Telicity: Difference between revisions

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(''Under construction'')

'''Telicity''' is a property of [[EDO]]s, which involves the given EDO being able to 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]] 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. Furthermore, since the 2-prime simply results in manifestations of the [[unison]] at different registers, thus leading to things like [[octave reduction]], the 2-prime is not a factor that affects what qualifies as telicity ''unless'' an interval in 2-prime chain itself serves as the target, or '''telos''', of a higher prime's patent interval chain. Given this, any sort of telicity involving the 2-prime cannot afford to temper out commas greater than half an EDO-step in size due to the unison being such a foundational interval to both EDOs and JI, and, the resultant inability to temper out commas greater than half a step in size without exceeding the 50% relative error threshold. Therefore, for the sake of consistency in definition, the commas that can be tempered out to achieve telicity ''must'' be less than half an EDO-step in size.

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			(''Under construction'')

	'''Telicity''' is a property of [[EDO]]s, which involves the given EDO being able to 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]] 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. Furthermore, since the 2-prime simply results in manifestations of the [[unison]] at different registers, thus leading to things like [[octave reduction]], the 2-prime is not a factor that affects what qualifies as telicity ''unless'' an interval in 2-prime chain itself serves as the target, or '''telos''', of a higher prime's patent interval chain. Given this, any sort of telicity involving the 2-prime cannot afford to temper out commas greater than half an EDO-step in size due to the unison being such a foundational interval to both EDOs and JI, and, the resultant inability to temper out commas greater than half a step in size without exceeding the 50% relative error threshold. Therefore, for the sake of consistency in definition, the commas that can be tempered out to achieve telicity ''must'' be less than half an EDO-step in size.		'''Telicity''' is a property of [[EDO]]s, which involves the given EDO being able to 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]] 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. Furthermore, since the 2-prime simply results in manifestations of the [[unison]] at different registers, thus leading to things like [[octave reduction]], the 2-prime is not a factor that affects what qualifies as telicity ''unless'' an interval in 2-prime chain itself serves as the target, or '''telos''', of a higher prime's patent interval chain. Given this, any sort of telicity involving the 2-prime cannot afford to temper out commas greater than half an EDO-step in size due to the unison being such a foundational interval to both EDOs and JI, and, the resultant inability to temper out commas greater than half a step in size without exceeding the 50% relative error threshold. Therefore, for the sake of consistency in definition, the commas that can be tempered out to achieve telicity ''must'' be less than half an EDO-step in size.