User talk:Frostburn/Geometric algebra for regular temperaments

Good stuff

The notion of using geometric algebra/Clifford algebra is pretty interesting - something we've talked about a little bit before but didn't get very far on. But yeah, the basic idea is that if you have the TE norm (which is just a scaled L2 norm) and the wedge product, those two automatically create a Clifford algebra. Thus, in a certain sense we already are using a Clifford algebra; we just haven't been doing that much with the Clifford product, which is basically the sum of the wedge product and the inner product. It probably makes the most sense to do this with vals, because in the space of monzos we tend to use the Tenney (scaled L1) norm instead. The L2 norm leads to some strange results on monzos. But it's still kind of interesting to look at it for vals, where the TE norm is a bit more natural.

I would not worry all that much about fitting into the "Douglas Blumeyer and Dave Keenan's Intro to exterior algebra for RTT" page; that's just one writeup of the material and it uses terminology that differs from most of the rest of the Wiki. Still a useful read though so we left it up on the main Mathematical Theory page. Mike Battaglia (talk) 23:15, 23 May 2022 (UTC)

Syntax hint

MediaWiki - the software that Wikipedia and this wiki is using - has an inter-wiki feature which eases linking to some dedicated external sites. So Wikipedia articles can be linked with the internal link syntax plus the Wikipedia: prefix (can also be lowercase), in the actual case I saw on your article it can be done like this: Wikipedia:Geometric algebra. BTW: Welcome to the XenWiki! Best regards --Xenwolf (talk) 17:37, 18 May 2022 (UTC)

Exterior algebra page

Hello Frostburn! Yes, welcome to the wiki.

Are you aware of the page Douglas Blumeyer and Dave Keenan's Intro to exterior algebra for RTT? I expect your content will overlap significantly with that effort. I'm curious if you're interested in editing or expanding that page, or if not, how you plan for work to contrast with it. --Cmloegcmluin (talk) 21:29, 18 May 2022 (UTC)

Thank you for the tips

I wasn't aware that Wikipedia links get special treatment. I'll fix my links in the draft I'm working on.

I'm aware of the various pages for algebra and RTT, but I'm still only a newbie getting into temperaments and geometric algebra. So that awareness hasn't matured into actually reading those pages. I'm doing write-ups to organize my thoughts and learn by doing. I'm currently interested in making open source software for microtonal musicians. I'm a physicist by education so I don't have too much mathematical rigor and don't yet feel comfortable making big contributions. I can provide feedback on your work if requested, but as said I'm mostly interested in the math for software's sake.

--Frostburn (talk) 15:29, 19 May 2022 (UTC)