Talk:Rodan

13-limit & overcomplex ratios

Imo the 13-limit should be in the main column of the interval table. It's not less accurate than the 11-limit at all and practically no competing extensions exist there. The 17-limit on the other hand is less accurate, so I gave it an extra column. Also I believe those two- or three-digit ratios should not be there when much simpler ones exist (superparticular commas & their inverses such as 160/81 should be exempt). For the classes where the simplest ratio is complex it may be reasonable e.g. for 50/27 it may be good to have 81/44 and 90/49 for reference. But why would one think of 55/48 or 63/55 when it's clearly 8/7? Those numbers are just noises that dilute the actually important information. FloraC (talk) 10:22, 15 June 2025 (UTC)

55/48 and 63/55 are in Mothra as well; 80/63 was the complex interval in the interval chain previously though it makes even less sense to keep that and not the 55-odds. The decision to make the cutoff at 11-limit vs 13-limit was somewhat of a close call; primarily 17-limit rodan doesn't really do much more damage on top of 13-limit either, so it feels weird for specifically 17-limit to get its own column but 13-limit to not. I don't think most of the ratios I kept are useless enough to be "noise", I think it's better to have complete odd limits in interval chains and it makes sense to consider at least 63-odd given the structure of slendric. -- Lériendil (talk) 13:10, 15 June 2025 (UTC)

Then I think 55/48, 63/55 and the like should get out of Mothra too. 80/63 was on this page, yes. I added it years ago. Now I want to remove it. Those ratios are absolutely overshadowed by the clarity of much simpler ones like 8/7 or 14/11. Even structurally, the comma steps should suffice for conceptualizing the temp and grabbing a feeling for it. To be realistic: 55/48 simply doesn't mean anything to anyone who hasn't memorized it's the difference between 5/4 and 12/11 or between 6/5 and 11/8, and there's very little reason to watch that difference cuz the two ratios have nothing in common in the first place. The difference between say 5/4 and 14/11 are more pertinent cuz the ratios sound similar enough to be put together and compared to each other.

87edo has a practically pure prime 13 whereas the prime 17 is several cents sharp with 17/14 and 21/17 being particularly off, so I'm afraid I still don't get why you set the cut between 11- and 13-limit rather than between 13- and 17-limit.

FloraC (talk) 14:35, 15 June 2025 (UTC)

I think these sorts of standards for intervals are present on other temperaments too; more temperaments have these kinds of extended odd-limits than not, and I personally value having all that information over the risk of "cluttering" - I've already accepted some compromises with you, such as only showing positive generator steps for long chains like this. If you want to make changes, it will have to be a more general discussion with the community rather than concerning a particular temperament page. I don't want to make a grandfathered exception for commas either. Odd 55 is very structural in slendric extensions anyhow.

As for 13-limit vs 17-limit, I'm not thinking in terms of 87edo exclusively. I think it's notable that the "chords of rodan" page focuses on 11-limit, and in general for slendric extensions 5 tends to partner with 11 and 13 with 17, since both 17/13 and 55/32 are easily accessible at low generators. I'd add that all edos between 41edo and 46edo tuning that support 7-limit rodan also support 11-limit rodan, and additional patent val deviations occur both at 13 and 17-limit. 13 and 17 are also distinctly more complex than 5 and 11 are. Though as I said, the big motivator is not wanting to leave 17 alone (which in addition to serving an aesthetic purpose also helps with removing the "clutter" you mentioned by shunting off ratios of higher limits that would otherwise go in the same column as the others) when it isn't clearly worse or structurally weird compared to lower primes; in rodan's case, the extensions to 11, 13, and 17 are all motivated by general tendencies for the tempering already established in the 7-limit. I'd even be willing to make the split between 7-limit and higher limits in order to more cleanly separate the complex ratios.

Although I suppose the issue is that this convention is used on temperaments where the extensions are significantly higher-damage than the core temperament in a lower limit/subgroup, and without clarification it might appear that rodan is one of those... -- Lériendil (talk) 15:48, 15 June 2025 (UTC)

The standards aren't as you described. Just take a look at the most typical and well-maintained temp pages: Magic, Sensi, Orwell, Porcupine, Negri, Miracle, and Valentine. Which has those two-digit ratios when there's LCJI/XLCJI ratios? Some of them have ~35/32 where ~11/10 and ~12/11 are, which I'm personally not fond of, but even that should be regarded as a carefully selected inclusion. So I'm afraid this isn't me making changes. Also, I don't consider comma steps being included an "grandfathered exception". They're genuinely useful information that readers can pull insight from.

