Talk:Color notation/Temperament names

both "contorsion" and "torsion"?

I disagree with the idea that a temperament can meaningfully have both contorsion and torsion. Actually I think that torsion only applies to periodicity blocks and doesn't exist for temperaments because they temper commas out. I recently published a new page here with more details: https://en.xen.wiki/w/Canonical_form#the_pathology_of_enfactoredness I'm interested in your thoughts on it when you get a chance. --Cmloegcmluin (talk) 19:19, 29 September 2021 (UTC)

Sorry, I didn't write that passage very well. I have since edited it. I meant that having both contorsion and torsion is a problem to be avoided. --TallKite (talk) 00:59, 30 September 2021 (UTC)

Okay, I see the edit. I think you've misunderstood my concern, though. It probably comes as a surprise because it runs counter to prevailing thinking about this topic. But Dave Keenan and I did a ton of research and discussion on this recently and we've come to the conclusion that temperaments cannot have torsion. It is not a problem to avoid, but an impossibility. Certainly, you can take a comma like [-4 4 -1⟩ and multiply it by 2 to get [-8 8 -2⟩. Our point is that while that has an effect on periodicity blocks, it has no effect on temperaments, because tempering out [-8 8 -2⟩ implies tempering out [-4 4 -1⟩. On the other hand, temperaments can have contorsion, because [24 38 56⟩ does mean something musically different in RTT than [12 19 38⟩; however, because temperaments can't have torsion, we don't think it makes sense to call this effect "contorsion"; we call it "enfactoring" instead. Actually, the section of my new page I linked you to in the previous post may not have been the best introduction to our finding. Please try this one instead: Canonical_form#enfactored.2C_to_replace_contorted --Cmloegcmluin (talk) 01:20, 30 September 2021 (UTC)

I totally agree about torsion. Been thinking that way for years. You can't hear periodicity blocks! Someone explained to me once that it's mathematically possible to temper the two [-4 4 -1⟩'s differently, but that's silly. That would be an irregular temperament, but the "R" in RTT means regular.

I agree about contorsion too. Contorsion is like saying that all 12edo music is really in 24edo, but half the notes don't happen to get used. :)

As for this article, sure, torsion in the comma list (in the sense that the pivot product is bigger than it needs to be) is not at all a problem musically or mathematically. Rule #2 says to avoid torsion only as a means to getting a canonical name for the temperament.

I will read your articles when I get a chance. --TallKite (talk) 01:46, 30 September 2021 (UTC)

This conversation moved here: User_talk:TallKite#having_torsion_vs._being_enfactored --Cmloegcmluin (talk) 14:54, 1 October 2021 (UTC)