Talk:Superpyth

5-limit superpyth?

I'm confused. Why is there no mention of the actual superpyth comma on this page?

According to the commas pages, the superpyth comma is 20480/19683, [12 -9 1⟩, 68.719¢. There's no dedicated page for this comma yet, but that is how it appears on the PTS diagram, and also how it is recognized in Graham Breed's temperament tool: http://x31eq.com/cgi-bin/uv.cgi?limit=5&uvs=%5B12%2C-9%2C1%3E.

I see that on the Tour of Regular Temperaments page a distinction is drawn between superpyth and suprapyth; you maybe don't get superpyth until you enter the 7-limit. But then shouldn't the 5-limit comma [12 -9 1⟩ be called the "suprapyth comma"? And does that mean the PTS diagram and Graham's tool need to be updated?

But wait - the distinction between suprapyth and superpyth is different as described on this page, relating to something in the 11-limit!

Maybe there's a bit of a mess here that has arisen from a failure to establish consensus around these names over the years. To be clear: I don't have a horse in the race. I just came here to add the valid tuning range for the 5-limit superpyth temperament as seen on PTS, but I discovered that there wasn't even a 5-limit superpyth temperament entry (with generators, vals, etc.) existing in the first place. So many we need some general consistency, and also for that temperament to find some place to exist.

--Cmloegcmluin (talk) 19:06, 25 May 2021 (UTC)

You're wrong about superpyth vs suprapyth. The 5-limit temperament is called "superpyth", and so is the 7-limit one, and back in the day the accepted way to name things was that only one extension to the higher limit (in this case 11-limit) gets the unaltered name. Usually a rather high-accuracy/high-complexity one was chosen. So in this case there's a complex mapping of 11 that's called "superpyth" and a simpler, higher-error mapping of 11 that's called "suprapyth". —Keenan Pepper (talk) 22:24, 25 May 2021 (UTC)

Thanks Keenan. That's good to know in general about the back-in-the-day naming approach to temperament extensions. All the stuff you say about suprapyth and superpyth makes sense and I assume you're correct about all of that. Also, this page I just found seems to confirm what you say. In that case, then, the information I used to try to figure this all out myself — which I found on the Tour of Regular Temperaments page above (link again here for convenience) — is either incorrect, incomplete, or otherwise misleading. Unfortunately I'm not confident enough about this stuff to correct it myself.

As for the actual page we're on the discussion page for here, it seems like it should include a 5-limit superpyth section at the beginning and define superpyth up front as the temperament family defined by tempering out the superpyth comma, which is 5-limit. Right? At present the page seems to say that superpyth is defined by tempering out 64/63 and there's no mention of anything below 7-limit here which is pretty confusing to me. --Cmloegcmluin (talk) 01:52, 26 May 2021 (UTC)

I considered 5-limit superpyth and could enter the data for it. But actually, whenever you use superpyth you get septimal intervals first, by the fact that prime 7 is only 2 steps on the chain of fifths, and then prime 5 is much farther, making the 5-limit version quite unuseful.

I'm simply removing superpyth family in Tour of regular temperaments. There's virtually no alternative 7-limit extensions. FloraC (talk) 04:08, 26 May 2021 (UTC)

Including the 5-limit comma sounds great, go ahead and do it. But this whole topic is related to the change in perspective Mike Battaglia wants to make, where instead of the old way of thinking where 5-limit always comes before 7-limit, we instead consider the simpler commas and closer (lower number of generators) intervals in the temperament first. So in this case superpyth would be considered a 2.3.5.7 extension of a 2.3.7 temperament (64/63, the one now called "archy"), rather than a 7-limit extension of a 5-limit temperament. —Keenan Pepper (talk) 05:46, 26 May 2021 (UTC)

Thanks for making the changes, FloraC. And thanks for expanding on FloraC's explanation, Keenan; I wasn't totally sure what was meant and I was afraid for a moment that my understandings were destabilized again, but now I see exactly what's happening and why. That's pretty cool work y'all're doing! --Cmloegcmluin (talk) 15:01, 26 May 2021 (UTC)