User talk:Xenwolf

When in the MonoBook skin, the Search bar is down, so it requires scrolling. PiotrGrochowski (talk) 11:47, 17 September 2018 (UTC)

I suggest not to use a user-defined skin. After Wikipedia switched to Vector, MonoBook seems to be no longer maintained by the MediaWiki team. Maybe you can still use MonoBook and change the search bar position via user-defined CSS and/or user-defined JavaScript, but I'm currently not able to help you with this issue. --Xenwolf (talk) 13:27, 17 September 2018 (UTC)

That's in Special:Preferences by the way. PiotrGrochowski (talk) 14:01, 17 September 2018 (UTC)

A nice advantage of MediaWiki is that broken links are immediately visible, which is helpful in pages like EDO#100...199. PiotrGrochowski (talk) 14:01, 17 September 2018 (UTC)

Absolutely. I even more like the MediaWiki tables, look here for a little table demo :) --Xenwolf (talk) 14:09, 17 September 2018 (UTC)

Why is there a site named dev.xen.wiki that copies the xenharmonic articles and uses Timeless as the default skin? What's the point of that site? PiotrGrochowski (talk) 13:10, 18 September 2018 (UTC)

It's a test page as it seems, there was a poll on Facebook which skin to prefer, it's still open, but a majority for Default (=Vector) is on the horizon. --Xenwolf (talk) 14:28, 18 September 2018 (UTC)

Why did you ban me?!

Allowing any list model is the exact opposite of a personal opinion! You are so ironic! PiotrGrochowski (talk) 07:04, 15 October 2018 (UTC)

Nobody disallows your opinion. But it's extremely disturbing that you tell people working on this wikis for years that they are childish if they use the simplest thing possible to write lists. Maybe it's a misconception to think that MediaWiki is about coding, it's about writing and communication. Did you read the help pages in Wikipedia or MediaWiki? What do you think about their expertise? They start with simple lists, later they explain HTML-like features, but they try to keep the wiki text as readable as possible and usable in diffs. Most (if not all lists we used in this wiki were simple enough for basic lists). Show me the actual problem that can be solved via template:list that cannot be solved via * and #. I mean: find an existing one, not construct one. I see a problem in very long lines containing a lot of </li><li> markup: they are not easy to change and they have a lower signal-to-noise ratio. And this can be solved by basic lists.
And as to answer your initial question: You try to invent Conventions for the wiki with a lot of effort and when I tried to correct you about this, you show how fast you can revert my justified changes and tell me that I'm vandalizing the wiki? I have not enough time to play this I'm better than you game. I have the feeling that you don't read carefully what other people write.
Best regards --Xenwolf (talk) 13:19, 15 October 2018 (UTC)

It's true that you are worse than me. You are the one trying to push a personal opinion. All list models are equally acceptable and a specific one should not be taught in en:Help:Wiki help, no matter what advantages it might have. PiotrGrochowski (talk) 14:42, 15 October 2018 (UTC)

I suggest to set up an own page "Help:Links" or "Help:Link" to contain the options <ul><li></li></ul> and <ol><li></li></ol> as well as your list template(s), provided that they are introduced with realistic use cases not as "just another opinion". Pages with style A ("my pages") and pages with style B ("your pages") without good reason will cause endless future wars, won't it? As for your claim that preferring * and # would show a "personal opinion": you remember your "unofficial poll"? I hope this helps you understand why a help page should start to teach the simplest way first. And when you claim "All list models are equally acceptable", this is wrong. A list template will have limits, and <br/> doesn't build a valid list, right? The HTML list tags are acceptable if they are well structured even in the source code since basically everyone should be able to edit the wiki not only those who are coding in HTML. Best regards --Xenwolf (talk) 15:37, 15 October 2018 (UTC)

Realistic use cases don't matter. Every single list model is subjectively best, so it's very wrong to include only one in en:Help:Wiki help. And all list models really are equally acceptable; it's racist to say that a plaintext or defined list model results in an invalid list. And the convention that an edit consisting only of a list model change should not be done is supposed to prevent the edit war bug. PiotrGrochowski (talk) 16:11, 15 October 2018 (UTC)

Maybe en:Help:Wiki help#Lists should soft redirect to en:List model, like dev:Help:Wiki help#Lists does? Whatever the final solution may be, it definitely must show all list models as possibilities that users may use, with no subjective recommendation or anything. The objective advantages and disadvantages are too specific to be shown in the xen.wiki school, and they can always be found out by users later on, so it's best to state all list models neutrally. Can't believe you are complaining while doing worse in en:Help:Wiki help. PiotrGrochowski (talk) 05:17, 16 October 2018 (UTC)

11-limit Intervals

Hello there, I see that the intervals 55/32 and 64/55 are not present in the chart on the Gallery of Just Intervals page, and I have no idea how to add them as I don't know how to add cells to the chart. As I told Mike Battaglia in a recent email, I've found both 55/32 and 64/55 extremely useful in 11-limit music as they help harmonically bridge the 16/11 fifth. They are made even more useful by the fact that they differ from septimal intervals such as 12/7 and 7/6 by only a Keenanisma. Accordingly, I use them in a 44:55:64 overtonal triads built on the octave-reduced eleventh harmonic of the tonic as a predominant chord, and this is one of the two best 11-limit chords to use for such a purpose as it is clearly distinct from a diminished chord. While this chord is strange-sounding, it can help to evoke a sense of both the strange and wonderful, particularly if followed up by a traditional dominant seventh built on the third harmonic of the tonic. Possible set-ups I've found so far include a 4:5:6 major triad built on the octave-reduced third harmonic, a 10:12:15 minor triad built on the octave-reduced fifth harmonic, a 27:32:40 minor third built on the octave-reduced twenty-seventh harmonic, and of course, the tonic triad itself. --Aura (talk) 12:15, 2 September 2020 (UTC)

Excuse me for the second message, and sorry if your user talk page isn't the right place for having this discussion, but I just found 64/55 on the list on the Gallery of Just Intervals page. However, 55/32 is still missing though, and I still don't know how to add it. --Aura (talk) 12:40, 2 September 2020 (UTC)

I tried to add some of the information (to 55/32, 64/55, Gallery of just intervals).

BTW: Welcome on board, Aura 🙂

--Xenwolf (talk) 16:48, 2 September 2020 (UTC)

Thanks! I took the time to complete the first sentence of information on 55/32, and I added information to 64/55 about the triad formed with a 5/4 major third and a 64/55 keenanismic subminor third. I hope you can test this triad out for yourself. --Aura (talk) 20:01, 2 September 2020 (UTC)

Links on my User Page

Hey, I just created an EDO impressions page- with the link at the bottom of my user page. However, the links on my user page need work in general, and I'm not sure how to go about fixing them, let alone getting my work seen on the Table of EDO impressions... Could you spare a moment and help me out? Thanks! --Aura (talk) 00:56, 4 September 2020 (UTC)

I tried my best. The links are relatively easy to understand. First remember square brackets (double for internal, single for external links). Internal links are automatically built from page titles (the case of the very first character is ignored). External links always start with http(s), the URL part stops at the first space, what follows (before the closing bracket) is taken as display text. Read the whole story under Help:Links. Have a nice day 🙂 --Xenwolf (talk) 08:36, 4 September 2020 (UTC)

Thanks a ton! Hopefully all I have to do now is study what you did this... --Aura (talk) 14:48, 4 September 2020 (UTC)

Diatonic Functions of Xenharmonic Intervals

Okay, so one thing I'm interested in is covering the diatonic functions of notes at various intervals' distance away from the tonic- you know, for microtonal composers who still want to work with tonality- I honestly think pages like 3/2 and 4/3 could benefit from having information on things like this. On another note, do we have information on the thirty-five 12edo proper modes? Pages documenting these modes would serve to gather variations and alternative tunings for these scales and modes into one place. For the record, I know that in my own microtonal composing, I tend not to go very far from my 12edo roots for reasons detaild in A recovering microtonalist's critical reaction to Why Microtonality, yet, I also can't help but agree with Mike S in his comments in Microtonalists critical reaction to a recovering microtonalists critical reaction to Why Microtonaltiy? on 7-limit and 11-limit being important- in fact, I would add the 13-limit to his list. --Aura (talk) 16:11, 5 September 2020 (UTC)

First, I guess that I'm not the right person to ask about diatonic functions of notes. Second, as far as I know there are no pages about the 35 12edo modes, but it could as well be that I only missed it/them. Third, I didn't compose anything yet. Currently I mostly help others to put information into the wiki ... I really like listening xen music of any kind, I also like "meditating" on intervals, that's why I uploaded several sound examples, especially those in prime limits above 5. But I also know that timbre is very important. BTW: today I discovered that 11/7 has a very convincing sound. --Xenwolf (talk) 19:33, 5 September 2020 (UTC)

Well, to be fair, you are one of the people who runs this wiki- at least to my knowledge- so you're one of the first people I can think of to ask about even the possibility of adding information to the wiki about the diatonic functions of notes at various intervals away from the tonic- just as a guide to help microtonal composers. Truth be told, I think Mike Battaglia could also be of help in deciding and working on the matter as he's got experience with jazz, but still, it's just as well that I approached you about this because I don't want to put stuff on this wiki if it doesn't belong here. As to whether or not there are pages on the 35 modes of 12edo that are "proper" in the sense mentioned on the Periodic scale page, I did find a page about what a Mode is. The reason I brought all this up in the first place is because I've found that in tunings closer to JI, the conventional Ionian, Dorian, Phrygian, Lydian, Mixolydian and Aeolian scales are not simply modes of the same diatonic scale, but rather, differing diatonic scales in their own right on account of using different tunings of their notes relative to one another for the purposes of establishing tonality. Locrian however proves to be an exception to this as according to my calculations, it is still a mode of the Lydian scale if you don't use 77/64 as the minor third above the tonic- I know I myself prefer to use 77/64 as the minor third above the tonic for Locrian as well as for minor scales in general so there's that. --Aura (talk) 00:40, 6 September 2020 (UTC)

If you wish to add information - including new pages - to the wiki, you are welcome. I'm very interested in learning about your perspective on modes. And should it still happen that you add duplicate information, others will point it out to us.--Xenwolf (talk) 12:06, 6 September 2020 (UTC)

Okay, so I've added the page on my diatonic scales, however, it needs a table of contents due to its size... --Aura (talk) 22:12, 6 September 2020 (UTC)

Continuation to the latter on User talk:Aura/Aura's Diatonic Scales. --Xenwolf (talk) 09:51, 7 September 2020 (UTC)

Unnoticeable Comma

Okay, so I've recently found an unnoticeable comma- 117440512/117406179- that is only slightly more than half a cent in size. It is the difference between five 33/32 quartertones and a 7/6 subminor third, as well as the difference between six 33/32 quartertones and a 77/64 minor third... I've only seen it mentioned once on this wiki aside from on talk pages- specifically on the page for 3125edo- and I've also been told that it doesn't have a name... Since this unnoticeable comma involves 11-limit quartertones, can we call it the "Quartisma"? If so, then when this comma is tempered out, then can we can call the resulting temperaments "Quartismatic"? --Aura (talk) 22:12, 6 September 2020 (UTC)

I have to ask about the name for the temperaments that temper out this comma because as I mentioned to Inthar on Sam's talk page, the comma's proposed name "Quartisma" comes from "Quarter" and "Schisma" on account of the comma both involving stacks of quartertones and being extremely small itself, and, the name for temperaments that temper out the Schisma is "Schismatic". --Aura (talk) 23:08, 6 September 2020 (UTC)

Never mind about the name for the temperaments now... I think we've settled on the name "Quartismic" for the temperament name. However, now I'm curious... I know that 159edo is the first EDO divisible by 53 to temper out the "Quartisma", however, I also see that 24edo tempers out this interval as well... So that leaves me with questions as to which EDOs temper out the "Quartisma" and which ones don't... --Aura (talk) 00:50, 7 September 2020 (UTC)

Since you're tempering out a comma in a rank-4 JI subgroup (2.3.7.11), you'll have to find 3 linearly independent (non-contorted) edos (not necessarily using their patent vals) that temper out the comma. None of the other relatively simple edos I can think of (17edo, 26edo, 34edo) do it, though. IlL (talk) 03:00, 7 September 2020 (UTC)

Apparently 46edo (using the patent val) does! So the edos that are quartismic are all edos of the form 24A + 46B + 159C, where A, B, C are integers (but the resulting edo might not be a patent val). IlL (talk) 03:04, 7 September 2020 (UTC)

I do know that the page for 3125edo makes mention of the Quartisma by way of it's ratio- 117440512/117406179. However, it's not totally clear from the text on that page whether 3125 actually tempers out the Quartisma or not. --Aura (talk) 03:18, 7 September 2020 (UTC)

I believe it does. (It's saying that all the 11 limit commas tempered out by 3125 can be found by taking linear combinations of the commas given.) IlL (talk) 03:39, 7 September 2020 (UTC)

So that's four different EDOs that temper out the quartisma, and none of these EDOs seem to have the exact same prime factorizations- though 46edo and 24edo do share a prime factor in 2... --Aura (talk) 03:49, 7 September 2020 (UTC)

I have to admit that I don't know all the necessary math for this, it is the patent vals for the intervals 33/32, 7/6 and 77/64 in 24edo and 159edo that make me suspect that these EDOs temper out the quartisma in the first place. It would be nice to confirm these findings with the more rigorous math- however, I'm not in a position to do this as I don't know the right equations and stuff, and chances are that I wouldn't even know the meanings of some of the symbols involved... --Aura (talk) 04:01, 7 September 2020 (UTC)

3125 = 17*159 + 5*46 + 8*24 so we're ok unless it's a non-patent val of 3125 or something. [It's not about the prime factorization of the edo number, it's about whether the edo is a sum of some number of the edos 24, 46 and 159 or not.] IlL (talk) 04:17, 7 September 2020 (UTC)

Okay then... With this knowledge in hand, let's see if we can find other quartismic EDOs... Chances are high that any additional EDOs we find are bound to have ridiculously small step sizes though... --Aura (talk) 04:27, 7 September 2020 (UTC)

Oh and before we continue, let's take this to your own talk page, shall we, Inthar?

Sorry about blowing up your talk page Xenwolf... --Aura (talk) 04:34, 7 September 2020 (UTC)

Have you been following the ongoing discussion on how I've dubbed 117440512/117406179 the "quartisma" and on what EDOs temper it out? I bring this up because when we gather enough data, I'm thinking we should add pages about both the quartisma and the temperaments that result from it being tempered out. That and I hope other people in the microtonal community like the name I've picked... --Aura (talk) 00:19, 8 September 2020 (UTC)

I, personally, am not a big friend of the name "Quartisma". Is it really obvious that it comes from "Quarter tone" and "Schisma"? But I do not want to stop you here in any way. Good luck! 🙂 --Xenwolf (talk) 06:53, 8 September 2020 (UTC)

Well, to be frank, even if it isn't obvious, the term "quart" itself often means "quarter"- even if "quart" is dated or even obsolete, see this Wiktionary entry. Besides, "quartertonisma" strikes me as being a bit too long and awkward... --Aura (talk) 12:32, 8 September 2020 (UTC)

Hey Xenwolf, I see you're doing work on microtemperaments right about now. For the record the quartisma is about 0.50619 cents in size, and so tempering it out results in a microtemperament. I figured I'd bring this up while you're at it. --Aura (talk) 17:10, 11 September 2020 (UTC)

Hi Aura, I'm only formally working on redirects and categories (gardening/housekeeping stuff). if you feel that something should be linked or categorized, don't hesitate to do it yourself! (to be honest I'm not an expert in (micro)temperament terminology).

Best regards --Xenwolf (talk) 17:22, 11 September 2020 (UTC)

Tridecimal Neutral Intervals

I don't know about you, but something tells me we need additional names for 39/32 and 64/39 that reference how they are tridecimal neutral intervals. I know that I personally would prefer to call 39/32 the "Tridecimal Narrow Neutral Third" while calling 16/13 the "Tridecimal Wide Neutral Third". Similarly, I would call 13/8 the "Tridecimal Narrow Neutral Sixth" while calling 64/39 the "Tridecimal Wide Neutral Sixth". --Aura (talk) 00:19, 8 September 2020 (UTC)

I have nothing against the names you suggest. In the opposite: I'm a bit lost with finding the right name. Please change the pages at your own free discretion. --Xenwolf (talk) 06:43, 8 September 2020 (UTC)

I suggest small tridecimal neutral third and (large/greater) tridecimal neutral third. FloraC (talk) 07:45, 8 September 2020 (UTC)

Okay then. --Aura (talk) 12:20, 8 September 2020 (UTC)

Linking Info on Articles to Relevant Comments on Talk Pages

Hello Xenwolf, I just recently modified the page on 3125edo to reflect how it is so far the only EDO known to have been confirmed as tempering out the quartisma prior to me finding out that comma's significance. I can see from the page's history at its current site address that the info on 3125edo tempering out the quartisma has been known at least since 2015 when it was imported here by Gene Ward Smith- or by someone else with the username "genewardsmith" on Wikispaces. However, I certainly can't forget the day I discovered the quartisma's significance, and thus, since the earliest comments about the quartisma's significance on this Wiki are dated September 6th, 2020, I'd like to see this confirmed by means of a link to the relevant discussions on Sam's talkpage and your talkpage. --Aura (talk) 02:54, 9 September 2020 (UTC)

If you link to talks, it could help to add the permanent link as well (see this example). --Xenwolf (talk) 05:45, 9 September 2020 (UTC)

Okay, here's a link to the other relevant comment... I hope this helps...

Cantonisma

Hey, I just checked the calculations with wolfram alpha, and it turns out that 159edo tempers out the cantonisma- the unnoticeable comma which is the difference between three 14/13 trienthirds and one 5/4 major third. I'm wondering if there should be a page on the cantonisma and those temperaments that temper it out... --Aura (talk) 15:18, 10 September 2020 (UTC)

Why not? --Xenwolf (talk) 21:16, 10 September 2020 (UTC)

Classifying Prime Limits by Diatonic Function

I have an idea as to how to classify primes based on their functions relative to the tonic, but I don't know if I should modify the harmonic limit page for this or not. I know I would classify the 2-limit as being the "Pitch Class Prime" in light of how pitches related to the tonic by powers of two naturally seem to our hearing to be the same as the tonic in ways that other primes don't. I would classify the 3-limit and the 5-limit as the "Diatonic Primes" for their key functions in just diatonic and just chromatic music. I would classify the 7-limit, 11-limit and 13-limit as the "Paradiatonic Primes because of their relative ease of use as accidentals in otherwise diatonic keys, and, due to the fact that these relatively low primes can create intervals that can be readily used as alongside diatonic intervals or even as substitutions for them. I'd go on to classify the 17-limit and 19-limit as "Quasidiatonic Primes" owing to the most basic intervals in these families having striking similarities to diatonic intervals, but with greater complexity. I'd then go on to label the 23-limit, the 29-limit, and 31-limit the "Pseudodiatonic Primes" because even though these primes are not diatonic by any stretch, they can still serve as substitutes for the paradiatonic primes in a pinch. Does all this sound like a good idea to you? --Aura (talk) 19:17, 11 September 2020 (UTC)

I think the harmonic limit page is a good place for your classification concept (maybe as a section?), but I must say that the classifications (especially the distinction between Quasi and Pseudo) after Paradiatonic look a bit strange (or artificial/sophisticated) to me. In general, I don't believe in such a high precision of the human ear. --Xenwolf (talk) 19:31, 11 September 2020 (UTC)

The distincton between "Quasidiatonic Primes" and "Pseudodiatonic Primes" boils down to the fact that the base 17-limit and 19-limit intervals closely resemble diatonic intervals, whereas this is not the case for the 23-limit, 29-limit, and 31-limit. This has the effect of determining how well the related ratios tend to blend in with diatonic harmonies. --Aura (talk) 19:42, 11 September 2020 (UTC)

Well, I'm not the one who will draw red lines here. Please add you ideas freely! --Xenwolf (talk) 19:46, 11 September 2020 (UTC)

Okay Xenwolf, I've posted my ideas of consonance, feel free to check this stuff out. --Aura (talk) 05:15, 12 September 2020 (UTC)

Spitting "Quartimic Temperaments" into multiple pages

Hey! Given what you are doing, I think it would be best if we split the page "Quartimic Temperaments" into "Quartisma" and "Quartismic Family". The page "Quartisma" would be the page containing the information on the quartisma itself, while the page "Quartismic Family" could contain the information on the various quartismic temperaments. With this in mind, the page "Quartisma" would read as follows:

The quartisma or Saquinlu-azo comma is a comma with a ratio of 117440512/117406179 and a monzo of [24 -6 0 1 -5⟩. It is an unnoticeable comma of the 11-limit- specifically one of the the 2.9.7.11 subgroup- with a value of approximately 0.50619 cents. The quartisma is significant on account of it being the difference between a stack of five 33/32 quartertones and one 7/6 subminor third in Just Intonation. The quartismic temperament or Saquinlu-azo temperament is the temperament that tempers out this comma, for the list of such temperaments, see Quartismic family.

Of course, while we're in the process of splitting things up, we need to keep the old "Quartimic Temperaments". Once all the data has been retrieved- including the data from the talk pages- then we can delete the old "Quartimic Temperaments" page.

I'd appreciate some help with this. --Aura (talk) 13:39, 13 September 2020 (UTC)

Looks good so far. Would it be okay to just rename the Quartismic temperaments article into Quartismic family? --Xenwolf (talk) 13:48, 13 September 2020 (UTC)

Actually, yes, but I don't know how to do that... --Aura (talk) 13:55, 13 September 2020 (UTC)

Done. (Renaming requires organizer rights which you haven't.) --Xenwolf (talk) 13:57, 13 September 2020 (UTC)

Quartismic family seems to have a good start now. --Xenwolf (talk) 14:22, 13 September 2020 (UTC)
PS: I'll be a bit AFK for now.

Neapolitan Augmented Sixth

Hey, Xenwolf, I know I gave 225/128 the name "Neapolitan Augmented Sixth" on this wiki on the assumption that there were other people who have also referred to this interval by that same name- even if there's only a handful, as the two Neapolitan scales don't seem to be all that well known by musicians at large. However, I can't help but wonder if I inadvertently coined my own name for 225/128, because I don't personally know of any other people besides me who refer to it by the name "Neapolitan Augmented Sixth". All I know for sure is that the Just Semitone has a ratio of 16/15, and that in any Neapolitan scale, there's an area where two semitones occur consecutively, adding up to a diminished third- the octave complement of this is an augmented sixth. So it stands to reason- at least from what I know- that in any 5-limit just Neapolitan scale, there's an area where two 16/15 semitones occur consecutively, adding up to a 256/225 diminished third, and the octave complement of this is a 225/128 augmented sixth... I just want to know for sure that I'm doing this right and not spreading misinformation... --Aura (talk) 19:35, 16 September 2020 (UTC)

I don't know if you are right. Let's see if another one knows better ... --Xenwolf (talk) 19:45, 16 September 2020 (UTC)

I should point out that if my assumption about the "Neapolitan Augmented Sixth" is correct, however, it might help explain why people say 7/4 is also an augmented sixth, as 7/4 is smaller than 225/128, and the two are equated in marvel temperaments- even though this sort of thing seems to bother Flora. --Aura (talk) 19:46, 16 September 2020 (UTC)

I see no problem with intervals serving two (or more) different functions. This is common in 12edo, the intervals (on interval pages) are not bound to any temperament or ET. --Xenwolf (talk) 19:51, 16 September 2020 (UTC)

Right then. I guess the secondary name "Neapolitan Augmented Sixth" for 225/128 stays. However, I should also point out that it seems that notes in the region roughly between 256/255 and 7/6 and in the region roughly between 12/7 and 225/128 are the most susceptible to having multiple functions even within the same system. If so, then I guess it's a good thing I labeled the paradiatonic functions of these regions "Varicant" and "Contravaricant", as "Varicant" means "straddling". For the record, if you want to know which region I've labeled what, well, all you have to do is look at the scale's direction of construction, as when you start from the Tonic and travel in this direction, the "Contravaricant" region is the one that's encountered first, with the "Varicant" region being its counterpart. --Aura (talk) 19:59, 16 September 2020 (UTC)

The (contra)varicant naming seems helpful. Have you maybe an image at hand for it, so your "all you have to do is look" would fit better. I'm really not great at finding/building scales. --Xenwolf (talk) 20:06, 16 September 2020 (UTC)

I'll be able to do this better once my theory on treble-down tonality and my terminology on these two pages become more firmly established, as this sort of theory is largely unique to me at this point. --Aura (talk) 20:16, 16 September 2020 (UTC)

Do also bear in mind that I'm having to make sure to pick the optimal boundaries for some of the different diatonic and paradiatonic regions at the moment. --Aura (talk) 20:26, 16 September 2020 (UTC)

Diatonic and Paradiatonic Function Map

Hey Xenwolf, remember when you asked for an image for the locations of different diatonic and paradiatonic regions? Well, here it is...

I hope you find this helpful... Do bear in mind that this is a preliminary version... --Aura (talk) 18:04, 17 September 2020 (UTC)

Thanks so much for the image. --Xenwolf (talk) 08:18, 18 September 2020 (UTC)

What do you plan on doing with the image? --Aura (talk) 09:02, 18 September 2020 (UTC)

Oh, and you're welcome... --Aura (talk) 09:03, 18 September 2020 (UTC)

It's interesting to see the regions (zones) and their names and the borders. Concerning the relation to known concepts, it could as well include the positions of some just intervals such as 5/4 or 7/4 (even if they don't represent zones or zone borders). And, well, the legend is a bit confusing (Where is up and down?). Wouldn't it be less confusing to use ratios below 1.0 for undertones (such as 1/2 .. 2/3 .. 3/4 .. 1/1 .. 4/3 .. 3/2 .. 2/1)? And, sorry for so much criticism, could you increase the resolution a bit? --Xenwolf (talk) 10:03, 18 September 2020 (UTC)

I could definitely make a larger chart and show the positions of some of the more well-known intervals. However, I need a good way to really show how Bass-Up contrasts with Treble-Down in terms of structure. The starting point is in the center of the chart as 1/1 is guaranteed to be your initial Tonic- as is 2/1- though I suppose it wouldn't hurt to make that clearer. The reason I used ratios above 1/1 for all intervals regardless of direction is to show distance from the Tonic in the center- I mean, the Dominant really is characterized by being situated at 3/2 away from the Tonic in the direction of construction. --Aura (talk) 10:22, 18 September 2020 (UTC)

Okay, I didn't know that the site wouldn't let me replace the older file with a new version... Let me try and post the newest version for real this time... --Aura (talk) 01:12, 19 September 2020 (UTC)

Very interesting graph. Thanks for sharing. --Xenwolf (talk) 19:50, 20 September 2020 (UTC)

Thanks, can you make more sense of this graph than you could the earlier version? --Aura (talk) 19:55, 20 September 2020 (UTC)

Names and functions of 45/44, 55/54 and 33/32

Hey Xenwolf, I see in your recent creation of the 242/225 article that you said that 45/44 felt like an undecimal chroma to you. You're not the first to say something to that effect, as I myself have called 45/44 the "greater undecimal parachroma" and 55/54 the "lesser undecimal parachroma". That said, since we've also decided that 33/32 is somewhat similar in the sense of having chroma-like properties, and since a "parachroma" is an interval with properties akin to a chroma, only involving primes 7, 11, and thirteen, I think we need to give 33/32 a name that both reflects its parachromatic nature and sets it apart from both 45/44 and 55/54. Do you have any ideas? --Aura (talk) 19:44, 20 September 2020 (UTC)

Just for the record, the only name I can currently think of for 33/32 is the "undecimal parachromatic quartertone". This name contrasts with other more complicated undecimal intervals in the area such as 512/495, which could perhaps be called the "undecimal paradiatonic quartertone"... --Aura (talk) 19:50, 20 September 2020 (UTC)

I have to admit that this observation is very new to me. I'm not even sure if I didn't mix things up. I need more time for this. BTW: I like the varicant/contravarivant regions of your graph. --Xenwolf (talk) 19:56, 20 September 2020 (UTC)

Trust me, you're right about 45/44. I know because I've attempted to use it before in my own compositions. Oh, and thanks for your comments on the graph! --Aura (talk) 19:58, 20 September 2020 (UTC)

If you're worried about whether or not you can use 45/44 in melodies, well, I can assure you from experience that you can use even 64/63 in melodies, and that's even smaller than 45/44. I'd only really be concerned on this front if the interval was smaller than 25 cents. --Aura (talk) 20:03, 20 September 2020 (UTC)

Names for New Third and Sixth

Xenwolf, there's already both a tridecimal minor third in 13/11 and a tridecimal major sixth in 22/13... We need to come up with some better names... --Aura (talk) 20:13, 21 September 2020 (UTC)

I see that this new minor third and new major sixth differ from the old ones by 693/676... Perhaps the new minor third and new major sixth should be named for this comma... That is, once we give it a name... --Aura (talk) 20:15, 21 September 2020 (UTC)

As to solve this issue, any suggestion is welcome. I already looked into the gallery of just intervals and saw the name clashes I caused. --Xenwolf (talk) 20:19, 21 September 2020 (UTC)

BTW: it can also be that these pages seem useless to you. I must honestly admit that sometimes I simply let myself be driven by curiosity for unusual sounds. --Xenwolf (talk) 20:21, 21 September 2020 (UTC)

No problem...

Hmm... I have to admit we need a good name for the 693/676 comma... Wait- this is no comma... it has a value of about 42.9985270 cents! --Aura (talk) 20:36, 21 September 2020 (UTC)

Yeah, calling 693/676 a "comma" is a bad idea... I mean, the idea of 33/32 being called a "comma" already bugs me considering it's a very useful quartertone, not something we want to try and temper out- unless of course we're talking about EDOs like 12edo or something... --Aura (talk) 20:41, 21 September 2020 (UTC)

Being a comma is not a death sentence for an interval ;) As I learned, we have these ranges: 0 .. 3.5 cents for unnoticeable, 3.5 .. 30 cents for "comma", 30 .. 100 cents for medium comma, and 100 cents and above for large commas. Especially the "commacity" is another dimension. I'd say even the Tone 9/8 is some kind of comma. I think that the higher the limit the more intervals fight for being the representative of that limit, the classic diatonic nomenclature (minor/major) helps a bit but this is also limited. --Xenwolf (talk) 21:02, 21 September 2020 (UTC)

At the same time, however, only intervals above 25 cents can be reasonably used as melodic intervals, and, the way I see it, commas in the purest sense can't really do that well. Yes, I'm aware that there are limitations to the classic diatonic nomenclature, however, said nomenclature is still needed, even if we must incorporate it into a larger system. --Aura (talk) 02:17, 22 September 2020 (UTC)

For now, what about "submajor" and "supraminor" for 26/21 and 63/52? Since there is septendecimal submajor third 21/17 and septendecimal supraminor third 17/14. FloraC (talk) 02:34, 22 September 2020 (UTC)

Hmm... I think that might work, but I can't speak for Xenwolf on this... --Aura (talk) 02:58, 22 September 2020 (UTC)

Thanks for the help, I changed the names of 26/21, 63/52, 104/63, and 21/13 accordingly. --Xenwolf (talk) 05:19, 22 September 2020 (UTC)

MOS scales of various EDOs

Hey, Xenwolf, since 159edo now has its own category, should we add 79MOS 159edo to said category? To be fair, I'm also proposing that we link 31edo MOS scales under Category:31edo in the same way, and that we do the same for other edos and their MOS scales. --Aura (talk) 18:18, 2 October 2020 (UTC)

This absolutely makes sense. Just don't be afraid to categorize pages! Categorizing is by no means reserved for organizers only, on the contrary: if you discover that a category is missing or too much, think about how it could be changed and express suggestions for improvement actively (by making appropriate changes). --Xenwolf (talk) 18:26, 2 October 2020 (UTC)

PS: (already changed in your comment): Linking categories is of course possible. It's done by placing a colon just after the opening bracket pair, like this [[:Category:31edo]]. --Xenwolf (talk) 18:33, 2 October 2020 (UTC)

Notation for 159edo

Excuse me, Xenwolf, I've been waiting for a response from Mike Battaglia on this, but he seems to be busy or something... I'd like to hear what y'all think of this proposed system for notation in 159edo- admittedly the drawing is a bit crude, but all the same, I'd like to know if this combination of mainstream quartertone accidentals, Helmholz notation, and Ups and Downs notation is any good...

You should notice right away that I'm combining simple accidentals to create composite accidentals- at least this way there aren't so many simple accidentals to memorize, and you won't loose track of all the iterations of the Ups and Downs accidentals... Any thoughts? --Aura (talk) 18:58, 2 October 2020 (UTC)

It's hard for me to value this: I have little experiences with high-order EDOs (well, I already know that 53edo (=159/3) has good approximations of 5-limit ratios). In the image, it's unclear to me where I am at a given tick. However, The idea of combining accidentals seems good to me, provided the (de)composition rules are simple and unambiguous. What about the "grammar" of this system: what kind of music (scales etc.) is this notation supposed to support? --Xenwolf (talk) 19:42, 2 October 2020 (UTC)

Well, how should I make it easier for you to keep track of where you are at any given tick?

As for what this is supposed to support, I'm looking to support things like different varieties of near-just diatonic scales, as well as near-just harmonic major scales, near-just harmonic minor scales, near-just melodic minor scales, and near-just neapolitan scales. I'm also thinking of supporting of at least two proper 7-limit heptatonic scales with modes and derivatives using supermajor and subminor triads, and I'm also looking to support basic 11-limit music. Basically, I'm trying to make high-order edos like 159edo more accessible to composers with a background in 12edo and 24edo. Still, it's clear that this system needs some work. --Aura (talk) 21:03, 2 October 2020 (UTC)

It seems to me that you are searching for a basis (or superset) of actual tonal systems. Do you know 205edo, which builds the basis of the Hunt System? Maybe the theory webpages of the author could be of help for you. About the ticks: you maybe show only the set of accidentals - I searched for the 159 relation in that graph. So the tick distance seem to be 1\159, right? --Xenwolf (talk) 08:52, 3 October 2020 (UTC)

The tick distance on that chart is indeed 1\159, and the distance between the larger ticks is one whole tone of 9/8. I feel it's necessary to show the ticks on some level to show how the accidentals relate to one another. That said, I wouldn't mind removing the composite accidentals and only showing the simple accidentals on the chart. That said, the Helmholz arrows indicating the raising or lowering by a syntonic comma seem to need a host accidental in order to even appear to begin with, and the only thing new about their appearance in this chart is that they can now be bound to mainstream quartertone accidentals. --Aura (talk) 10:04, 3 October 2020 (UTC)

There is another issue with the graphics that I should have pointed out a long time ago, I'm sorry it's only now: it's the resolution again: the symbols are to small. I'm trying to make a SVG image myself of it (right now installing font QMuML9.ttf that should contain quarter tone accidentals...) --Xenwolf (talk) 10:29, 3 October 2020 (UTC)

Well, the thing is that I'm not exactly the best one to ask for high-resolution images without large image size seeing as I'm stuck with MS paint for creating images in the first place... --Aura (talk) 10:33, 3 October 2020 (UTC)

Did I mention that chances are high that one might have difficulty combining the Helmholz syntonic comma arrows with the quartertone accidentals using existing fonts? I mean, the idea of combining these two things together seems fairly new, as Helmholz notation itself has a different symbols for 11-limit demisharps and seems to lack symbols for both 11-limit sesquisharps and sesquiflats... --Aura (talk) 10:38, 3 October 2020 (UTC)

[MS paint] I guessed that, and that's why I decided to try a version myself (SVG images, supported by the wiki software, can be created with Inkscape, but it's not as easy for beginners, I have some experiences with it). [Did I mention] The font mentioned above was a miss, as was the Unicode "Musical Symbols Block", the latter only contains one flavor for quarter-tone accidentals, so I have to pick the ones you use from Wikipedia Commons. --Xenwolf (talk) 10:50, 3 October 2020 (UTC)

For the record, MuseScore 3 seems to support both Helmholz notation and the quartertone accidentals I use. However, I'm again confronted with the problem of combining the Helmholtz syntonic comma arrows with the mainstream quartertone accidentals... --Aura (talk) 11:15, 3 October 2020 (UTC)

PS: please be a bit less agile on your questions/comments. Changing questions afterwards creates edit conflicts to the one who want's to answer (this is the 5th time I try to save my answer). --Xenwolf (talk) 10:50, 3 October 2020 (UTC)

Sorry about that... I must confess I feel the need to get the comments and questions down as quickly as possible before I forget about them... --Aura (talk) 11:06, 3 October 2020 (UTC)

I can't believe I forgot about this, but I honestly think that there are other 11-limit chromas that need to be addressed besides just 33/32, as 45/44 and 55/54 seem to also be worth taking account of. Even though I'm in favor of not only making a new version of Helmholtz/Ellis notation in which the current symbol for raising by 33/32 is replaced by the mainstream demi-sharp accidental but also putting the current Helmholtz/Ellis symbol for raising by 33/32 to use in representing one of the other 11-limit chromas instead, the fact is that I don't have the capabilities nor the permissions to do such a thing myself... --Aura (talk) 10:47, 3 October 2020 (UTC)

[...unindenting...]

I finally got the picture done, as said with Inkscape (originally in SVG format), here is a PNG preview:

It's not perfect, but hopefully better to read now. Well, a bit of legend is still missing. Are the accidentals reproduced correctly? --Xenwolf (talk) 13:28, 3 October 2020 (UTC)

I think that the sharps, flats, naturals, demisharps, demiflats, sesquisharps and sesquiflats are indeed reproduced correctly, as are the Ups-and-Downs-derived accidentals- which I'll simply call up-darts and down-darts. However, when it come to both the Helmholtz syntonic comma arrows, as wells as the Helmholtz septimal accidentals, you might find help in reproducing them by looking at the Helmholtz-Ellis notation page. On another note, I realized in looking this over that I myself botched some of the composite accidentals. Specifically, for the composite accidentals comprised of the sesquisharp and the different varieties of down-darts, as the two elements in these composite accidentals should be arranged in the same order as in the combinations of the sesquisharp and the up-darts... --Aura (talk) 16:58, 3 October 2020 (UTC)

I reworked the file (same filename, if you don't see changes, force a browser reload). The symbols are now based on the HEJI SVG we already have. I'd upload the combinations you used for your notation that are not part of HEJI (of quartertone accidentals with syntonic commas). I also started the page 159edo notation with a table that contains inline combinations of some symbols, I hope I counted correctly. --Xenwolf (talk) 12:23, 4 October 2020 (UTC)

After I made a few corrections in the table, I checked things over, and I'd definitely say you've counted correctly. --Aura (talk) 17:10, 4 October 2020 (UTC)

[...unindenting...]

Okay, so, I'm considering the idea of extending the current 159edo notation system to the 13-limit, with this being the highest prime extension due to the 13-limit being the last paradiatonic prime, and the last one that offers something new other than modulation possibilities. However, this would involve further modifying Helmholtz-Ellis notation to better accommodate trientones (one third tones) and stuff such, and I'm also considering other alterations along the same lines- for instance, reviving the original Helmholtz-Ellis 11-limit quartertone glyph and putting it to a different use relative to the 11-limit to represent a raising by 45/44, and pairing it with a new symbol to represent a lowering by 45/44. However, I need more feedback on our current 159edo system first, and so far, all I know is that I need to build on the familiar in order to create this notation system, which, if all goes well, can be integrated with an improved version of the SHEFKHED interval naming system that has been extended to 171edo... --Aura (talk) 21:36, 6 October 2020 (UTC)

I think it is good to have a basis for discussion at all, it does not have to be perfect. --Xenwolf (talk) 21:57, 6 October 2020 (UTC)

What do you mean by that? --Aura (talk) 22:00, 6 October 2020 (UTC)

I picked out your more feedback on our current 159edo system because I find that it would be helpful to wait for responses from people who did not participate in the development, like Kite. I'm still not experienced with high-order EDOs. I think all these additional characters reduce the legibility of the notation in a considerable way. When I compare this with the conventional system, say for baroque music, where I casually pick up the accidentals and do not really have to decipher them, also because there is usually only one variant that makes musical sense, I get almost dizzy in our "battle of symbols". In the classic notation, accidentals are not just modifiers for single notes, but signs that indicate the change of the tonal base. I'm still searching for a parallel in alternative tonal systems. --Xenwolf (talk) 22:36, 6 October 2020 (UTC)

You are right in saying that in the classic notation, accidentals are not just modifiers for single notes, but signs that indicate the change of the tonal base. The classical and quartertone accidentals as found in this system actually have the same function, believe it or not- yes, this is even true of the combinations of these accidentals and the syntonic comma arrows. I mean, if Jacob Collier can seamlessly modulate from E-Natrual Major to G-Demisharp Major, I want to know the specifics of the notes he uses, and if changing keys seamlessly like that involves using different tunings for notes, I want to see the tuning changes in action- hence the need for so many accidentals. --Aura (talk) 22:50, 6 October 2020 (UTC)

Nevertheless, we do need feedback from others who did not participate in the development, and I'm hoping that my reasoning for the sheer number of accidentals- namely my need to see tuning changes in action- makes sense to these other people as well. --Aura (talk) 23:08, 6 October 2020 (UTC)

[...unindenting...]

Hey, Xenwolf, I just realized- the rastma, 243/242, is something akin to an 11-limit version of the syntonic comma... What's more striking is that a stack of three rastmas differs from a syntonic comma by 1771561/1771470, which has a value of only about 0.08893 cents... So, perhaps 243/242 is the interval that we need to consider as a JI basis for the single step of 159edo... --Aura (talk) 07:21, 7 October 2020 (UTC)

So, based on Kite's feedback, I have several proposals for modifying the current Helmholtz-Ellis-based system- see our discussion on dart symbols. --Aura (talk) 15:01, 7 October 2020 (UTC)

Xenwolf, do you have time to help me rework our Helmholtz-Ellis-based notations system? --Aura (talk) 14:10, 8 October 2020 (UTC)

Hardly this time, but it depends on whether there are concrete questions to answer (easy), to discuss topics in their full breadth (hard), or to make glyphs (impossible). For me it's still unclear how your approach relates to 205edo one of Hunt. Did you have a look on it (41x5 leads to a system with a perfect 3-limit approximation and very good to fair approximations of other limits)? --Xenwolf (talk) 14:28, 8 October 2020 (UTC)

Okay, firstly, the steps of 205edo are a bit too small, and are likely to blend into one another, whereas 159edo doesn't have that problem as the step size is greater than 7 cents. In comparing the patent vals up to the 17-limit, I can see that the approximations of the 3-limit, 7-limit and 11-limit in 159edo are superior to those of 205edo in terms of absolute error, though the reverse is true when it comes to the 5-limit, the 13-limit and the 17-limit. Considering that the 3-limit is the major diatonic navigational prime for the main key signatures, while the 11-limit is the major paradiatonic navigational prime for things like quartertone key signatures, and that both of these prime limits are significant for the many microtonalists who end up starting with 24edo on account of 24edo being perhaps one the best known microtonal systems, I'd say that 159edo's better performance in these limits is a major factor to be considered, as are the issues with 205edo's smaller stepsize. Are there any other facets of the relationship between my approach to 159edo and Hunt's approach to 205edo that you wish to know about? --Aura (talk) 16:02, 8 October 2020 (UTC)

Thanks for having a look into it.

You wrote: the approximations of the 3-limit, 7-limit and 11-limit in 159edo are superior - I guess you mean p-limit intervals here? How do you measure approximation quality (I mean 9/7 is also a 7-limit interval)? I tried this calculator but was not satisfied with the idea of averaging. For me it is also still unclear which set of musical intervals can be regarded as sufficiently representative, if such an idea makes sense at all... --Xenwolf (talk) 18:59, 8 October 2020 (UTC)

For the record, that whole phrase reads: the approximations of the 3-limit, 7-limit and 11-limit in 159edo are superior to those of 205edo in terms of absolute error. Long story short, I measure the absolute errors in cents as they accumulate when tempered p-limit intervals are stacked, and the number of such intervals I can stack without the absolute error exceeding an unnoticeable comma's distance of 3.5 cents determines the quality of representation, and thus the portions of the harmonic lattice that can be sufficiently represented by any given EDO. --Aura (talk) 19:44, 8 October 2020 (UTC)

For prime limits that form the backbone of key signature navigation such as the 3-limit and the 11-limit, having a high number of tempered intervals that can be stacked without exceeding an unnoticeable comma's distance of 3.5 cents is actually pretty important. --Aura (talk) 19:52, 8 October 2020 (UTC)

In the case of 9/7, we have two prime factors to consider- the 3-limit, and the 7-limit. Now, I can already assure you that you can only use one tempered 7-limit interval max before the absolute error exceeds 3.5 cents, as after 7/4, the next interval in the 7-limit chain is 49/32, and the difference between the JI version and the 159edo-tempered version exceeds 3.5 cents, and this is also true for the 205edo-tempered version of 49/32. However, when two different EDOs have the same number of intervals of a given p-limit that can be stacked before the absolute error exceeds 3.5 cents, it is the absolute error in cents of the tempered stack relative to the JI equvalent that determines which EDO is superior for representing that p-limit, with the better EDO for representation having the smaller absolute error in cents. --Aura (talk) 20:05, 8 October 2020 (UTC)

