User:Kaiveran/OLITTA Distance: Difference between revisions
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'''Odd-limit-integrating triangularized taxicab distance''' (or '''OLITTA Distance''', for short) is a modified form of triangularized [[Commas by taxicab distance#Triangularizing proposal|taxicab distance]], developed by Kaiveran in response to an issue raised by Kite Giedraitis in his original formulation, namely that the procedure can designate certain intervals as "2-steps" (e.g [[9/7]]) which are in fact less complex both in prime- and odd-limit than some "1-steps" (e.g [[11/7]]). | '''Odd-limit-integrating triangularized taxicab distance''' (or '''OLITTA Distance''', for short) is a modified form of triangularized [[Commas by taxicab distance#Triangularizing proposal|taxicab distance]], developed by [[User:Kaiveran|Kaiveran]] in response to an issue raised by Kite Giedraitis in his original formulation, namely that the procedure can designate certain intervals as "2-steps" (e.g [[9/7]]) which are in fact less complex both in prime- and odd-limit than some "1-steps" (e.g [[11/7]]). | ||
== Default Procedure == | == Default Procedure == | ||
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== Examples == | == Examples == | ||
( | (comparative btw all 3 methods. you might not always want OLITTA, esp. for comma pump progressions) | ||
Revision as of 12:25, 9 September 2022
Odd-limit-integrating triangularized taxicab distance (or OLITTA Distance, for short) is a modified form of triangularized taxicab distance, developed by Kaiveran in response to an issue raised by Kite Giedraitis in his original formulation, namely that the procedure can designate certain intervals as "2-steps" (e.g 9/7) which are in fact less complex both in prime- and odd-limit than some "1-steps" (e.g 11/7).
Default Procedure
(bleh, odd-number step down, include adjacent non-primes [e.g 13-prime-limit automatically extends to 15], open with comparison to Kite)
Tweaks
(you can include more or less odd non-primes into the OLITTA measure, like a 7-limit that doesn't include 9s, or a 23-limit that includes both 25 and 27
The chief disadvantage of this case is that there then ceases to be a singular OLITTA measure. Or, more accurately, your OLITTA measure has a designated odd-limit just like your piece of music does.)
Examples
(comparative btw all 3 methods. you might not always want OLITTA, esp. for comma pump progressions)