Talk:Interval of equivalence: Difference between revisions
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: That term also happens to be used commonly to refer to an octave flat or sharp by a comma-sized interval, so that conflicting usage should at least be mentioned if this term is added to the equave article. --[[User:CompactStar|CompactStar]] ([[User talk:CompactStar|talk]]) 08:20, 6 March 2024 (UTC) | : That term also happens to be used commonly to refer to an octave flat or sharp by a comma-sized interval, so that conflicting usage should at least be mentioned if this term is added to the equave article. --[[User:CompactStar|CompactStar]] ([[User talk:CompactStar|talk]]) 08:20, 6 March 2024 (UTC) | ||
: I added ''formal octave'' (from Scala mostly) and ''pseudo-octave'', with a note about CompactStar's comment, as well as ''formal fifth'' for [[generator]], with new redirects to go with all that. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 05:15, 7 March 2024 (UTC) | : I added ''formal octave'' (from Scala mostly) and ''pseudo-octave'', with a note about CompactStar's comment, as well as ''formal fifth'' for [[generator]], with new redirects to go with all that. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 05:15, 7 March 2024 (UTC) | ||
== "Tempering" equaves == | |||
This passage doesn't really make sense, and would be really confusing to someone just learning RTT. I vote it gets removed. | This passage doesn't really make sense, and would be really confusing to someone just learning RTT. I vote it gets removed. | ||
"If intervals and notes an equave apart are considered to be wholly equivalent to one another, and are collapsed down to a single representative interval (as is usually the case when constructing lattices), this is mathematically identical to tempering out the equave, as it is an interval separating notes that are treated as the same thing. This gives us a tool to formalize the notion of equivalence in the language of regular temperament theory – for example, octave-equivalent meantone is a rank-1 temperament that tempers out 81/80, but also "tempers out" 2/1 (although the kinds of "tempering" are treated completely differently musically, both define an equivalence class of intervals)" | "If intervals and notes an equave apart are considered to be wholly equivalent to one another, and are collapsed down to a single representative interval (as is usually the case when constructing lattices), this is mathematically identical to tempering out the equave, as it is an interval separating notes that are treated as the same thing. This gives us a tool to formalize the notion of equivalence in the language of regular temperament theory – for example, octave-equivalent meantone is a rank-1 temperament that tempers out 81/80, but also "tempers out" 2/1 (although the kinds of "tempering" are treated completely differently musically, both define an equivalence class of intervals)" | ||
--[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 20:58, 24 April 2025 (UTC) | --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 20:58, 24 April 2025 (UTC) | ||
: I've removed it for now. There is an interesting interpretation in terms of quotient groups, but really it is a completely different interpretation from what we understand as tempering, even if it might (mathematically) look similar. | |||
:– [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 21:01, 24 April 2025 (UTC) | |||