Scala analysis: prop19_8c
Third proper 8-note 19-et scale, single larger 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: 315.789 cents 315.789474 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: 189.4737 cents 189.4737 3: 63.1579 cents 63.1579 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: 1 63.15789 cents 1: 3 126.31579 cents 1: 4 189.47368 cents 2: 2 252.63158 cents 2: 6 315.78947 cents 3: 2 378.94737 cents 3: 3 442.10526 cents 3: 3 505.26316 cents 4: 4 568.42105 cents 4: 4 631.57895 cents 5: 3 694.73684 cents 5: 3 757.89474 cents 5: 2 821.05263 cents 6: 6 884.21053 cents 6: 2 947.36842 cents 7: 4 1010.52632 cents 7: 3 1073.68421 cents 7: 1 1136.84211 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.57143 = 18/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 126.3 315.8 378.9 568.4 694.7 884.2 1010.5 1200.0 126.3 : 189.5 252.6 442.1 568.4 757.9 884.2 1073.7 1200.0 315.8 : 63.2 252.6 378.9 568.4 694.7 884.2 1010.5 1200.0 378.9 : 189.5 315.8 505.3 631.6 821.1 947.4 1136.8 1200.0 568.4 : 126.3 315.8 442.1 631.6 757.9 947.4 1010.5 1200.0 694.7 : 189.5 315.8 505.3 631.6 821.1 884.2 1073.7 1200.0 884.2 : 126.3 315.8 442.1 631.6 694.7 884.2 1010.5 1200.0 1010.5: 189.5 315.8 505.3 568.4 757.9 884.2 1073.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.1579 .. 189.4737 cents 126.31579 cents 63.15789 cents 2: 252.6316 .. 315.7895 cents 63.15790 cents 63.15789 cents 3: 378.9474 .. 505.2632 cents 126.31579 cents 63.15789 cents 4: 568.4211 .. 631.5789 cents 63.15790 cents 63.15789 cents 5: 694.7368 .. 821.0526 cents 126.31579 cents 63.15789 cents 6: 884.2105 .. 947.3684 cents 63.15790 cents 63.15789 cents 7: 1010.5263 .. 1136.8421 cents 126.31579 cents 63.15789 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 63.15789 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 189.47368 cents Average / Smallest step : 2.375000 Largest / Average step : 1.263158 Largest / Smallest step : 3.000000 Median interval of one step : 157.89474 cents, amount: 0 Most common interval of one step : 189.47368 cents, amount: 4 Least squares average step : 145.20124 cents, oct.: 1161.60991 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 5 6 9 11 14 16 19 Least number of segments generator : 14 of 884.211 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 14 of 884.211 cents and inv. generated superset size: 11 = 3 more = 137.500% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABCBABAB Step pattern size order : MLSLMLML Interval vector is [ 1 3 4 2 6 2 3 3 4 ] Scale is a Constant Structure, by a margin of 63.15789 cents Scale diversity : 1.415976 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.421053 Rothenberg efficiency : 0.555357 redundancy: 0.444643 Efficiency x scale size : 4.442857 Number of different interval sizes : 18 = 2.57143 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.57143 = 18/7 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 : 3, average 694.7368 cents Formal octave complements present : 3 = 37.5000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 6-7 -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 38.2712 c. M:-71.0526 c. 9: 1 1 1 1 1 2 1 1 P M ME SD: 36.2101 c. M:-56.1404 c. 10: 1 2 0 2 1 1 1 2 N D3 SD: 32.5891 c. M: 50.5263 c. 11: 1 2 0 2 1 2 1 2 P D3 SD: 27.8336 c. M: 51.6746 c. 12: 1 2 1 2 1 2 1 2 SP B ME SD: 18.6081 c. M:-31.5789 c. Octatonic, Messiaen mode 2, Dominant Diminished, Diminished Blues, Half-Whole step scale 15: 2 2 1 2 2 2 2 2 SP M ME SD: 19.9723 c. M:-33.6842 c. Pentadecaphonic "Major", Jones's Porcupine-8 19: 2 3 1 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: 14.4530 cents 6 x 7 x 8:9:10:11:12 S SD: 15.7288 cents 7 x 8:9:10 x 12:13:14 S SD: 22.8850 cents 8:9 x 10:11:12:13:14:16 S SD: 14.3334 cents 9:10 x 11 x 13:15:16:18 SD: 14.6504 cents 10:11:12 x 14:15:17:18:20 SD: 7.8024 cents 13:14 x 16:18:19:22:23:26 SD: 7.9014 cents 14:15:17 x 19:21:23:25:28 SD: 7.4918 cents 15:16:18:19:21:22:25:27:30 SD: 6.1024 cents 16:17:19:20:22:24:27:29:32 SD: 5.6195 cents 18:19 x 22:25:27:30:32:36 SD: 6.8890 cents 20:22:24:25:28:30:33:36:40 SD: 5.7951 cents 21:23:25:26:29:31:35:38:42 SD: 5.6263 cents 24:26:29:30:33:36:40:43:48 SD: 3.2837 cents 29:31:35:36:40:43:48:52:58 SD: 3.2480 cents 36:39:43:45:50:54:60:65:72 SD: 2.7316 cents 39:42:47:49:54:58:65:70:78 SD: 2.5242 cents 41:44:49:51:57:61:68:74:82 SD: 2.2661 cents 49:53:59:61:68:73:82:88:98 SD: 1.8027 cents 54:58:65:67:75:81:90:97:108 SD: 1.4169 cents 65:70:78:81:90:97:108:117:130 SD: 1.3299 cents 69:74:83:86:96:103:115:124:138 SD: 1.1137 cents 90:97:108:112:125:134:150:161:180 SD: 0.9420 cents 95:102:114:118:132:142:158:170:190 SD: 0.8619 cents 105:113:126:131:146:157:175:188:210 SD: 0.6823 cents 131:141:157:163:182:196:218:235:262 SD: 0.6015 cents 134:144:161:167:186:200:223:240:268 SD: 0.5954 cents 144:155:173:179:200:215:240:258:288 SD: 0.4257 cents 160:172:192:199:222:239:267:287:320 SD: 0.4235 cents 213:229:256:265:296:318:355:382:426 SD: 0.4156 cents 221:238:265:275:307:330:368:396:442 SD: 0.3889 cents 225:242:270:280:312:336:375:403:450 SD: 0.3715 cents 237:255:284:295:329:354:395:425:474 SD: 0.3434 cents 249:268:299:310:346:372:415:446:498 SD: 0.2963 cents 265:285:318:330:368:396:442:475:530 SD: 0.2315 cents 360:387:432:448:500:538:600:645:720 SD: 0.2182 cents 381:410:457:474:529:569:635:683:762 SD: 0.1855 cents 409:440:491:509:568:611:682:733:818 SD: 0.1611 cents 425:457:510:529:590:635:708:762:850 SD: 0.1472 cents 450:484:540:560:625:672:750:807:900 SD: 0.1224 cents 555:597:666:691:771:829:925:995:1110 SD: 0.1087 cents