Talk:Optimal ET sequence: Difference between revisions

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:::: I've never heard of ET standing for "equal tuning", only "equal temperament". I do not say that ETs ''are'' maps (vals), but rather that ETs ''have'' maps (vals), because an ET can just as well be defined by its comma basis (monzo list). So, to me, those sequences are not sequences of any kind of map or val. That would look like: ⟨12 19 28], ⟨17 27 40], ... They are sequences of ETs. I agree it would be interesting to know if an ET with a non-uniform map could ever make it into such list, given only the requirement of decreasing error with increasing ET number. I'm sorry I can't answer that. I expect that Flora could easily perform some experiments in that regard. But we don't need to know that to resolve this issue, since we agree we can (and would want to) simply add the uniformity (GPV) requirement as part of what it means to be "optimal" here. [[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 04:06, 4 May 2023 (UTC)

::::: I don't think ET is used often for "equal tuning" by the way, I was just noticing the coincidence. Also, I would rather say that ETs ''can be expressed'' as maps, rather than "have" maps, but I might just be playing with words here. Anyway, since optimal GPV sequences enumerate ETs with warts, and since 17c is a shorthand for ⟨17 27 40], it means that including 17c is equivalent to including ⟨17 27 40] in the list. A list of comma bases would essentially serve the same purpose, but we don't choose that form for essentially the same reason we don't write out the maps in full. In any case, that doesn't change that "optimal ET sequence" still looks like the best option to me so far. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 06:51, 4 May 2023 (UTC)

Revision as of 04:11, 4 May 2023 view source Dave Keenan (talk \| contribs) autopatrolled, emailconfirmed 1,671 edits Changed "we agree we can" to "we agree we can (and would want to)". ← Older edit		Revision as of 06:51, 4 May 2023 view source Fredg999 (talk \| contribs) autopatrolled, Interface administrators, Sysops 6,129 edits →Is "Val list" the best name for this thing?: re Newer edit →
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	:::: I've never heard of ET standing for "equal tuning", only "equal temperament". I do not say that ETs ''are'' maps (vals), but rather that ETs ''have'' maps (vals), because an ET can just as well be defined by its comma basis (monzo list). So, to me, those sequences are not sequences of any kind of map or val. That would look like: ⟨12 19 28], ⟨17 27 40], ... They are sequences of ETs. I agree it would be interesting to know if an ET with a non-uniform map could ever make it into such list, given only the requirement of decreasing error with increasing ET number. I'm sorry I can't answer that. I expect that Flora could easily perform some experiments in that regard. But we don't need to know that to resolve this issue, since we agree we can (and would want to) simply add the uniformity (GPV) requirement as part of what it means to be "optimal" here. [[User:Dave Keenan\|Dave Keenan]] ([[User talk:Dave Keenan\|talk]]) 04:06, 4 May 2023 (UTC)		:::: I've never heard of ET standing for "equal tuning", only "equal temperament". I do not say that ETs ''are'' maps (vals), but rather that ETs ''have'' maps (vals), because an ET can just as well be defined by its comma basis (monzo list). So, to me, those sequences are not sequences of any kind of map or val. That would look like: ⟨12 19 28], ⟨17 27 40], ... They are sequences of ETs. I agree it would be interesting to know if an ET with a non-uniform map could ever make it into such list, given only the requirement of decreasing error with increasing ET number. I'm sorry I can't answer that. I expect that Flora could easily perform some experiments in that regard. But we don't need to know that to resolve this issue, since we agree we can (and would want to) simply add the uniformity (GPV) requirement as part of what it means to be "optimal" here. [[User:Dave Keenan\|Dave Keenan]] ([[User talk:Dave Keenan\|talk]]) 04:06, 4 May 2023 (UTC)

			::::: I don't think ET is used often for "equal tuning" by the way, I was just noticing the coincidence. Also, I would rather say that ETs ''can be expressed'' as maps, rather than "have" maps, but I might just be playing with words here. Anyway, since optimal GPV sequences enumerate ETs with warts, and since 17c is a shorthand for ⟨17 27 40], it means that including 17c is equivalent to including ⟨17 27 40] in the list. A list of comma bases would essentially serve the same purpose, but we don't choose that form for essentially the same reason we don't write out the maps in full. In any case, that doesn't change that "optimal ET sequence" still looks like the best option to me so far. --[[User:Fredg999\|Fredg999]] ([[User talk:Fredg999\|talk]]) 06:51, 4 May 2023 (UTC)