81/80: Difference between revisions

Line 36:

=== 31edo as splitting the fifth into two, three and nine ===

[[31edo]] is unique as combining all aforementioned tempering strategies into one elegant [[11-limit]] meantone temperament; it also combines yet more extensions of meantone not discussed here, and it has a very accurate [[5/4]] and [[7/4]] and an even more accurate [[35/32]], so that it is very strong in the 2.5.7 subgroup. A tempering strategy not mentioned is splitting a flattened [[3/2]] into nine sharpened [[25/24]]'s, resulting in the 5-limit version of [[valentine]] so that 31edo is uniquely meantone + valentine. Valentine is a natural [[11-limit]] temperament that tempers [[121/120]] so for this reason might be natural to combine with meantone. Furthermore, splitting the meantone fifth into two and three in the ways described above leads to meantone + miracle, which interestingly, though a rank 2 temperament, only has [[31edo]] as a [[patent val]] tuning.

[[31edo]] is unique as combining all aforementioned tempering strategies into one elegant [[11-limit]] meantone temperament; it also combines yet more extensions of meantone not discussed here, and it has a very accurate [[5/4]] and [[7/4]] and an even more accurate [[35/32]], so that it is very strong in the 2.5.7 subgroup (leading to [[birds]] if you want a better fifth). A tempering strategy not mentioned is splitting a flattened [[3/2]] into nine sharpened [[25/24]]'s, resulting in the 5-limit version of [[valentine]] so that 31edo is uniquely meantone + valentine. Valentine is a natural [[11-limit]] temperament that tempers [[121/120]] so for this reason might be natural to combine with meantone. Furthermore, splitting the meantone fifth into two and three in the ways described above leads to meantone + miracle, which interestingly, though a rank 2 temperament, only has [[31edo]] as a [[patent val]] tuning.

== Relations to other superparticular ratios ==

@@ Line 36: / Line 36: @@
 === 31edo as splitting the fifth into two, three and nine ===
-[[31edo]] is unique as combining all aforementioned tempering strategies into one elegant [[11-limit]] meantone temperament; it also combines yet more extensions of meantone not discussed here, and it has a very accurate [[5/4]] and [[7/4]] and an even more accurate [[35/32]], so that it is very strong in the 2.5.7 subgroup. A tempering strategy not mentioned is splitting a flattened [[3/2]] into nine sharpened [[25/24]]'s, resulting in the 5-limit version of [[valentine]] so that 31edo is uniquely meantone + valentine. Valentine is a natural [[11-limit]] temperament that tempers [[121/120]] so for this reason might be natural to combine with meantone. Furthermore, splitting the meantone fifth into two and three in the ways described above leads to meantone + miracle, which interestingly, though a rank 2 temperament, only has [[31edo]] as a [[patent val]] tuning.
+[[31edo]] is unique as combining all aforementioned tempering strategies into one elegant [[11-limit]] meantone temperament; it also combines yet more extensions of meantone not discussed here, and it has a very accurate [[5/4]] and [[7/4]] and an even more accurate [[35/32]], so that it is very strong in the 2.5.7 subgroup (leading to [[birds]] if you want a better fifth). A tempering strategy not mentioned is splitting a flattened [[3/2]] into nine sharpened [[25/24]]'s, resulting in the 5-limit version of [[valentine]] so that 31edo is uniquely meantone + valentine. Valentine is a natural [[11-limit]] temperament that tempers [[121/120]] so for this reason might be natural to combine with meantone. Furthermore, splitting the meantone fifth into two and three in the ways described above leads to meantone + miracle, which interestingly, though a rank 2 temperament, only has [[31edo]] as a [[patent val]] tuning.
 == Relations to other superparticular ratios ==

81/80: Difference between revisions

Godtone (talk | contribs)