Talk:Optimal ET sequence: Difference between revisions

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:::: I expect that most readers who see "optimal GPV sequence" in temperament catalogs, if they can figure it out at all, will assume that "GPV" must mean "supporting ET" (i.e. "ET that supports this temperament"), which of course it does not. So I think these should be called "optimal supporting-ET sequence" or if that's considered too long then "optimal ET sequence" since why would it be listed against the temperament if it didn't support it. Is there such a thing as an ET that doesn't have a uniform map/GPV? If so, the uniform map/GPV requirement can simply be made part of the optimality requirement. [[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 02:13, 4 May 2023 (UTC)

::::: I recall reading that there are infinitely many ET for each EDO (or equal tuning) out there, alluding to the fact that an ET is defined by a temperament map (val), and you could technically use any kind of map, even wonky ones, with any tuning. The use of wart notation in this sequence confirms that we're really enumerating equal ''temperaments'', not equal ''tunings'' (both of which can abbreviate to ET, that's annoying, but I'm using ET for equal temperament here). After all, putting something like 17c in a sequence is exactly the same as spelling out the corresponding map in full, it's just that wart notation makes the sequence look like a list of equal ''tunings'' when it actually isn't. Now, uniform maps (GPVs) are a special kind of ET that excludes the "wonky ones", and in a given prime limit (or domain), there are finitely many uniform maps that map a given prime to the same number of steps; [[:File:Generalized Patent Vals.png]] offers a nice visualization of this. I believe it's reasonable to only include uniform maps in these lists, because most people interested in temperament data want maps that actually try to approximate JI logically, and it would only be less clear what exactly is being listed if we switched from GPV to ET. If people understand it as "supporting ET", while it's not the full picture, it's not completely off track either, unless I am myself off track of course. My current concern would be "GPV" vs. "uniform map" (UM?). "Optimal uniform map sequence" is a mouthful, and "Optimal UM sequence" looks weird because it's new although I bet I could get used to it quickly. On the other hand, since it's an "optimal sequence", one might expect that the ETs listed would also be uniform maps. From that perspective, I agree that "optimal ET sequence" is the most straightforward choice. However, I wonder if non-uniform maps can make it in the sequences even with the restriction of decreasing error, so maybe someone could help me clear that up? --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 03:10, 4 May 2023 (UTC)

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	:::: I expect that most readers who see "optimal GPV sequence" in temperament catalogs, if they can figure it out at all, will assume that "GPV" must mean "supporting ET" (i.e. "ET that supports this temperament"), which of course it does not. So I think these should be called "optimal supporting-ET sequence" or if that's considered too long then "optimal ET sequence" since why would it be listed against the temperament if it didn't support it. Is there such a thing as an ET that doesn't have a uniform map/GPV? If so, the uniform map/GPV requirement can simply be made part of the optimality requirement. [[User:Dave Keenan\|Dave Keenan]] ([[User talk:Dave Keenan\|talk]]) 02:13, 4 May 2023 (UTC)		:::: I expect that most readers who see "optimal GPV sequence" in temperament catalogs, if they can figure it out at all, will assume that "GPV" must mean "supporting ET" (i.e. "ET that supports this temperament"), which of course it does not. So I think these should be called "optimal supporting-ET sequence" or if that's considered too long then "optimal ET sequence" since why would it be listed against the temperament if it didn't support it. Is there such a thing as an ET that doesn't have a uniform map/GPV? If so, the uniform map/GPV requirement can simply be made part of the optimality requirement. [[User:Dave Keenan\|Dave Keenan]] ([[User talk:Dave Keenan\|talk]]) 02:13, 4 May 2023 (UTC)

			::::: I recall reading that there are infinitely many ET for each EDO (or equal tuning) out there, alluding to the fact that an ET is defined by a temperament map (val), and you could technically use any kind of map, even wonky ones, with any tuning. The use of wart notation in this sequence confirms that we're really enumerating equal ''temperaments'', not equal ''tunings'' (both of which can abbreviate to ET, that's annoying, but I'm using ET for equal temperament here). After all, putting something like 17c in a sequence is exactly the same as spelling out the corresponding map in full, it's just that wart notation makes the sequence look like a list of equal ''tunings'' when it actually isn't. Now, uniform maps (GPVs) are a special kind of ET that excludes the "wonky ones", and in a given prime limit (or domain), there are finitely many uniform maps that map a given prime to the same number of steps; [[:File:Generalized Patent Vals.png]] offers a nice visualization of this. I believe it's reasonable to only include uniform maps in these lists, because most people interested in temperament data want maps that actually try to approximate JI logically, and it would only be less clear what exactly is being listed if we switched from GPV to ET. If people understand it as "supporting ET", while it's not the full picture, it's not completely off track either, unless I am myself off track of course. My current concern would be "GPV" vs. "uniform map" (UM?). "Optimal uniform map sequence" is a mouthful, and "Optimal UM sequence" looks weird because it's new although I bet I could get used to it quickly. On the other hand, since it's an "optimal sequence", one might expect that the ETs listed would also be uniform maps. From that perspective, I agree that "optimal ET sequence" is the most straightforward choice. However, I wonder if non-uniform maps can make it in the sequences even with the restriction of decreasing error, so maybe someone could help me clear that up? --[[User:Fredg999\|Fredg999]] ([[User talk:Fredg999\|talk]]) 03:10, 4 May 2023 (UTC)