Talk:Rodan: Difference between revisions

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::::::: Yeah, I'll likely continue to disagree. I side with Osmium in regard to 63edo. -- [[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 12:17, 16 June 2025 (UTC)

:::::::: If you don't have anything to add, I'll wait for your revision of other sections first. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:32, 17 June 2025 (UTC)

::: Re: 17-limit rodan. While it's less accurate than 13-limit one (not dramatically so - 17 is about as off as 7, though in the opposite direction), I'd like to highlight that it's generally much harder to approximate the full 17-limit well than the 13-limit. So temps should rather be compared with others of the same rank and group than with their own restrictions to smaller groups. Rodan is 2.1x Dirichlet-worse in the 13-limit than its leader abigail, but only 1.4x Dirichlet-worse in the 17-limit than its leader hendec. (Well, abigail is impractical, but harry is still 1.4x better than rodan in the 13-limit, and the latter is slightly worse than manna in both - by 1.08x and 1.14x.) Rodan is remarkably good for a 17-limit temp that 41 supports, is one of the few sensible ways of detempering 41 considering that the latter has relatively terrible prime 17.

::: As for rodan's rank-3 detempers: while akea indeed extends poorly to the 17-limit, recall that rodan is portending akea, and portending does extend unambiguously by 273/272, yielding a portent extension that's closely tied with ominous in Dirichlet badness. Generally, rodan's structure reminds me more about its portent aspect than its hemifamity aspect. And btw, prime 5 doesn't make much sense in portent without prime 11, so I'm against treating rodan's full 7-limit as much more important than its 11-limit, whereas 2.3.7 is too small a group that doesn't explain the whole interval table well and doesn't warrant a separate column.

::: Besides, 13/11 is at -9 gens. That's fairly few by the standards of such a complex temp as rodan, so I'd consider 11 and 13 somewhat paired too. So I'm seeing little sense in sorting the equivalents by prime groups at all.

::: However, 55/48 and 63/55 are too complex to be mentioned in the first ratio column because, if one wanted to distinguish them from 8/7, then they wouldn't use a gamelismic temp at all, would rather use some lehmerismic non-gamelismic temp that's way more accurate.

::: So I'd rather have 17-prime-limited 27-odd-limit equivalents in one column (with the sole exception of 96/49 that can't be simplified) and possibly more complex equivalents in another column.

::: [[User:VIxen|VIxen]] ([[User talk:VIxen|talk]]) 21:07, 19 June 2025 (UTC)

:::: It seems discussion on Discord strongly points to not wanting to see intervals like 63/55 in the same entry as 8/7, so once I finish the tuning spectrum I'll go back and get rid of a lot of those, though only in cells that have a simple (11-odd) LCJI interpretation. Further discussion can be had about your system, again it'll have to be discussed in the context of more temperaments than rodan. And yeah, thanks for elaborating on the fact that rodan is exceptional in how easily it extends to the full 17-limit. -- [[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 21:59, 19 June 2025 (UTC)

== Notation vs interval chain ==

Another thing I'm not so sure about is placing notation above interval chain. In my mind, the notation section will eventually address lots of different schemes (e.g. ups and downs, sagittal, and extended diatonic notation) so it will be longer than it is now, which will make it unwieldy. Furthermore, an effective discussion on notation should be based on the knowledge of how the temp maps intervals. It seems the only reason to present notation first is to introduce the "super" and "sub" categories in the interval table. I believe since the introduction is just a one-liner we could put it at the top of the interval chain. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:32, 17 June 2025 (UTC)

: Alright, that's fair. I'll move it to the position it is in e.g. [[Mothra]]. -- [[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 13:54, 17 June 2025 (UTC)

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 ::::::: Yeah, I'll likely continue to disagree. I side with Osmium in regard to 63edo. -- [[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 12:17, 16 June 2025 (UTC)
+:::::::: If you don't have anything to add, I'll wait for your revision of other sections first. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:32, 17 June 2025 (UTC)
+::: Re: 17-limit rodan. While it's less accurate than 13-limit one (not dramatically so - 17 is about as off as 7, though in the opposite direction), I'd like to highlight that it's generally much harder to approximate the full 17-limit well than the 13-limit. So temps should rather be compared with others of the same rank and group than with their own restrictions to smaller groups. Rodan is 2.1x Dirichlet-worse in the 13-limit than its leader abigail, but only 1.4x Dirichlet-worse in the 17-limit than its leader hendec. (Well, abigail is impractical, but harry is still 1.4x better than rodan in the 13-limit, and the latter is slightly worse than manna in both - by 1.08x and 1.14x.) Rodan is remarkably good for a 17-limit temp that 41 supports, is one of the few sensible ways of detempering 41 considering that the latter has relatively terrible prime 17.
+::: As for rodan's rank-3 detempers: while akea indeed extends poorly to the 17-limit, recall that rodan is portending akea, and portending does extend unambiguously by 273/272, yielding a portent extension that's closely tied with ominous in Dirichlet badness. Generally, rodan's structure reminds me more about its portent aspect than its hemifamity aspect. And btw, prime 5 doesn't make much sense in portent without prime 11, so I'm against treating rodan's full 7-limit as much more important than its 11-limit, whereas 2.3.7 is too small a group that doesn't explain the whole interval table well and doesn't warrant a separate column.
+::: Besides, 13/11 is at -9 gens. That's fairly few by the standards of such a complex temp as rodan, so I'd consider 11 and 13 somewhat paired too. So I'm seeing little sense in sorting the equivalents by prime groups at all.
+::: However, 55/48 and 63/55 are too complex to be mentioned in the first ratio column because, if one wanted to distinguish them from 8/7, then they wouldn't use a gamelismic temp at all, would rather use some lehmerismic non-gamelismic temp that's way more accurate.
+::: So I'd rather have 17-prime-limited 27-odd-limit equivalents in one column (with the sole exception of 96/49 that can't be simplified) and possibly more complex equivalents in another column.
+::: [[User:VIxen|VIxen]] ([[User talk:VIxen|talk]]) 21:07, 19 June 2025 (UTC)
+:::: It seems discussion on Discord strongly points to not wanting to see intervals like 63/55 in the same entry as 8/7, so once I finish the tuning spectrum I'll go back and get rid of a lot of those, though only in cells that have a simple (11-odd) LCJI interpretation. Further discussion can be had about your system, again it'll have to be discussed in the context of more temperaments than rodan. And yeah, thanks for elaborating on the fact that rodan is exceptional in how easily it extends to the full 17-limit. -- [[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 21:59, 19 June 2025 (UTC)
+== Notation vs interval chain ==
+Another thing I'm not so sure about is placing notation above interval chain. In my mind, the notation section will eventually address lots of different schemes (e.g. ups and downs, sagittal, and extended diatonic notation) so it will be longer than it is now, which will make it unwieldy. Furthermore, an effective discussion on notation should be based on the knowledge of how the temp maps intervals. It seems the only reason to present notation first is to introduce the "super" and "sub" categories in the interval table. I believe since the introduction is just a one-liner we could put it at the top of the interval chain. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:32, 17 June 2025 (UTC)
+: Alright, that's fair. I'll move it to the position it is in e.g. [[Mothra]]. -- [[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 13:54, 17 June 2025 (UTC)