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)

Naming, the eternal question

Once again, 'archy' was basically forced upon us by Gene, and the discussion goes back all the way to 2012, where there is a clear consensus that it is fine to call the 2.3.7 temperament "superpyth".

This also matches how people actually use the term, which is what we should be documenting! I'm tired of the idea that something is somehow 'canonical' just because it's how it was written on the wiki and nobody dared to change it before.

For reference: https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104738.html

– Sintel🎏 (talk) 17:10, 26 April 2025 (UTC)

Thanks for the context! I personally use "archy", and basically only a couple days ago I learned that "superpyth" IS actually the more common name. And personally, I agree: any piece in a temperament can just as much be said to be in that temperament's restriction, so there is no need to distinguish 2.3.5, 2.3.7, and 2.3.5.7 versions of a temperament if a canonical mapping exists for the full subgroup. --VectorGraphics (talk) 18:06, 26 April 2025 (UTC)

That's interesting. I had the opposite experience. Where did you learn about the name? – Sintel🎏 (talk) 20:11, 26 April 2025 (UTC)

I don't know. I guess it's because my basic conception of the temperament was in the 2.3.7 limit, and the full 7-limit extension was just an... extra thing defined for the purpose of having a full 7-limit version, basically, since you're probably not interested in the 5-limit in the first place if you're using (a strong extension of) archy.

Tuning spectrum error

I get why FloraC reverted the tuning spectrum changes, but isn't the diamond monotone still wrong? Tunings flatter than 22edo swap 7/5 and 10/7.--Overthink (talk) 22:02, 6 October 2025 (UTC)

You're right. Fixed. FloraC (talk) 11:38, 7 October 2025 (UTC)

Chords page

Many temperaments like meantone, orwell, and miracle have pages listing all of their chords, most often in the 11-limit. This temperament is important and needs to have its own chords page as well. As of now, I have made a draft at User:Overthink/Chords of superpyth.--Overthink (talk) 17:05, 10 November 2025 (UTC)

Chromatic alterations

In the chords section, it says:

1–9/8–9/7–3/2 chord may be altered to 1–9/8–11/8–3/2 (8:9:11:12), which is impressive-sounding, resembling a sus4 but with even more tension; it resolves quite nicely to 1–9/8–9/7–3/2.

The alteration from 9/7 to 11/8 is +16 - (+4) = +12 generators. The page should clarify what it means by a "chromatic" alteration. This was copied from the page for 17edo, where the chromatic semitone is 2 steps. The chromatic semitone is +7 generators, which would alter the chord to 1–9/8–7/5–3/2. In superpyth the most important interval for alterations is actually the limma, representing 256/243, 28/27, 36/35, and 81/80. Here, 1–9/8–9/7–3/2 still can't be altered to 1–9/8–11/8–3/2, but can instead be altered to 1–9/8–5/4–3/2 or 1–10/9–9/7–3/2. The info about chromatic alterations should make sense in superpyth, not 17edo.

Also, the 6:7:8 paragraph should be expanded to include larger chords like 28:36:42:49.

--Overthink (talk) 03:28, 3 January 2026 (UTC)