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 simpler and more complex ratios. -- Lériendil (talk) 15:37, 15 June 2025 (UTC)