User talk:Xenoindex: Difference between revisions

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::: For its part, "telic", when used to describe an EDO, can be defined as "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 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 – all by means of tempering one or more commas smaller than half a step". From this, we get the definition of "telic" when used to describe a comma, which "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, and "M" is the [[monzo]] of "r", the equation {N, round(log2(3)*N), round(log2(5)*N), round(log2(7)*N), round(log2(11)*N), ...}.{M} = round(log2(r)*N) must hold true along both prime chains up to and including the point of connection. Telic commas themselves satisfy this same equation when [[tempered out]] for the given EDO in question.

::: 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, and "M" is the [[monzo]] of "r", the equation {N, round(log2(3)*N), round(log2(5)*N), round(log2(7)*N), round(log2(11)*N), ...}.{M} = round(log2(r)*N) must hold true along both prime chains up to and including the point of connection. Telic commas themselves satisfy this same equation when [[tempered out]] for the given EDO in question in addition to being able to join distinct prime chains.

::: Anyhow, with this in mind, "multitelicity" means "the quality or state of being multitelic", while "multitelic", for its part, is an adjective describing an EDO that is telic in a given multiprime relationship by more than one means. Also, it is from the sense of "telic" used to describe a comma that we get "telicity range", which is "the numerical range in which a given comma is telic" – this range is often designated by the number of the steps in the highest EDO to fall in this range, as the lowest EDO to fall in this range is always assumed to be 1edo.

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 ::: For its part, "telic", when used to describe an EDO, can be defined as "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 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 – all by means of tempering one or more commas smaller than half a step". From this, we get the definition of "telic" when used to describe a comma, which "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, and "M" is the [[monzo]] of "r", the equation {N, round(log2(3)*N), round(log2(5)*N), round(log2(7)*N), round(log2(11)*N), ...}.{M} = round(log2(r)*N) must hold true along both prime chains up to and including the point of connection.  Telic commas themselves satisfy this same equation when [[tempered out]] for the given EDO in question.
+::: 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, and "M" is the [[monzo]] of "r", the equation {N, round(log2(3)*N), round(log2(5)*N), round(log2(7)*N), round(log2(11)*N), ...}.{M} = round(log2(r)*N) must hold true along both prime chains up to and including the point of connection.  Telic commas themselves satisfy this same equation when [[tempered out]] for the given EDO in question in addition to being able to join distinct prime chains.
 ::: Anyhow, with this in mind, "multitelicity" means "the quality or state of being multitelic", while "multitelic", for its part, is an adjective describing an EDO that is telic in a given multiprime relationship by more than one means. Also, it is from the sense of "telic" used to describe a comma that we get "telicity range", which is "the numerical range in which a given comma is telic" – this range is often designated by the number of the steps in the highest EDO to fall in this range, as the lowest EDO to fall in this range is always assumed to be 1edo.