Talk:Telicity

Meaning and unit

I think the article should start with a general classification. Since here is spoken of a property, the next question is, whether this property is of qualitative or quantitative nature, connected with it would be then questions about the domain of values and about possible units. What do you think? --Xenwolf (talk) 07:28, 20 January 2021 (UTC)

I do think that there are both qualitative as well as quantitative aspects to telicity- especially when you apply this to the JND. As to the domain of values and the possible units, those are definitely good questions, though to be fair this portion covers the telicity range of commas and other small music intervals like the JND. I should point out that "telicity" itself seems to almost exist on a true or false basis for any given type, such as 3-to-2, 5-to-3, 11-to-3, etcetera, while the related "telicity range" denotes the numerical range in which a given type of telicity, as achieved by either the tempering of a given comma, or, as in the case of the JND, the direct mapping to the unison, can potentially be true. --Aura (talk) 08:41, 20 January 2021 (UTC)

One part of the quantitative aspect of this is particularly clear, the unit for used for the measurement of telicity range represents the number of steps in a given EDO. Meanwhile, I do know that when a single type of telicity is accomplished in a given EDO through the tempering of multiple commas, the EDO can be said to demonstrate "multitelicity" of that given type, the specific nature of the multitelicity being expressed by a numerical prefix, such as uni-, bi-, tri-, etcetera, attached to the word "telicity". Perhaps it can be said that telicity itself is multifaceted... --Aura (talk) 09:10, 20 January 2021 (UTC)

Now that I'm really thinking about it, I'm thinking that we're actually dealing with a collection of closely intertwined properties, some of which are qualitative, others of which are quantitative. Judging from the definition of "telicity" itself as presented by the article's first paragraph, I'd say that telicity itself is ultimately a qualitative property. I mean, things like 3-to-2 telicity, 5-to-3 telicity, 5-to-2 telicity and 11-to-3 telicity are definitely qualitative. However, the details on how and where telicity is achieved- which are covered by ideas like "multitelicity" and "telicity range", are all quantitative things that have measurements. Does this sound right? --Aura (talk) 16:44, 20 January 2021 (UTC)

I also thought of reach first. Interesting that you brought up "telicity range" in the end. I'm not so happy with the new term "multitelicity"; as long "telicity" as is not completely clear, "multitelicity" will be even harder to define. --Xenwolf (talk) 23:20, 20 January 2021 (UTC)

How then do we make the concept of "telicity" itself more clear?

I mean, I know for sure that "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.

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 can possibly be 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.

Does this all make more sense now? --Aura (talk) 02:56, 21 January 2021 (UTC)

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. Any further thoughts? --Aura (talk) 19:23, 21 January 2021 (UTC)