Talk:Douglas Blumeyer's RTT How-To: Difference between revisions

← Older edit

VisualWikitext

@@ Line 12: / Line 12: @@
 ::::: Thanks for that. I tried using this star instead and it does seem to still work on my mobile device. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 17:01, 21 May 2021 (UTC)
+== "regular" ==
+The article says:
+> We’ve made it to a critical point here: we are now able to explain why RTT is called “regular” temperament theory. Regular here is a mathematical term, and I don’t have a straightforward definition of it for you, but it apparently refers to the fact that all intervals in the tuning are combinations of only these specified generators. So there you go.
+As far as i know, regular here isn't a mathematical term at all. (If I'm wrong please point me to the right definition!) It seems like it was chosen to mean "linear" but "linear temperament" already means something else.
+- [[User:Sintel|Sintel]] ([[User talk:Sintel|talk]]) 21:11, 30 December 2021 (UTC)
+: Interesting. Back in April I asked for the meaning of the "regular" in RTT and I got various answers. From Keenan Pepper, a couple:
+: 'It's regular because wherever two tempered intervals represent the same JI interval, they are exactly the same size. This means the temperament is an abelian group and the mapping is a morphism.'
+: 'Once a tuning of each generator is provided the tuning of any interval can be computed as an integer linear combination of generator tunings. This property that all intervals are linear combinations of the generators is in fact what makes a temperament "regular".'
+: Then, from Paul Erlich:
+: 'Every generator always appears in (close enough to) the same size; and every instance of a prime is arrived at via generators in EXACTLY the same way.'
+: to which Keenan replied:
+: 'Oh, this is interesting because it's slightly different from the definition I gave. I suppose what I defined could be called a "regular tuning of a regular temperament". An example that passes your definition but not mine is a well-temperament of 12edo. The generators are slightly different sizes, but the mapping is still regular (it's only the realization in tuning that is irregular).'
+: And then Mike Battaglia said:
+: 'Keenan Pepper I don't think the tunings have to be the same size; rather the mapping has to be the same. Graham Breed and I were just talking about this'
+: and Paul felt that was the same thing as his definition.
+: So maybe it's not a mathematical term after all. Probably this tidbit could stand to be updated. Thanks for bringing this to my attention. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 04:50, 31 December 2021 (UTC)