Talk:EDO vs ET: Difference between revisions

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:: Interestingly, [[ET]] currently redirects to [[EDO]]; since ET is an abbreviation of equal temperament, certainly they should go to the same place, yeah? But this is another aspect to the extended problem. I suspect "Equal temperament" should probably not be a redirect page at all, but should be the place where we find the sort of historical information you and I have started writing about here and which is mentioned on the EDO page. Also, [[Rank-1 temperament]] should probably exist (as [[Rank-2 temperament]] and [[Rank-3 temperament]] do), and address the modern RTT interpretation of the term. Most of these pages can be quite brief, I think. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 16:04, 21 June 2023 (UTC)

::: I'll clarify why I associate edos with tuning maps, and more specifically '''generator tuning maps'''. In non-RTT jargon, a specific edo is usually defined by its number of steps to the octave. If we assume the octave to be just, which is often the case (or not always critically important anyway), then that definition is equivalent to a definition by step size. In other words, 12edo can be defined either by its 12 tones per octave or by its 100¢ step size. Now, we know that an edo's step corresponds to its generator, from an RTT point of view. The generator tuning map for a rank-1 regular temperament is a 1x1 row vector containing, as its only element, the size of the generator, which we know is exactly the edo's step size. That is to say, the tuning map is a generalization of the concept of "step size" to higher dimensions. This idea might need a bit more work to be conveyed fluently, but I still believe it is a useful way to bridge edos and ETs.

::: I agree that several related pages would also need coherent work alongside the revision of the page here. The excerpts you quoted here give a good idea of the work to do. As for the pages for rank-''n'' temperaments, it's good to keep in mind that wiki pages should be about concepts, not words or expressions. [[Rank-1 temperament]] can redirect to [[Equal temperament]] or to whatever "Equal temperament" redirects to. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 19:28, 21 June 2023 (UTC)

== "Supports" ==

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 :: Interestingly, [[ET]] currently redirects to [[EDO]]; since ET is an abbreviation of equal temperament, certainly they should go to the same place, yeah? But this is another aspect to the extended problem. I suspect "Equal temperament" should probably not be a redirect page at all, but should be the place where we find the sort of historical information you and I have started writing about here and which is mentioned on the EDO page. Also, [[Rank-1 temperament]] should probably exist (as [[Rank-2 temperament]] and [[Rank-3 temperament]] do), and address the modern RTT interpretation of the term. Most of these pages can be quite brief, I think. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 16:04, 21 June 2023 (UTC)
+::: I'll clarify why I associate edos with tuning maps, and more specifically '''generator tuning maps'''. In non-RTT jargon, a specific edo is usually defined by its number of steps to the octave. If we assume the octave to be just, which is often the case (or not always critically important anyway), then that definition is equivalent to a definition by step size. In other words, 12edo can be defined either by its 12 tones per octave or by its 100¢ step size. Now, we know that an edo's step corresponds to its generator, from an RTT point of view. The generator tuning map for a rank-1 regular temperament is a 1x1 row vector containing, as its only element, the size of the generator, which we know is exactly the edo's step size. That is to say, the tuning map is a generalization of the concept of "step size" to higher dimensions. This idea might need a bit more work to be conveyed fluently, but I still believe it is a useful way to bridge edos and ETs.
+::: I agree that several related pages would also need coherent work alongside the revision of the page here. The excerpts you quoted here give a good idea of the work to do. As for the pages for rank-''n'' temperaments, it's good to keep in mind that wiki pages should be about concepts, not words or expressions. [[Rank-1 temperament]] can redirect to [[Equal temperament]] or to whatever "Equal temperament" redirects to. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 19:28, 21 June 2023 (UTC)
 == "Supports" ==