Telicity: Difference between revisions

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Combinations of primes are more complicated, but it's safe to say that there are more types of telicity available in such cases- namely "full telicity" and "partial telicity". Full telicity for combinations involving multiple primes occurs when the EDO in question is able to stack a number of instances of a given combination's patent interval to connect with an interval belonging to a chain created by the patent interval for a prime that is lower than the lowest prime in the initial combination after octave reduction is taken into account. In contrast, partial telicity for combinations involving multiple primes occurs when the EDO in question is able to stack a number of instances of a given combination's patent interval to connect with an interval belonging to a chain created by the patent interval for a prime that is lower than the highest prime in the initial combination after octave reduction is taken into account.

Given that different EDOs can temper out different commas to achieve the same type of telicity – for example, [[12edo]] tempers out the [[Pythagorean comma]] to achieve 3-to-2 telicity, while [[53edo]] tempers out [[Mercator's comma]] to achieve 3-to-2 telicity – it can thus be argued that sequences of different EDOs demonstrating one or more types of telicity can be compiled. For instance, the first seven EDOs to demonstrate 3-to-2 telicity specifically are {{EDOs| 2, 5, 12, 24, 53, 106, 159 }}. In addition, one can compare multiple such telicity sequences, and see how frequently the various prime chains connect to one another across various EDOs, revealing which portions of the harmonic lattice are best utilized by a given EDO. Furthermore, this also enables one to examine the properties of the various prime chains themselves and provides cause to look for unexpectedly useful commas that, as of yet, are still unknown.

Given that different EDOs can temper out different commas to achieve the same type of telicity – for example, [[12edo]] tempers out the [[Pythagorean comma]] to achieve 3-to-2 telicity, while [[53edo]] tempers out [[Mercator's comma]] to achieve 3-to-2 telicity – it can thus be argued that sequences of different EDOs demonstrating one or more types of telicity can be compiled. For instance, the first seven EDOs to demonstrate 3-to-2 telicity specifically are {{EDOs| 2, 5, 12, 24, 53, 106, 159 }}. In addition, one can compare multiple such telicity sequences, and see how frequently the various prime chains connect to one another across various EDOs, revealing which portions of the harmonic lattice are best utilized by any given EDO. Furthermore, this also enables one to examine the properties of the various prime chains themselves and provides cause to look for unexpectedly useful commas that, as of yet, are still unknown.

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	Combinations of primes are more complicated, but it's safe to say that there are more types of telicity available in such cases- namely "full telicity" and "partial telicity". Full telicity for combinations involving multiple primes occurs when the EDO in question is able to stack a number of instances of a given combination's patent interval to connect with an interval belonging to a chain created by the patent interval for a prime that is lower than the lowest prime in the initial combination after octave reduction is taken into account. In contrast, partial telicity for combinations involving multiple primes occurs when the EDO in question is able to stack a number of instances of a given combination's patent interval to connect with an interval belonging to a chain created by the patent interval for a prime that is lower than the highest prime in the initial combination after octave reduction is taken into account.		Combinations of primes are more complicated, but it's safe to say that there are more types of telicity available in such cases- namely "full telicity" and "partial telicity". Full telicity for combinations involving multiple primes occurs when the EDO in question is able to stack a number of instances of a given combination's patent interval to connect with an interval belonging to a chain created by the patent interval for a prime that is lower than the lowest prime in the initial combination after octave reduction is taken into account. In contrast, partial telicity for combinations involving multiple primes occurs when the EDO in question is able to stack a number of instances of a given combination's patent interval to connect with an interval belonging to a chain created by the patent interval for a prime that is lower than the highest prime in the initial combination after octave reduction is taken into account.

	Given that different EDOs can temper out different commas to achieve the same type of telicity – for example, [[12edo]] tempers out the [[Pythagorean comma]] to achieve 3-to-2 telicity, while [[53edo]] tempers out [[Mercator's comma]] to achieve 3-to-2 telicity – it can thus be argued that sequences of different EDOs demonstrating one or more types of telicity can be compiled. For instance, the first seven EDOs to demonstrate 3-to-2 telicity specifically are {{EDOs\| 2, 5, 12, 24, 53, 106, 159 }}. In addition, one can compare multiple such telicity sequences, and see how frequently the various prime chains connect to one another across various EDOs, revealing which portions of the harmonic lattice are best utilized by a given EDO. Furthermore, this also enables one to examine the properties of the various prime chains themselves and provides cause to look for unexpectedly useful commas that, as of yet, are still unknown.		Given that different EDOs can temper out different commas to achieve the same type of telicity – for example, [[12edo]] tempers out the [[Pythagorean comma]] to achieve 3-to-2 telicity, while [[53edo]] tempers out [[Mercator's comma]] to achieve 3-to-2 telicity – it can thus be argued that sequences of different EDOs demonstrating one or more types of telicity can be compiled. For instance, the first seven EDOs to demonstrate 3-to-2 telicity specifically are {{EDOs\| 2, 5, 12, 24, 53, 106, 159 }}. In addition, one can compare multiple such telicity sequences, and see how frequently the various prime chains connect to one another across various EDOs, revealing which portions of the harmonic lattice are best utilized by any given EDO. Furthermore, this also enables one to examine the properties of the various prime chains themselves and provides cause to look for unexpectedly useful commas that, as of yet, are still unknown.