User:Kaiveran/OLITTA Distance - Revision history

Kaiveran at 09:03, 14 September 2022

2022-09-14T09:03:48Z

← Older revision		Revision as of 09:03, 14 September 2022
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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 [[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]]).		'''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 ==		== Procedure ==
	(bleh, odd-number step down, include adjacent non-primes [e.g 13-prime-limit automatically extends to 15], open with comparison to Kite)		(bleh, odd-number step down, include adjacent non-primes [e.g 13-prime-limit automatically extends to 15], open with comparison to Kite)

	== ~~Tweaks~~ ==		== Advantages & Disadvantages ==
	(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~~		(simplify and gives you more moves to use)

	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.)		The chief disadvantage is that OLITTA distance (as formulated above) is not a deterministic measure, unlike both regular and Kite-triangularized taxicab distance. Or, put another way, OLITTA measure ''has a designated odd-limit'', just like your piece of music does.

			This might be interesting for certain purposes, but most people would prefer a measure that does not change arbitrarily, and whose results depend only on the prime factors involved in the ratio.

			(prime gap splitting method, with adjacent non-primes and midpoints between prime gaps always included:

			7-limit automatically includes ratios of 9

			13-limit automatically includes ratios of 15

			23-limit automatically includes ratios of 25

			89-limit automatically includes ratios of 91 and 93)

	== Examples ==		== Examples ==
	(comparative btw all 3 methods. you might not always want OLITTA, esp. for comma pump progressions)		(comparative btw all 3 methods. you might not always want OLITTA, esp. for comma pump progressions)

Kaiveran: basic structure

2022-09-09T12:25:27Z

basic structure

← Older revision		Revision as of 12:25, 9 September 2022
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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 ==
Line 10:		Line 10:

	== Examples ==		== Examples ==
	(~~yah~~)		(comparative btw all 3 methods. you might not always want OLITTA, esp. for comma pump progressions)

Kaiveran at 12:21, 9 September 2022

2022-09-09T12:21:30Z

← Older revision		Revision as of 12:21, 9 September 2022
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	(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		(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.)		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 ==		== Examples ==
	(yah)		(yah)

Kaiveran: Created page with "'''Odd-limit-integrating triangularized taxicab distance''' (or '''OLITTA Distance''', for short) is a modified form of triangularized Commas by taxicab distance#Triangulari..."

2022-09-09T12:20:16Z

Created page with "'''Odd-limit-integrating triangularized taxicab distance''' (or '''OLITTA Distance''', for short) is a modified form of triangularized Commas by taxicab distance#Triangulari..."

New page

'''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]]).

== 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.)

== Examples ==
(yah)