User talk:Godtone: Difference between revisions

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== Comment on Your Proposal ==

I don't know about you, but when it comes to picking EDOs based on Subgroups, I'm actually kind of big on something I call "[[telicity]]". While I admit that I haven't managed to express the concept very well as of yet, perhaps we could talk about this and clarify the concept, as I'd like to see this sort of thing mentioned in terms of how well an EDO approximates a given subgroup structure-wise. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:26, 22 January 2021 (UTC)

: For the record, "telicity", as a concept, builds on Inthar's concept of "Consistency to distance ''d''" in terms of its core definition. While I often use the term "telicity" to refer to this concept as a whole, perhaps in order to define this concept itself more clearly, we need to look at the adjective "telic", as "telicity" itself means "the quality or state of being telic".

: 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".

: I'm not going over the parts of these definitions concerning combinations of primes yet, as we need to find the right way to express these.

~~I don't know about you~~, ~~but when~~ it ~~comes~~ to ~~picking EDOs based on Subgroups~~, I'm ~~actually kind~~ of ~~big~~ on ~~something I call "[[telicity]]"~~. ~~While~~ I ~~admit~~ that I haven't ~~managed~~ to ~~express~~ the concept ~~very well~~ as ~~of yet~~, ~~perhaps we could talk about~~ this ~~and clarify the concept~~, as I'd like to ~~see this sort~~ of ~~thing mentioned in terms~~ of ~~how well an EDO approximates~~ a ~~given subgroup structure-wise~~. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:26, 22 January 2021 (UTC)

: 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.

: For the record, part of the reason I'm limiting myself to chains of prime intervals at the moment is because judging from my own exploration of Alpharabian tuning, pure prime chains seem to have a way of acting as the borders for the tuning space of the various combinations of the primes in question. When two primes come together via telicity, the tuning space for combinations of those two primes seems to be finite, and thus, more manageable- on one corner is the unison, and on the other corner is the place where the two primes come together. Aside from this, the other part of the reason I'm limiting myself to pure prime chains is that in some respects, I haven't gotten around to those combinations yet- after all, I need to start with the basics of the concept first. It is true that there are less-straight paths available in the harmonic lattice, but when you want to return to the initial Tonic, as I myself often do, those less-straight paths are often more difficult to navigate, especially when you're dealing with higher primes in higher EDOs- I know this from experience, as I really like working in 159edo. Telicity gives easier-to-navigate paths for modulation, and sometimes, those paths are quite unexpected. For example, suppose you want to modulate down by a 32/27 minor third from your initial Tonic, but you know that the most expected way to get there is by chains of 3/2 fifths- well, it turns out that the nexus comma, which is unnoticeable and thus has a pretty high telicity range, joins the 11/8 prime chain together with the 3/2 prime chain at just that particular point, thus, going up by a chain of six 11/8 intervals allows you to reach the note at 32/27 below your original tonic by unexpected means. From there, you can simply modulate by a chain of perfect 3/2 fifths back to your original Tonic. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:32, 22 January 2021 (UTC)

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 == Comment on Your Proposal ==
+I don't know about you, but when it comes to picking EDOs based on Subgroups, I'm actually kind of big on something I call "[[telicity]]".  While I admit that I haven't managed to express the concept very well as of yet, perhaps we could talk about this and clarify the concept, as I'd like to see this sort of thing mentioned in terms of how well an EDO approximates a given subgroup structure-wise. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:26, 22 January 2021 (UTC)
+: For the record, "telicity", as a concept, builds on Inthar's concept of "Consistency to distance ''d''" in terms of its core definition.  While I often use the term "telicity" to refer to this concept as a whole, perhaps in order to define this concept itself more clearly, we need to look at the adjective "telic", as "telicity" itself means "the quality or state of being telic".
+: 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".
+: I'm not going over the parts of these definitions concerning combinations of primes yet, as we need to find the right way to express these.
-I don't know about you, but when it comes to picking EDOs based on Subgroups, I'm actually kind of big on something I call "[[telicity]]".  While I admit that I haven't managed to express the concept very well as of yet, perhaps we could talk about this and clarify the concept, as I'd like to see this sort of thing mentioned in terms of how well an EDO approximates a given subgroup structure-wise. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:26, 22 January 2021 (UTC)
+: 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.
+: For the record, part of the reason I'm limiting myself to chains of prime intervals at the moment is because judging from my own exploration of Alpharabian tuning, pure prime chains seem to have a way of acting as the borders for the tuning space of the various combinations of the primes in question. When two primes come together via telicity, the tuning space for combinations of those two primes seems to be finite, and thus, more manageable- on one corner is the unison, and on the other corner is the place where the two primes come together. Aside from this, the other part of the reason I'm limiting myself to pure prime chains is that in some respects, I haven't gotten around to those combinations yet- after all, I need to start with the basics of the concept first. It is true that there are less-straight paths available in the harmonic lattice, but when you want to return to the initial Tonic, as I myself often do, those less-straight paths are often more difficult to navigate, especially when you're dealing with higher primes in higher EDOs- I know this from experience, as I really like working in 159edo. Telicity gives easier-to-navigate paths for modulation, and sometimes, those paths are quite unexpected. For example, suppose you want to modulate down by a 32/27 minor third from your initial Tonic, but you know that the most expected way to get there is by chains of 3/2 fifths- well, it turns out that the nexus comma, which is unnoticeable and thus has a pretty high telicity range, joins the 11/8 prime chain together with the 3/2 prime chain at just that particular point, thus, going up by a chain of six 11/8 intervals allows you to reach the note at 32/27 below your original tonic by unexpected means. From there, you can simply modulate by a chain of perfect 3/2 fifths back to your original Tonic. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:32, 22 January 2021 (UTC)