Scala analysis: xen18-ayers-table-40
7 Generalized Root Harmonic Square Means between 1.0 and 1.6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 101.711 cents 101.711000 2: 203.422 cents 203.422000 3: 305.132 cents 305.132000 4: 406.843 cents 406.843000 5: 508.554 cents 508.554000 6: 610.265 cents 610.265000 7: 711.976 cents 711.976000 8: 813.686 cents 813.686000
SHOW/INTERVAL
0: 101.7100 cents 101.7100 1: 101.7110 cents 101.7110 2: 101.7110 cents 101.7110 3: 101.7100 cents 101.7100 4: 101.7110 cents 101.7110 5: 101.7110 cents 101.7110 6: 101.7110 cents 101.7110 7: 101.7110 cents 101.7110 8: 101.7100 cents 101.7100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 101.71000 cents 1: 6 101.71100 cents 2: 4 203.42100 cents 2: 4 203.42200 cents 3: 6 305.13200 cents 3: 2 305.13300 cents 4: 1 406.84200 cents 4: 6 406.84300 cents 4: 1 406.84400 cents 5: 2 508.55300 cents 5: 6 508.55400 cents 6: 4 610.26400 cents 6: 4 610.26500 cents 7: 6 711.97500 cents 7: 2 711.97600 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.14286 = 15/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 101.7 203.4 305.1 406.8 508.6 610.3 712.0 813.7 101.7: 101.7 203.4 305.1 406.8 508.6 610.3 712.0 813.7 203.4: 101.7 203.4 305.1 406.8 508.6 610.3 712.0 813.7 305.1: 101.7 203.4 305.1 406.8 508.6 610.3 712.0 813.7 406.8: 101.7 203.4 305.1 406.8 508.6 610.3 712.0 813.7 508.6: 101.7 203.4 305.1 406.8 508.6 610.3 712.0 813.7 610.3: 101.7 203.4 305.1 406.8 508.6 610.3 712.0 813.7 712.0: 101.7 203.4 305.1 406.8 508.6 610.3 712.0 813.7 813.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 101.7100 .. 101.7110 cents 0.00100 cents 101.71000 cents 2: 203.4210 .. 203.4220 cents 0.00100 cents 101.71000 cents 3: 305.1320 .. 305.1330 cents 0.00100 cents 101.71000 cents 4: 406.8420 .. 406.8440 cents 0.00200 cents 101.70900 cents 5: 508.5530 .. 508.5540 cents 0.00100 cents 101.70900 cents 6: 610.2640 .. 610.2650 cents 0.00100 cents 101.71000 cents 7: 711.9750 .. 711.9760 cents 0.00100 cents 101.71000 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 101.71000 cents, class 1 Average step (divided formal octave): 101.7108 cents Largest one step interval : 101.71100 cents Average / Smallest step : 1.000007 Largest / Average step : 1.000002 Largest / Smallest step : 1.000010 Median interval of one step : 101.71100 cents, amount: 6 Most common interval of one step : 101.71100 cents, amount: 6 Least squares average step : 101.71080 cents, oct.: 813.68639 cents Scale is strictly proper Scale is 3-distributional even Scale is a mode of a 8-tone equal temperament with octave 813.686 cents degrees: 1 2 3 4 5 6 7 8 Least number of segments generator : 5 of 508.554 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 5 of 508.554 cents and inv. generated superset size: 8 = 0 more = 100.000% Number of contiguous 1-step segments: 1 Step pattern alph. order: AABAAAAB Step pattern size order : LLSLLLLS Interval vector is [ 6 4 2 3 ] Scale is a Constant Structure, by a margin of 101.70900 cents Scale diversity : 0.918277 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.999990 Rothenberg efficiency : 0.637500 redundancy: 0.362500 Efficiency x scale size : 5.100000 Number of different interval sizes : 15 = 2.14286 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.14286 = 15/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 0.00100 cents Number of recognisable fifths : 8, average 711.9753 cents Number of recognisable fourths : 8, average 508.5537 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 4 = 50.