User talk:FloraC: Difference between revisions

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You are now member of dev.xen.wiki. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:42, 12 January 2021 (UTC)

== Telicity ==

Hey, Flora, I finally have a name for the collection of properties which I once dubbed as being a sort of "consistency". Now that I have terminology to talk about this concept, which I call "telicity", I'm hoping we can discuss this some, as I'm hoping this topic is worthy of an article here. Perhaps I ought to lay down what I know about telicity here so you can evaluate the concept for yourself.

Telicity- as I'm defining it here- 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 lower prime's [[patent interval]] without accumulating 50% relative error or more at any point in the process on the part of either prime's chain.

Given this definition, the only type of telicity available to the 3-prime is 3-to-2 telicity, as the 3-prime can only connect with the 2-prime in this fashion, and since the 2-prime simply results in manifestations of the [[unison]] at different registers- meaning that the unison is the only available target- that means that the 3-prime requires a complete [[circle of fifths]] without accumulating 50% relative error or more. 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-to-3 and 5-to-2 telicity available to it.

Combinations of primes are more complicated, and some of the nuances are yet to be considered in this realm, 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. 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.

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 }}- I checked this without an algorithm available to me, and this is the result I got.

I hope this idea makes more sense than my initial attempts to talk about it on the [[Talk:159edo|159edo talk page]]. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 07:03, 19 January 2021 (UTC)

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 You are now member of dev.xen.wiki. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:42, 12 January 2021 (UTC)
+== Telicity ==
+Hey, Flora, I finally have a name for the collection of properties which I once dubbed as being a sort of "consistency".  Now that I have terminology to talk about this concept, which I call "telicity", I'm hoping we can discuss this some, as I'm hoping this topic is worthy of an article here.  Perhaps I ought to lay down what I know about telicity here so you can evaluate the concept for yourself.
+Telicity- as I'm defining it here- 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 lower prime's [[patent interval]] without accumulating 50% relative error or more at any point in the process on the part of either prime's chain.
+Given this definition, the only type of telicity available to the 3-prime is 3-to-2 telicity, as the 3-prime can only connect with the 2-prime in this fashion, and since the 2-prime simply results in manifestations of the [[unison]] at different registers- meaning that the unison is the only available target- that means that the 3-prime requires a complete [[circle of fifths]] without accumulating 50% relative error or more.  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-to-3 and 5-to-2 telicity available to it.
+Combinations of primes are more complicated, and some of the nuances are yet to be  considered in this realm, 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.  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.
+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 }}- I checked this without an algorithm available to me, and this is the result I got.
+I hope this idea makes more sense than my initial attempts to talk about it on the [[Talk:159edo|159edo talk page]]. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 07:03, 19 January 2021 (UTC)