Talk:17L 2s: Difference between revisions

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:: I also noticed that problem with 36/25 (unless you make a nonstandard subgroup notation extension that lets you use both a prime and a multiple of that prime or both flat and sharp versions of that prime, depending upon a simple selection rule). Probably should add a note about that to what I proposed above. With respect to fitting into the range, if you DON'T do that (and depending upon generator constitution, often even if you do), you end up with an awful lot of EDOs where the generator doesn't map correctly — for instance, both 23/16 and 13/9 have spotty mapping in this tuning table (although at least covering enough EDOs to be useful for a decent subset of it), while the Alphatricot generator doesn't map correctly for anything other than a very narrow band close to 53edo. I've been working on this under Musical Mad Science under my user page (but it's ''nowhere near ready'' to put here or on any other official page), and found that 62/43 maps correctly to almost everything (and the very small number of exceptions are candidates for wart rescue). [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:25, 1 May 2025 (UTC)

==== Proposed text to add to introduction section (revised) ====

From a regular temperament theory perspective, this scale is notable for corresponding to the mega chromatic scale of the [[Alphatricot family]] temperaments. Unfortunately, its generator does not have a convenient rational representation — the simple ratios [[23/16]] and even [[36/25]] are off-scale flat, while the simple ratio [[13/9]] is off-scale sharp. The Alphatricot family uses ~[[59049/40960]] as a generator. Note that although the comparitively simple 36/25 is just barely off-scale flat (being near just in the equalized endpoint [[19edo]]), using it effectively depends upon direct approximation of the 25th harmonic, while one might also need to use the 5th harmonic as opposed to its square, requiring the use of a 2.3.5♯.5♭ (or 2.3.5.25) subgroup temperament that includes a rule on when to use each flavor of 5th harmonic (or when to use the 5th harmonic and when to use direct approximation of the 25th harmonic).

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:14, 2 May 2025 (UTC)

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 :: I also noticed that problem with 36/25 (unless you make a nonstandard subgroup notation extension that lets you use both a prime and a multiple of that prime or both flat and sharp versions of that prime, depending upon a simple selection rule).  Probably should add a note about that to what I proposed above.  With respect to fitting into the range, if you DON'T do that (and depending upon generator constitution, often even if you do), you end up with an awful lot of EDOs where the generator doesn't map correctly &mdash; for instance, both 23/16 and 13/9 have spotty mapping in this tuning table (although at least covering enough EDOs to be useful for a decent subset of it), while the Alphatricot generator doesn't map correctly for anything other than a very narrow band close to 53edo.  I've been working on this under Musical Mad Science under my user page (but it's ''nowhere near ready'' to put here or on any other official page), and found that 62/43 maps correctly to almost everything (and the very small number of exceptions are candidates for wart rescue).  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:25, 1 May 2025 (UTC)
+==== Proposed text to add to introduction section (revised) ====
+From a regular temperament theory perspective, this scale is notable for corresponding to the mega chromatic scale of the [[Alphatricot family]] temperaments. Unfortunately, its generator does not have a convenient rational representation &mdash; the simple ratios [[23/16]] and even [[36/25]] are off-scale flat, while the simple ratio [[13/9]] is off-scale sharp. The Alphatricot family uses ~[[59049/40960]] as a generator. Note that although the comparitively simple 36/25 is just barely off-scale flat (being near just in the equalized endpoint [[19edo]]), using it effectively depends upon direct approximation of the 25th harmonic, while one might also need to use the 5th harmonic as opposed to its square, requiring the use of a 2.3.5♯.5♭ (or 2.3.5.25) subgroup temperament that includes a rule on when to use each flavor of 5th harmonic (or when to use the 5th harmonic and when to use direct approximation of the 25th harmonic).
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:14, 2 May 2025 (UTC)