Talk:EDO vs ET: Difference between revisions

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: RTT distinguishes "temperament map" and "tuning map". An abstract ET only has information on the temperament map (defaulting to the simple map), while a concrete ET also assumes a tuning map. On the other hand, an EDO only has information on the tuning map (defaulting to a generator of 1200{{cent}}/n), even though calling it a tuning map is a bit of a stretch. From there, I believe these are the two key concepts that should be used to explain in more detail the points you raised: stretched/compressed octaves, relation to JI (or other pitch set to be approximated), rounding (or direct mapping) vs. regular mapping, the existence of multiple ETs for each EDO, the ambiguity contained in statements like "n-EDO supports", and so on. I don't think the lead section should mention all of these topics, but it should at least summarize why the concepts are similar and why they are distinct (which is already what the page does, but I think it could be improved).

: To summarize, this page should do its best to answer the question "what is the difference between an EDO and an ET" without needlessly repeating what's already on the other pages (by referencing these pages instead) while bringing a sense of progression that goes from general to specific. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 20:43, 20 June 2023 (UTC)

:: Thanks for your reply, Fredg999. You make very good points. In particular, yes, I'd definitely meant to make some historical notes along the lines of what you wrote up here, but I completely forgot! And in forgetting this, my statements about ETs completely assumed the modern regular temperament interpretation of that term, ignoring the fact that historically "equal temperament" was shorthand for "12-tone equal temperament", and that it didn't need to make any distinction between rounding and mapping in the way I described.

:: Your suggestion that temperament maps and tuning maps would be excellent keys to unlock this understanding for readers is interesting; however, I feel your concern that tying tuning maps to EDOs may be a stretch. I think that could cause more confusion than insight. Maybe there's another better way.

:: I support your progression from general overview to specific details, and think this page could be revised to fit that better.

:: You bring up another good point, which is avoiding repeating what is already written on other pages. Ideally, all these pages should be considered simultaneously, and each piece of information should end up in the ideal form in each ideal place. Though that's a bit of an endeavor, to be sure. Here's what I found on the [[Equal-step tuning]] page, which is what [[Equal temperament]] redirects to:

When a tuning is called '''''n''-tone equal temperament''' (abbreviated ''n''-tet or ''n''-et), this usually means "''n'' divisions of 2/1, the octave, or some approximation thereof", but it also implies a mindset of [[Regular Temperaments|temperament]] – that is, of a JI-approximation-based understanding of the scale. If you are wondering how equal divisions of the octave can become associated with temperaments, the page [[EDOs to ETs]] may help clarify. There are many reasons why one might choose to not consider JI approximations when dealing with equal tunings, and thus not treat equal tunings as temperaments. In such case, the less theory-laden term '''edo''' (occasionally written '''ed2'''), meaning '''equal divisions of the octave''' (or '''equal divisions of 2/1'''), leaves comparison to JI out of the picture, aside from the octave itself (which is assumed to be just).

:: And on the [[EDO]] page, in its History section, we currently find:

Tuning theorists first used the term "equal temperament" for edos designed to approximate low-complexity just intervals. The same term is still used today for all rank-1 temperaments. For example, 15edo can be referred to as 15-tone equal temperament (15-TET, 15-tET, 15tet, etc.), or more simply 15 equal temperament (15-ET, 15et, etc.).

:: 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)

== "Supports" ==

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: Following by reply to the topic above, I think this can be explained by the two kinds of map; an ET implies a particular temperament map, while an EDO doesn't, so it's ambiguous for EDO (unless everyone agrees to assume patent val, but I'd rather say it's ambiguous). I agree that the so-called "debate" doesn't really make sense if you look at the definitions properly. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 20:43, 20 June 2023 (UTC)

:: Agreed, except that (as I mentioned in the other topic of this discussion page) I don't think the other type of map — the tuning map — is a good idea to bring up with respect to EDOs. And that's okay because I don't think we even need to mention it here. We can simply explain that ETs have a temperament map and EDOs don't. If you like, I can take a first attempt at improving this section now. Let me know. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 16:04, 21 June 2023 (UTC)

