Telicity: Difference between revisions

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== Telicity Type Designations ==

Different EDOs have different relationships among the various primes that are used to define their [[patent val]]s, and thus, there is a need to designate these relationships. Given that EDOs specifically are defined as equal divisions of the [[octave]], the 2-prime – which defines the octave – is always listed last, with the largest prime being listed first, and other primes being listed in the middle from largest to smallest thus, for example a telic connection between the 3-prime and the 2-prime is denoted as 3-2 telicity. It should be noted that the only type of telicity available to the 3-prime is 3-2 telicity, as 2 is the only positive prime lower than 3, and since octave equivalency renders the unison as the only available target, that means that the 3-prime requires a complete [[circle of fifths]] without accumulating 50% relative error or more in order to achieve telicity. However, higher primes have more options for achieving a form of telicity as there are multiple lower primes to chose from to potentially connect with. For instance, the 5-prime has both 5-3 and 5-2 telicity available to it. Not only that, but in cases where multiple overlapping telic relationships exist for a given EDO without the largest tempered comma failing to satisfy the telicity equation, one can express all of these telic relationships within a single designation. For example, [[12edo]], which simultaneously demonstrates 3-2 telicity, 5-3 telicity, and 5-2 telicity, can be said to ~~have~~ 5-3-2 telicity.

Different EDOs have different relationships among the various primes that are used to define their [[patent val]]s, and thus, there is a need to designate these relationships. Given that EDOs specifically are defined as equal divisions of the [[octave]], the 2-prime – which defines the octave – is always listed last, with the largest prime being listed first, and other primes being listed in the middle from largest to smallest thus, for example a telic connection between the 3-prime and the 2-prime is denoted as 3-2 telicity. It should be noted that the only type of telicity available to the 3-prime is 3-2 telicity, as 2 is the only positive prime lower than 3, and since octave equivalency renders the unison as the only available target, that means that the 3-prime requires a complete [[circle of fifths]] without accumulating 50% relative error or more in order to achieve telicity. However, higher primes have more options for achieving a form of telicity as there are multiple lower primes to chose from to potentially connect with. For instance, the 5-prime has both 5-3 and 5-2 telicity available to it. Not only that, but in cases where multiple overlapping telic relationships exist for a given EDO without the largest tempered comma failing to satisfy the telicity equation, one can express all of these telic relationships within a single designation. For example, [[12edo]], which simultaneously demonstrates 3-2 telicity, 5-3 telicity, and 5-2 telicity, can be said to demonstrate 5-3-2 telicity.

== Applications ==

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 == Telicity Type Designations ==
-Different EDOs have different relationships among the various primes that are used to define their [[patent val]]s, and thus, there is a need to designate these relationships. Given that EDOs specifically are defined as equal divisions of the [[octave]], the 2-prime – which defines the octave – is always listed last, with the largest prime being listed first, and other primes being listed in the middle from largest to smallest thus, for example a telic connection between the 3-prime and the 2-prime is denoted as 3-2 telicity.  It should be noted that the only type of telicity available to the 3-prime is 3-2 telicity, as 2 is the only positive prime lower than 3, and since octave equivalency renders the unison as the only available target, that means that the 3-prime requires a complete [[circle of fifths]] without accumulating 50% relative error or more in order to achieve telicity.  However, higher primes have more options for achieving a form of telicity as there are multiple lower primes to chose from to potentially connect with.  For instance, the 5-prime has both 5-3 and 5-2 telicity available to it.  Not only that, but in cases where multiple overlapping telic relationships exist for a given EDO without the largest tempered comma failing to satisfy the telicity equation, one can express all of these telic relationships within a single designation.  For example, [[12edo]], which simultaneously demonstrates 3-2 telicity, 5-3 telicity, and 5-2 telicity, can be said to have 5-3-2 telicity.
+Different EDOs have different relationships among the various primes that are used to define their [[patent val]]s, and thus, there is a need to designate these relationships. Given that EDOs specifically are defined as equal divisions of the [[octave]], the 2-prime – which defines the octave – is always listed last, with the largest prime being listed first, and other primes being listed in the middle from largest to smallest thus, for example a telic connection between the 3-prime and the 2-prime is denoted as 3-2 telicity.  It should be noted that the only type of telicity available to the 3-prime is 3-2 telicity, as 2 is the only positive prime lower than 3, and since octave equivalency renders the unison as the only available target, that means that the 3-prime requires a complete [[circle of fifths]] without accumulating 50% relative error or more in order to achieve telicity.  However, higher primes have more options for achieving a form of telicity as there are multiple lower primes to chose from to potentially connect with.  For instance, the 5-prime has both 5-3 and 5-2 telicity available to it.  Not only that, but in cases where multiple overlapping telic relationships exist for a given EDO without the largest tempered comma failing to satisfy the telicity equation, one can express all of these telic relationships within a single designation.  For example, [[12edo]], which simultaneously demonstrates 3-2 telicity, 5-3 telicity, and 5-2 telicity, can be said to demonstrate 5-3-2 telicity.
 == Applications ==