Talk:Pajara

Minimax tunings

Although I'd like to have any excuse for the 7th harmonic to be more in tune, I don't think it makes much sense to call the tuning with eigenmonzo 7/6 the "7-odd-limit minimax".

If I understand correctly, this generator size was chosen because it balances 10/7, which is 17.5 cents flat, with 6/5, which is 17.5 cents sharp, but in pajara 10/7 is always 17.5 cents flat, so there is no point in balancing it. With the same reasoning you can say that the tuning where 5/4 is eigenmonzo, with a fifth of 706.843 cents, is the 7-odd limit minimax, because it balances the two worst intervals – 10/7 with 7/4, which are both, again, 17.5 cents sharp/flat respectively. If you take the term "minimax" literally, i.e. "The tuning in which the maximal error of any consonance is minimal", you get that any tuning between them is also a minimax, because in all of them the maximal error is 17.5 cents – that of 10/7.

I suggest labeling the tuning with eigenminzo 48/35 the 7-off limit minimax, because that's where 6/5 and 8/7 are balanced. That's also what you get if you take the minimum of the p-norm (Wikipedia) of the errors when p approaches infinity. I haven't checked but some other odd-limit minimax tunings may be changed too. Roeesi (talk) 13:56, 16 October 2022 (UTC)

Unclear/questionable paragraph

> Pajara has fundamentally different categories, as a conventional semifourth (~250 cents) is now a neutral interval of some variety.

Different from what? Is this talking about Pajara[10] or Pajara[12]? Afaik pajara doesn't have an exact hemifourth.

> A unique feature of pajara is [1–6/5–3/2–12/7] as an essentially tempered alteration to [1–5/4–3/2–7/4] where both the third and the harmonic seventh are flattened by a chroma.

Isn't it a feature of all jubilismic temperaments? Also "essentially tempered alteration" doesn't make sense to me.

FloraC (talk) 15:05, 2 August 2025 (UTC)

Pajara has "~900-1000c" as an interval category. The meaning of "essentially tempered alteration" is clear. Flattening these two intervals by the same amount cannot produce this chord in JI. And be free to rewrite that section in terms of jubilismic temperaments.

Additionally, you have been previously advised to discuss things on the talk page instead of force-removing them from articles. This does not mean do both at once. -- VectorGraphics (talk) 01:42, 3 August 2025 (UTC)

> Pajara has [~900–1000 ¢] as an interval category.

I suppose this is about Pajara[10], the 2L 8s scale. It's clearly not the case in Pajara[12].

> The meaning of "essentially tempered alteration" is clear.

I suppose the term was coined by analogy to essentially tempered chord, in which case, since it doesn't share the basics of essentially tempered chords, I'm afraid it's not a great idea, as Fred related to you on Discord.

> You have been previously advised to discuss things on the talk page instead of force-removing them from articles. This does not mean do both at once.

In fact, the advised cycle was edit–revert–discuss, becuz we obviously have the right to review your edits. This includes reversion.

FloraC (talk) 09:32, 3 August 2025 (UTC)

Redundant tables

There are two tables for the intervals of pajara (canonical 11-limit), just with different optimization. One of them should be removed.--Overthink (talk) 16:25, 28 September 2025 (UTC)

Patent vals

Planning to revert edit by FloraC that is justified by the entirely opinion-based statement that "patent vals are overrated". To many people, there is no reason to consider non-patent vals.

-- VectorGraphics (talk) 21:50, 22 November 2025 (UTC)

Still, 22edo is the only patent val supporting pajara with 11-odd-limit consistency, so those who don't consider non-patent vals would only use 22edo for a tuning, and not use 32edo or 54edo. --Overthink (talk) 21:52, 22 November 2025 (UTC)

Oops, forgot pajara is defined most simply in the 7-limit and not 11-limit. The only 7-odd-limit consistent EDOs supporting pajara are 10, 12, and 22, and someone who uses only patent vals probably cares about consistency, so wouldn't use anything else anyways. --Overthink (talk) 21:57, 22 November 2025 (UTC)

32edo and 54edo support pajara in the 7-limit. -- VectorGraphics (talk) 22:20, 22 November 2025 (UTC)

I have to agree that "being supported by all patent vals that support pajara save 12edo" seems like an arbitrary fact and not a specific advantage. Can you explain why it is useful? – Sintel🎏 (talk) 01:25, 23 November 2025 (UTC)

I honestly don't see why everyone sees patent vals as so arbitrary. To me the patent val essentially is the edo, non-patent vals really just exist to define wedgies/ET joins and that's it. -- VectorGraphics (talk) 06:44, 23 November 2025 (UTC)