Using the same calculator that you linked, I tested how 159edo and 205edo each represent this set of intervals- 3/2, 9/8, 27/16, 81/64, 243/128, 729/512, 5/4, 25/16, 125/64, 625/512, 7/4, 49/32, 343/256, 11/8, 121/64, 13/8, 169/128, 17/16 and 289/256- and as I'm forced to limit the interval set somehow, I've decided that the odd-limit of any interval in the set has to be less than 1024. I looked for the number of "P" ratings given by both 205edo and 159edo, as "P" ratings are the only ratings I'm really interested in at this point, and I also looked at their distribution. Both 205edo and 159edo give 7 "P" ratings total out of this set, and are surpassed in this respect by 147edo, which has 8. However, one of the P-rated intervals for 147edo is for 343/326, the best approximation of which cannot be reached by stacking three of 147edo's best tempered version of 7/4 and octave reducing, thus resulting in this interval's disqualification. Furthermore, the 147edo-tempered versions of six of the other 7 intervals in the starting interval set given a "P" rating in Hunt's system have absolute errors in cents that are greater than those of their 159edo-tempered counterparts which are also P-rated- a decisive loss for 147edo. --Aura (talk) 02:13, 9 October 2020 (UTC)

As for the remaining head to head comparison of 159edo and 205edo in terms of how good their representation is, one of the P-rated intervals for 205edo is 49/32, the best approximation of which cannot be reached by stacking two of 205edo's best tempered version of 7/4 and octave reducing, resulting in this interval's disqualification. Four of 205edo's remaining P-rated intervals are all solidly in the in the 5-limit chain, and another P-rated interval is 17/16- the 205edo-tempered version of which is better than the 159edo-tempered version- the final P-rated interval for 205edo is 3/2, and 159edo-tempered version of this interval has less absolute error in cents than the 205edo-tempered version, leaving 205edo with only 5 P-rated intervals that are not outperformed by their 159edo counterparts. This means a decisive loss for 205edo. --Aura (talk) 02:40, 9 October 2020 (UTC)

Sorry about the long string of comments... I hope you can get through them all, because I want to know your thoughts on the process I used and my reasoning for choosing 159edo over 205edo. --Aura (talk) 03:09, 9 October 2020 (UTC)

[...unindenting...]

Xenwolf, do you have time to help me remake glyphs and stuff for a new notation system? I want to take the feedback from Sam and Kite into account for this... --Aura (talk) 15:28, 13 October 2020 (UTC)

That depends on how well you can explain what you need. I think it should be possible to describe a toolbox, graphical elements, layout aspects. A rough sketch might also help to illustrate things. --Xenwolf (talk) 18:46, 13 October 2020 (UTC)

Right. I hope my descriptions in the new section of the relevant talk page can be of help. The only issue I can think of so far is that I need to come up with a good way to represent the rastma... --Aura (talk) 19:01, 13 October 2020 (UTC)

New Interval Categorizations

Continuing our discussion from the 5/4 talk page, do you think my proposal for new interval categorizations is at least half decent? I mean, if "classic" is too ambiguous, we need to find better descriptors for intervals like 5/4, don't we? --Aura (talk) 16:56, 9 October 2020 (UTC)

Sorry, I'm not in the mood to participate in this discussion right now. --Xenwolf (talk) 17:36, 9 October 2020 (UTC)

Ah. Perhaps we can have this discussion at another time then. --Aura (talk) 18:30, 9 October 2020 (UTC)

Another Comma

Hey Xenwolf, I've found this unnoticeable comma- 1771561/1769472- that marks the difference between three 128/121 semitones and one 32/27 minor third, and I would like to give it a name... Since the 3-limit and the 11-limit are both major navigational primes, I think we can call this comma the "nexusma", or the "nexus comma" or something like that... What do you think? --Aura (talk) 06:06, 14 October 2020 (UTC)

Sorry I don't see how you reach "nexus" here. --Xenwolf (talk) 12:27, 14 October 2020 (UTC)

Tempering out 1771561/1769472 leads to the joining of two navigational primes limits- the 3-limit and the 11-limit- and "nexus" means "a connection or series of connections linking two or more things". --Aura (talk) 14:53, 14 October 2020 (UTC)

If "nexus" isn't a good basis for a name, what's another term that reflects this joining of two navigational primes? --Aura (talk) 17:39, 14 October 2020 (UTC)

If I understand you right, you say 3 and 11 are "navigational primes"; That they are primes is of course already known to me, but I lack any idea what exactly you could mean by "navigational".

BTW: your image File:Possible Quartertone Accidentals.png looks quite clear to me. --Xenwolf (talk) 18:01, 14 October 2020 (UTC)

Navigational primes are those that lay the groundwork for defining key signatures. The 3-limit defines the primary diatonic key signatures, while the 11-limit defines paradiatonic and secondary diatonic key signatures. While the 5-limit, the 7-limit and the 13-limit also help define key signatures, they only define the exact variant of any given key signature- for instance, in distinguishing an Intense Major key from the standard Pythagorean Major key. --Aura (talk) 18:41, 14 October 2020 (UTC)

Examples of primary diatonic key signatures include C Major, G Major, G-Sharp Minor, B-Flat Minor, and so on. Examples of secondary diatonic key signatures include G-Demisharp Major, F-Demisharp Minor, B-Demiflat Major, and D-Demisharp Minor. --Aura (talk) 18:48, 14 October 2020 (UTC)

So, does my definition of "navigational primes" as per this page make sense? If so, does my idea of calling 1771561/1769472 the "nexusma", or the "nexus comma" also make sense? --Aura (talk) 17:27, 15 October 2020 (UTC)

Yeah, that kind of makes sense. But I'm not fully convinced by the high priority you assign to 11 after 3. --Xenwolf (talk) 17:50, 15 October 2020 (UTC)

So, anything I need to think about in terms of my reasoning for assigning the 11-limit such a high priority? What are the objections I need to answer? --Aura (talk) 18:06, 15 October 2020 (UTC)

I currently have not the time to read and study a lot of text. I read your last additions but maybe not as carefully as you may expect. I have no experience with quartertone music so far, so I probably have difficulties with things that are obvious in your eyes. If I look at it from a mathematical perspective, I only see that the higher the p-limit, the higher the density of fractions between 1 and 2. But please don't let my personal objections stop you from working out your theories in the Wiki. You are welcome to do so in the main namespace of the wiki; it's really not that new pages would have to be created as subpages of the user page and then go through a review process. And I have far too little knowledge of and experience with microtonal music to be a suitable "examiner". --Xenwolf (talk) 18:35, 15 October 2020 (UTC)

Okay, if that's the case, do you think that Kite and Flora could be of help? --Aura (talk) 18:58, 15 October 2020 (UTC)

I'm not sure. Maybe. Kite does a lot of practical work in microtonality 41edo guitars etc. Flora is new, but seems to have good mathematical skills. --Xenwolf (talk) 19:31, 15 October 2020 (UTC)

Oh yes, regarding the 12 sign symbols you suggested, I was really close to starting the detail work, but then realized that we have to consider the graphical context. After all, these symbols will be on and between staves, and yet you have to be able to recognize them and distinguish them safely. So this will also make a bit more work. Maybe I'll try a first rough draft showing the 12 symbols in 2 positions each. --Xenwolf (talk) 19:31, 15 October 2020 (UTC)

Right then. In the meantime, I'd best get to work putting the theory I've come up with here down on the page detailing my Concepts of Tonality... --Aura (talk) 19:35, 15 October 2020 (UTC)

All I know in this case is that if the 3-limit is used to assign pitch relations between the standard notes, and you want to have a standard for assigning pitch relations for keys like G-Demisharp Major, which Jacob Collier uses in his rendition of "In the Bleak Midwinter", we need some sort of relatively simple limit by which we can build off of the 3-limit in order to access such keys. Furthermore, we need to ensure maximal separation from the standard keys in a case like this. It may be true that when the rastma isn't tempered out, there's multiple possibilities, but given what I demonstrated on constructing a 9/8 whole tone using just four 11-limit intervals in my recent response to Kite's recent comments on the talk page for 159edo notation, I can't help but think that 33/32 is bound to be perhaps the most important among quartertones, especially in light of the one example of a stack of three 33/32 parachromatic quartertones plus a 4096/3993 paradiatonic quartertone adding up to a full 9/8 whole tone- you can't get much more straightforward in adding up quartertones than that. --Aura (talk) 18:19, 15 October 2020 (UTC)

Your Ideas seem interesting and may make sense musically. But the process of underpinning these musically appealing ideas with a solid theoretical foundation seems very complicated and nerve-racking to me. --Xenwolf (talk) 18:35, 15 October 2020 (UTC)

It is a very complicated job, but someone has to do it, and since I work more extensively with the 11-limit than most people here, it looks like that job falls largely to me. --Aura (talk) 18:42, 15 October 2020 (UTC)

If you're looking for a definition of "parachromatic" and "paradiatonic" as it relates to quartertones, let's look at the traditional distinction between "diatonic" and "chromatic" amongst semitones. From my observations so far, two parachromatic quartertones add up to a chromatic semitone, while a parachromatic quartertone and a paradiatonic quartertone add up to make a diatonic semitone. Therefore, it takes three parachromatic quartertones and one paradiatonic quartertone to make a 9/8 whole tone. --Aura (talk) 18:47, 15 October 2020 (UTC)

Alpharabian Comma

Hey Xenwolf, I botched the title of the Alpharabian comma page, as the word "comma" should not be capitalized. I'm hoping you can fix it. Thanks! --Aura (talk) 23:15, 16 October 2020 (UTC)

Link on Nexuma Page

Hey, Xenwolf, I figured that when you said the "demonstrably" link on the Nexuma page was questionable, you were talking about the way that link was written, but were you also talking about the content of that link? I asked Kite to look over that particular page to make sure the content there was up to snuff... --Aura (talk) 09:56, 17 October 2020 (UTC)

I find the linking style questionable, not the referred text.

