Scala analysis: prop19_9b
Alternative proper 9-note 19-et scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 126.316 cents 126.315789 2: 315.789 cents 315.789474 3: 378.947 cents 378.947368 4: 568.421 cents 568.421053 5: 694.737 cents 694.736842 6: 821.053 cents 821.052632 7: 947.368 cents 947.368421 8: 1073.684 cents 1073.684211 9: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 126.3158 cents 126.3158 1: 126.3158 cents 126.3158 2: 189.4737 cents 189.4737 3: 63.1579 cents 63.1579 4: 189.4737 cents 189.4737 5: 126.3158 cents 126.3158 6: 126.3158 cents 126.3158 7: 126.3158 cents 126.3158 8: 126.3158 cents 126.3158 9: 126.3158 cents 126.3158
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 63.15789 cents 1: 6 126.31579 cents 1: 2 189.47368 cents 2: 7 252.63158 cents 2: 2 315.78947 cents 3: 6 378.94737 cents 3: 3 442.10526 cents 4: 5 505.26316 cents 4: 4 568.42105 cents 5: 4 631.57895 cents 5: 5 694.73684 cents 6: 3 757.89474 cents 6: 6 821.05263 cents 7: 2 884.21053 cents 7: 7 947.36842 cents 8: 2 1010.52632 cents 8: 6 1073.68421 cents 8: 1 1136.84211 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.25000 = 9/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 126.3 315.8 378.9 568.4 694.7 821.1 947.4 1073.7 1200.0 126.3 : 189.5 252.6 442.1 568.4 694.7 821.1 947.4 1073.7 1200.0 315.8 : 63.2 252.6 378.9 505.3 631.6 757.9 884.2 1010.5 1200.0 378.9 : 189.5 315.8 442.1 568.4 694.7 821.1 947.4 1136.8 1200.0 568.4 : 126.3 252.6 378.9 505.3 631.6 757.9 947.4 1010.5 1200.0 694.7 : 126.3 252.6 378.9 505.3 631.6 821.1 884.2 1073.7 1200.0 821.1 : 126.3 252.6 378.9 505.3 694.7 757.9 947.4 1073.7 1200.0 947.4 : 126.3 252.6 378.9 568.4 631.6 821.1 947.4 1073.7 1200.0 1073.7: 126.3 252.6 442.1 505.3 694.7 821.1 947.4 1073.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.1579 .. 189.4737 cents 126.31579 cents 63.15789 cents 2: 252.6316 .. 315.7895 cents 63.15790 cents 63.15789 cents 3: 378.9474 .. 442.1053 cents 63.15790 cents 63.15789 cents 4: 505.2632 .. 568.4211 cents 63.15789 cents 63.15789 cents 5: 631.5789 .. 694.7368 cents 63.15790 cents 63.15789 cents 6: 757.8947 .. 821.0526 cents 63.15790 cents 63.15790 cents 7: 884.2105 .. 947.3684 cents 63.15789 cents 63.15789 cents 8: 1010.5263 .. 1136.8421 cents 126.31579 cents 63.15789 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 63.15789 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 189.47368 cents Average / Smallest step : 2.111111 Largest / Average step : 1.421053 Largest / Smallest step : 3.000000 Median interval of one step : 126.31579 cents, amount: 6 Most common interval of one step : 126.31579 cents, amount: 6 Least squares average step : 135.40166 cents, oct.: 1218.61496 cents Scale is strictly proper Scale is 3-distributional even Scale is a mode of a 19-tone equal temperament with octave 1200.000 cents degrees: 2 5 6 9 11 13 15 17 19 Least number of segments generator : 11 of 694.737 cents and inv. number of contiguous generator circle segments: 2 Shortest superset generator : 17 of 1073.684 cents and inv. generated superset size: 11 = 2 more = 122.222% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABCBAAAAA Step pattern size order : MLSLMMMMM Interval vector is [ 1 6 2 7 2 6 3 5 4 ] Scale is a Constant Structure, by a