Sengic family: Difference between revisions

(4 intermediate revisions by 3 users not shown)

Line 1:

'''~~Sengic~~ family''' ~~is a collection~~ of ~~the~~ [[~~planar~~ temperament]]s tempering out the senga comma, [[686/675]].

The '''sengic family''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the senga a.k.a. sengic comma, [[686/675]].

Temperament discussed elsewhere include [[sensigh]] (→ [[Sensamagic family #Sensigh|Sensamagic family]]). Considered below are demeter and krypton.

== Sengic ==

Sengic is naturally a 2.3.5.7.13 subgroup temperament due to the identity 686/675 = (91/90)(196/195) and 91/90 = (169/168)(196/195). This identifies the last generator as 13/12~14/13~15/14.

Sengic is naturally a 2.3.5.7.13 subgroup temperament due to the identity 686/675 = (91/90)(196/195) and 91/90 = (169/168)(196/195). This identifies the last generator as 13/12~14/13~15/14. The 7-limit parent was discovered and named in 2005, whereas the extension was noted by [[Keenan Pepper]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19390.html Yahoo! Tuning Group | ''It's the "thirds", stupid!'']</ref>.

[[Subgroup]]: 2.3.5.7

Line 36:

Line 37:

== Demeter ==

Named by [[Graham Breed]] in 2011, demeter was found to be locally efficient in the 17-limit among all rank-3 temperaments<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19673.html Yahoo! Tuning Group | ''Artemis and friends'']</ref>.

[[Subgroup]]: 2.3.5.7.11

Line 109:

Line 112:

Projection pairs: ~5 = 6912/1331, ~7 = 854/121, ~13 = 144/11 to 2.3.11

== Notes ==

[[Category:Temperament families]]

[[Category:Pages with mostly numerical content]]

[[Category:Sengic family| ]]

[[Category:Sengic| ]]

[[Category:Rank 3]]

@@ Line 1: / Line 1: @@
-'''Sengic family''' is a collection of the [[planar temperament]]s tempering out the senga comma, [[686/675]].
+{{Technical data page}}
+The '''sengic family''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the senga a.k.a. sengic comma, [[686/675]].
 Temperament discussed elsewhere include [[sensigh]] (→ [[Sensamagic family #Sensigh|Sensamagic family]]). Considered below are demeter and krypton.
 == Sengic ==
-Sengic is naturally a 2.3.5.7.13 subgroup temperament due to the identity 686/675 = (91/90)(196/195) and 91/90 = (169/168)(196/195). This identifies the last generator as 13/12~14/13~15/14.
+Sengic is naturally a 2.3.5.7.13 subgroup temperament due to the identity 686/675 = (91/90)(196/195) and 91/90 = (169/168)(196/195). This identifies the last generator as 13/12~14/13~15/14. The 7-limit parent was discovered and named in 2005, whereas the extension was noted by [[Keenan Pepper]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19390.html Yahoo! Tuning Group | ''It's the "thirds", stupid!'']</ref>.
 [[Subgroup]]: 2.3.5.7
@@ Line 36: / Line 37: @@
 == Demeter ==
+Named by [[Graham Breed]] in 2011, demeter was found to be locally efficient in the 17-limit among all rank-3 temperaments<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19673.html Yahoo! Tuning Group | ''Artemis and friends'']</ref>.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 109: / Line 112: @@
 Projection pairs: ~5 = 6912/1331, ~7 = 854/121, ~13 = 144/11 to 2.3.11
+== Notes ==
 [[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Sengic family| ]] <!-- main article -->
 [[Category:Sengic| ]] <!-- key article -->
 [[Category:Rank 3]]