Scala analysis: diff19-9-4
Scale derived from (19,9,4) Type Q cyclic difference set, 19edo
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 63.158 cents 63.157890 2: 252.632 cents 252.631580 3: 315.789 cents 315.789470 4: 378.947 cents 378.947370 5: 442.105 cents 442.105260 6: 568.421 cents 568.421050 7: 694.737 cents 694.736840 8: 1010.526 cents 1010.526320 9: 1073.684 cents 1073.684210 10: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 126.3158 cents 126.3158 1: 63.1579 cents 63.1579 2: 189.4737 cents 189.4737 3: 63.1579 cents 63.1579 4: 63.1579 cents 63.1579 5: 63.1579 cents 63.1579 6: 126.3158 cents 126.3158 7: 126.3158 cents 126.3158 8: 315.7895 cents 315.7895 9: 63.1579 cents 63.1579 10: 126.3158 cents 126.3158
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 63.15789 cents 1: 3 126.31579 cents 1: 1 189.47369 cents 1: 1 315.78948 cents 2: 2 126.31579 cents 2: 3 189.47368 cents 2: 3 252.63158 cents 2: 1 378.94737 cents 2: 1 442.10527 cents 3: 1 189.47368 cents 3: 2 252.63158 cents 3: 3 315.78947 cents 3: 1 378.94737 cents 3: 2 505.26316 cents 3: 1 568.42106 cents 4: 1 315.78947 cents 4: 3 378.94737 cents 4: 2 442.10526 cents 4: 1 568.42105 cents 4: 3 631.57895 cents 5: 2 442.10526 cents 5: 3 505.26316 cents 5: 3 694.73685 cents 5: 2 757.89474 cents 6: 3 568.42105 cents 6: 1 631.57895 cents 6: 2 757.89474 cents 6: 3 821.05263 cents 6: 1 884.21053 cents 7: 1 631.57894 cents 7: 2 694.73684 cents 7: 1 821.05263 cents 7: 3 884.21053 cents 7: 2 947.36843 cents 7: 1 1010.52632 cents 8: 1 757.89473 cents 8: 1 821.05263 cents 8: 3 947.36842 cents 8: 3 1010.52632 cents 8: 2 1073.68421 cents 9: 1 884.21052 cents 9: 1 1010.52631 cents 9: 3 1073.68421 cents 9: 5 1136.84211 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.88889 = 44/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 63.2 252.6 315.8 378.9 442.1 568.4 694.7 1010.5 1073.7 1200.0 63.2 : 189.5 252.6 315.8 378.9 505.3 631.6 947.4 1010.5 1136.8 1200.0 252.6 : 63.2 126.3 189.5 315.8 442.1 757.9 821.1 947.4 1010.5 1200.0 315.8 : 63.2 126.3 252.6 378.9 694.7 757.9 884.2 947.4 1136.8 1200.0 378.9 : 63.2 189.5 315.8 631.6 694.7 821.1 884.2 1073.7 1136.8 1200.0 442.1 : 126.3 252.6 568.4 631.6 757.9 821.1 1010.5 1073.7 1136.8 1200.0 568.4 : 126.3 442.1 505.3 631.6 694.7 884.2 947.4 1010.5 1073.7 1200.0 694.7 : 315.8 378.9 505.3 568.4 757.9 821.1 884.2 947.4 1073.7 1200.0 1010.5: 63.2 189.5 252.6 442.1 505.3 568.4 631.6 757.9 884.2 1200.0 1073.7: 126.3 189.5 378.9 442.1 505.3 568.4 694.7 821.1 1136.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.1579 .. 315.7895 cents 252.63159 cents 63.15789 cents 2: 126.3158 .. 442.1053 cents 315.78948 cents -189.47369 cents 3: 189.4737 .. 568.4211 cents 378.94738 cents -252.63159 cents 4: 315.7895 .. 631.5790 cents 315.78948 cents -252.63159 cents 5: 442.1053 .. 757.8947 cents 315.78948 cents -189.47369 cents 6: 568.4211 .. 884.2105 cents 315.78948 cents -189.47369 cents 7: 631.5789 .. 1010.5263 cents 378.94738 cents -252.63159 cents 8: 757.8947 .. 1073.6842 cents 315.78948 cents -252.63159 cents 9: 884.2105 .. 1136.8421 cents 252.63159 cents -189.47369 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 63.15789 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 315.78948 cents Average / Smallest step : 1.900000 Largest / Average step : 2.631579 Largest / Smallest step : 5.000000 Median interval of one step : 94.73684 cents, amount: 0 Most common interval of one step : 63.15789 cents, amount: 5 Least squares average step : 112.37184 cents, oct.: 1123.71839 cents Scale is not proper Scale is a mode of a 19-tone equal temperament with octave 1200.000 cents degrees: 1 4 5 6 7 9 11 16 17 19 Least number of segments generator : 10 of 631.579 cents and inv. number of contiguous generator circle segments: 3 Shortest