User talk:FloraC

• User talk:FloraC/Archive 2020

Fractions vs. names in interval lemmas

What about moving the limit to 9 digits, or 4 digits in the denominator? Kite already suggested this for comma tables, I run an (in my opinion) acceptable test on 41edo#Commas. I'd also like to be more consistent in this aspect, i.e. pages that can easily be linked by just copying their title. So the limits about comma tables should maybe also been applied to (comma) page titles itself. What do you think? --Xenwolf (talk) 17:30, 9 January 2021 (UTC)

The change for page titles is minimal, as I don't remember of a single 9-digit comma. I'm not fond of comma tables also subjecting to that rule though. Comma tables can afford to show more digits, and hiding them removes the aspect of the sensation of complexity by the sheer length. FloraC (talk) 16:25, 10 January 2021 (UTC)

The 9-digit rule is nothing other than an extended 8-digit rule. With octave-reduced fractions, cases are possible with 5-digit nominators with a 1 as leading digit. In my opinion, the comma tables on the EDO pages are overloaded anyway. There all the information we have about commas is repeated, I assume that most of this information is obtained by copying from other pages, so there could be a number of errors to correct multiple times. And this tendency will rather increase if we don't push back this kind of duplicates. --Xenwolf (talk) 17:15, 10 January 2021 (UTC)

I agree the comma tables in edo pages are overloaded. What should be there and what should not, then? FloraC (talk) 07:25, 11 January 2021 (UTC)

I'd say limit and one name or fraction (depending on target lemma) with link, maybe a column for comments. The comments column can be used to contain the information if there is no comma page to link to, but I think we should soon create these pages and link to them as well from the global comma tables. I now think I probably should have started this discussion in the Xenharmonic Wiki namespace. I now try to move it to there: Xenharmonic Wiki: Things to do #Comma tables in EDO_pages. Sorry for the trouble. --Xenwolf (talk) 08:57, 11 January 2021 (UTC)

dev

You are now member of dev.xen.wiki. --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 EDOs, 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 2, 5, 12, 24, 53, 106, 159- yes, I checked this without a computer 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 159edo talk page. --Aura (talk) 07:03, 19 January 2021 (UTC)

For single-ring edos, every interval is on the chain of 3s. Take 31edo for example, isn't its first step of harmonic 5, 10\31, already on the circle of fifths, for the tempering of 81/80? FloraC (talk) 07:34, 19 January 2021 (UTC)

Let's see, for 31edo, 81/80 is larger than half of a step in size, so 31edo actually fails to demonstrate 5-to-3 telicity as the relative error induced by the comma is liable to be greater than 50%. --Aura (talk) 07:38, 19 January 2021 (UTC)

For the sure-fire examples of telicity, the comma being tempered out has to be less than half an EDO step in size. --Aura (talk) 07:42, 19 January 2021 (UTC)

Such commas are ubiquitous. What about 8 steps of 10\31 to 3/2, for the tempering of würschmidt comma? FloraC (talk) 08:04, 19 January 2021 (UTC)

Ah, this makes more sense for 5-to-3 telicity. Sorry about that, looks like 31edo does demonstrate 5-to-3 telicity after all, my mistake. It may be true that commas that are less than half a step in size are ubiquitous, but I've also noticed in my explorations that sometimes commas of this sort fail to be tempered out. Truth be told, the reason I'm tying to limit my idea of telic commas to commas that are less than half an EDO-step in size is because any instance of telicity involving the 2-prime cannot afford to temper out commas greater than half an EDO-step in size due to the unison being such a foundational interval to both EDOs and JI, and, the resultant inability to temper out commas greater than half a step in size without exceeding the 50% relative error threshold. Thus, I'm trying to impose a uniform standard for this across the board just to make it easier. --Aura (talk) 08:17, 19 January 2021 (UTC)

To state the definition of telicity 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. Does this make more sense?

Discord

Hello Flora, I see that you're on Discord. Since I myself am also on Discord, and since this Microtonal Server was established by another user here last year, I feel that you would be quite welcome. --Aura (talk) 17:24, 21 January 2021 (UTC)

It's not an invite link. You should get the invite link so that I can join. FloraC (talk) 06:47, 22 January 2021 (UTC)

Right. I'll get to that in a bit.