TallKite

== having torsion vs. being enfactored ==

I'm glad you agree about torsion. I like the way you explained it, pointing to the name of RTT itself. As a nit-pick, though, I can't agree with the statement that "you can't hear periodicity blocks". That wasn't what I was trying to say. In fact, I was trying to say something like the opposite. My point was that using e.g. {{vector|-8 8 -2}} instead of {{vector|-4 4 -1}} has an audible effect on periodicity blocks but not on temperaments. For a periodicity block, it causes the size of the scale to double, but half of the notes are a redundant copy of the other half, simply offset. Because this is a real audible effect, and I understand there are maybe even some uses for it or cases where it's desirable, it has a name, "torsion". But for a temperament, though, where the comma is by definition tempered out, there is no audible effect, and thus using {{vector|-8 8 -2}} instead of {{vector|-4 4 -1}} is meaningless. It's just pathological enfactoring that is removed when the comma basis is put into canonical form.

:: Ah, I see. What you're talking about is completely different. I started making some corrections to my previous statements before I'd noticed you'd replied already. So I'm going to go ahead and make those rather than leave the misinformation up and correct it here, if that's okay (my incorrectness is still preserved in the edit history). I think I probably shouldn't try to say more about the Lp norms yet until I have a better handle on them, so never mind for now, especially since it's irrelevant to your purpose anyway. Sorry for the confusion. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 23:42, 22 January 2022 (UTC)