Valentine extensions: Difference between revisions

Created page with "Valentine has various competing extensions to the 13-limit. == Interval chain == In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''..."
 
Expand
Line 1: 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.  


== Interval chain ==
== Interval chain ==