Telicity: Difference between revisions

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'''Telicity''' is a property of both [[equal temperament]]s and [[comma]]s and how they relate to each other. Specifically, for [[EDO]]s, it is the quality or state of being able 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, ~~or even~~ the tempered comma connecting the two prime chains in question, ~~failing to~~ satisfy the following equation 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:

'''Telicity''' is a property of both [[equal temperament]]s and [[comma]]s and how they relate to each other. Specifically, for [[EDO]]s, it is the quality or state of being able 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''' – so that all of the tempered intervals on either prime's patent interval chain, and the tempered comma connecting the two prime chains in question, satisfy the following equation 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:

<math>\text{val} (N) \cdot \text{monzo} (r) = \text{round} (N \log_2 (r))</math>

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	'''Telicity''' is a property of both [[equal temperament]]s and [[comma]]s and how they relate to each other. Specifically, for [[EDO]]s, it is the quality or state of being able 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, ~~or even~~ the tempered comma connecting the two prime chains in question, ~~failing to~~ satisfy the following equation 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:		'''Telicity''' is a property of both [[equal temperament]]s and [[comma]]s and how they relate to each other. Specifically, for [[EDO]]s, it is the quality or state of being able 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''' – so that all of the tempered intervals on either prime's patent interval chain, and the tempered comma connecting the two prime chains in question, satisfy the following equation 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:

	<math>\text{val} (N) \cdot \text{monzo} (r) = \text{round} (N \log_2 (r))</math>		<math>\text{val} (N) \cdot \text{monzo} (r) = \text{round} (N \log_2 (r))</math>