Scala analysis: prop19_8b
Second proper 8 note scale in 19-et, two sizes of interval
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: 568.421 cents 568.421053 5: 694.737 cents 694.736842 6: 884.211 cents 884.210526 7: 1010.526 cents 1010.526316 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 189.4737 cents 189.4737 1: 126.3158 cents 126.3158 2: 126.3158 cents 126.3158 3: 126.3158 cents 126.3158 4: 189.4737 cents 189.4737 5: 126.3158 cents 126.3158 6: 189.4737 cents 189.4737 7: 126.3158 cents 126.3158 8: 189.4737 cents 189.4737
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 126.31579 cents 1: 3 189.47369 cents 2: 2 252.63158 cents 2: 6 315.78947 cents 3: 1 378.94737 cents 3: 5 442.10526 cents 3: 2 505.26316 cents 4: 4 568.42105 cents 4: 4 631.57895 cents 5: 2 694.73684 cents 5: 5 757.89474 cents 5: 1 821.05263 cents 6: 6 884.21053 cents 6: 2 947.36842 cents 7: 3 1010.52632 cents 7: 5 1073.68421 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.28571 = 16/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 126.3 252.6 378.9 568.4 694.7 884.2 1010.5 1200.0 126.3 : 126.3 252.6 442.1 568.4 757.9 884.2 1073.7 1200.0 252.6 : 126.3 315.8 442.1 631.6 757.9 947.4 1073.7 1200.0 378.9 : 189.5 315.8 505.3 631.6 821.1 947.4 1073.7 1200.0 568.4 : 126.3 315.8 442.1 631.6 757.9 884.2 1010.5 1200.0 694.7 : 189.5 315.8 505.3 631.6 757.9 884.2 1073.7 1200.0 884.2 : 126.3 315.8 442.1 568.4 694.7 884.2 1010.5 1200.0 1010.5: 189.5 315.8 442.1 568.4 757.9 884.2 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 63.15789 cents 63.15789 cents 3: 378.9474 .. 505.2632 cents 126.31579 cents 63.15789 cents 4: 568.4211 .. 631.5789 cents 63.15789 cents 63.15789 cents 5: 694.7368 .. 821.0526 cents 126.31579 cents 63.15790 cents 6: 884.2105 .. 947.3684 cents 63.15790 cents 63.15789 cents 7: 1010.5263 .. 1073.6842 cents 63.15790 cents 63.15789 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 126.31579 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 189.47369 cents Average / Smallest step : 1.187500 Largest / Average step : 1.263158 Largest / Smallest step : 1.500000 Median interval of one step : 126.31579 cents, amount: 5 Most common interval of one step : 126.31579 cents, amount: 5 Least squares average step : 144.58204 cents, oct.: 1156.65635 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 4 6 9 11 14 16 19 Least number of segments generator : 12 of 757.895 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 12 of 757.895 cents and inv. generated superset size: 10 = 2 more = 125.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABABAB Step pattern size order : SSSLSLSL Interval vector is [ 0 5 3 2 6 1 5 2 4 ] Scale is a Constant Structure, by a margin of 63.15789 cents Scale diversity : 1.324098 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.526316 Rothenberg efficiency : 0.589286 redundancy: 0.410714 Efficiency x scale size : 4.714286 Number of different interval sizes : 16 = 2.28571 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.28571 = 16/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 63.15789 cents Most common intervals : 315.78947 cents & inv., amount: 6 Most common triad is 0.0 315.789 884.211 cents, amount: 4 Number of recognisable fifths : 2, average 694.7368 cents Formal octave complements present : 1 = 12.5000% Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 5-6 -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 41.4003 c. M:-71.0526 c. 9: 1 1 1 1 1 2 1 1 P M ME SD: 32.1584 c. M:-56.1404 c. 10: 1 1 1 2 1 1 1 2 P B ME SD: 28.9426 c. M: 50.5263 c. 11: 1 1 1 2 1 2 1 2 P D3 SD: 30.1093 c. M: 51.6746 c. 12: 1 2 1 2 1 2 1 2 SP B ME SD: 24.4043 c. M:-47.3684 c. Octatonic, Messiaen mode 2, Dominant Diminished, Diminished Blues, Half-Whole step scale 13: 1 2 1 2 2 2 1 2 P D3 SD: 26.2191 c. M:-43.7247 c. 15: 2 1 2 2 2 2 2 2 SP M ME SD: 20.4113 c. M:-33.6842 c. 18: 2 2 2 3 1 3 2 3 P D3 SD: 19.0171 c. M:-31.5789 c. 19: 2 2 2 3 2 3 2 3 SP D3 SD: 0.0000 c. M:-0.0000 c.
