TallKite
Joined 19 September 2018
Cmloegcmluin (talk | contribs) →Chessboard distance: new section |
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Anyway, just thought you might like to revise that original paragraph to use established nomenclature, or at least reference it! You may not have been aware of it; I only just learned it myself a few months back. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:04, 19 January 2022 (UTC) | Anyway, just thought you might like to revise that original paragraph to use established nomenclature, or at least reference it! You may not have been aware of it; I only just learned it myself a few months back. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:04, 19 January 2022 (UTC) | ||
: Hmm, interesting. But actually, what I'm proposing is different from all of these. In the 2-D case I propose a shearing so that the rectangular lattice becomes triangular. | |||
{| class="wikitable" | |||
|+triangularized | |||
|1 | |||
|1 | |||
|2 | |||
|- | |||
|1 | |||
|0 | |||
|1 | |||
|- | |||
|2 | |||
|1 | |||
|1 | |||
|} | |||
: This applies to all prime subgroups, but let's assume 2.3.5 and see what the ratios are. Note that the ratios that are now two moves away are the ones with the much higher odd-limit of 15. Thus it does seem to reflect the actual musical distance better than any of the 3 ways you listed. | |||
{| class="wikitable" | |||
|+ratios | |||
|5/3 | |||
|5/4 | |||
|15/8 | |||
|- | |||
|4/3 | |||
|1/1 | |||
|3/2 | |||
|- | |||
|16/15 | |||
|8/5 | |||
|6/5 | |||
|} | |||
: In 3-D, 4-D etc., it's better thought of not as shearing but as higher primes cancelling lower primes that are on the opposite side of the ratio. | |||
: I'm not following the L1 stuff. Can you give some actual examples? --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 07:47, 20 January 2022 (UTC) | |||