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 concept by going over 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 out for the given EDO in question in addition to being able to join distinct prime chains.

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)

At the end of the day, the article on telicity needs to be rewritten to more clearly communicate the concept, and its applicability, and it implications, and finding these connections between various primes is part of demonstrating the structure of various EDOs in terms of how they relate to the harmonic lattice. --Aura (talk) 20:44, 24 January 2021 (UTC)

For the record, I do have some idea as to the expected results as to the sequence of EDOs demonstrating 3-to-2 telicity, as, without algorithms, I've calculated the first seven EDOs demonstrating this type of telicity to be the EDOs 2, 5, 12, 24, 53, 106, 159, with the lattermost being my favorite Mega-EDO for a number of reasons. --Aura (talk) 20:50, 24 January 2021 (UTC)

I implemented your equation and it seems to work, but what exactly did you want me to compute? A list of EDOs that have patent vals that line up with a chain of primes? And is this chain of primes JI primes or each respective EDO's patent val primes? --Xenoindex (talk) 04:16, 25 January 2021 (UTC)

In effect, I am looking to see a table with rows corresponding to all the EDOs between 1 and 400, with different columns in the table indicating different types of telicity, namely 3-to-2 telicity, 5-to-3 telicity, 5-to-2 telicity, 7-to-5 telicity, 7-to-3 telicity, 7-to-2 telicity, 11-to-7 telicity, 11-to-5 telicity, 11-to-3 telicity and 11-to-2 telicity. An EDO that demonstrates one of these types of telicity has a ✓ in the cell matching the telicity column in question or ✓✓ if it demonstrates multitelicity for that particular type. This is what I'm actually looking for. Later on, we can make diagrams that help us map out the structure of these EDOs based on this table. Does this make sense? --Aura (talk) 14:18, 25 January 2021 (UTC)

Oh, and as for your question as to whether this chain of primes is JI primes or each respective EDO's patent val primes, given that we're working with EDOs, it follows that the 2-prime is just, though for everything else... well... let's say 49/32 is "r", since this interval is made by stacking two instance of 7/4 then octave-reducing. There's a difference between say, the direct mapping of your example interval (represented by the right side of the equation), which is the step of the EDO that most closely approximates the just interval in question, and the patent-val-based traditional mapping of that same interval (represented by the left side of the equation), which depends on the mapping generated by stacking multiple instances of the EDO's best approximation of the patent prime interval and octave reducing. The equation tests to see if the results of both of these mappings are identical (indicated by the equation being "true") or not. From there, the only way I can think of to answer that is to say that you need to study the definition of "telicity" itself. Does this make sense? --Aura (talk) 14:41, 25 January 2021 (UTC)

Hi! You have some neat things here, wow! --Arseniiv (talk) 17:21, 11 October 2021 (UTC)

Thank you! come join us on the discord server if you wanna chat about it (linked in the side bar under connect). --Xenoindex (talk) 18:16, 11 October 2021 (UTC)

Table usability

I doubt that NEJI Tables/Average Error or NEJI Tables/Greatest Error will be of high value to readers. Did you ever try to view the information (about 41EDO) on a mobile device? I think it would be better to provide some examples for illustration and some script (or pseudo code) that would enable readers to get the specific information they want. --Xenwolf (talk) 22:19, 27 June 2021 (UTC)

Several XA Discord users have expressed to me the immediate usefulness of these tables. They're meant to be accessed on a PC where a user can select which EDO they want a NEJI of from the table of contents then copy and paste different scales to try. But I understand if you deem it necessary to remove them. --Xenoindex (talk) 00:19, 28 June 2021 (UTC)

There is no need to remove tables if they are helpful. But maybe it would be good to ask (on XA Discord) which specific parts are useful. We already have a lot of tables that try to be complete in an area where completeness is impossible. I see a problem in long static pages, when most users wait for them to load, only to find afterwards that the content is (for the most part) irrelevant to them. Isn't this exactly the occasion for a dynamic web application where users can specify exactly what kind of data they want? --Xenwolf (talk) 08:11, 28 June 2021 (UTC)

BTW: which code/script are you using? Wouldn't it make sense to add it as well? --Xenwolf (talk) 08:13, 28 June 2021 (UTC)

I've shortened the tables by about half, I hope this is adequate. And my code is written in SuperCollider, I suppose I could upload the source but I can't imagine the intersection of SuperCollider users and NEJI users is very large. --Xenoindex (talk) 08:53, 28 June 2021 (UTC)

In that case I think it would help to show the core algorithm to get the NEJIs that correspond to EDOs. This could also be in SuperCollider:

// Print "Hello world!"
"Hello world!".postln;

we have syntax highlighting for it (lang="sc"). Maybe someone will be able to translate it into Python, JavaScript, Lua or whatever. --Xenwolf (talk) 13:33, 28 June 2021 (UTC)