Scala analysis: semisixths-8
8-note MOS of Semisixths [7, 9, 13, -2, 1, 5] temperament, TOP tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 131.091 cents 131.091350 2: 262.183 cents 262.182700 3: 443.160 cents 443.160290 4: 574.252 cents 574.251640 5: 705.343 cents 705.342990 6: 886.321 cents 886.320590 7: 1017.412 cents 1017.411930 8: 1198.390 cents 1198.389530
SHOW/INTERVAL
0: 180.9776 cents 180.9776 1: 131.0913 cents 131.0913 2: 131.0913 cents 131.0913 3: 180.9776 cents 180.9776 4: 131.0913 cents 131.0913 5: 131.0913 cents 131.0913 6: 180.9776 cents 180.9776 7: 131.0913 cents 131.0913 8: 180.9776 cents 180.9776
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 131.09135 cents 1: 3 180.97759 cents 2: 2 262.18270 cents 2: 6 312.06894 cents 3: 7 443.16029 cents 3: 1 493.04654 cents 4: 4 574.25164 cents 4: 4 624.13789 cents 5: 1 705.34299 cents 5: 7 755.22924 cents 6: 6 886.32059 cents 6: 2 936.20683 cents 7: 3 1017.41193 cents 7: 5 1067.29818 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 : 131.1 262.2 443.2 574.3 705.3 886.3 1017.4 1198.4 131.1 : 131.1 312.1 443.2 574.3 755.2 886.3 1067.3 1198.4 262.2 : 181.0 312.1 443.2 624.1 755.2 936.2 1067.3 1198.4 443.2 : 131.1 262.2 443.2 574.3 755.2 886.3 1017.4 1198.4 574.3 : 131.1 312.1 443.2 624.1 755.2 886.3 1067.3 1198.4 705.3 : 181.0 312.1 493.0 624.1 755.2 936.2 1067.3 1198.4 886.3 : 131.1 312.1 443.2 574.3 755.2 886.3 1017.4 1198.4 1017.4: 181.0 312.1 443.2 624.1 755.2 886.3 1067.3 1198.4 1198.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 131.0913 .. 180.9776 cents 49.88624 cents 131.09135 cents 2: 262.1827 .. 312.0689 cents 49.88624 cents 81.20511 cents 3: 443.1603 .. 493.0465 cents 49.88625 cents 131.09135 cents 4: 574.2516 .. 624.1379 cents 49.88625 cents 81.20510 cents 5: 705.3430 .. 755.2292 cents 49.88625 cents 81.20510 cents 6: 886.3206 .. 936.2068 cents 49.88624 cents 131.09135 cents 7: 1017.4119 .. 1067.2982 cents 49.88625 cents 81.20510 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 131.09134 cents, class 1 Average step (divided formal octave): 149.7987 cents Largest one step interval : 180.97759 cents Average / Smallest step : 1.142705 Largest / Average step : 1.208139 Largest / Smallest step : 1.380546 Median interval of one step : 131.09135 cents, amount: 5 Most common interval of one step : 131.09135 cents, amount: 5 Least squares average step : 146.25285 cents, oct.: 1170.02284 cents Scale is strictly proper Scale has Myhill's property chromas: 49.88624 cents and 81.20511 cents, ratio: 1.627806 generators: 3 of 443.16029 cents and 755.22924 cents ET pair of linear temperament : 19&27 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1033-tone equal temperament with octave 1198.390 cents degrees: 113 226 382 495 608 764 877 1033 generators: 382 and 651 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAABAB Step pattern size order : SSLSSLSL Scale is a Constant Structure, by a margin of 81.20510 cents Scale diversity : 1.226367 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.708606 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 : 49.88624 cents Most common intervals : 443.16029 cents & inv., amount: 7 Scale