Scala analysis: 08_kleismic
Proper subset of Kleismic (in 19-tET).
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 63.158 cents 63.158000 2: 315.789 cents 315.789000 3: 378.947 cents 378.947000 4: 631.579 cents 631.579000 5: 694.737 cents 694.737000 6: 947.368 cents 947.368000 7: 1010.526 cents 1010.526000 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 189.4740 cents 189.4740 1: 63.1580 cents 63.1580 2: 252.6310 cents 252.6310 3: 63.1580 cents 63.1580 4: 252.6320 cents 252.6320 5: 63.1580 cents 63.1580 6: 252.6310 cents 252.6310 7: 63.1580 cents 63.1580 8: 189.4740 cents 189.4740
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 63.15800 cents 1: 1 189.47400 cents 1: 2 252.63100 cents 1: 1 252.63200 cents 2: 2 252.63200 cents 2: 4 315.78900 cents 2: 2 315.79000 cents 3: 1 315.79000 cents 3: 2 378.94700 cents 3: 1 378.94800 cents 3: 2 505.26300 cents 3: 2 568.42100 cents 4: 4 568.42100 cents 4: 4 631.57900 cents 5: 2 631.57900 cents 5: 2 694.73700 cents 5: 1 821.05200 cents 5: 2 821.05300 cents 5: 1 884.21000 cents 6: 2 884.21000 cents 6: 4 884.21100 cents 6: 2 947.36800 cents 7: 1 947.36800 cents 7: 2 947.36900 cents 7: 1 1010.52600 cents 7: 4 1136.84200 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.71429 = 26/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 63.2 315.8 378.9 631.6 694.7 947.4 1010.5 1200.0 63.2 : 252.6 315.8 568.4 631.6 884.2 947.4 1136.8 1200.0 315.8 : 63.2 315.8 378.9 631.6 694.7 884.2 947.4 1200.0 378.9 : 252.6 315.8 568.4 631.6 821.1 884.2 1136.8 1200.0 631.6 : 63.2 315.8 378.9 568.4 631.6 884.2 947.4 1200.0 694.7 : 252.6 315.8 505.3 568.4 821.1 884.2 1136.8 1200.0 947.4 : 63.2 252.6 315.8 568.4 631.6 884.2 947.4 1200.0 1010.5: 189.5 252.6 505.3 568.4 821.1 884.2 1136.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.1580 .. 252.6320 cents 189.47400 cents 63.15800 cents 2: 252.6320 .. 315.7900 cents 63.15800 cents 1/1, 0.0000 cents 3: 315.7900 .. 568.4210 cents 252.63100 cents 1/1, 0.0000 cents 4: 568.4210 .. 631.5790 cents 63.15800 cents 1/1, 0.0000 cents 5: 631.5790 .. 884.2100 cents 252.63100 cents 1/1, 0.0000 cents 6: 884.2100 .. 947.3680 cents 63.15800 cents 1/1, 0.0000 cents 7: 947.3680 .. 1136.8420 cents 189.47400 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 63.15800 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 252.63200 cents Average / Smallest step : 2.374996 Largest / Average step : 1.684213 Largest / Smallest step : 4.000000 Median interval of one step : 126.31600 cents, amount: 0 Most common interval of one step : 63.15800 cents, amount: 4 Least squares average step : 147.98759 cents, oct.: 1183.90071 cents Scale is proper Scale is a mode of a 19-tone equal temperament with octave 2/1 degrees: 1 5 6 10 11 15 16 19 Least number of segments generator : 10 of 631.579 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 14 of 884.211 cents and inv. generated superset size: 8 = 0 more = 100.000% Number of contiguous 1-step segments: 4 Step pattern alph. order: ABACABAD Step pattern size order : ACADACAB Interval vector is [ 4 0 1 3 3 1 0 2 6 ] Scale is not a Constant Structure Scale diversity : 1.246993 Rothenberg stability : 0.571429 = 4/7 Lumma stability : 0.105263 Rothenberg efficiency : 0.546429 redundancy: 0.453571 Efficiency x scale size : 4.371429 Number of different interval sizes : 20 = 2.85714 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 3.71429 = 26/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 0.00100 cents Most common intervals : 568.42100 cents & inv., amount: 6 Most common triad is 0.0 568.421 631.579 cents, amount: 4 Number of recognisable fifths : 2, average 694.7370 cents Scale contains two identical disjunct tetrachords Formal octave complements present : 1 = 12.5000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 7-8 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
