Template talk:Infobox ET: Difference between revisions

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:::: I guess because the 41 fifths doesn't close at the octave in 53edo. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:12, 3 December 2020 (UTC)

Hmm... Perhaps the type tempered fifth- particularly for those EDO fifths that more closely approximate the [[3/2]] just fifth than their neighbors- should have categories involving the 2.3 comma that's tempered out- e.g. the type of fifth that 53edo has should just be called "Mercator" because [[Mercator's comma]] is tempered out. Similarly, the type of fifth that ~~53edo~~ has should just be called "Pythagorean" because the [[Pythagorean comma]] is tempered out. I hope this is at least a start... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:52, 4 December 2020 (UTC)

Hmm... Perhaps the type tempered fifth- particularly for those EDO fifths that more closely approximate the [[3/2]] just fifth than their neighbors- should have categories involving the 2.3 comma that's tempered out- e.g. the type of fifth that 53edo has should just be called "Mercator" because [[Mercator's comma]] is tempered out. Similarly, the type of fifth that 12edo has should just be called "Pythagorean" because the [[Pythagorean comma]] is tempered out. I hope this is at least a start... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:52, 4 December 2020 (UTC)

: "Similarly, the type of fifth that 53edo has should just be called "Pythagorean"" - did you mean 12edo? Every edo tempers out only one 2.3 comma (not counting multiples of this comma). For N-edo, the comma's 3-exponent is ±N/GCD(M,N), where the best 3/2 is M\N. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 22:38, 7 December 2020 (UTC)

:: Yes, I did mean that the type of fifth that 12edo has should just be called "Pythagorean". I fixed that in the above comment. Thank you. I don't know how I botched that. Unfortunately, I don't see what you're getting at with much of the rest of your comment. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 08:00, 18 December 2020 (UTC)

I agree with FloraC, fifth type is not rigorously defined. Every comma that contains primes 2 and 3 and only 1 other prime implies a fifth size, or a narrow range of fifth sizes. But the exact range is disputable, and also there are an infinite number of possible commas. There is already a lengthy table of commas on every edo page. By Xenwolf's "indisputable and concise" rule, we should not list the fifth type. I propose there only be fifth size in edosteps and cents, e.g. for 24edo, "14\24 700¢". The shorter the better. We could possibly have IlL's categories of mavila, 7edo, hypopent, (just 3/2), hyperpent, 5edo, father. (BTW these are quite similar to my edo categories superflat, perfect, diatonic, pentatonic and supersharp.) But once you know the fifth size, it's easy to tell what category it's in. The 7edo category is obvious -- the edo must be a smallish (< 50) multiple of 7, and the 5th must be 680-something cents. The 5edo category is even more obvious. Mavila and father are also obvious, the 5th is < 680¢ or > 720¢. It's not like there are edos who's fifths are only a cent or two away from 4\7 or 3\5. Hypopent and hyperpent are mostly easy to tell too, as long as you know how many cents 3/2 is. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 22:38, 7 December 2020 (UTC)

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 :::: I guess because the 41 fifths doesn't close at the octave in 53edo. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:12, 3 December 2020 (UTC)
-Hmm...  Perhaps the type tempered fifth- particularly for those EDO fifths that more closely approximate the [[3/2]] just fifth than their neighbors- should have categories involving the 2.3 comma that's tempered out- e.g. the type of fifth that 53edo has should just be called "Mercator" because [[Mercator's comma]] is tempered out.  Similarly, the type of fifth that 53edo has should just be called "Pythagorean" because the [[Pythagorean comma]] is tempered out.  I hope this is at least a start... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:52, 4 December 2020 (UTC)
+Hmm...  Perhaps the type tempered fifth- particularly for those EDO fifths that more closely approximate the [[3/2]] just fifth than their neighbors- should have categories involving the 2.3 comma that's tempered out- e.g. the type of fifth that 53edo has should just be called "Mercator" because [[Mercator's comma]] is tempered out.  Similarly, the type of fifth that 12edo has should just be called "Pythagorean" because the [[Pythagorean comma]] is tempered out.  I hope this is at least a start... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:52, 4 December 2020 (UTC)
 : "Similarly, the type of fifth that 53edo has should just be called "Pythagorean"" - did you mean 12edo? Every edo tempers out only one 2.3 comma (not counting multiples of this comma). For N-edo, the comma's 3-exponent is ±N/GCD(M,N), where the best 3/2 is M\N. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 22:38, 7 December 2020 (UTC)
+:: Yes, I did mean that the type of fifth that 12edo has should just be called "Pythagorean".  I fixed that in the above comment.  Thank you.  I don't know how I botched that.  Unfortunately, I don't see what you're getting at with much of the rest of your comment. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 08:00, 18 December 2020 (UTC)
 I agree with FloraC, fifth type is not rigorously defined. Every comma that contains primes 2 and 3 and only 1 other prime implies a fifth size, or a narrow range of fifth sizes. But the exact range is disputable, and also there are an infinite number of possible commas. There is already a lengthy table of commas on every edo page. By Xenwolf's "indisputable and concise" rule, we should not list the fifth type. I propose there only be fifth size in edosteps and cents, e.g. for 24edo, "14\24 700¢". The shorter the better. We could possibly have IlL's categories of mavila, 7edo, hypopent, (just 3/2), hyperpent, 5edo, father. (BTW these are quite similar to my edo categories superflat, perfect, diatonic, pentatonic and supersharp.) But once you know the fifth size, it's easy to tell what category it's in. The 7edo category is obvious -- the edo must be a smallish (< 50) multiple of 7, and the 5th must be 680-something cents. The 5edo category is even more obvious. Mavila and father are also obvious, the 5th is < 680¢ or > 720¢. It's not like there are edos who's fifths are only a cent or two away from 4\7 or 3\5. Hypopent and hyperpent are mostly easy to tell too, as long as you know how many cents 3/2 is. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 22:38, 7 December 2020 (UTC)