Talk:Fokker block

Math styles

This is what I'm sticking to:

• Matrices should be uppercase and roman italic, e.g. V V.
• Vectors or matrix rows should be roman bolded roman, e.g. v v.
• Scalar variables or matrix/vector entries should be italic, e.g. n.
• Letter-denoted functions should generally be italic, e.g. f (x), except when interpreted as vectors, e.g. v (c).
• Word-denoted functions should be roman, e.g. log (x).
• Use <math> $$ for "newline math" (in contrast to inline math).

Good enough?

And btw, is there a reason for the S[i] to have brackets instead of parentheses? I see this is used to denote index offset.

FloraC (talk) 10:28, 15 January 2021 (UTC) (updated FloraC (talk) 10:31, 22 March 2025 (UTC))

@FloraC: Yes it looks better in the rendered HTML page, but it looks worse in wikitext because it's to much control chars (ticks and tags) between the meaningful content. As I know, math can be configured to use text output for simple formatting. (Another option would be to roll our own template, module whatever to transform ^ and _ in sup and sub tags.) For example, here is what I see in the first paragraph of the current version of section "Second definition of a Fokker block":

Let us define a new set of vals by u<sub>''k''</sub> = ''P''v<sub>''k''</sub> - v<sub>''k''</sub> (2) v<sub>''n''</sub>. To apply these vals 
to S[''i''], note first that floor ((''e''<sub>''n''</sub>''i'' + ''a''<sub>''n''</sub>)/''P'') = floor (''i'' + ''a''<sub>''n''</sub>/''P'') 
= ''i'', so that v<sub>''n''</sub> (S[''i'']) = ''i''. Hence u<sub>''n''</sub> (S[''i'']) = ''P''v<sub>''n''</sub> - v<sub>''n''</sub> (2) 
v<sub>''n''</sub> = 0, while for ''k'' < ''n'', u<sub>''k''</sub> (S[''i'']) = ''P''v<sub>''k''</sub>(S[''i'']) - v<sub>''k''</sub> (2) 
''i''. Since ''x'' - 1 < floor(''x'') ≤ ''x'', we have (''e''<sub>''k''</sub>''i'' + ''a''<sub>''k''</sub>)/''P'' - 1 < floor 
((''e''<sub>''k''</sub>''i'' + ''a''<sub>''k''</sub>)/''P'') ≤ (''e''<sub>''k''</sub>''i'' + ''a''<sub>''k''</sub>)/''P'', so that 
''e''<sub>''k''</sub>''i'' + ''a''<sub>''k''</sub> - ''P'' < ''P''v<sub>''k''</sub> (S[''i'']) ≤ ''e''<sub>''k''</sub>''i'' + 
''a''<sub>''k''</sub>. Since ''e''<sub>''k''</sub> = v<sub>''k''</sub> (2), this gives us ''a''<sub>''k''</sub> - ''P'' < 
u<sub>''k''</sub> (S[''i'']) ≤ ''a''<sub>''k''</sub>. This means that for each of the vals u<sub>''k''</sub>, the scale is mapped to a set of 
''P'' integers.

I hope you see my point. Maybe this is exactly what Inthar expresses in the proposal Xenharmonic Wiki:Things to do#Improve accessibility of wiki and present info in a non-technical way (BTW: I'm sure we need a shortcut for this, let's try Xenwiki:Accessibility). --Xenwolf (talk) 12:39, 16 January 2021 (UTC)

Yeah and it was super tedious to work on, and hopefully no one is gonna work on it anymore. I'm considering using more newline maths.

I believe Inthar proposed a different problem though. FloraC (talk) 16:07, 16 January 2021 (UTC)

Flora, do you feel able to explain some of the mathematics in the wiki to a non-mathematician audience. For instance, what does wedgie mean? I tried to read about wedge products but finally gave up. --Xenwolf (talk) 11:37, 17 January 2021 (UTC)

Unfortunately, the only thing I know about wedgies is an ad hoc method to calculate them. FloraC (talk) 16:32, 17 January 2021 (UTC)

Rename to "periodicity block"?

