Valentine extensions: Difference between revisions

(5 intermediate revisions by 2 users not shown)

Line 1:

[[Valentine]] has various competing [[extension]]s to the [[13-limit]].

[[Valentine]] has various competing [[extension]]s to the [[13-limit]]. The following temperaments are discussed in this article:

* '''Valentino''' (31 & 46) – tempering out 121/120, 126/125, 176/175, and 196/195;

* '''Lupercalia''' (31 & 46f) – tempering out 66/65, 105/104, 121/120, and 126/125;

* '''Dwynwen''' (31f & 46) – tempering out 91/90, 121/120, 126/125, and 176/175.

The most important of these is valentino, which tempers out [[196/195]] and may also be characterized by tempering out [[351/350]] or [[352/351]] instead. It is [[support]]ed by [[77edo|77]]. However, it does come at the cost of a way increased complexity level. A low-complexity low-accuracy mapping is given by lupercalia, where the ~13/8 is conflated with the ~18/11. Dwynwen is a more perculiar case: the mapping is not very simple to start with, and the approximation is not ideal if we just use the tunings optimized for valentine or valentino. However, a sharper tuning especially from those sharper than [[46edo]] may do the trick.

Another path that relates a sense of compromise is to temper out [[169/168]], leading to [[semivalentine]]. This has the effect of slicing the period in two, and is supported by [[30edo|30]], [[46edo|46]], and [[62edo|62]]. Yet another possibility is given by [[hemivalentine]], with the effect of slicing the generator of 21/20~25/24 into two [[40/39]]'s. Finally, tempering out [[676/675]] leads to [[demivalentine]], with the effect of slicing the generator of 21/10~25/12 (one octave above 21/20~25/24) into two [[13/9]]'s, and is supported by 62 and 77.

See [[Gamelismic clan #Valentino]], [[Gamelismic clan #Lupercalia|#Lupercalia]], and [[Gamelismic clan #Dwynwen|#Dwynwen]] for technical data.

== Interval chain ==

Line 246:

Line 257:

[[Category:Valentine]]

[[Category:Temperament extensions]]

[[Category:Rank-2 temperaments]]

@@ Line 1: / Line 1: @@
-[[Valentine]] has various competing [[extension]]s to the [[13-limit]].
+{{Breadcrumb|Valentine}}
+[[Valentine]] has various competing [[extension]]s to the [[13-limit]]. The following temperaments are discussed in this article:
+* '''Valentino''' (31 & 46) – tempering out 121/120, 126/125, 176/175, and 196/195;
+* '''Lupercalia''' (31 & 46f) – tempering out 66/65, 105/104, 121/120, and 126/125;
+* '''Dwynwen''' (31f & 46) – tempering out 91/90, 121/120, 126/125, and 176/175.
+The most important of these is valentino, which tempers out [[196/195]] and may also be characterized by tempering out [[351/350]] or [[352/351]] instead. It is [[support]]ed by [[77edo|77]]. However, it does come at the cost of a way increased complexity level. A low-complexity low-accuracy mapping is given by lupercalia, where the ~13/8 is conflated with the ~18/11. Dwynwen is a more perculiar case: the mapping is not very simple to start with, and the approximation is not ideal if we just use the tunings optimized for valentine or valentino. However, a sharper tuning especially from those sharper than [[46edo]] may do the trick.
+Another path that relates a sense of compromise is to temper out [[169/168]], leading to [[semivalentine]]. This has the effect of slicing the period in two, and is supported by [[30edo|30]], [[46edo|46]], and [[62edo|62]]. Yet another possibility is given by [[hemivalentine]], with the effect of slicing the generator of 21/20~25/24 into two [[40/39]]'s. Finally, tempering out [[676/675]] leads to [[demivalentine]], with the effect of slicing the generator of 21/10~25/12 (one octave above 21/20~25/24) into two [[13/9]]'s, and is supported by 62 and 77.
+See [[Gamelismic clan #Valentino]], [[Gamelismic clan #Lupercalia|#Lupercalia]], and [[Gamelismic clan #Dwynwen|#Dwynwen]] for technical data.
 == Interval chain ==
@@ Line 246: / Line 257: @@
 [[Category:Valentine]]
 [[Category:Temperament extensions]]
+[[Category:Rank-2 temperaments]]