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 1 2 3 4 5 6 7 Limited inverse transpositions : 1 2 3 4 5 6 7 Inversional symmetry on degrees : 0 1 2 3 4 5 6 7 Inversional symmetry on intervals : 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0004 c. M: 0.0007 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 386.3140 cents 2 x x x x x x 3 x S SD: 10.0210 cents 3 x x x x 4 x x 5 S SD: 35.7249 cents 4 x x x 5 x x 6 x S SD: 11.4223 cents 5 x x 6 x x 7 x 8 S SD: 9.8920 cents 6 x x 7 x 8 x 9:10 S SD: 20.4166 cents 7 x 8 x 9 x 10 x 11 S SD: 12.7303 cents 8 x 9 x 10:11 x 12:13 S SD: 11.0839 cents 9 x 10:11 x 12:13 x 14 S SD: 14.7139 cents 10 x 11:12:13 x 14:15:16 S SD: 11.4273 cents 11:12 x 13:14:15:16:17:18 S SD: 13.0091 cents 12:13 x 14:15:16:17:18:19 S SD: 8.8484 cents 13:14:15 x 16:17:19:20:21 SD: 14.6124 cents 14:15:16:17:18:19:20:21:22 H SD: 8.2670 cents 15:16:17:18:19:20:21:23:24 SD: 5.6719 cents 26:28:29:31:33:35:37:39:42 SD: 4.6107 cents 30:32:34:36:38:40:43:45:48 SD: 3.4731 cents 31:33:35:37:39:42:44:47:50 SD: 3.4320 cents 33:35:37:39:42:44:47:50:53 SD: 3.0810 cents 38:40:43:45:48:51:54:57:61 SD: 2.9996 cents 45:48:51:54:57:60:64:68:72 S SD: 2.8252 cents 47:50:53:56:59:63:67:71:75 SD: 2.0447 cents 63:67:71:75:80:85:90:95:101 SD: 2.0024 cents 64:68:72:76:81:86:91:97:102 SD: 1.7139 cents 67:71:75:80:85:90:95:101:107 SD: 1.5254 cents 79:84:89:94:100:106:112:119:126 SD: 1.3774 cents 82:87:92:98:104:110:117:124:131 SD: 1.2543 cents 83:88:93:99:105:111:118:125:133 SD: 1.1720 cents 88:93:99:105:111:118:125:133:141 SD: 1.1425 cents 97:103:109:116:123:130:138:146:155 SD: 1.0481 cents 102:108:115:122:129:137:145:154:163 SD: 0.9819 cents 114:121:128:136:144:153:162:172:182 SD: 0.7415 cents 120:127:135:143:152:161:171:181:192 SD: 0.6811 cents 135:143:152:161:171:181:192:204:216 SD: 0.5906 cents 167:177:188:199:211:224:238:252:267 SD: 0.5798 cents 182:193:205:217:230:244:259:275:291 SD: 0.5500 cents 185:196:208:221:234:248:263:279:296 SD: 0.4653 cents 232:246:261:277:293:311:330:350:371 SD: 0.4548 cents 234:248:263:279:296:314:333:353:374 SD: 0.3316 cents 249:264:280:297:315:334:354:376:398 SD: 0.3305 cents 295:313:332:352:373:396:420:445:472 SD: 0.3123 cents 313:332:352:373:396:420:445:472:501 SD: 0.2843 cents 328:348:369:391:415:440:467:495:525 SD: 0.2687 cents 348:369:391:415:440:467:495:525:557 SD: 0.2673 cents 362:384:407:432:458:486:515:546:579 SD: 0.2523 cents 378:401:425:451:478:507:538:570:605 SD: 0.2144 cents 393:417:442:469:497:527:559:593:629 SD: 0.2047 cents 442:469:497:527:559:593:629:667:707 SD: 0.1873 cents 483:512:543:576:611:648:687:729:773 SD: 0.1776 cents 513:544:577:612:649:688:730:774:821 SD: 0.1115 cents