Scala analysis: prop19_10
Negri[10] = 10-19.scl, Negri's 10+9 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: 252.632 cents 252.631579 3: 378.947 cents 378.947368 4: 505.263 cents 505.263158 5: 631.579 cents 631.578947 6: 694.737 cents 694.736842 7: 821.053 cents 821.052632 8: 947.368 cents 947.368421 9: 1073.684 cents 1073.684211 10: 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: 126.3158 cents 126.3158 6: 63.1579 cents 63.1579 7: 126.3158 cents 126.3158 8: 126.3158 cents 126.3158 9: 126.3158 cents 126.3158 10: 126.3158 cents 126.3158
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 63.15790 cents 1: 9 126.31579 cents 2: 2 189.47368 cents 2: 8 252.63158 cents 3: 3 315.78947 cents 3: 7 378.94737 cents 4: 4 442.10526 cents 4: 6 505.26316 cents 5: 5 568.42105 cents 5: 5 631.57895 cents 6: 6 694.73684 cents 6: 4 757.89474 cents 7: 7 821.05263 cents 7: 3 884.21053 cents 8: 8 947.36842 cents 8: 2 1010.52632 cents 9: 9 1073.68421 cents 9: 1 1136.84210 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 10 0.0 : 126.3 252.6 378.9 505.3 631.6 694.7 821.1 947.4 1073.7 1200.0 126.3 : 126.3 252.6 378.9 505.3 568.4 694.7 821.1 947.4 1073.7 1200.0 252.6 : 126.3 252.6 378.9 442.1 568.4 694.7 821.1 947.4 1073.7 1200.0 378.9 : 126.3 252.6 315.8 442.1 568.4 694.7 821.1 947.4 1073.7 1200.0 505.3 : 126.3 189.5 315.8 442.1 568.4 694.7 821.1 947.4 1073.7 1200.0 631.6 : 63.2 189.5 315.8 442.1 568.4 694.7 821.1 947.4 1073.7 1200.0 694.7 : 126.3 252.6 378.9 505.3 631.6 757.9 884.2 1010.5 1136.8 1200.0 821.1 : 126.3 252.6 378.9 505.3 631.6 757.9 884.2 1010.5 1073.7 1200.0 947.4 : 126.3 252.6 378.9 505.3 631.6 757.9 884.2 947.4 1073.7 1200.0 1073.7: 126.3 252.6 378.9 505.3 631.6 757.9 821.1 947.4 1073.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.1579 .. 126.3158 cents 63.15789 cents 63.15790 cents 2: 189.4737 .. 252.6316 cents 63.15789 cents 63.15790 cents 3: 315.7895 .. 378.9474 cents 63.15789 cents 63.15790 cents 4: 442.1053 .. 505.2632 cents 63.15789 cents 63.15790 cents 5: 568.4211 .. 631.5789 cents 63.15789 cents 63.15790 cents 6: 694.7368 .. 757.8947 cents 63.15789 cents 63.15790 cents 7: 821.0526 .. 884.2105 cents 63.15789 cents 63.15790 cents 8: 947.3684 .. 1010.5263 cents 63.15789 cents 63.15790 cents 9: 1073.6842 .. 1136.8421 cents 63.15789 cents 63.15790 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 63.15790 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 126.31579 cents Average / Smallest step : 1.900000 Largest / Average step : 1.052632 Largest / Smallest step : 2.000000 Median interval of one step : 126.31579 cents, amount: 9 Most common interval of one step : 126.31579 cents, amount: 9 Least squares average step : 119.75393 cents, oct.: 1197.53930 cents Scale is strictly proper Scale has Myhill's property chromas: 63.15789 cents and 0.00000 cents, ratio: 63157873.464038 generators: 1 of 126.31579 cents and 9 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 10 11 13 15 17 19 generators: 2 and 17 Number of contiguous 1-step segments: 1 Scale is fully connected major-minor triadic in 19-tone equal temperament Scale is a Winograd/Gamer deep scale Step pattern alph. order: AAAAABAAAA Step pattern size order : LLLLLSLLLL Interval vector is [ 1 9 2 8 3 7 4 6 5 ] Scale is a Constant Structure, by a margin of 63.15790 cents Scale diversity : 1.278754 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.526316 