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: 3.6091 cents 3 x x x 4 x 5 x 6 S SD: 23.4587 cents 4 x x 5 x 6 x 7:8 S SD: 10.7392 cents 5 x 6 x 7 x 8:9:10 S SD: 19.1754 cents 6 x 7 x 8:9:10:11:12 S SD: 13.6585 cents 7 x 8:9:10 x 12:13:14 S SD: 18.3748 cents 8 x 9:10:11:12:13:14:16 S SD: 11.4462 cents 9:10 x 11 x 13:15:16:18 SD: 14.6504 cents 10:11:12 x 14:15:17:18:20 SD: 11.9122 cents 11:12:13:14:15:16:18:20:22 S SD: 11.2683 cents 12:13:14:15:17:18:20:22:24 SD: 7.0305 cents 13:14:15:16:18:19:22:23:26 SD: 6.9407 cents 18:19:21:22:25:27:30:32:36 SD: 6.2852 cents 20:22:23:25:28:30:33:36:40 SD: 5.9466 cents 23:25:27:29:32:34:38:41:46 SD: 5.7337 cents 24:26:28:30:33:36:40:43:48 SD: 3.4297 cents 36:39:42:45:50:54:60:65:72 SD: 3.0957 cents 37:40:43:46:51:55:62:66:74 SD: 2.8947 cents 38:41:44:47:53:57:63:68:76 SD: 2.3334 cents 44:47:51:55:61:66:73:79:88 SD: 2.2964 cents 49:53:57:61:68:73:82:88:98 SD: 2.0136 cents 52:56:60:65:72:78:87:93:104 SD: 1.8636 cents 57:61:66:71:79:85:95:102:114 SD: 1.3205 cents 69:74:80:86:96:103:115:124:138 SD: 1.0831 cents 77:83:89:96:107:115:128:138:154 SD: 0.8416 cents 119:128:138:148:165:178:198:213:238 SD: 0.8254 cents 120:129:139:149:167:179:200:215:240 SD: 0.8223 cents 121:130:140:151:168:181:202:217:242 SD: 0.7937 cents 132:142:153:164:183:197:220:237:264 SD: 0.7559 cents 134:144:155:167:186:200:223:240:268 SD: 0.5452 cents 159:171:184:198:221:238:265:285:318 SD: 0.5049 cents 160:172:185:199:222:239:267:287:320 SD: 0.4527 cents 172:185:199:214:239:257:287:308:344 SD: 0.4012 cents 237:255:274:295:329:354:395:425:474 SD: 0.2190 cents 332:357:384:413:461:496:553:595:664 SD: 0.2172 cents 381:410:441:474:529:569:635:683:762 SD: 0.1624 cents 478:514:553:595:664:714:797:857:956 SD: 0.1595 cents 502:540:581:625:697:750:837:900:1004 SD: 0.1395 cents 515:554:596:641:715:769:858:923:1030 SD: 0.1296 cents 555:597:642:691:771:829:925:995:1110 SD: 0.1258 cents 579:623:670:721:804:865:965:1038:1158 SD: 0.1205 cents 597:642:691:743:829:892:995:1070:1194 SD: 0.1186 cents