@@ Line 25: / Line 25: @@
 : RTT distinguishes "temperament map" and "tuning map". An abstract ET only has information on the temperament map (defaulting to the simple map), while a concrete ET also assumes a tuning map. On the other hand, an EDO only has information on the tuning map (defaulting to a generator of 1200{{cent}}/n), even though calling it a tuning map is a bit of a stretch. From there, I believe these are the two key concepts that should be used to explain in more detail the points you raised: stretched/compressed octaves, relation to JI (or other pitch set to be approximated), rounding (or direct mapping) vs. regular mapping, the existence of multiple ETs for each EDO, the ambiguity contained in statements like "n-EDO supports", and so on. I don't think the lead section should mention all of these topics, but it should at least summarize why the concepts are similar and why they are distinct (which is already what the page does, but I think it could be improved).
 : To summarize, this page should do its best to answer the question "what is the difference between an EDO and an ET" without needlessly repeating what's already on the other pages (by referencing these pages instead) while bringing a sense of progression that goes from general to specific. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 20:43, 20 June 2023 (UTC)
+:: Thanks for your reply, Fredg999. You make very good points. In particular, yes, I'd definitely meant to make some historical notes along the lines of what you wrote up here, but I completely forgot! And in forgetting this, my statements about ETs completely assumed the modern regular temperament interpretation of that term, ignoring the fact that historically "equal temperament" was shorthand for "12-tone equal temperament", and that it didn't need to make any distinction between rounding and mapping in the way I described.
+:: Your suggestion that temperament maps and tuning maps would be excellent keys to unlock this understanding for readers is interesting; however, I feel your concern that tying tuning maps to EDOs may be a stretch. I think that could cause more confusion than insight. Maybe there's another better way.
+:: I support your progression from general overview to specific details, and think this page could be revised to fit that better.
+:: You bring up another good point, which is avoiding repeating what is already written on other pages. Ideally, all these pages should be considered simultaneously, and each piece of information should end up in the ideal form in each ideal place. Though that's a bit of an endeavor, to be sure. Here's what I found on the [[Equal-step tuning]] page, which is what [[Equal temperament]] redirects to:
+ When a tuning is called '''''n''-tone equal temperament''' (abbreviated ''n''-tet or ''n''-et), this usually means "''n'' divisions of 2/1, the octave, or some approximation thereof", but it also implies a mindset of [[Regular Temperaments|temperament]] – that is, of a JI-approximation-based understanding of the scale. If you are wondering how equal divisions of the octave can become associated with temperaments, the page [[EDOs to ETs]] may help clarify. There are many reasons why one might choose to not consider JI approximations when dealing with equal tunings, and thus not treat equal tunings as temperaments. In such case, the less theory-laden term '''edo''' (occasionally written '''ed2'''), meaning '''equal divisions of the octave''' (or '''equal divisions of 2/1'''), leaves comparison to JI out of the picture, aside from the octave itself (which is assumed to be just).
+:: And on the [[EDO]] page, in its History section, we currently find:
+ Tuning theorists first used the term "equal temperament" for edos designed to approximate low-complexity just intervals. The same term is still used today for all rank-1 temperaments. For example, 15edo can be referred to as 15-tone equal temperament (15-TET, 15-tET, 15tet, etc.), or more simply 15 equal temperament (15-ET, 15et, etc.).
+:: 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)
 == "Supports" ==
@@ Line 37: / Line 50: @@
 : Following by reply to the topic above, I think this can be explained by the two kinds of map; an ET implies a particular temperament map, while an EDO doesn't, so it's ambiguous for EDO (unless everyone agrees to assume patent val, but I'd rather say it's ambiguous). I agree that the so-called "debate" doesn't really make sense if you look at the definitions properly. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 20:43, 20 June 2023 (UTC)
+:: Agreed, except that (as I mentioned in the other topic of this discussion page) I don't think the other type of map — the tuning map — is a good idea to bring up with respect to EDOs. And that's okay because I don't think we even need to mention it here. We can simply explain that ETs have a temperament map and EDOs don't. If you like, I can take a first attempt at improving this section now. Let me know. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 16:04, 21 June 2023 (UTC)