Valentine extensions: Difference between revisions

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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.

== Interval chain ==

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 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.
 == Interval chain ==