It doesn't seem like there are many things called "periodicity block" in general, so I think it would be more logical to simply use the term "periodicity block" chosen by Fokker himself. There doesn't seem to be a problem with the term "periodicity block" by itself, except maybe that there's potentially a better option out there that hasn't been considered yet (or hasn't been considered here at least), and I don't think we need to add Fokker's name to make it somehow clearer. Wikipedia seems to prefer "Fokker periodicity block", but I couldn't find the reasoning for this choice.

That said, it's a quite low priority issue to me, but if further work is going to be done to improve this page, I'd like to see the occasion taken to choose descriptive terms over ones based on people's names, especially for fundamental theory concepts like this one. --Fredg999 (talk) 04:46, 22 March 2025 (UTC)

I agree with this change, ABSOLUTELY. Heck, let's go ahead and find other stuff like this that could do with more descriptive names (I'd keep "monzo" though, since it's too ingrained). --VectorGraphics (How do I add a timestamp)

The math

"Do not edit math you clearly do not understand." Well, if I do not understand the math even after watching two 3B1B videos and stepping through it meticulously, then maybe the math is the problem. -- VectorGraphics (talk) 16:29, 25 June 2025 (UTC)

Most of the math is due to GWS, who is good at math. Math is either correct or incorrect; there is hardly a third category for "unclear" unless you're Mochizuki. I would guess that this math in particular is correct. --hkm (talk) 16:46, 25 June 2025 (UTC)

This math in particular makes a couple of logical leaps; these leaps were probably filled better by articles which this one linked to when all of the wiki was more math-focused. --hkm (talk) 17:00, 25 June 2025 (UTC)

To understand the section about finding the epimorph val, do cofactor expansion on the top row, then realize that the monzos when stripped of (for example) their first coordinate span ALL the intervals which are octave-equivalent to the origin. In the example given, they span 1/22 of all the intervals since the determinant of those three monzos is 22, so 1/22 of all intervals must be octave-equivalent to the origin; thus our rank-1 temperament must map 2/1 to 22 steps. --hkm (talk) 17:08, 25 June 2025 (UTC)

This page is just bad, it should be rewritten from the ground up. In the meantime, the article on wikipedia is much better. – Sintel🎏 (talk) 18:50, 25 June 2025 (UTC)

What do you think of moving the mathematics section to a separate article called Mathematical theory of Fokker blocks, similar to the Mathematical theory of regular temperaments article, so that we can start over? FloraC (talk) 18:55, 25 June 2025 (UTC)

Sure, sounds like a decent start. I think the content of this page is actually pretty interesting, but after not having read it for a while it takes me like 20 minutes to even understand all the definitions so I can read through it. I guess for the new page we can literally just follow the Wikipedia outline, or the original article. – Sintel🎏 (talk) 19:03, 25 June 2025 (UTC)

I agree. We should also attempt to weed out wedgies from the mathematics section, as per Operation Loosen Underpants. -- VectorGraphics (talk) 22:49, 27 June 2025 (UTC)

A fresh start

Thanks FloraC for going ahead and making the move. I tried to make a starting point for the new article, following the example given in the Wikipedia article. There's lots of examples and illustrations to make! We can start by trying to synthesize the original article, Erlich's introduction and the page on Wikipedia (which is surprisingly good actually).

More specifically, what's missing currently is a proper treatment of domes/modes and how to find them. Following Erlich, I think we should first give a graphical example in 2D that shows how moving the parallelogram gives you different resulting scales. Later we can move some things back from the old article, like how to find the intervals from the change of basis matrix.

– Sintel🎏 (talk) 20:05, 29 June 2025 (UTC)

Weak vs strong

So-called "weak" Fokker blocks are Fokker blocks. In practice this rarely matters, and you can bring it up when it does. The todo note isn't helpful as it distracts from the articles content.

Why should we bring this up here? It is not discussed on the page for constant structure either, but it applies very much in the same way. Another example, when discussing the fact that meantone generates a diatonic scale, nobody really cares that it may produce a scale with negative steps if I were to pick a particularly awful generator tuning. It's just pedantry.

– Sintel🎏 (talk) 22:32, 29 June 2025 (UTC)

The note's here to warn readers that the page is wrong: the second and third paragraphs in "Theory" are incorrect if we say that weak Fokker blocks are Fokker blocks. If it's not important to talk about strong and weak Fokker blocks on this page, those paragraphs can be deleted. --hkm (talk) 02:04, 30 June 2025 (UTC)