Talk:EDO vs ET: Difference between revisions
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::: 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'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) | ::: 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) | ||
:::: Ah ha! Yes, before I got a chance to read this, while I was drifting off to sleep last night, the thought suddenly occurred to me that perhaps you had been thinking specifically of ''generator'' tuning maps. And in that case, yes, I totally agree that this could be a great way to get at the difference between EDOs and ETs, for the reasons you describe. | |||
:::: Also agreed re: pages being for concepts, not terms. So the RTT interpretation of equal temperament should be a section on this new non-redirect [[Equal temperament]] page, and [[Rank-1 temperament]] should redirect to that section. | |||
:::: If I don't get any pushback here or further suggestions, I can take a crack at making these improvements next week. | |||
:::: --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 17:07, 22 June 2023 (UTC) | |||
== "Supports" == | == "Supports" == | ||