User talk:FloraC

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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)


You are now member of --Xenwolf (talk) 06:42, 12 January 2021 (UTC)


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?


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.
Excuse me, but I'm not sure how to invite users who are not on my friends list... --Aura (talk) 16:00, 22 January 2021 (UTC)

Inharmonic vs subgroup TE

Would you happen to know the difference between "inharmonic TE" and "subgroup TE" tunings on x31eq for subgroup temperaments? For 13&18 temperament, the POTE generator is 464.1396c using inharmonic TE but 464.3865c using subgroup TE. Is subgroup TE specifically intended for approximating JI subgroups? Inthar (talk) 11:39, 4 February 2021 (UTC)

I'm only able to reproduce the results of "inharmonic TE". It finds the least square in the TE weighted space by treating any basis just like prime ones. FloraC (talk) 12:01, 4 February 2021 (UTC)

Val vs Vals

Hi Flora,
Sorry that I wasn't aware of this problem, when I suggested to branch out Vals from Template:EDOs. The distance pattern of vals and val is one of the worst possible, in the same class of coding horror with valf vs vals (slightly better) and sonth and sonth (even worse). While val is for formatting one val (long form), vals is for adding links to EDO pages. As a programmer, I'd like to get rid of val being a sub string of the other, but maybe this is too much to change and also means more typing in the future ...
Do you have any ideas how to solve it?
Best regards --Xenwolf (talk) 09:53, 7 February 2021 (UTC)

Just an idea: what about {{List of vals|...}}? --Xenwolf (talk) 09:55, 7 February 2021 (UTC)
Maybe we add Not to be confused with Template:Vals to Template:Val and vice versa. Does it solves the problem? If not, we can go for {{val list| ... }}. FloraC (talk) 10:23, 7 February 2021 (UTC)
I think {{val list}} is great. This way we can wait to point out the possible confusion until we actually observe the first confusion. Of course, in this solution the search for "val" will return both.--Xenwolf (talk) 18:04, 7 February 2021 (UTC)

159edo Notation System

Hey, Flora, I've been talking with a few other people about my proposed system for notating 159edo on my user talk page and elsewhere, and I'm getting the sense that my system is clear and straightforward. My question now is whether or not it's feasible to try and finalize the system. --Aura (talk) 06:19, 20 February 2021 (UTC)

To say "finalize" is like you don't take long-term maintenance of your system, but I reckon it more sensible to iterate it whenever you feel the need in the course of use.
If you plan on the MuseScore plugin, you'll want to consider that MuseScore doesn't allow freely combined accidentals. To access each step you need independent symbols. MuseScore's current sagittal coverage isn't enough for 159edo, either. FloraC (talk) 07:00, 20 February 2021 (UTC)
In this case, I say "finalize" in regards to the selection of symbols themselves and their design- the remaining symbols are made from single symbols that have been strung together. Also, I'm wondering if support for custom accidentals can be incorporated into MuseScore 4. --Aura (talk) 07:18, 20 February 2021 (UTC)
I'd say the selection of symbols and their design could be iterated through use as well. As for software, if Dorico can do it, I believe MuseScore too. Let's wait and see. FloraC (talk) 07:30, 20 February 2021 (UTC)
Well, the better the selection is to begin with, the fewer changes will have to be made later- aside from those caused by things like font changes in general. So, I'm looking to get the designs for this iteration finalized- however, Xenwolf seems to be quite busy at the moment. --Aura (talk) 07:42, 20 February 2021 (UTC)
Only through real application can you evaluate your selection. I don't know if the double dart is clear enough when stacked notes are present, for example. You'll have to check that in a real score. FloraC (talk) 08:10, 20 February 2021 (UTC)

Will you check up my implementation of the traditional Chinese tonal system?

Hi FloraC,

I assume you are more into Chinese culture than I am. :-)

Would you take a look at my Microtonal Playground platform and, among other things, provide some feedback on the implementation of the Chinese scales?

With my system, you can play music directly in your browser. The entire introductory part can be found on my page: Microtonal Fabric.

The particular application I'm asking you to look at is called Microtonal Playground.