margin of 63.15789 cents Scale diversity : 1.340072 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.473684 Rothenberg efficiency : 0.582011 redundancy: 0.417989 Efficiency x scale size : 5.238095 Number of different interval sizes : 18 = 2.25000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.25000 = 9/4 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 63.15789 cents Most common intervals : 252.63158 cents & inv., amount: 7 Most common triad is 0.0 252.632 947.368 cents, amount: 5 Number of recognisable fifths : 5, average 694.7368 cents Best minor thirds form a closed circle Formal octave complements present : 5 = 55.5556% Limited inverse transpositions : 5 Inversional symmetry on degrees : 7 Inversional symmetry on intervals : 2-3 -- Rational properties --
FIT/MODE
9: 1 1 1 1 1 1 1 1 1 SP B ME I SD: 24.9756 c. M: 49.1228 c. Pelog Nawanada: Sunda 10: 1 2 0 2 1 1 1 1 1 P D3 S SD: 22.4781 c. M:-44.2105 c. 15: 2 2 1 2 2 1 2 1 2 P D3 SD: 21.1925 c. M: 33.6842 c. 16: 2 2 1 3 1 2 2 1 2 P D3 SD: 19.8680 c. M:-31.5789 c. 19: 2 3 1 3 2 2 2 2 2 SP D3 S SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x 4 S SD: 3.6091 cents 3 x x x 4 x x 5 x 6 S SD: 31.4872 cents 4 x x 5 x 6 x 7 x 8 S SD: 5.9518 cents 5 x 6 x 7 x 8 x 9:10 S SD: 11.6597 cents 6 x 7 x 8:9 x 10:11:12 S SD: 18.2267 cents 7 x 8:9:10 x 11:12:13:14 S SD: 17.1501 cents 8:9 x 10:11:12:13:14:15:16 S SD: 10.8052 cents 9:10 x 11 x 13:14:16:17:18 SD: 16.7772 cents 10:11:12 x 14:15:16:17:19:20 SD: 7.9396 cents 13:14 x 16:18:19:21:22:24:26 SD: 7.2958 cents 14:15:17 x 19:21:23:24:26:28 SD: 7.6779 cents 15:16:18:19:21:22:24:26:28:30 SD: 5.5095 cents 16:17:19:20:22:24:26:28:30:32 SD: 5.2606 cents 18:19 x 22:25:27:29:31:33:36 SD: 6.5775 cents 20:22:24:25:28:30:32:35:37:40 SD: 5.4335 cents 21:23:25:26:29:31:34:36:39:42 SD: 5.1426 cents 23:25:28:29:32:34:37:40:43:46 SD: 4.9498 cents 24:26:29:30:33:36:39:41:45:48 SD: 4.5699 cents 25:27:30:31:35:37:40:43:46:50 SD: 3.5091 cents 26:28:31:32:36:39:42:45:48:52 SD: 3.1977 cents 28:30:34:35:39:42:45:48:52:56 SD: 3.1457 cents 29:31:35:36:40:43:47:50:54:58 SD: 3.1066 cents 36:39:43:45:50:54:58:62:67:72 SD: 2.1853 cents 41:44:49:51:57:61:66:71:76:82 SD: 1.4458 cents 65:70:78:81:90:97:104:112:121:130 SD: 1.2373 cents 69:74:83:86:96:103:111:119:128:138 SD: 1.0829 cents 91:98:109:113:126:136:146:157:169:182 SD: 0.9855 cents 95:102:114:118:132:142:153:164:177:190 SD: 0.8556 cents 106:114:127:132:147:158:170:183:197:212 SD: 0.7339 cents 119:128:143:148:165:178:191:206:221:238 SD: 0.6494 cents 134:144:161:167:186:200:215:232:249:268 SD: 0.6095 cents 144:155:173:179:200:215:231:249:268:288 SD: 0.5247 cents 160:172:192:199:222:239:257:277:297:320 SD: 0.5120 cents 170:183:204:212:236:254:273:294:316:340 SD: 0.4302 cents 185:199:222:230:257:276:297:320:344:370 SD: 0.4045 cents 196:211:235:244:272:293:315:339:364:392 SD: 0.3990 cents 213:229:256:265:296:318:342:368:396:426 SD: 0.3959 cents 221:238:265:275:307:330:355:382:411:442 SD: 0.3046 cents 249:268:299:310:346:372:400:430:463:498 SD: 0.2739 cents 265:285:318:330:368:396:426:458:493:530 SD: 0.1913 cents 409:440:491:509:568:611:657:707:760:818 SD: 0.1465 cents 450:484:540:560:625:672:723:778:837:900 SD: 0.1221 cents 555:597:666:691:771:829:892:959:1032:1110 SD: 0.1211 cents