Talk:EDO vs ET: Difference between revisions

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::::::: Yes, it's ''a trivial temperament where no tempering is happening: no commas are tempered out''. Well... EDO is simple and appear in many places in theory. We must say this first. Next, I think about it according to the title ''EDO vs ET'', I dare to position them on the same layer (as a regular temperament) for a clear comparison. Clear comparison means simply and mathematically pointing out the difference, not long descriptions of different layers.

::::::: Sorry I can't judge if it will be an easy-to-understand explanation for beginners ...　--[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 14:12, 25 June 2023 (UTC)

:::::::: Ah, ok. Thanks for explaining, Fredg999. It was the "domain" part that threw me off.

:::::::: Dummy index, what you wrote would have made sense to me if you had simply written "basis" instead of "domain basis". That's because "domain" is a mathematical term in that context, and what it refers to is a space ''before some mapping occurs'', or the space that something gets mapped from. The opposite word of domain in this sense is "range"; that's the space ''after'' mapping, or the space that we map into. So when we apply this mathematical concept to our xenharmonic topic, the domain is our JI lattice, the mapping is tempering, and the range is our tempered lattice. Does that make sense? So you can see that in an EDO, no mapping happens; there's no domain or range, or said another way, it is a system that doesn't require any before-and-after aspect to understand. Yes, we can certainly look at an EDO on a 1D lattice, and say that 12-EDO has a basis of 2<sup>1/12</sup>, but this basis wouldn't be called a ''domain'' basis.

:::::::: As for your most recent message:

:::::::: * I do not think it is reasonable to say that an EDO is "a trivial temperament where no tempering is happening: no commas are tempered out"; that's a description I've used often for JI. I would say that JI does not need to be looked at as a temperament, but it's possible to look at it as a trivial temperament if you want. EDOs, on the other hand, cannot be looked at as temperaments in any meaningful way, trivial or otherwise. They just don't have anything to do with tempering at all.

:::::::: * I also think it would be a bad idea to describe both EDOs and ETs as regular temperaments. I agree we should clearly/simply/mathematically point out their differences, but this way would be inaccurate and confusing.

:::::::: Perhaps, though, all you mean is, again, not that EDOs and ETs are both regular temperaments, but that they are both ''generated tunings'', as Fredg999 described, or in other words, that they can be visualized on a lattice. Even more specifically, they can both be visualized on 1D lattices. And one other thing they have in common is that both lattices' single dimension's generators represent an interval 2<sup>1/n</sup>, whether that's for n-ET or n-EDO, and whether or not this interval is tuned exactly. That much I can certainly agree with.

:::::::: --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 15:55, 25 June 2023 (UTC)

== "Supports" ==

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 ::::::: Yes, it's ''a trivial temperament where no tempering is happening: no commas are tempered out''. Well... EDO is simple and appear in many places in theory. We must say this first. Next, I think about it according to the title ''EDO vs ET'', I dare to position them on the same layer (as a regular temperament) for a clear comparison. Clear comparison means simply and mathematically pointing out the difference, not long descriptions of different layers.
 ::::::: Sorry I can't judge if it will be an easy-to-understand explanation for beginners ...　--[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 14:12, 25 June 2023 (UTC)
+:::::::: Ah, ok. Thanks for explaining, Fredg999. It was the "domain" part that threw me off.
+:::::::: Dummy index, what you wrote would have made sense to me if you had simply written "basis" instead of "domain basis". That's because "domain" is a mathematical term in that context, and what it refers to is a space ''before some mapping occurs'', or the space that something gets mapped from. The opposite word of domain in this sense is "range"; that's the space ''after'' mapping, or the space that we map into. So when we apply this mathematical concept to our xenharmonic topic, the domain is our JI lattice, the mapping is tempering, and the range is our tempered lattice. Does that make sense? So you can see that in an EDO, no mapping happens; there's no domain or range, or said another way, it is a system that doesn't require any before-and-after aspect to understand. Yes, we can certainly look at an EDO on a 1D lattice, and say that 12-EDO has a basis of 2<sup>1/12</sup>, but this basis wouldn't be called a ''domain'' basis.
+:::::::: As for your most recent message:
+:::::::: * I do not think it is reasonable to say that an EDO is "a trivial temperament where no tempering is happening: no commas are tempered out"; that's a description I've used often for JI. I would say that JI does not need to be looked at as a temperament, but it's possible to look at it as a trivial temperament if you want. EDOs, on the other hand, cannot be looked at as temperaments in any meaningful way, trivial or otherwise. They just don't have anything to do with tempering at all.
+:::::::: * I also think it would be a bad idea to describe both EDOs and ETs as regular temperaments. I agree we should clearly/simply/mathematically point out their differences, but this way would be inaccurate and confusing.
+:::::::: Perhaps, though, all you mean is, again, not that EDOs and ETs are both regular temperaments, but that they are both ''generated tunings'', as Fredg999 described, or in other words, that they can be visualized on a lattice. Even more specifically, they can both be visualized on 1D lattices. And one other thing they have in common is that both lattices' single dimension's generators represent an interval 2<sup>1/n</sup>, whether that's for n-ET or n-EDO, and whether or not this interval is tuned exactly. That much I can certainly agree with.
+:::::::: --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 15:55, 25 June 2023 (UTC)
 == "Supports" ==