8: 0 2 0 2 0 2 0 2 P B DE SD: 66.0520 c. M: 110.5260 c. 9: 0 2 1 1 1 2 0 2 N D3 SD: 54.1306 c. M: 98.2457 c. 11: 1 2 1 2 0 3 0 2 N SD: 34.8069 c. M:-57.4166 c. 12: 1 2 1 2 1 2 1 2 SP B ME SD: 26.0512 c. M: 47.3680 c. Octatonic, Messiaen mode 2, Dominant Diminished, Diminished Blues, Half-Whole step scale 13: 1 2 1 3 1 2 1 2 P D3 SD: 25.4769 c. M:-43.7245 c. 14: 1 3 0 3 1 3 1 2 N SD: 22.2727 c. M: 36.0899 c. 15: 1 3 1 3 1 3 1 2 P G SD: 17.6140 c. M:-29.4740 c. 19: 1 4 1 4 1 4 1 3 P G SD: 0.0003 c. M:-0.0005 c. Kleismic-8
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 3.6090 cents 3 x x 4 x x 5 x 6 S SD: 44.9129 cents 4 x x 5 x 6:7 x 8 S SD: 5.9519 cents 5 x 6 x 7 x x 9:10 SD: 12.3935 cents 6 x 7 x x 9:10:11:12 SD: 17.8029 cents 7 x 8:9:10 x 12:13:14 S SD: 20.0380 cents 8 x x 10 x 12:14 x 16 S SD: 5.9519 cents 9:10 x 11:13 x x 16:18 SD: 24.8580 cents 10:11:12 x 14:15:17:18:20 SD: 16.7256 cents 11:12:13:14:16 x 19:20:22 SD: 14.8039 cents 12:13:14:15:17:18:21:22:24 SD: 13.0935 cents 13:14 x 16:19 x 22:23:26 SD: 14.0681 cents 14:15:17 x 20:21:24:25:28 SD: 9.1254 cents 15:16:18:19:22 x 26:27:30 SD: 9.4130 cents 16:17:19:20:23:24:28:29:32 SD: 6.8713 cents 18:19 x 22:26:27:31:32:36 SD: 6.7710 cents 19:20:23:24:27:28:33:34:38 SD: 6.4950 cents 20:21:24:25:29:30:35:36:40 SD: 4.3435 cents 24:25:29:30:35:36:41:43:48 SD: 4.2959 cents 25:26:30:31:36:37:43:45:50 SD: 2.6335 cents 29:30:35:36:42:43:50:52:58 SD: 2.5371 cents 45:47:54:56:65:67:78:81:90 SD: 2.0857 cents 49:51:59:61:71:73:85:88:98 SD: 1.9754 cents 50:52:60:62:72:75:86:90:100 SD: 1.9337 cents 54:56:65:67:78:81:93:97:108 SD: 1.7047 cents 59:61:71:73:85:88:102:106:118 SD: 1.6788 cents 61:63:73:76:88:91:105:109:122 SD: 1.6576 cents 73:76:88:91:105:109:126:131:146 SD: 1.3953 cents 75:78:90:93:108:112:130:134:150 SD: 1.3873 cents 77:80:92:96:111:115:133:138:154 SD: 1.1185 cents 81:84:97:101:117:121:140:145:162 SD: 0.9252 cents 105:109:126:131:151:157:181:188:210 SD: 0.9246 cents 106:110:127:132:153:158:183:190:212 SD: 0.8107 cents 110:114:132:137:158:164:190:197:220 SD: 0.7898 cents 111:115:133:138:160:166:192:199:222 SD: 0.5982 cents 130:135:156:162:187:194:225:233:260 SD: 0.5847 cents 134:139:161:167:193:200:232:240:268 SD: 0.5832 cents 136:141:163:169:196:203:235:244:272 SD: 0.5423 cents 159:165:191:198:229:238:275:285:318 SD: 0.5381 cents 164:170:197:204:236:245:283:294:328 SD: 0.4835 cents 184:191:221:229:265:275:318:330:368 SD: 0.3002 cents 241:250:289:300:347:360:417:432:482 SD: 0.2963 cents 245:254:294:305:353:366:423:439:490 SD: 0.2904 cents 265:275:318:330:382:396:458:475:530 SD: 0.2638 cents 270:280:324:336:389:403:467:484:540 SD: 0.2429 cents 295:306:354:367:425:441:510:529:590 SD: 0.2276 cents 375:389:450:467:540:560:648:672:750 SD: 0.1698 cents 405:420:486:504:583:605:700:726:810 SD: 0.1241 cents 486:504:583:605:700:726:840:871:972 SD: 0.1170 cents 589:611:707:733:848:880:1018:1056:1178 SD: 0.1163 cents