Telicity: Difference between revisions

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'''Telicity''' is a property of both [[EDO]]s and [[commas]] and how they relate to each other. Specifically, for EDOs, it is the quality or state of being able, by means of tempering one or more commas smaller than half a step, to successfully stack a number of instances of a given prime's [[patent interval]] to connect with an interval belonging to a chain created by a lower prime's patent interval – designated as the '''telos''' – without ~~either accumulating 50% relative error or more at~~ any ~~point in~~ the ~~process~~ on ~~the part of~~ either prime's patent interval chain~~, or, creating as mismatch in results between~~ the ~~direct mapping and the more complicated traditional mapping for any~~ interval ~~along the chain~~. For commas, telicity is the quality of being able to join two distinct prime interval chains in the aforementioned manner by being tempered.

'''Telicity''' is a property of both [[EDO]]s and [[commas]] and how they relate to each other. Specifically, for EDOs, it is the quality or state of being able, by means of tempering one or more commas smaller than half a step, to successfully stack a number of instances of a given prime's [[patent interval]] to connect with an interval belonging to a chain created by a lower prime's patent interval – designated as the '''telos''' – without any of the tempered intervals on either prime's patent interval chain failing to be the closest approximation of said interval. For commas, telicity is the quality of being able to join two distinct prime interval chains in the aforementioned manner by being tempered.

Stated more mathematically, where ''N'' is the number of steps in a given EDO, ''r'' is the ratio of an interval in one of the two prime chains in question, and val (''N'') denotes the [[patent val]] of ''N''-EDO, the following equation must hold true along both prime chains up to and including the point of connection:

Revision as of 21:57, 30 January 2021 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 6,010 edits No edit summary ← Older edit		Revision as of 05:32, 8 February 2021 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 6,010 edits Hopefully simplified the intro some. Newer edit →
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	'''Telicity''' is a property of both [[EDO]]s and [[commas]] and how they relate to each other. Specifically, for EDOs, it is the quality or state of being able, by means of tempering one or more commas smaller than half a step, to successfully stack a number of instances of a given prime's [[patent interval]] to connect with an interval belonging to a chain created by a lower prime's patent interval – designated as the '''telos''' – without ~~either accumulating 50% relative error or more at~~ any ~~point in~~ the ~~process~~ on ~~the part of~~ either prime's patent interval chain~~, or, creating as mismatch in results between~~ the ~~direct mapping and the more complicated traditional mapping for any~~ interval ~~along the chain~~. For commas, telicity is the quality of being able to join two distinct prime interval chains in the aforementioned manner by being tempered.		'''Telicity''' is a property of both [[EDO]]s and [[commas]] and how they relate to each other. Specifically, for EDOs, it is the quality or state of being able, by means of tempering one or more commas smaller than half a step, to successfully stack a number of instances of a given prime's [[patent interval]] to connect with an interval belonging to a chain created by a lower prime's patent interval – designated as the '''telos''' – without any of the tempered intervals on either prime's patent interval chain failing to be the closest approximation of said interval. For commas, telicity is the quality of being able to join two distinct prime interval chains in the aforementioned manner by being tempered.

	Stated more mathematically, where ''N'' is the number of steps in a given EDO, ''r'' is the ratio of an interval in one of the two prime chains in question, and val (''N'') denotes the [[patent val]] of ''N''-EDO, the following equation must hold true along both prime chains up to and including the point of connection:		Stated more mathematically, where ''N'' is the number of steps in a given EDO, ''r'' is the ratio of an interval in one of the two prime chains in question, and val (''N'') denotes the [[patent val]] of ''N''-EDO, the following equation must hold true along both prime chains up to and including the point of connection: