Sirius: Difference between revisions
m Recategorize |
No edit summary Tags: Mobile edit Mobile web edit |
||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
{{ | {{Infobox regtemp | ||
| Title = Sirius | |||
| Subgroups = 3.5.7 | |||
| Comma basis = [[3125/3087]] | |||
| Edo join 1 = b13 | Edo join 2 = b19 | |||
| Mapping = 1; 3 5 | |||
| Generators = 25/21 | |||
| Generators tuning = 293.759 | |||
| Optimization method = CWE | |||
| MOS scales = [[1L 5s (3/1-equivalent)|1L 5s <3/1>]], [[6L 1s (3/1-equivalent)|6L 1s <3/1>]], [[6L 7s (3/1-equivalent)|6L 7s <3/1>]] | |||
| Color name = | |||
| Odd limit 1 = 3.5.7 7 | Mistuning 1 = 4.236 | Complexity 1 = 6 | |||
| Odd limit 2 = 3.5.7 49 | Mistuning 2 = 8.472 | Complexity 2 = 13 | |||
}} | |||
'''Sirius''' is a no-twos temperament which tempers out the gariboh comma, [[3125/3087]] (also known as major BP diesis). | |||
== | See [[Gariboh clan #Sirius]] and [[No-twos subgroup temperaments #Sirius]] for technical data. | ||
== EDTs compatible with the Sirius triskaidecatonic scale == | |||
The Sirius [[MOS]] families of [[6L 7s]] and 6L 7s are good scales to know for representing "ordinary" diminished chords with stack of their generators. In fact, 0-1-2-3-4 generators is an "ordinary" dim7dim9 [[pentad]], and by a weird coincidence, numbered 1-3-5-7-9 just as if arranged in an "ordinary" [[diatonic scale]]. Below is a list of the equal-temperaments which contain a [[6L 1s]] scale using [[generator]]s between 271.7 [[cents]] and 317.0 cents. | The Sirius [[MOS]] families of [[6L 7s]] and 6L 7s are good scales to know for representing "ordinary" diminished chords with stack of their generators. In fact, 0-1-2-3-4 generators is an "ordinary" dim7dim9 [[pentad]], and by a weird coincidence, numbered 1-3-5-7-9 just as if arranged in an "ordinary" [[diatonic scale]]. Below is a list of the equal-temperaments which contain a [[6L 1s]] scale using [[generator]]s between 271.7 [[cents]] and 317.0 cents. | ||
L=1 s=0 [[6edt|6]] and [[7edt|7]] edt | * L=1 s=0 [[6edt|6]] and [[7edt|7]] edt | ||
* L=1 s=1 [[13edt|13 edt]] | |||
L=1 s=1 [[13edt|13 edt]] | * L=2 s=1 [[19edt|19]] (~[[12edo]]) and [[20edt|20]] | ||
* L=3 s=1 [[25edt|25]] and [[27edt|27]] (~[[17edo]]) | |||
L=2 s=1 [[19edt|19]] (~[[12edo]]) and [[20edt|20]] | * L=3 s=2 [[32edt|32]] and [[33edt|33]] (~[[21edo]]) | ||
* L=4 s=1 [[31edt|31]] and [[34edt|34]] | |||
L=3 s=1 [[25edt|25]] and [[27edt|27]] (~[[17edo]]) | * L=4 s=3 [[45edt|45]] and [[46edt|46]] (~[[29edo]]) | ||
* L=5 s=1 [[37edt|37]] and [[41edt|41]] | |||
L=3 s=2 [[32edt|32]] and [[33edt|33]] (~[[21edo]]) | * L=5 s=2 [[44edt|44]] and [[47edt|47]] | ||
* L=5 s=3 [[51edt|51]] (~[[32edo]]) and [[53edt|53]] | |||
L=4 s=1 [[31edt|31]] and [[34edt|34]] | * L=5 s=4 [[58edt|58]] and [[59edt|59]] (~[[37edo]]) | ||
* L=6 s=1 [[43edt|43]] (~[[27edo]]) and [[48edt|48]] | |||
L=4 s=3 [[45edt|45]] and [[46edt|46]] (~[[29edo]]) | * L=6 s=5 [[71edt|71]] and [[72edt|72]] | ||
* L=7 s=1 [[49edt|49]] (~[[31edo]]) and [[55edt|55]] | |||
L=5 s=1 [[37edt|37]] and [[41edt|41]] | * L=7 s=2 [[56edt|56]] and [[61edt|61]] | ||
* L=7 s=3 [[63edt|63]] (~[[40edo]]) and [[67edt|67]] (~[[42edo]]) | |||
L=5 s=2 [[44edt|44]] and [[47edt|47]] | * L=7 s=4 [[64edt|64]] and [[68edt|68]] (~[[43edo]]) | ||
* L=7 s=5 [[77edt|77]] and [[79edt|79]] (~[[50edo]]) | |||
L=5 s=3 [[51edt|51]] (~[[32edo]]) and [[53edt|53]] | * L=7 s=6 [[84edt|84]] (~[[53edo]]) and [[85edt|85]] | ||
L=5 s=4 [[58edt|58]] and [[59edt|59]] (~[[37edo]]) | |||
L=6 s=1 [[43edt|43]] (~[[27edo]]) and [[48edt|48]] | |||
L=6 s=5 [[71edt|71]] and [[72edt|72]] | |||
L=7 s=1 [[49edt|49]] (~[[31edo]]) and [[55edt|55]] | |||
L=7 s=2 [[56edt|56]] and [[61edt|61]] | |||
L=7 s=3 [[63edt|63]] (~[[40edo]]) and [[67edt|67]] (~[[42edo]]) | |||
L=7 s=4 [[64edt|64]] and [[68edt|68]] (~[[43edo]]) | |||
L=7 s=5 [[77edt|77]] and [[79edt|79]] (~[[50edo]]) | |||
L=7 s=6 [[84edt|84]] (~[[53edo]]) and [[85edt|85]] | |||
[For what it's worth, as [[6edt]] and [[7edt]] are comparable to [[5edo]] and [[7edo]], then the "counterparts" of [[Blackwood]] and [[Whitewood]] would be found in multiples therein and would be [[Category:12-tone scales|dodecatonic]] and [[Category:14-tone scales|tetradecatonic]], eg. [[18edt]] and [[21edt]].] | [For what it's worth, as [[6edt]] and [[7edt]] are comparable to [[5edo]] and [[7edo]], then the "counterparts" of [[Blackwood]] and [[Whitewood]] would be found in multiples therein and would be [[Category:12-tone scales|dodecatonic]] and [[Category:14-tone scales|tetradecatonic]], eg. [[18edt]] and [[21edt]].] | ||
| Line 48: | Line 45: | ||
|- | |- | ||
! colspan="7" | Generator | ! colspan="7" | Generator | ||
! Cents<br | ! Cents <br>Hekts | ||
! L | ! L | ||
! s | ! s | ||
| Line 63: | Line 60: | ||
| | | | ||
| | | | ||
| colspan="2" | 316.99<br | | colspan="2" | 316.99 <br>216.67 | ||
| 0 | | 0 | ||
| 633.985<br | | 633.985 <br>433.33 | ||
| 950.98<br | | 950.98 <br>650 | ||
| 1267.97<br | | 1267.97 <br>866.67 | ||
| | | | ||
|- | |- | ||