The Chord of rodan page focusing on the 11-limit has no signficance. Most of the Chords of [temperament name] pages focus on the 11-limit. It's just an artifact from the original author of those pages. Your addition on the complexity of both 13 and 17 is a thing. You're right about that. Still, I'd like to reiterate the 17 is several cents sharp at the 13-limit optimum and tuning it closer to 46edo doesn't quite fix it. And by the logic of what tends to partner with what, remember rodan tempers out 896/891, which due to parapyth seems like a good enough bridge for 7, 11, and 13. Of course, I understand the aesthetical purpose and the idea of not leaving the 17-limit alone, but what clutters the table are the ratios of 49, 55, 63, …, not 13 or 17 really, which is why I suppose I don't feel so strongly about this issue compared to the one above. If anything, one single column for the 17-limit is an option.

FloraC (talk) 22:05, 15 June 2025 (UTC)

A lot of ratios of 49, 63, etc. are simple subgroup ratios. I disagree with a wholesale removal of those intervals. MCJI interpretations of LCJI ratios can come into sufficient use in complex chords, for one. I might clean things up once I revise other sections of the page, i.e. discard complex interpretations where simple ones exist, prioritizing harmonics and low-limit intervals when it comes to culling the complex ones. However, I personally believe those other temperament pages would benefit from more of these than currently exist, honestly, and if I had the power to revise their interval chains, I would do so. Also keep in mind that all of the pages you mentioned are very old articles, and I don't believe they're entirely reflective of current wiki consensus.

As for the 11 vs 13 vs 17-limit issue, I feel it's an arbitrary choice, and so I stand by a point that making a cutoff based on generator-complexity of primes makes sense here. All of 7-limit, 11-limit, 13-limit, and 17-limit rodan are pretty coherent structures in their own right, though I'd argue that 13-limit is the least "harmonically complete" (sensu Osmium) out of all of these. -- Lériendil (talk) 23:57, 15 June 2025 (UTC)

These temps have little MCJI capability anyway. The MCJI ratios aren't even distinguished from the LCJI/XLCJI ones. For example ~55/48 isn't even different from ~8/7 so the harmonic clarity of 8/7 dominates. Calling them simple subgroup ratios apparently gives them structural significance, but I think exactly the opposite cuz when a composer thinks about the major third in meantone for example they think about ~5/4, not ~81/64 even tho it structurally is. It being ~81/64 is a trivial piece of information cuz of course it's ~(9/8)². Similarly, ~64/49 is trivial cuz it's ~(8/7)² and more importantly no one thinks about the step as that when it's tempered to 17/13~21/16. ~64/49 is a result from some arithmetic; that's all. It doesn't add any insight. Compare it to comma steps such as ~56/55, which separates ~11/8 and ~7/5 with real consequences on the characteristics of the temp.

The articles I cited are the core-RTT and well-maintained ones. The fact that they are old but means they are the best models to follow. At least, they bear greater credibility than the recent niche turf made by inexperienced editors that few other editors will ever notice and care enough to rectify, such as CompactStar's non-octave temps, Vector's Fendo, Ntiscifer or less peculiarly the pre-cleanup version of Ultrapyth. Again, I can't emphasise enough how much concise and clean tables enhance reading experience and make readers stay (I might wanna mention the interval table of 58edo has been enjoyable to read while Godtone's table for 63edo has driven me nuts; this could have to do with how our brains are built differently).

Given all that, I still think we should generally only present the harmonically significant intervals and structurally significant comma steps in the interval tables.

I'd argue 13-limit rodan is the most harmonically coherent out of all of the extensions thanks to parapyth/pele/sensamagic, but that's really an insignificant point now, given there are plenty of other reasons that help to determine where to set the cut.

FloraC (talk) 10:51, 16 June 2025 (UTC)

Yeah, I'll likely continue to disagree. I side with Osmium in regard to 63edo. -- 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. 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.

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. -- 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. 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. -- Lériendil (talk) 13:54, 17 June 2025 (UTC)