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 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 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 [[EDO]]s and [[commas]] and how they relate to each other. Specifically, for EDOs, 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 the tempered comma 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:

<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 [[EDO]]s and [[commas]] and how they relate to each other. Specifically, for EDOs, 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 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 [[EDO]]s and [[commas]] and how they relate to each other. Specifically, for EDOs, 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 the tempered comma 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:

	<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>