 0 0 0 0 0 10 2 0 0 0 0 0 0 0 5 1 ] Scale is a Constant Structure, by a margin of 71.18644 cents Scale diversity : 1.134829 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.830508 Rothenberg efficiency : 0.472222 redundancy: 0.527778 Efficiency x scale size : 5.666667 Number of different interval sizes : 31 = 2.81818 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.81818 = 31/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 10.16949 cents Most common intervals : 498.30508 cents & inv., amount: 10 Most common triad is 0.0 498.305 701.695 cents, amount: 9 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 2 different sizes of fifth Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Formal octave complements present : 5 = 41.6667% Limited transpositions with margin 20.3390 cents: 5 7 9 Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 9 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.2241 c. M:-13.5593 c. Twelve-tone Chromatic (1/11-comma) 40: 3 4 3 3 4 3 3 3 4 3 3 4 SP D3 SD: 8.0209 c. M: 13.2203 c. 41: 3 4 3 3 4 3 4 3 3 4 3 4 SP M ME SD: 5.7750 c. M: 16.8665 c. Schismic-12 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 6.7326 c. M:-12.0615 c. Meantone Chromatic (1/5-comma) 49: 4 4 4 4 4 4 5 3 5 4 3 5 SP D3 SD: 7.4225 c. M:-11.2072 c. 51: 4 5 4 3 5 4 5 4 4 4 4 5 SP D3 SD: 6.3530 c. M:-10.9671 c. 52: 4 5 4 4 5 4 4 4 5 4 4 5 SP D3 SD: 6.3892 c. M:-10.1695 c. 53: 4 5 4 4 5 4 5 4 5 4 4 5 SP M ME SD: 3.2035 c. M:-10.7451 c. 63: 5 6 4 5 6 5 6 5 5 5 5 6 SP D3 SD: 4.7869 c. M: 9.2010 c. 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 2.6121 c. M: 8.7614 c. 67: 5 6 5 6 6 5 6 5 6 6 5 6 SP M ME SD: 4.8359 c. M: 8.3481 c. 72: 5 7 6 5 7 5 7 6 6 6 5 7 SP T3 SD: 4.7297 c. M: 8.1921 c. 75: 6 7 5 6 7 6 7 6 6 6 6 7 SP D3 SD: 3.8600 c. M: 6.9153 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 2.5235 c. M: 6.6036 c. 82: 6 8 6 6 8 6 8 6 7 7 6 8 SP D3 S SD: 3.1716 c. M: 5.9529 c. 89: 7 8 7 7 8 7 8 7 7 8 7 8 SP M ME SD: 2.7913 c. M: 5.0276 c. 94: 7 9 7 7 9 7 9 7 8 8 7 9 SP D3 S SD: 1.8445 c. M: 3.4620 c. 106: 8 10 8 8 10 8 10 8 9 9 8 10 SP D3 S SD: 0.8178 c. M: 1.5350 c. 118: 9 11 9 9 11 9 11 9 10 10 9 11 SP D3 S SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.1300 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.5199 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.9464 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.3278 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.1673 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.8313 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.3792 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.0374 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.6517 cents 11 x 12:13:14:15 x x 17:18:20:21:22 SD: 11.6994 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.7545 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 9.2052 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.9052 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.3256 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 5.0956 cents 21:22:24:25:26:28:30:31:33:35:37:39:42 SD: 4.9241 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 3.9302 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.4155 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 3.1405 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1694 cents 40:42:45:47:50:53:56:60:63:67:71:75:80 SD: 1.9271 cents 48:51:54:57:60:64:67:72:76:80:85:90:96 SD: 1.8882 cents 54:57:61:64:68:72:76:81:85:91:96:101:108 SD: 1.6216 cents 55:58:62:65:69:73:77:82:87:92:98:103:110 SD: 1.5507 cents 56:59:63:66:70:75:79:84:89:94:100:105:112 SD: 1.5237 cents 64:67:72:76:80:85:90:96:101:107:114:120:128 SD: 1.3233 cents 71:75:80:84:89:95:100:106:112:119:126:133:142 SD: 1.1697 cents 72:76:81:85:90:96:101:108:114:121:128:135:144 SD: 0.8216 cents 96:101:108:114:120:128:135:144:152:161:171:180:192 SD: 0.4872 cents 167:176:188:198:209:223:235:250:264:280:297:313:334 SD: 0.4216 cents 168:177:189:199:210:224:236:252:266:282:299:315:336 SD: 0.3489 cents 200:211:225:237:250:267:281:300:316:335:356:375:400 SD: 0.3321 cents 216:228:243:256:270:288:304:324:342:362:384:405:432 SD: 0.3263 cents 256:270:288:304:320:341:360:384:405:429:455:480:512 SD: 0.3171 cents 258:272:290:306:323:344:363:387:408:433:459:484:516 SD: 0.3043 cents 264:278:297:313:330:352:371:396:417:443:469:495:528 SD: 0.3021 cents 279:294:314:331:349:372:392:418:441:468:496:523:558 SD: 0.2639 cents 296:312:333:351:370:395:416:444:468:496:526:555:592 SD: 0.1951 cents 312:329:351:370:390:416:439:468:493:523:555:585:624 SD: 0.1770 cents 384:405:432:455:480:512:540:576:607:644:683:720:768 SD: 0.1416 cents 480:506:540:569:600:640:675:720:759:805:854:900:960 SD: 0.1047 cents