Nobody is happy to get a long text to find (theirselves) the answer for a seemingly simple question, so this "'demonstrably' trap" is (in my opinion) a good example for the problem referred by

If I had more time, I would have written a shorter letter.

Well, of course not a big issue, but for me it's kind of important. --Xenwolf (talk) 10:56, 17 October 2020 (UTC)

Well, I've never been good with shorter stuff- it doesn't feel like I can say what I need to say in shorter writings. Oh, and the very first sentence of that lengthy page says, and I quote:

"It seems that some people in the community want to know how my system relates to the more well-known approach of Aaron Hunt- a simple question with a complicated answer."

I must confess, I'm on the Autism spectrum- I have Asperger's specifically- and yes verbose writing like that is classic Asperger's for you... --Aura (talk) 12:13, 17 October 2020 (UTC)

Writing/reading is a great tool but it takes time. If we consider that writing time is spent once and reading time is again and again, we understand that it pays off to invest in a great reading experience. --Xenwolf (talk) 13:35, 17 October 2020 (UTC)

If someone needs to create a more reader-friendly version of my writings on the not-so-simple subject of music theory, then so be it. In the meantime, I can remove the "demonstrably" link. --Aura (talk) 12:20, 17 October 2020 (UTC)

For working together on such ideas, it could be better to place them (maybe in parts) in the article namespace as soon as you feel that you are done with it... --Xenwolf (talk) 13:35, 17 October 2020 (UTC)

A small addition: I'm not sure that I am the only one who is interested in the relation of your system to the Hunt system. (I'm not even sure if the H-System has gained any special popularity at all.) --Xenwolf (talk) 13:50, 17 October 2020 (UTC)

Who else do you think might be interested in my system besides you and Sam? --Aura (talk) 05:27, 18 October 2020 (UTC)

I think, it will interest a lot of people if it turns out to be consistent (I have to read your latest additions (ca. 7000 characters)) ... ---Xenwolf (talk) 09:44, 18 October 2020 (UTC)

Music in an Approximation of 94edo

Hello, Xenwolf, have you noticed how on my user page there are two new songs? I just wondered if you had seen them- they were posted here because they were written in an approximation of 94edo, so there's that. --Aura (talk) 22:17, 21 October 2020 (UTC)

Yes of course, quite nice compositions. Of course you have to stay in the background if it is to serve as music for a computer game or movie. To me, the tonal base mostly sounds close to 12edo - maybe my personal JND is a lot above average. --Xenwolf (talk) 07:05, 22 October 2020 (UTC)

It is no surprise that when you work in diatonic keys in other EDOs, you end up with a sound that is close to 12edo, but in this case, the sound is better. --Aura (talk) 08:42, 22 October 2020 (UTC)

Well, there are some passages where I found the sound not better. I'll give the details later. --Xenwolf (talk) 09:01, 22 October 2020 (UTC)

If you're talking about the parts where I used the grave fifth, well, I have to say that the dissonance of the grave fifth is actually a way of bringing out the functions of a Minor VI chord in Major, as ending the phrase with a dissonant grave fifth really seems to hit home that "we're not done yet". I mean, isn't that kind of the point of a deceptive cadence anyway? --Aura (talk) 09:22, 22 October 2020 (UTC)

On a similar note, dissonance of the fifth on the Major III chord in Minor is a way of preventing the tonicization of that chord as well as giving it more propulsive force. --Aura (talk) 09:28, 22 October 2020 (UTC)

With all that said, I have to admit that at the time I wrote these pieces, I didn't exactly have an appreciation for how the dissonance of the grave fifth affects the flow of the music. It's the same way with the 11-limit chords that I use in these songs. --Aura (talk) 09:43, 22 October 2020 (UTC)

Contributions

Hey, Xenwolf, I can't help but wonder what y'all think of my contributions to both this wiki and to microtonality in general at this point. I mean, I'm pretty new here and here I am seemingly upending stuff with new music theory and what not. Then there's the fact that I talk to people on this wiki a lot... I hope I'm not being disruptive in the wrong sorts of ways... --Aura (talk) 16:15, 29 October 2020 (UTC)

I think it's all good. I think people are busy with their stuff, so the responses to contents is currently low. If you are on facebook, there are some groups, which are - as I remember - more responsive (I'm not there any more, it's too time wasting). --Xenwolf (talk) 16:22, 29 October 2020 (UTC)

Heh, I don't mess with Facebook. I have enough to keep track of on Reddit and Discord... --Aura (talk) 16:28, 29 October 2020 (UTC)

Reddit seems me a better place, aren't some of the other xenharmonists active there? I try to restrict my social energy 😉 here in the Xenwiki. --Xenwolf (talk) 18:39, 29 October 2020 (UTC)

Not going to lie, I don't know who's who on Reddit... --Aura (talk) 19:00, 29 October 2020 (UTC)

The Song that Started It All for Me

Hey, Xenwolf, I've finally gotten the courage to release "Folly of a Drunk"- the piece that started it all. It's now on my user page, and I want to hear what you think of it. --Aura (talk) 18:19, 29 October 2020 (UTC)

Thanks so far, I'll soon take the time to listen to it; right now, I have to do some important (but completely unrelated) stuff. --Xenwolf (talk) 18:41, 29 October 2020 (UTC)

Right. I hope to hear what you have to say. --Aura (talk) 18:50, 29 October 2020 (UTC)

So, do you have the chance to listen now? --Aura (talk) 20:06, 29 October 2020 (UTC)

You should not have mentioned the name Jacob Collier, I did not know him at all, now I spent hours on YouTube and stirred up my whole environment (not to mention the age depression of the amateur musician).

I also heard your piece, it has some very interesting twists and turns, but on the other hand it is not easy to follow them. The more ornamental quarter notes for example at the beginning are of course no problem. Unfortunately, where the modulation enters unfamiliar paths, it becomes quite difficult to penetrate acoustically. Certainly these twists and turns seem surprising.But the overall logic is quite difficult for me to understand (also because my ear is very much at home in the range between meantone and Pythagorean tuning), maybe it would help to look into the notes. But the overall logic is quite difficult for me to understand (also because my ear is very much at home in the range between midrange and Pythagorean tuning), maybe it would help to look into the notes.

In conclusion, I must admit that I tend to respond more to contemplative pieces (much to the chagrin of my wife, who always has to listen to such "sad things") and your piece starts off in such a cheerful marching rhythm, which is quite a bit of an effort. --Xenwolf (talk) 10:47, 31 October 2020 (UTC)

The song "Folly of a Drunk", is a song that is meant to go along with a scene of a book I'm trying to write. Specifically, as per the name, it goes together with a scene in which a character gets drunk and makes a fool of himself while humming snatches of this same tune- unaware that the song was written in part to basically make fun of the stupid things that drunks do. I hope this make some level of sense. --Aura (talk) 12:46, 31 October 2020 (UTC)

I also listened to the tune just now and I agree that melodic quartertones are easy for my ear to follow (albeit I’ll agree with George Secor that as a melodic step quartertone is a bit small and tends to be recognized more as a dynamics feature, like a glide, and not an element of melody; but here that glide-iness AFAIU is just bull’s eye), but the harmonic shifts are sudden and quick and I’m left puzzled but can’t grow an anticipation for harmonic movements. This is easily an effect of that this harmonic system is novel to me and those moves aren’t repeated several times like e. g. Sevish does. Aura, thank you for showing this piece to us, but I’d be glad if maybe in another piece the interesting harmony bits would be exposed in more detail and a bit slower for an untrained ear to follow! :) --Arseniiv (talk) 18:51, 31 October 2020 (UTC)

Let's be honest, the sudden and quick modulations are a good reflection of a drunk's likelihood of following the first impulse that comes to mind, as well as the possibility of things going from good to either awkward or bad at the drop of a hat.