is a chain of 4 triads 0.0 131.091 755.229 cents Most common triad is 0.0 443.160 755.229 cents, amount: 6 Number of recognisable fifths : 1, average 705.3430 cents Number of recognisable fourths : 1, average 493.0465 cents Scale contains two identical conjunct tetrachords Best fifths form a closed circle Formal octave complements present : 1 = 12.5000% 2/1 octave complements present : 0 = 0.0000% 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: 26.0861 c. M:-43.6505 c. 13: 1 2 2 1 2 2 1 2 P M ME SD: 24.4644 c. M: 38.9075 c. Kadathian 14: 2 1 2 2 1 2 2 2 P D3 S SD: 22.1567 c. M:-40.1072 c. 15: 2 1 3 1 2 2 2 2 P D3 SD: 21.0886 c. M:-36.1955 c. 17: 2 2 2 2 2 3 1 3 SP D3 SD: 18.8418 c. M: 30.5029 c. 18: 2 2 3 2 2 2 2 3 SP D3 S SD: 18.3076 c. M:-27.0062 c. 19: 2 2 3 2 2 3 2 3 SP M ME SD: 6.8956 c. M: 11.5385 c. Oljare Octatonic, Sensi-8 27: 3 3 4 3 3 4 3 4 SP M ME SD: 2.8768 c. M:-4.8138 c. Sensi-8 46: 5 5 7 5 5 7 5 7 SP M DE SD: 1.1596 c. M: 1.9404 c. Sensi-8 73: 8 8 11 8 8 11 8 11 SP M DE SD: 0.3333 c. M:-0.5577 c. Sensi-8 119: 13 13 18 13 13 18 13 18 SP M DE SD: 0.2438 c. M: 0.4080 c. 192: 21 21 29 21 21 29 21 29 SP M DE SD: 0.0244 c. M: 0.0408 c. 649: 71 71 98 71 71 98 71 98 SP M DE SD: 0.0158 c. M:-0.0265 c. 841: 92 92 127 92 92 127 92 127 SP M DE SD: 0.0067 c. M:-0.0111 c. 1033: 113 113 156 113 113 156 113 156 SP M DE SD: 0.0009 c. M:-0.0015 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 1.6105 cents 2 x x x x 3 x x 4 S SD: 1.8756 cents 3 x x 4 x x 5 x 6 S SD: 18.3145 cents 4 x x 5 x 6 x 7:8 S SD: 18.7187 cents 5 x 6 x 7 x 8:9:10 S SD: 18.1157 cents 6 x 7:8 x 9:10:11:12 S SD: 10.6368 cents 7 x 8:9:10:11:12:13:14 S SD: 16.8965 cents 8 x 9:10:11:12:13:14:16 S SD: 15.4027 cents 9:10 x 12:13:14:15:16:18 S SD: 16.6260 cents 10:11:12:13:14:15:17:18:20 SD: 9.0632 cents 12:13:14:16:17:18:20:22:24 S SD: 8.7995 cents 13:14:15:17:18:20:22:23:26 SD: 7.8101 cents 16:17:19:21:22:24:27:29:32 SD: 7.6692 cents 18:19:21:23:25:27:30:32:36 SD: 5.9737 cents 20:22:23:26:28:30:33:36:40 SD: 5.7804 cents 23:25:27:30:32:35:38:41:46 SD: 5.2097 cents 24:26:28:31:33:36:40:43:48 SD: 3.2678 cents 30:32:35:39:42:45:50:54:60 SD: 3.0750 cents 36:39:42:47:50:54:60:65:72 SD: 2.7863 cents 38:41:44:49:53:57:63:68:76 SD: 2.2332 cents 48:52:56:62:67:72:80:86:96 SD: 1.6158 cents 61:66:71:79:85:92:102:110:122 SD: 1.3267 cents 66:71:77:85:92:99:110:119:132 SD: 1.2406 cents 79:85:92:102:110:119:132:142:158 SD: 0.9022 cents 99:107:115:128:138:149:165:178:198 SD: 0.7748 cents 117:126:136:151:163:176:195:211:234 SD: 0.7262 cents 127:137:148:164:177:191:212:229:254 SD: 0.5969 cents 165:178:192:213:230:248:275:297:330 SD: 0.3607 cents 244:263:284:315:340:367:407:439:488 SD: 0.3550 cents 280:302:326:362:390:421:467:504:559 SD: 0.3375 cents 295:318:343:381:411:443:492:531:589 SD: 0.3360 cents 305:329:355:394:425:458:509:549:609 SD: 0.2594 cents 354:382:412:457:493:532:591:637:707 SD: 0.2587 cents 356:384:414:460:496:535:594:641:711 SD: 0.1898 cents 404:436:470:522:563:607:674:727:807 SD: 0.1693 cents 435:469:506:562:606:654:726:783:869 SD: 0.1638 cents 470:507:547:607:655:706:784:846:939 SD: 0.1609 cents 483:521:562:624:673:726:806:869:965 SD: 0.0935 cents