Talk:Meantone family: Difference between revisions

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:::: Meridetone ''is'' the counterpart of grosstone across 43edo, but its join is 43 & 55de. Again, as Lucius said, sharp of 43edo is outside the septimal meantone range. So I'd concede a point here, though I still think that sauveuric is the best meridetone extension. Note however that 19-limit meridetonic follows what I've called the "mediantone" extension to 17 and 19; however that extension is specifically 74 & 43 (supported by 117d), and due to its sheer complexity should serve nowhere else other than grosstone. I'd suggest "meridian" as a name for this 19-limit grosstone extension.

:::: For further elaboration on grosstone extensions: ⟨0 1 4 10 18 -16 -5 -3] (31 & 43) is the current canonical 19-limit grosstone. However it is not supported by the optimal grosstone edos (74, 105, and 117d). My suggestion above was the inclusion of two alternate 19-limit extensions, based on 19-limit didacus extensions, that are quite complex but supported by 74edo. These are ⟨0 1 4 10 18 -16 38 40] (74 & 43) "meridian" and ⟨0 1 4 10 18 -16 -36 -34] (31 & 74) "name TBD". However, due to their complexity and lack of coverage of the whole 31-to-43 range, I suggest neither of these should be canonical. Either ~~the current 19-limit grosstone~~ should remain canonical, or none of these three should be. In the latter case we could call 31 & 43 "grosstonian" and 31 & 74 "grosstonic", or something along those lines.

:::: For further elaboration on grosstone extensions: ⟨0 1 4 10 18 -16 -5 -3] (31 & 43) is the current canonical 19-limit grosstone. However it is not supported by the optimal grosstone edos (74, 105, and 117d). My suggestion above was the inclusion of two alternate 19-limit extensions, based on 19-limit didacus extensions, that are quite complex but supported by 74edo. These are ⟨0 1 4 10 18 -16 38 40] (74 & 43) "meridian" and ⟨0 1 4 10 18 -16 -36 -34] (31 & 74) "name TBD". However, due to their complexity and lack of coverage of the whole 31-to-43 range, I suggest neither of these should be canonical. Either 31 & 43 should remain canonical, or none of these three should be. In the latter case we could call 31 & 43 "grosstonian" and 31 & 74 "grosstonic", or something along those lines.

:::: > The 19-limit extensions of meridetone aren't worth preserving if the 19-limit extensions of tridecimal meantone are removed

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 :::: Meridetone ''is'' the counterpart of grosstone across 43edo, but its join is 43 & 55de. Again, as Lucius said, sharp of 43edo is outside the septimal meantone range. So I'd concede a point here, though I still think that sauveuric is the best meridetone extension. Note however that 19-limit meridetonic follows what I've called the "mediantone" extension to 17 and 19; however that extension is specifically 74 & 43 (supported by 117d), and due to its sheer complexity should serve nowhere else other than grosstone. I'd suggest "meridian" as a name for this 19-limit grosstone extension.
-:::: For further elaboration on grosstone extensions: ⟨0 1 4 10 18 -16 -5 -3] (31 & 43) is the current canonical 19-limit grosstone. However it is not supported by the optimal grosstone edos (74, 105, and 117d). My suggestion above was the inclusion of two alternate 19-limit extensions, based on 19-limit didacus extensions, that are quite complex but supported by 74edo. These are ⟨0 1 4 10 18 -16 38 40] (74 & 43) "meridian" and ⟨0 1 4 10 18 -16 -36 -34] (31 & 74) "name TBD". However, due to their complexity and lack of coverage of the whole 31-to-43 range, I suggest neither of these should be canonical. Either the current 19-limit grosstone should remain canonical, or none of these three should be. In the latter case we could call 31 & 43 "grosstonian" and 31 & 74 "grosstonic", or something along those lines.
+:::: For further elaboration on grosstone extensions: ⟨0 1 4 10 18 -16 -5 -3] (31 & 43) is the current canonical 19-limit grosstone. However it is not supported by the optimal grosstone edos (74, 105, and 117d). My suggestion above was the inclusion of two alternate 19-limit extensions, based on 19-limit didacus extensions, that are quite complex but supported by 74edo. These are ⟨0 1 4 10 18 -16 38 40] (74 & 43) "meridian" and ⟨0 1 4 10 18 -16 -36 -34] (31 & 74) "name TBD". However, due to their complexity and lack of coverage of the whole 31-to-43 range, I suggest neither of these should be canonical. Either 31 & 43 should remain canonical, or none of these three should be. In the latter case we could call 31 & 43 "grosstonian" and 31 & 74 "grosstonic", or something along those lines.
 :::: > The 19-limit extensions of meridetone aren't worth preserving if the 19-limit extensions of tridecimal meantone are removed