Scala analysis: prop19_8a
Sensi[8] = Mandelbaum 8/19 = Oljare Octatonic
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: 442.105 cents 442.105263 4: 568.421 cents 568.421053 5: 757.895 cents 757.894737 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: 189.4737 cents 189.4737 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: 189.4737 cents 189.4737
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 126.31579 cents 1: 3 189.47368 cents 2: 2 252.63158 cents 2: 6 315.78947 cents 3: 7 442.10526 cents 3: 1 505.26316 cents 4: 4 568.42105 cents 4: 4 631.57895 cents 5: 1 694.73684 cents 5: 7 757.89474 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: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 126.3 315.8 442.1 568.4 757.9 884.2 1010.5 1200.0 126.3 : 189.5 315.8 442.1 631.6 757.9 884.2 1073.7 1200.0 315.8 : 126.3 252.6 442.1 568.4 694.7 884.2 1010.5 1200.0 442.1 : 126.3 315.8 442.1 568.4 757.9 884.2 1073.7 1200.0 568.4 : 189.5 315.8 442.1 631.6 757.9 947.4 1073.7 1200.0 757.9 : 126.3 252.6 442.1 568.4 757.9 884.2 1010.5 1200.0 884.2 : 126.3 315.8 442.1 631.6 757.9 884.2 1073.7 1200.0 1010.5: 189.5 315.8 505.3 631.6 757.9 947.4 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 63.15789 cents 63.15789 cents 3: 442.1053 .. 505.2632 cents 63.15790 cents 126.31579 cents 4: 568.4211 .. 631.5789 cents 63.15789 cents 63.15789 cents 5: 694.7368 .. 757.8947 cents 63.15790 cents 63.15789 cents 6: 884.2105 .. 947.3684 cents 63.15790 cents 126.31579 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 : 189.47368 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 : 147.67802 cents, oct.: 1181.42415 cents Scale is strictly proper Scale has Myhill's property chromas: 63.15790 cents and 63.15789 cents, ratio: 1.000000 generators: 3 of 442.10526 cents and 5 of 757.89474 cents Scale is maximally even in 19-tone equal temperament ET pair of linear temperament : 11&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 5 7 9 12 14 16 19 generators: 7 and 12 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAAB Step pattern size order : SLSSLSSL Interval vector is [ 0 5 3 2 6 0 7 1 4 ] Scale is a Constant Structure, by a margin of 63.15789 cents Scale diversity : 1.246989 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.631579 Rothenberg efficiency : 0.750000 redundancy: 0.250000 Efficiency x scale size : 6.000000 Number of different interval sizes : 14 = 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 : 442.10526 cents & inv., amount: 7 Scale is a chain of 4 triads 0.0 126.316 757.895 cents Most common triad is 0.0 442.105 757.895 cents, amount: 6 Number of recognisable fifths : 1, average 694.7368 cents Scale contains two identical conjunct tetrachords Best fifths form a closed circle Formal octave complements present : 5 = 62.5000% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 4-5 -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 21.6206 c. M:-39.4737 c. 11: 1 2 1 1 2 1 1 2 P M ME SD: 15.7241 c. M: 28.7081 c. 19: 2 3 2 2 3 2 2 3 SP M ME SD: 0.0000 c. M:-0.0000 c. Mandelbaum Eight out of 19
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: 27.9699 cents 3 x x 4 x x 5 x 6 S SD: 18.6466 cents 4 x x 5 x 6 x 7:8 S SD: 22.3339 cents 5 x 6 x 7:8 x 9:10 S SD: 11.5953 cents 6 x 7:8 x 9:10:11:12 S SD: 16.7993 cents 7 x 8:9:10:11:12:13:14 S SD: 18.2707 cents 8:9 x 10:11:12:13:14:16 S SD: 18.1841 cents 9:10:11:12:13:14:15:16:18 S SD: 13.7973 cents 10:11:12:13:14:16:17:18:20 S SD: 9.8347 cents 11:12:13:14:15:17:18:20:22 SD: 8.3946 cents 13:14:16:17:18:20:22:23:26 SD: 7.7134 cents 14:15:17:18:19:22:23:25:28 SD: 7.2375 cents 15:16:18:19:21:23:25:27:30 SD: 5.3926 cents 24:26:29:31:33:37:40:43:48 SD: 3.2040 cents 38:41:46:49:53:59:63:68:76 SD: 2.5531 cents 39:42:47:50:54:60:65:70:78 SD: 2.4235 cents 44:47:53:57:61:68:73:79:88 SD: 2.2289 cents 49:53:59:63:68:76:82:88:98 SD: 1.9361 cents 51:55:61:66:71:79:85:91:102 SD: 1.5604 cents 54:58:65:70:75:84:90:97:108 SD: 1.5143 cents 65:70:78:84:90:101:108:117:130 SD: 1.4566 cents 66:71:79:85:92:102:110:118:132 SD: 1.3707 cents 69:74:83:89:96:107:115:124:138 SD: 1.0992 cents 80:86:96:103:111:124:133:143:160 SD: 1.0292 cents 90:97:108:116:125:139:150:161:180 SD: 0.9789 cents 93:100:112:120:129:144:155:167:186 SD: 0.8927 cents 106:114:127:137:147:164:177:190:212 SD: 0.7396 cents 120:129:144:155:167:186:200:215:240 SD: 0.5295 cents 131:141:157:169:182:203:218:235:262 SD: 0.5067 cents 144:155:173:186:200:223:240:258:288 SD: 0.3358 cents 240:258:288:310:333:372:400:430:480 SD: 0.3038 cents 255:274:306:329:354:395:425:457:510 SD: 0.2860 cents 275:296:330:355:382:426:458:493:550 SD: 0.2081 cents 371:399:445:479:515:575:618:665:742 SD: 0.1997 cents 381:410:457:492:529:590:635:683:762 SD: 0.1886 cents 399:429:479:515:554:618:665:715:798 SD: 0.1660 cents 450:484:540:581:625:697:750:807:900 SD: 0.1133 cents 530:570:636:684:736:821:883:950:1060 SD: 0.1080 cents 594:639:713:767:825:920:990:1065:1188 SD: 0.1053 cents