Valinorsmic clan: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Some cleanup; remove varda (covered by diaschismic family)
m Finish cleanup
Line 1: Line 1:
__FORCETOC__
This is a collection of rank-3 temperaments tempering out the valinorsma, [[176/175]], which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does).
The valinorsmic rank three temperaments temper out the [[valinorsma]], 176/175, which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does.)
 
Discussed elsewhere are:
* [[Julius]] or [[varda]], {176/175, 896/891} → [[Diaschismic rank three family #Julius aka varda]]
 
Considered below are manwe, mandos and ulmo, but we can begin with the rank-4 temperament.  


== Valinorsmic ==
== Valinorsmic ==
Comma list: 176/175
Subgroup: 2.3.5.7.11


Mapping: [<1 0 0 0 -4|, <0 1 0 0 0|, <0 0 1 0 2|, <0 0 0 1 1|]
[[Comma list]]: [[176/175]]


EDOs: 22, 31, 46, 53, 58, 80, 111
[[Mapping]]: [{{val| 1 0 0 0 -4 }}, {{val| 0 1 0 0 0 }}, {{val| 0 0 1 0 2 }}, {{val| 0 0 0 1 1 }}]
 
{{Val list|legend=1| 22, 31, 46, 53, 58, 80, 111 }}


== Manwe ==
== Manwe ==
Comma list: 176/175, 1331/1323
Subgroup: 2.3.5.7.11


Mapping: [<1 0 0 12 8|, <0 1 0 3 3|, <0 0 1 -6 -4|]
[[Comma list]]: 176/175, 1331/1323


EDOs: 15, 31, 46, 77, 80, 111
[[Mapping]]: [{{val| 1 0 0 12 8 }}, {{val| 0 1 0 3 3 }}, {{val| 0 0 1 -6 -4 }}]


Badness: 0.000679
{{Val list|legend=1| 15, 31, 46, 77, 80, 111 }}
 
[[Badness]]: 0.679 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 1331/1323, 351/350
Comma list: 176/175, 1331/1323, 351/350


Mapping: [&lt;1 0 0 12 8|, &lt;0 1 0 3 3|, &lt;0 0 1 -6 -4|]
Mapping: [{{val| 1 0 0 12 8 }}, {{val| 0 1 0 3 3 }}, {{val| 0 0 1 -6 -4 }}]


EDOs: 31, 46, 77, 80, 111
Vals: {{val list| 31, 46, 77, 80, 111 }}


Badness: 0.001147
Badness: 1.147 × 10<sup>-3</sup>


== Mandos ==
== Mandos ==
Comma list: 176/175, 243/242
Subgroup: 2.3.5.7.11


Mapping: [&lt;1 1 0 6 2|, &lt;0 2 0 5 5|, &lt;0 0 1 -2 0|]
[[Comma list]]: 176/175, 243/242


EDOs: 7, 24, 31, 58, 89
[[Mapping]]: [{{val| 1 1 0 6 2 }}, {{val| 0 2 0 5 5 }}, {{val| 0 0 1 -2 0 }}]


Badness: 0.000751
{{Val list|legend=1| 7, 24, 31, 58, 89 }}
 
[[Badness]]: 0.751 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 176/175, 243/242
Comma list: 144/143, 176/175, 243/242


Mapping: [&lt;1 1 0 6 2 4|, &lt;0 2 0 5 5 -1|, &lt;0 0 1 -2 0 0|]
Mapping: [{{val| 1 1 0 6 2 4 }}, {{val| 0 2 0 5 5 -1 }}, {{val| 0 0 1 -2 0 0 }}]


EDOs: 7, 24, 31, 58
Vals: {{val list| 7, 24, 31, 58 }}


Badness: 0.000923
Badness: 0.923 × 10<sup>-3</sup>


== Ulmo ==
== Ulmo ==
Comma list: 176/175, 2200/2187
Subgroup: 2.3.5.7.11
 
[[Comma list]]: 176/175, 2200/2187


Mapping: [&lt;1 0 0 1, -3|, &lt;0 1 0 7 7|, &lt;0 0 1 -4 -2|]
[[Mapping]]: [{{val| 1 0 0 1, -3 }}, {{val| 0 1 0 7 7 }}, {{val| 0 0 1 -4 -2 }}]


EDOs: 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd
{{Val list|legend=1| 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd }}


Badness: 0.00123
[[Badness]]: 1.23 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 176/175, 325/324
Comma list: 169/168, 176/175, 325/324


Mapping: [&lt;1 0 0 1, -3 2|, &lt;0 1 0 7 7 4|, &lt;0 0 1 -4 -2 -2|]
Mapping: [{{val| 1 0 0 1, -3 2 }}, {{val| 0 1 0 7 7 4 }}, {{val| 0 0 1 -4 -2 -2 }}]


EDOs: 7, 39, 46, 53, 80, 133d, 179, 312cdf
Vals: {{val list| 7, 39, 46, 53, 80, 133d, 179, 312cdf }}


Badness: 0.000932
Badness: 0.932 × 10<sup>-3</sup>


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]

Revision as of 09:42, 15 June 2021

This is a collection of rank-3 temperaments tempering out the valinorsma, 176/175, which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does).

Discussed elsewhere are:

Considered below are manwe, mandos and ulmo, but we can begin with the rank-4 temperament.

Valinorsmic

Subgroup: 2.3.5.7.11

Comma list: 176/175

Mapping: [⟨1 0 0 0 -4], ⟨0 1 0 0 0], ⟨0 0 1 0 2], ⟨0 0 0 1 1]]

Template:Val list

Manwe

Subgroup: 2.3.5.7.11

Comma list: 176/175, 1331/1323

Mapping: [⟨1 0 0 12 8], ⟨0 1 0 3 3], ⟨0 0 1 -6 -4]]

Template:Val list

Badness: 0.679 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 1331/1323, 351/350

Mapping: [⟨1 0 0 12 8], ⟨0 1 0 3 3], ⟨0 0 1 -6 -4]]

Vals: Template:Val list

Badness: 1.147 × 10-3

Mandos

Subgroup: 2.3.5.7.11

Comma list: 176/175, 243/242

Mapping: [⟨1 1 0 6 2], ⟨0 2 0 5 5], ⟨0 0 1 -2 0]]

Template:Val list

Badness: 0.751 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 176/175, 243/242

Mapping: [⟨1 1 0 6 2 4], ⟨0 2 0 5 5 -1], ⟨0 0 1 -2 0 0]]

Vals: Template:Val list

Badness: 0.923 × 10-3

Ulmo

Subgroup: 2.3.5.7.11

Comma list: 176/175, 2200/2187

Mapping: [⟨1 0 0 1, -3], ⟨0 1 0 7 7], ⟨0 0 1 -4 -2]]

Template:Val list

Badness: 1.23 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 176/175, 325/324

Mapping: [⟨1 0 0 1, -3 2], ⟨0 1 0 7 7 4], ⟨0 0 1 -4 -2 -2]]

Vals: Template:Val list

Badness: 0.932 × 10-3

Retrieved from "https://en.xen.wiki/index.php?title=Valinorsmic_clan&oldid=72625"