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.
- 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". 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. -- Lériendil (talk) 15:37, 15 June 2025 (UTC)