Scala analysis: prop19_9a
Negri[9] = 09-19.scl
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: 252.632 cents 252.631579 3: 378.947 cents 378.947368 4: 505.263 cents 505.263158 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: 126.3158 cents 126.3158 3: 126.3158 cents 126.3158 4: 126.3158 cents 126.3158 5: 189.4737 cents 189.4737 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: 8 126.31579 cents 1: 1 189.47368 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: 1 1010.52632 cents 8: 8 1073.68421 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 126.3 252.6 378.9 505.3 694.7 821.1 947.4 1073.7 1200.0 126.3 : 126.3 252.6 378.9 568.4 694.7 821.1 947.4 1073.7 1200.0 252.6 : 126.3 252.6 442.1 568.4 694.7 821.1 947.4 1073.7 1200.0 378.9 : 126.3 315.8 442.1 568.4 694.7 821.1 947.4 1073.7 1200.0 505.3 : 189.5 315.8 442.1 568.4 694.7 821.1 947.4 1073.7 1200.0 694.7 : 126.3 252.6 378.9 505.3 631.6 757.9 884.2 1010.5 1200.0 821.1 : 126.3 252.6 378.9 505.3 631.6 757.9 884.2 1073.7 1200.0 947.4 : 126.3 252.6 378.9 505.3 631.6 757.9 947.4 1073.7 1200.0 1073.7: 126.3 252.6 378.9 505.3 631.6 821.1 947.4 1073.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 126.3158 .. 189.4737 cents 63.15790 cents 126.31579 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 63.15790 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 63.15789 cents 7: 884.2105 .. 947.3684 cents 63.15790 cents 63.15789 cents 8: 1010.5263 .. 1073.6842 cents 63.15790 cents 63.15789 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 126.31579 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 189.47368 cents Average / Smallest step : 1.055556 Largest / Average step : 1.421053 Largest / Smallest step : 1.500000 Median interval of one step : 126.31579 cents, amount: 8 Most common interval of one step : 126.31579 cents, amount: 8 Least squares average step : 134.07202 cents, oct.: 1206.64820 cents Scale is strictly proper Scale has Myhill's property chromas: 63.15790 cents and 63.15789 cents, ratio: 1.000000 generators: 1 of 126.31579 cents and 8 of 1073.68421 cents Scale is maximally even in 19-tone equal temperament ET pair of linear temperament : 10&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 19-tone equal temperament with octave 1200.000 cents degrees: 2 4 6 8 11 13 15 17 19 generators: 2 and 17 Number of contiguous 1-step segments: 0 Scale is a Winograd/Gamer deep scale Step pattern alph. order: AAAABAAAA Step pattern size order : SSSSLSSSS Interval vector is [ 0 8 1 7 2 6 3 5 4 ] Scale is a Constant Structure, by a margin of 63.15789 cents Scale diversity : 1.253119 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.578947 Rothenberg efficiency : 0.740741 redundancy: 0.259259 Efficiency x scale size : 6.666667 Number of different interval sizes : 16 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 63.15789 cents Most common intervals : 126.31579 cents & inv., amount: 8 Scale is a chain of 4 triads 0.0 505.263 1073.684 cents Number of recognisable fifths : 5, average 694.7368 cents Scale contains two identical disjunct pentachords Best minor thirds form a closed circle Formal octave complements present : 9 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 4-5 -- Rational properties --
FIT/MODE
9: 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.1192 c. M: 28.0702 c. Pelog Nawanada: Sunda 10: 1 1 1 1 2 1 1 1 1 P M ME I SD: 16.3073 c. M:-25.2632 c. Yoyo & Latrizo-9 19: 2 2 2 2 3 2 2 2 2 SP M ME I SD: 0.0000 c. M: 0.0000 c. Negri-9
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: 21.1406 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: 22.9240 cents 6 x 7 x 8:9 x 10:11:12 S SD: 11.6294 cents 7 x 8:9 x 10:11:12:13:14 S SD: 15.1676 cents 8 x 9:10:11:12:13:14:15:16 S SD: 9.3988 cents 9:10 x 11:12:13:14:16:17:18 S SD: 14.7077 cents 10:11:12 x 13:15:16:17:19:20 SD: 12.7549 cents 11:12:13:14:15:16:18:19:20:22 S SD: 10.5611 cents 12:13:14:15:16:18:19:21:22:24 SD: 5.2274 cents 23:25:27:29:31:34:37:40:43:46 SD: 5.1106 cents 24:26:28:30:32:36:39:41:45:48 SD: 4.3233 cents 25:27:29:31:33:37:40:43:46:50 SD: 4.1921 cents 26:28:30:32:35:39:42:45:48:52 SD: 3.1169 cents 36:39:42:45:48:54:58:62:67:72 SD: 2.6636 cents 38:41:44:47:51:57:61:66:71:76 SD: 2.1182 cents 44:47:51:55:59:66:71:76:82:88 SD: 2.0501 cents 50:54:58:62:67:75:80:86:93:100 SD: 1.8923 cents 51:55:59:63:68:76:82:88:95:102 SD: 1.8637 cents 53:57:61:66:71:79:85:92:99:106 SD: 1.6894 cents 56:60:65:70:75:84:90:97:104:112 SD: 1.5736 cents 65:70:75:81:87:97:104:112:121:130 SD: 1.2315 cents 77:83:89:96:103:115:124:133:143:154 SD: 0.7648 cents 107:115:124:133:143:160:172:185:199:214 SD: 0.6009 cents 147:158:170:183:197:220:236:254:273:294 SD: 0.5298 cents 148:159:171:184:198:221:238:256:275:296 SD: 0.5263 cents 171:184:198:213:229:255:275:296:318:342 SD: 0.5074 cents 172:185:199:214:230:257:276:297:320:344 SD: 0.4337 cents 184:198:213:229:246:275:296:318:342:368 SD: 0.3945 cents 209:225:242:260:280:312:336:361:389:418 SD: 0.3851 cents 221:238:256:275:296:330:355:382:411:442 SD: 0.3322 cents 249:268:288:310:333:372:400:430:463:498 SD: 0.3210 cents 254:273:294:316:340:379:408:439:472:508 SD: 0.3143 cents 262:282:303:326:351:391:421:453:487:524 SD: 0.2825 cents 306:329:354:381:410:457:492:529:569:612 SD: 0.2275 cents 318:342:368:396:426:475:511:550:591:636 SD: 0.2074 cents 356:383:412:443:477:532:572:615:662:712 SD: 0.2044 cents 369:397:427:459:494:551:593:638:686:738 SD: 0.1622 cents 478:514:553:595:640:714:768:826:889:956 SD: 0.1076 cents 490:527:567:610:656:732:787:847:911:980 SD: 0.0998 cents 567:610:656:706:759:847:911:980:1054:1134 SD: 0.0980 cents