Believe it or not, one of the key notes in the modulation, D-Demisharp- the note situated at an 11/8 fourth above the main tonic of A-Natural- actually occurs once in the bass near the end of each major section of the song up until the modulation, and the same chord in which it occurs is actually a simpler and slightly modified version of one of the chords used in the modulation itself. If you want, I'll be happy to make separate practice pieces demonstrating the chord progressions in question. --Aura (talk) 19:32, 31 October 2020 (UTC)

Yeah, it would be interesting to listen to. --Arseniiv (talk) 19:54, 31 October 2020 (UTC)

Right then. Let me get to work on it. For the record, I'll have to put all the elements of the individual chords together for these demos rather than staggering the chords like in the actual song. --Aura (talk) 21:05, 31 October 2020 (UTC)

Here's a practice piece containing the key chord progressions of "Folly of a Drunk" that you might have missed due to the speed of the piece... --Aura (talk) 09:26, 1 November 2020 (UTC)

One more thing... At the request of Kite, I've put the score for the song up on my user page, so if you want to check that out, feel free. --Aura (talk) 10:52, 1 November 2020 (UTC)

Thanks! I decided to move at least my part of the discussion to your page as it doesn’t concern Xenwolf. Here. --Arseniiv (talk) 14:27, 1 November 2020 (UTC)

Xenwolf, I think I can explain the logic of some of the weirder chord progressions in the modulation as well as why they work. One thing I seem to notice is that root motion by 3/2 and 4/3 works musically because of a strong harmonic affiliation. This same mechanism is at play for root motion by 5/4, 8/5, 8/7 and 7/4. On the other hand, root motion by roughly 600 cents also works musically, but by a different mechanism- that of sheer contrast. Root motion by 11/8 and 16/11 essentially brings both mechanisms into play at once- harmonic affiliation because 11/8 and 16/11 are the 11th harmonic and 11th subharmonic respectively, and sheer contrast because these pitches are located between 525 cents and 675 cents. The fact that this works musically is attested to by the number of people who actually find Folly of a Drunk catchy and actually enjoy the strange, unexpected modulation. --Aura (talk) 15:02, 1 November 2020 (UTC)

How about a page for discussing the current wiki projects and ideas what to do and their state?

I have seen such a page on a couple of wikis but now I can’t find how it was called. Something like Xenharmonic Wiki:Things to do or Xenharmonic Wiki:Noticeboard? I think a page like that would be good to make a rough list of mechanical mundane tasks a user like me may be able to do. I noticed you added a monzo and other information to an interval page and wondered if there many pages like this to help with. I already thought about writing a code snippet to print an interval’s mathematical stats like monzo formatted with use of this wiki’s templates, if it would be useful. Then it would find a rightful place in a section of this “what’s up now” page.

On minutiae: the page itself might contain concise desctiptions of various things and tasks and have links to subpages dedicated to them where they can be further guided with help messages and specs if needed, discussed on Talk:s etc., and Talk: for the central page would naturally be a place to discuss interesting global movements which one is shy to post right into the central page. (Like, “we need these pages made clearer” doesn’t need any discussion but “we need to style the wiki in Comic Sans” obviously does.)

Though by no means I propose strict organization: first and foremost just a dump of what everyone considers useful and interesting to do together and have help with, and in which manner it’s seen to be to do best, and what useful tools are suggested — all like that.

Anything in that vein. What do you think? (If there’s already a page with that purpose, yay! I didn’t search very thoroughly.) --Arseniiv (talk) 15:18, 5 November 2020 (UTC)

I fully agree with you in this. There are pages that could have turned into this root page, the one linked in the sidebar as Conventions is such a thing, but its discussion is quite old. I was also looking for a suitable place where proposals could be published that - after reaching an acceptable positive quota - could turn into conventions. What I think is obvious: all that should take place in the Project namespace (Xenharmonic Wiki:...). Find a good root name for such a community project and we'll start it right now! 🙂 There is already a lot to do, for instance provide support for archiving outdated discussions. --Xenwolf (talk) 16:49, 5 November 2020 (UTC)

Cool! Yeah I agree about placing it in XW namespace, as Help: looks like it’s more for established tools, not discussion. So I’ll write something on Xenharmonic Wiki:Things to do, and later if a better name arrives, let it be renamed. --Arseniiv (talk) 17:13, 5 November 2020 (UTC)

Great! I am looking forward to joining the project! We will probably have to reintegrate things like Migration FAQ, Wikifuture, and Bugs/Talk:Bugs sometime. --Xenwolf (talk) 17:23, 5 November 2020 (UTC)

Previewing math

Did you notice previewing on edit doesn’t display math? (Test: [math]\displaystyle{ \cos\frac{\pi}7 }[/math].) Looking at the HTML code, it seems MathJax script isn’t added for the editing page. Maybe it can be configured somewhere? (I know it’s possibly excluded when editing because it’s heavy, but maybe that won’t end up as an issue?) --Arseniiv (talk) 15:54, 9 November 2020 (UTC)

I don't observe that. It takes a bit time, but works (I changed your test for testing: [math]\displaystyle{ \cos\frac{\pi}{17} }[/math]). --Xenwolf (talk) 15:59, 9 November 2020 (UTC)

Oh… :( In my case it shows up as precisely this: <span style="opacity:0.5">[math]\cos\frac{\pi}{17}[/math]</span>. I’m not sure it can shed some light on the issue but it’s all I have. Checked ad-blocking extensions and found none that could cut MathJax off. I’ll check my wiki preferences, maybe I switched something off unknowingly… (But math shows up normally when I load the page not as a preview, in case I may have written that unclearly.) --Arseniiv (talk) 17:21, 9 November 2020 (UTC)

Oops, it gets rendered when the page is loaded normally. Changed to <nowiki. --Arseniiv (talk) 17:22, 9 November 2020 (UTC)

Quick Questions

Would you mind if I ask several quick questions? At the moment, I have four:

1. External links cause rendering of the big margin after the anchor text before next work; it breaks the layout and the look pretty badly. Can it be fixed?
2. I found another problem: there is the URL probably registered as the user: ../w/User:Contribution, so it appears in the “Special pages” list. At the same time, the page shows the contributions. Don't you think it needs some fix? — SA 08:26, 27 November 2020 (UTC)
3. The problems with that very bad yet important page MicrotonalInstruments referenced from the main navigation bar: it gives the title header "MicrotonalInstruments", must become "Microtonal Instruments", at the same time, the change should not break possible existing links (redirection?). (I want to wikify this page well because I already put some important fixes. But they go nowhere, because it is mostly dirty HTML inside wiki, not wiki — not maintainable. Before it is wikified, further effort would be a waste of time. I would do it, but not at once, and only when I'm tired of main work, that will require keeping this page "Under construction" for a short period of time.) — SA 17:44, 27 November 2020 (UTC)
4. Do we have a proper place for posting publications, like articles? It seems obvious: no. Say, we have the section "Theory", but no publications can be added to any of the first 3 items, which are already the self-consistent publications, only a new tool can be added to "Useful Tools". But not every publication can be classified as "Theory" or "Tools". So, don't you think we need a section "Articles" or "Publications" referenced from the main toolbar and the page similar to Practice/Instruments, Practice/Software, or Practice/Projects? — SA 19:19, 27 November 2020 (UTC)

On the MicrotonalInstruments item above: I've found your comment in the history: "please resist any dd-"workarounds" the wiki will get fixed soon". I totally agree. I was about to show to you this kind of work-around, sorry that I make some redundant noise. I'm interested in resolving of the issue with the page name and "MicrotonalInstruments" vs. "Microtonal Instruments". When I have time, I can start to wikify the page without waiting to the fix of externally reference margin and other fixes. Would you agree is the only reasonable way to fix this content is to wikify it first? If I start, could we possibly clash if you do some fixes in parallel? Hope not... — SA 19:07, 27 November 2020 (UTC) By the way, I didn't get notification on your comment I mentioned above, just happened to look in the history and see it, even though this page is on my Watchlist. It is supposed to work this way? — SA 19:07, 27 November 2020 (UTC)

(Just for the record: we do have the history of changes and archiving, but these wiki techniques are badly outdated and not so operational. The civilized approach is the coupling with some appropriate revision control system, the way it is done by GitHub and its embedded Wiki (multiple standards with the default in the form of Markdown). By the way, I'm one of the collaborates at Microsoft Visual Studio Code, the author of Markdown extension written in JavaScript; it does a lot of things related to the document self-consistency, automatic TOC and links with advanced options, and, importantly, does typographic corrections on output, for example, converts --, ---, or "" into typographically correct Unicode, and a lot more, anyway, I got tons of experience with that. These typographical problems are very irritating to me. I examine the possibility of improving things by Mediawiki scripting — not at all sure if it may make sense. First of all, not so unsafe. Then, corrections wiki to wiki is bad: wiki source should remain clear, the corrections should be done on the fly between wiki and resulting HTML rendering, but it may work only globally, not on the per-user basis. Besides, JavaScript is badly outdated here. So, probably nothing would pay off the effort.) — SA 19:05, 27 November 2020 (UTC)

Thank you!

— SA (talk), 21:46, 25 November 2020 (UTC)

If I understand you correctly, you asking for the space after external links? This is an issue that is seemingly caused by the update. We have to wait for it to be fixed at least until next week, I fear. Unfortunately, I can't tell you more about this. I'm not the maintainer of the wiki nor have access to the configuration, so we have to be patient ... --Xenwolf (talk) 23:35, 25 November 2020 (UTC)

That's right, after the external links. I will be patient, no problem with that :-). Thank you anyway. I'm an impossible perfectionist and think about changing the layouts in case the problem is permanent. — SA (talk), 04:57, 26 November 2020 (UTC)

Yes, there is a user named Contribution. It may be confusing sometimes but I think there is nothing to fix. --Xenwolf (talk) 08:53, 27 November 2020 (UTC)