Sirius: Difference between revisions

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{{Infobox regtemp

~~Technical data:~~ [[~~Gariboh clan#Sirius~~]]

| 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).

== ~~Edts~~ compatible with the Sirius triskaidecatonic scale ==

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.

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]].]

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|-

! colspan="7" | Generator

! Cents Hekts

! Cents Hekts

! L

! s

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|

| colspan="2" | 316.99 216.67

| colspan="2" | 316.99 216.67

| 0

| 633.985 433.33

| 633.985 433.33

| 950.98 650

| 950.98 650

| 1267.97 866.67

| 1267.97 866.67

|

|-

@@ Line 1: / Line 1: @@
-{{URWTC}}
+{{Infobox regtemp
-Technical data: [[Gariboh clan#Sirius]]
+| 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).
-== Edts compatible with the Sirius triskaidecatonic scale ==
+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&nbsp;7s]] and 6L&nbsp;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&nbsp;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]].]
@@ Line 48: / Line 45: @@
 |-
 ! colspan="7" | Generator
-! Cents<br />Hekts
+! Cents <br>Hekts
 ! L
 ! s
@@ Line 63: / Line 60: @@
 |
 |
-| colspan="2" | 316.99<br />216.67
+| colspan="2" | 316.99 <br>216.67
 | 0
-| 633.985<br />433.33
+| 633.985 <br>433.33
-| 950.98<br />650
+| 950.98 <br>650
-| 1267.97<br />866.67
+| 1267.97 <br>866.67
 |
 |-