Scala analysis: prop19_7f
Sixth 7-note 19-et strictly proper scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 189.474 cents 189.473684 2: 378.947 cents 378.947368 3: 568.421 cents 568.421053 4: 694.737 cents 694.736842 5: 821.053 cents 821.052632 6: 1010.526 cents 1010.526316 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 189.4737 cents 189.4737 1: 189.4737 cents 189.4737 2: 189.4737 cents 189.4737 3: 189.4737 cents 189.4737 4: 126.3158 cents 126.3158 5: 126.3158 cents 126.3158 6: 189.4737 cents 189.4737 7: 189.4737 cents 189.4737
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 126.31579 cents 1: 5 189.47368 cents 2: 1 252.63158 cents 2: 2 315.78947 cents 2: 4 378.94737 cents 3: 2 442.10526 cents 3: 2 505.26316 cents 3: 3 568.42105 cents 4: 3 631.57895 cents 4: 2 694.73684 cents 4: 2 757.89474 cents 5: 4 821.05263 cents 5: 2 884.21053 cents 5: 1 947.36842 cents 6: 5 1010.52632 cents 6: 2 1073.68421 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.66667 = 8/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 189.5 378.9 568.4 694.7 821.1 1010.5 1200.0 189.5 : 189.5 378.9 505.3 631.6 821.1 1010.5 1200.0 378.9 : 189.5 315.8 442.1 631.6 821.1 1010.5 1200.0 568.4 : 126.3 252.6 442.1 631.6 821.1 1010.5 1200.0 694.7 : 126.3 315.8 505.3 694.7 884.2 1073.7 1200.0 821.1 : 189.5 378.9 568.4 757.9 947.4 1073.7 1200.0 1010.5: 189.5 378.9 568.4 757.9 884.2 1010.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 126.3158 .. 189.4737 cents 63.15789 cents 126.31579 cents 2: 252.6316 .. 378.9474 cents 126.31579 cents 63.15790 cents 3: 442.1053 .. 568.4211 cents 126.31579 cents 63.15790 cents 4: 631.5789 .. 757.8947 cents 126.31579 cents 63.15790 cents 5: 821.0526 .. 947.3684 cents 126.31579 cents 63.15790 cents 6: 1010.5263 .. 1073.6842 cents 63.15790 cents 63.15789 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 126.31579 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 189.47368 cents Average / Smallest step : 1.357143 Largest / Average step : 1.105263 Largest / Smallest step : 1.500000 Median interval of one step : 189.47368 cents, amount: 5 Most common interval of one step : 189.47368 cents, amount: 5 Least squares average step : 171.42857 cents, oct.: 1200.00000 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: 3 6 9 11 13 16 19 Least number of segments generator : 13 of 821.053 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 11 of 694.737 cents and inv. generated superset size: 11 = 4 more = 157.143% Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABBAA Step pattern size order : LLLSSLL Interval vector is [ 0 2 5 1 2 4 2 2 3 ] Scale is a Constant Structure, by a margin of 63.15789 cents Scale diversity : 1.414959 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.473684 Rothenberg efficiency : 0.537415 redundancy: 0.462585 Efficiency x scale size : 3.761905 Number of different interval sizes : 16 = 2.66667 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.66667 = 8/3 Median interval variety : 2.5 Lowest interval variety : 2 Smallest interval difference : 63.15789 cents Most common intervals : 189.47368 cents & inv., amount: 5 Most common triad is 0.0 189.474 1010.526 cents, amount: 4 Number of recognisable fifths : 2, average 694.7368 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 5 = 71.4286% Limited inverse transpositions : 1 Inversional symmetry on degrees : 4 Inversional symmetry on intervals : 0-1 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 29.9244 c. M: 54.1353 c. Lebeng 10: 2 1 2 1 1 1 2 N D3 SD: 32.6437 c. M:-50.5263 c. 11: 2 1 2 1 1 2 2 N D3 SD: 37.3363 c. M: 57.4163 c. 12: 2 2 2 1 1 2 2 P D3 S SD: 17.4559 c. M:-31.5789 c. Lydian Minor, Mela Rishabhapriya, Raga Ratipriya, Mixolydian sharp 4 flat 6 15: 2 3 2 2 1 3 2 P T3 SD: 21.8206 c. M:-29.4737 c. 17: 3 2 3 2 2 2 3 P D3 SD: 18.8394 c. M:-26.0062 c. Otonal 17 19: 3 3 3 2 2 3 3 SP D3 S SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 3.6091 cents 3 x x 4 x 5 x 6 S SD: 31.5532 cents 4 x 5 x 6 x 7:8 S SD: 10.7392 cents 5 x 6:7 x 8:9:10 S SD: 13.1308 cents 6:7 x 8:9:10:11:12 S SD: 21.4160 cents 7:8:9:10 x 11:13:14 SD: 18.6541 cents 8:9:10:11:12:13:14:16 S SD: 7.4580 cents 9:10:11 x 13:14:16:18 SD: 14.7029 cents 10:11:12:14:15:16:18:20 S SD: 10.0624 cents 15:17:19:21:22:24:27:30 SD: 7.7793 cents 16:18:20:22:24:26:29:32 SD: 5.2479 cents 18:20:22:25:27:29:32:36 SD: 5.2032 cents 20:22:25:28:30:32:36:40 SD: 4.5354 cents 24:27:30:33:36:39:43:48 SD: 4.4892 cents 25:28:31:35:37:40:45:50 SD: 3.6350 cents 28:31:35:39:42:45:50:56 SD: 2.6918 cents 33:37:41:46:49:53:59:66 SD: 2.2882 cents 44:49:55:61:66:71:79:88 SD: 1.9446 cents 49:55:61:68:73:79:88:98 SD: 1.8992 cents 53:59:66:74:79:85:95:106 SD: 1.6191 cents 61:68:76:85:91:98:109:122 SD: 1.2522 cents 69:77:86:96:103:111:124:138 SD: 0.9073 cents 77:86:96:107:115:124:138:154 SD: 0.7594 cents 111:124:138:154:166:178:199:222 SD: 0.7530 cents 139:155:173:193:208:223:249:278 SD: 0.6232 cents 155:173:193:215:232:249:278:310 SD: 0.6026 cents 164:183:204:228:245:264:294:328 SD: 0.5577 cents 172:192:214:239:257:276:308:344 SD: 0.4943 cents 180:201:224:250:269:289:323:360 SD: 0.4067 cents 188:210:234:261:281:302:337:376 SD: 0.3511 cents 208:232:259:289:311:334:373:416 SD: 0.3492 cents 216:241:269:300:323:347:387:432 SD: 0.3363 cents 241:269:300:335:360:387:432:482 SD: 0.3163 cents 257:287:320:357:384:413:461:514 SD: 0.3156 cents 270:301:336:375:403:434:484:540 SD: 0.2910 cents 294:328:366:408:439:472:527:588 SD: 0.2853 cents 338:377:421:469:505:543:606:676 SD: 0.2768 cents 348:388:433:483:520:559:624:696 SD: 0.2560 cents 356:397:443:494:532:572:638:712 SD: 0.2533 cents 363:405:452:504:542:583:651:726 SD: 0.2149 cents 371:414:462:515:554:596:665:742 SD: 0.1887 cents 381:425:474:529:569:612:683:762 SD: 0.1618 cents 425:474:529:590:635:683:762:850 SD: 0.1353 cents 458:511:570:636:684:736:821:916 SD: 0.0671 cents