Live play with different systems is [here].

I reproduced intervals, modes, the names of notes, and modes based on the Wikipedia article referenced in the Tonal System Metadata (will see it when you start the application).

I'll be very grateful if you take a look. Does it make sense? Can you see any mistakes in sound and names?

If you have any questions, I'll gladly answer. What I do is all open-source and a non-commercial project project, open for many kinds of collaboration for mutual benefits. For example, I could make the tonal system you suggested playable.

Thank you. — SASunday 2021 February 21, 05:16 UTC

I'm afraid I'm not as familiar with traditional Chinese tonal system as you've hoped. But if you're talking about Shí-èr-lǜ specifically, afaik it's very similar to Pythagorean tuning, except that every block of notes in an octave is stretched by a Pythagorean comma – at least that's how I interpret the sources. In your app the jiázhōng and zhònglǚ clearly doesn't sound right though. FloraC (talk) 10:03, 21 February 2021 (UTC)
Thank you! This is not so much of musical knowledge, but rather a fresh look. For example, as I don't understand the words, I could have messed them up. It looks like you do understand the words, even though they are spelled in some Latin-based rendering. I do hear the problematic sounds; it looks like a recent regression bug, so I just did not re-test it after some latest changes. The data describing the system is here. — SASunday 2021 February 21, 15:29 UTC
I checked the file and it turns out an asterisk is missing for jiázhōng and zhònglǚ. I tried fixing it (see your pull request). For musicians, the words are nothing but note names like ABCDEFG. Yet still, it's not really different from Pythagorean tuning if you don't apply the octave stretch. FloraC (talk) 16:02, 21 February 2021 (UTC)
You are right. I've fixed it and pushed the code. Thank you for your help!
My impression of this system is: the goal was the equidistant tone arrangement, without any concerns of better harmony. Even obvious perfect 4th 4/3 is 3**11/2**17 there. To me, it looks like if the system was changed to 12-EDO even for traditional music, it would lose nothing. What do you think? — SASunday 2021 February 21, 16:42 UTC
I suppose it is, and it motivated prince Zhū Zǎiyù to compute the twelfth root of 2. FloraC (talk) 17:52, 21 February 2021 (UTC)
Very interesting. I'm very curious: when it happened? Was the notion of irrational numbers also introduced or proven? — SASunday 2021 February 21, 19:51 UTC
It's published in 1581. By the time irrational numbers had been recognized across the world. FloraC (talk) 07:02, 22 February 2021 (UTC)
Thank you! Any links? I'm asking because I was unaware of this; and it is very interesting and dramatically related to music. You know, the discovery on the irrational numbers is often attributed to Híppasos (c. 530 — c. 450 BC, by the way), but this is not known for certain, it could have been found by some other person of that time, but this is also not completely certain. And then, all that story about the death of Híppasos, who could have been killed by Pythagoreans... The entire idea of mystical Pythagorean... how to call it?... something closer to superstition than to science makes the idea of thinking of Pythagoreans and Pythagoras himself as of advanced mathematicians very questionable. No wonder some argue that the mathematical achievements of Pythagoras were faked, attributing them to, surprisingly, Híppasos. By the way, some scholars believe the irrationality proof was related to √2, which is the tritone in music, exactly half of the octave, «most disharmonic» and a very important interval. — SATuesday 2021 February 23, 03:16 UTC
See Wikipedia: 12 equal temperament #History for the history of 12edo (but the Baroque era section is probably incorrect as it confuses well temperaments for equal temperament). FloraC (talk) 04:06, 23 February 2021 (UTC)
Got it. Thank you! — SATuesday 2021 February 23, 07:31 UTC


Thanks, that clarifies all :-) --Xenwolf (talk) 13:53, 26 February 2021 (UTC)

Tour of Regular Temperaments

Hey, I'm curious why you deleted Laconic and Comic. --TallKite (talk) 05:18, 17 March 2021 (UTC)

There's no alternative extensions to them, so it seems unnecessary to keep the "families". I moved all the data (including the 5-limit version) to the related clan pages. FloraC (talk) 06:11, 17 March 2021 (UTC)