Rothenberg efficiency : 0.733333 redundancy: 0.266667 Efficiency x scale size : 7.333333 Number of different interval sizes : 18 = 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: 9 Scale is a chain of 5 triads 0.0 505.263 1073.684 cents Most common triad is 0.0 126.316 1073.684 cents, amount: 8 Number of recognisable fifths : 6, average 694.7368 cents Scale contains two identical disjunct pentachords Formal octave complements present : 9 = 90.0000% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 5-6 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.4135 c. M: 31.5789 c. 17: 2 2 1 2 2 1 2 1 2 2 P D3 SD: 19.5532 c. M: 29.7214 c. 19: 2 2 2 2 2 1 2 2 2 2 SP M ME SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 3.6091 cents 3 x x x 4 x x x 5 x 6 S SD: 21.1406 cents 4 x x 5 x x 6 x 7 x 8 S SD: 5.9518 cents 5 x 6 x x 7 x 8 x 9:10 S SD: 19.5733 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 11.6294 cents 7 x 8:9 x 10 x 11:12:13:14 S SD: 10.5983 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 9.3988 cents 9:10 x 11:12:13 x 14:16:17:18 S SD: 12.8037 cents 10:11:12 x 13:14:15:16:17:19:20 SD: 12.5804 cents 11:12:13:14:15:16 x 18:19:20:22 S SD: 9.4320 cents 12:13:14:15:16:17:18:19:21:22:24 SD: 5.5046 cents 13:14:15:16:17:19 x 21:22:24:26 SD: 7.2801 cents 14:15:16:17:19:20:21:23:24:26:28 SD: 6.9436 cents 15:16:17:19:20:22 x 24:26:28:30 SD: 6.6579 cents 18:19:21:22:24:26:27:29:31:33:36 SD: 5.5218 cents 20:22:23:25:27:29:30:32:35:37:40 SD: 5.1452 cents 21:23:24:26:28:30:31:34:36:39:42 SD: 5.0657 cents 23:25:27:29:31:33:34:37:40:43:46 SD: 4.6464 cents 24:26:28:30:32:35:36:39:41:45:48 SD: 4.4506 cents 25:27:29:31:33:36:37:40:43:46:50 SD: 3.7730 cents 26:28:30:32:35:37:39:42:45:48:52 SD: 3.4900 cents 30:32:35:37:40:43:45:48:52:56:60 SD: 3.1087 cents 36:39:42:45:48:52:54:58:62:67:72 SD: 2.4496 cents 38:41:44:47:51:55:57:61:66:71:76 SD: 2.0889 cents 41:44:47:51:55:59:61:66:71:76:82 SD: 1.9714 cents 50:54:58:62:67:72:75:80:86:93:100 SD: 1.7033 cents 53:57:61:66:71:76:79:85:92:99:106 SD: 1.6985 cents 56:60:65:70:75:81:84:90:97:104:112 SD: 1.5986 cents 63:68:73:78:84:91:94:101:109:117:126 SD: 1.5136 cents 64:69:74:80:86:92:96:103:111:119:128 SD: 1.4701 cents 65:70:75:81:87:94:97:104:112:121:130 SD: 1.3155 cents 77:83:89:96:103:111:115:124:133:143:154 SD: 0.7061 cents 107:115:124:133:143:154:160:172:185:199:214 SD: 0.5538 cents 147:158:170:183:197:212:220:236:254:273:294 SD: 0.5302 cents 148:159:171:184:198:213:221:238:256:275:296 SD: 0.4904 cents 172:185:199:214:230:248:257:276:297:320:344 SD: 0.4359 cents 184:198:213:229:246:265:275:296:318:342:368 SD: 0.3551 cents 209:225:242:260:280:301:312:336:361:389:418 SD: 0.3467 cents 221:238:256:275:296:318:330:355:382:411:442 SD: 0.3392 cents 236:254:273:294:316:340:353:379:408:439:472 SD: 0.3279 cents 254:273:294:316:340:366:379:408:439:472:508 SD: 0.2950 cents 298:321:345:371:399:429:445:479:515:554:596 SD: 0.2845 cents 306:329:354:381:410:441:457:492:529:569:612 SD: 0.2333 cents 318:342:368:396:426:458:475:511:550:591:636 SD: 0.1867 cents 413:444:478:514:553:595:617:664:714:768:826 SD: 0.1664 cents 425:457:492:529:569:612:635:683:735:790:850 SD: 0.1582 cents 478:514:553:595:640:688:714:768:826:889:956 SD: 0.1467 cents 490:527:567:610:656:706:732:787:847:911:980 SD: 0.1129 cents 593:638:686:738:794:854:886:953:1025:1103:1186 SD: 0.1046 cents