Talk:Kite's 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)