superset generator : 10 of 631.579 cents and inv. generated superset size: 15 = 5 more = 150.000% Number of contiguous 1-step segments: 3 Step pattern alph. order: ABAAACCDAC Step pattern size order : ACAAABBDAB Interval vector is [ 5 5 5 5 5 5 5 5 5 ] Scale is not a Constant Structure Scale diversity : 1.278754 Lumma stability : 0.105263 Lumma impropriety factor : 0.789474 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 : 4 Highest interval variety : 6 Mean interval variety : 4.88889 = 44/9 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 63.15789 cents Number of recognisable fifths : 5, average 694.7369 cents Formal octave complements present : 1 = 10.0000% -- Rational properties --
FIT/MODE
10: 1 1 1 0 1 1 1 3 0 1 N SD: 36.9352 c. M:-69.4737 c. 11: 0 2 1 0 1 1 1 3 1 1 N SD: 33.5775 c. M: 63.1579 c. 12: 1 2 0 1 1 1 1 3 1 1 N SD: 30.7794 c. M:-57.8947 c. 13: 1 2 1 0 1 1 2 3 1 1 N SD: 28.4117 c. M:-53.4413 c. 14: 1 2 1 1 0 2 1 4 1 1 N SD: 26.3823 c. M:-49.6241 c. 15: 1 2 1 1 1 1 2 4 1 1 N SD: 24.6235 c. M:-46.3158 c. 16: 1 2 1 1 1 1 2 4 1 2 N SD: 23.0845 c. M: 43.4211 c. 17: 1 2 1 1 1 2 2 4 1 2 N SD: 21.7266 c. M: 40.8669 c. 18: 1 3 1 1 1 2 2 4 1 2 N SD: 20.5196 c. M:-38.5965 c. 19: 1 3 1 1 1 2 2 5 1 2 N 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 x 3 x x 4 S SD: 3.6091 cents 3 x x x x 4 x x 5 x 6 S SD: 46.0043 cents 4 x x x 5 x x 6:7 x 8 S SD: 10.7392 cents 5 x x 6 x x 7 x 9 x 10 SD: 3.9415 cents 6 x 7 x x 8 x 9 x 11:12 SD: 12.6105 cents 7 x 8 x x 9:10 x x 13:14 SD: 10.8096 cents 8 x 9 x 10 x 11:12:14:15:16 S SD: 9.8191 cents 9 x 10 x 11:12 x 13:16:17:18 SD: 16.5312 cents 10 x x 12 x 13:14:15:18:19:20 S SD: 6.1523 cents 11:12 x 13 x 14:15:16:20 x 22 S SD: 16.0829 cents 12:13:14 x 15 x 17:18 x 22:24 SD: 12.6037 cents 13:14:15 x 16:17:18:19:23:24:26 SD: 9.4702 cents 14:15:16:17 x 18:19:21:25:26:28 SD: 8.4411 cents 15:16:17:18:19 x 21:22:27:28:30 SD: 8.5123 cents 16:17 x 19:20:21:22:24:29:30:32 SD: 6.9192 cents 17:18:20 x 21:22:24:25:30:32:34 S SD: 7.8904 cents 18:19:21 x 22:23:25:27:32:33:36 SD: 6.3744 cents 20:21:23:24:25:26:28:30:36:37:40 SD: 3.3829 cents 24:25:28:29:30:31:33:36:43:45:48 SD: 3.1823 cents 30:31:35:36:37:39:42:45:54:56:60 SD: 3.1465 cents 31:32:36:37:39:40:43:46:56:58:62 SD: 3.1124 cents 34:35:39:41:42:44:47:51:61:63:68 SD: 2.8404 cents 44:46:51:53:55:57:61:66:79:82:88 SD: 2.0369 cents 49:51:57:59:61:63:68:73:88:91:98 SD: 1.5491 cents 65:67:75:78:81:84:90:97:117:121:130 SD: 1.5113 cents 69:72:80:83:86:89:96:103:124:128:138 SD: 1.3870 cents 75:78:87:90:93:97:104:112:134:139:150 SD: 1.2842 cents 77:80:89:92:96:99:107:115:138:143:154 SD: 1.1596 cents 83:86:96:100:103:107:115:124:149:154:166 SD: 1.0774 cents 85:88:98:102:106:110:118:127:152:158:170 SD: 0.9830 cents 101:105:117:121:126:130:140:151:181:188:202 SD: 0.9352 cents 103:107:119:124:128:133:143:154:185:192:206 SD: 0.9277 cents 106:110:123:127:132:137:147:158:190:197:212 SD: 0.7581 cents 110:114:127:132:137:142:153:164:197:205:220 SD: 0.7474 cents 114:118:132:137:142:147:158:170:204:212:228 SD: 0.7347 cents 131:136:152:157:163:169:182:196:235:244:262 SD: 0.7238 cents 134:139:155:161:167:173:186:200:240:249:268 SD: 0.3902 cents 216:224:250:259:269:279:300:323:387:402:432 SD: 0.3423 cents 241:250:279:289:300:311:335:360:432:448:482 SD: 0.2490 cents 299:310:346:359:372:386:415:447:536:556:598 SD: 0.2109 cents 375:389:434:450:467:484:521:560:672:697:750 SD: 0.1686 cents 433:449:501:520:539:559:601:647:776:805:866 SD: 0.1672 cents 478:496:553:574:595:617:664:714:857:889:956 SD: 0.1622 cents 510:529:590:612:635:658:708:762:914:948:1020 SD: 0.1534 cents 515:534:596:618:641:665:715:769:923:958:1030 SD: 0.1391 cents 535:555:619:642:666:691:743:799:959:995:1070 SD: 0.1194 cents 540:560:625:648:672:697:750:807:968:1004:1080 SD: 0.1083 cents