User talk:Xenoindex

Hi

Hello there! Judging from your gratuitously massive list of EDOs that make progressively better approximation of 3/2, it seems you like math. A lot. Did you use an algorithm to make that list? If so, I have a project that I'm hoping you can help me with, since I don't have those kinds of skills. --Aura (talk) 17:13, 24 January 2021 (UTC)

Yep it's an algorithm. I'll hear you out, what's your project? --Xenoindex (talk) 20:22, 24 January 2021 (UTC)

I'm hoping to eventually create a map involving multiple instances of a property which I call telicity as it occurs between various primes. However, the current article on it, which I admit to having created, doesn't express the concept all that well- since I'm not the best at communicating. Perhaps I should begin by unpacking the meanings of the various words associated with it. 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".

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 for the given EDO in question.

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.

I hope this is at least a good starting point, and that I've communicated this well. --Aura (talk) 20:35, 24 January 2021 (UTC)