Talk:31st-octave temperaments

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sad enfactoring?

Trying to understand this statement in the Birds section: "It also tempers out the 31-7 comma, but sadly, combining the two commas leads to torsion."

When the commas listed — 3136/3125 and 823543/819200 — are expressed as the comma basis for this temperament, we get [6 0 -5 2 [-15 0 -2 7]. This matches with the mapping provided [31 49 72 87] 0 1 0 0], i.e. it is its null-space. In canonical form this mapping and comma basis are [31 0 72 87] 0 1 0 0] and [-72 0 31 0 [-33 0 13 1], respectively.

Elsewhere description claims that this temperament could be defined by tempering out the 31-5 and the 31-7 commas, were it not for torsion. I don't know what is "sad" about the torsion. Simply remove it by defactoring, right? When these two commas are expressed as a comma basis for a temperament it looks like [-87 0 0 31 [72 0 -31 0], and then if we put it in canonical form (which defactors it), we get the same thing [-72 0 31 0 [-33 0 13 1] as what's there.

So can't we just remove the part where it says "but sadly, combining the two commas leads to torsion"? Otherwise, can we clarify what is sad?

If this clause is retained, then I have a revision request. As you can read about on the page re: defactoring, I am recommending we not use the word "torsion" for temperaments, but only for periodicity blocks. A temperament may "be enfactored", but it shouldn't be said to "have torsion". --Cmloegcmluin (talk) 16:24, 30 September 2021 (UTC)

I don't understand that part either. That said, this entire page may use some improvements. FloraC (talk) 16:56, 30 September 2021 (UTC)

Bold lemma?

If there is no way to present the lemma (in bold) in the introduction, this seems to indicate a problem. Any ideas about that? --Xenwolf (talk) 22:21, 23 February 2022 (UTC)

Plenty of Wikipedia articles don't have a bolded lemma (e.g. Wikipedia: List of compositions by Johann Sebastian Bach). It's more common when the article is not about a concept but about a collection. FloraC (talk) 10:01, 24 February 2022 (UTC)
I saw that the page was moved to this lemma and wondered if the current name is really the best choice. So I took a look at the article and found the term "31st octave" neither mentioned nor explained here. To be more specific, I have no trouble with the word "temperaments" at all, but simply wish that some explanation of the term "31st octave" would come out of the article. Thank you in advance for this! --Xenwolf (talk) 12:49, 24 February 2022 (UTC)
Thanks for helping me understand. BTW: Did you know that subpages are disabled for the article namespace? So even "1/31 octave" would have been possible. Maybe for English natives this isn't a problem, but I'm often confused by the duality of ordinals and fractions. --Xenwolf (talk) 13:11, 24 February 2022 (UTC)
Yea I'm aware. This page was moved following another similar page (→ 26th-octave temperaments). I think either title would be ok, but changes must be made to both pages. FloraC (talk) 16:25, 24 February 2022 (UTC)