# Xenharmonic Wiki talk:Things to do

## Automatic color names?

Has somebody mused about generating suitable humane color names for intervals and other things? For example, for an interval, one needs to know whether to name it a third, a fourth, a sixth, but AFAIU they are often scale-dependent, and the same interval can have a “(color 1) third” name and a “(color 2) fourth” name. What can be done obviously is to enumerate the most sensible of potential cases (like if the interval is between 5/4 and 4/3, likely it will function more often as a third or fourth and less often as a second or fifth), but one needs to be able to tell for example if 7/5 may called a fourth, or there’s a sense it should be called a fifth way more often than a fourth. I’d try to write some code to guess appropriate color names, but having advice beforehand would be very nice. --Arseniiv (talk) 18:08, 5 November 2020 (UTC)

- Oops, I hadn’t read the description well enough! The matter is way simpler and there is no guessing at all. --Arseniiv (talk) 20:10, 5 November 2020 (UTC)

It would be also worth it to add this page to the navigation close to Help and Conventions, even if later. --Arseniiv (talk) 21:09, 5 November 2020 (UTC)

- We'll do that soon. But I think that we should first have to clarify its structure. I'd prefer dedicated pages one per task (maybe as sub pages). We should have a handful of clearly defined projects available before we link this overview in the navigation. The style of the existing ones will silently work as a blueprint for future projects, so we better limit confusion to a minimum. a bit of styling (for the intro in the header) could also help to make this site as inviting as possible. --Xenwolf (talk) 21:40, 5 November 2020 (UTC)

`Template:Stub`

I hope that would be found useful to automatically categorize pages as needing attention (maybe even different kinds of attention?), as well as marking the places needing elaboration. For example, right on this page until it’s “production ready” ;-) I’ll investigate later if I’m up to the task to desigh a nice-looking template but if you know how to do it easily, please feel free to! --Arseniiv (talk) 17:43, 5 November 2020 (UTC)

- Before thinking about an appropriate Template:Stub, I think Category:Todo is worth a look, as well as its sub categories, these category developed out of wikispaces tags and are maybe more specific then just
*stub*. --Xenwolf (talk) 18:24, 5 November 2020 (UTC)

- The template with an example of how it looks: User:Arseniiv/TodoTest. It seems to apply the category correctly. Maybe that can find some use still, but if not, no problem. --Arseniiv (talk) 19:51, 5 November 2020 (UTC)

- I moved this discussion from Xenharmonic Wiki:Things to do to here, since it's not decided yet whether it should go into the list. --Xenwolf (talk) 12:42, 7 November 2020 (UTC)

- Now that two days have passed and no new things to add or remove arose, maybe we should now migrate the Todo template to the template namespace and start sticking it everywhere :) Also it’s very nice Template:Infobox interval automatically adds todo categories, I think this is a way to go with other specialized templates, should they apper later. --Arseniiv (talk) 14:28, 7 November 2020 (UTC)

## Infobox for EDO pages

Let’s list what should be present in the template:

- step count (
`steps`

)

- period? (for EDT and several others?)
- [Xenwolf: no need, consider other templates for other EDs]

`step size`

- [Xenwolf: size alone isn't clear]

- commas tempered out
- [FloraC: too many stuff]

- notable commas not tempered out? (possibly with an example of distinguished JI intervals?)
- [FloraC: too many stuff]

- family?

- JI subgroup represented fairly well? (and a patent val?)

- notable modes?
- [FloraC: no consensus]
- [Arseniiv: now I come to think including entire modes would also bloat the table]

- related EDOs? (maybe more specific relations, like “refines 11edo”?)
- [Xenwolf: include predecessor and successor EDOs]

Thoughts? --Arseniiv (talk) 14:44, 7 November 2020 (UTC)

- The parameters
`step count`

(or`step size`

) and`size`

seem indisputable to me, EDO implies 2/1 as`period`

(I'd consider to make other templates for other EDs). What about prime factorization? Relates would be great for navigational purposes (for instance predecessor and successor). As far as the parameters can be filled without headaches and without edit wars they should be included. Maybe we can get a community process started about that. --Xenwolf (talk) 18:31, 7 November 2020 (UTC)

- I'm afraid
`Commas tempered out`

and`Commas not tempered out`

are too many stuff. And there's no consensus what constitutes "notable". FloraC (talk) 18:47, 7 November 2020 (UTC)

- (To all:) Is there a consensus about patent vals for EDOs? I seem to remember in several cases there were at least two vals which would be as good, so I don’t know if it’s a good for the template. Also the same about well-representedness of JI subgroups.

- I suggest listing the # of edosteps that the 3-limit M2 and m2 span. If the best 3/2 of n-edo is m/n, that would be 2m-n and 3n-5m. This instantly gives you the "flavor" of the edo. --TallKite (talk) 02:35, 26 November 2020 (UTC)

- @TallKite, @FloraC, Isn't
*A1 := M2 - m2*? Why not all three? Maybe also*m*itself that should probably better be renamed in, say,*f*or*fifth*?

Of course a collection of name-values pairs will not look that great, but maybe something like*M2=m2+A1:*(as label) and*3=2+1*(as value), as a rough sketch?

--Xenwolf (talk) 10:03, 26 November 2020 (UTC)

- @TallKite, @FloraC, Isn't

- Yes, A1 = M2 - m2, so A1 isn't needed. Sure, we could have all three. If we have only two, M2 and m2 are the most useful for finding your way around a microtonal guitar. For example, hand a guitarist a 31-edo guitar tuned EADGBE and say M2 = 5 frets and m2 = 3 frets, and they can figure it out pretty quickly.
- And yes, for certain edos like 6-edo, it's not that helpful. But for most edos it's very useful, so we might as well include it for all of them. Even if the M2 is not the same as the best approximation of 9/8. Because M2 is always the distance between the best approximation of 4/3 and the best approximation of 3/2. --TallKite (talk) 07:34, 27 November 2020 (UTC)

- To all: Inthar has got Template:Infobox ET constructed and has implemented it(!) in many edo pages. Let's move on to Template talk:Infobox ET. FloraC (talk) 06:49, 3 December 2020 (UTC)

## Relations of various interval categories

There are Category:Interval, Category:Just interval, Category:Interval ratio and Category:Ratio with different content of *m*/*n* pages like 3/2. Maybe someone knows if there was an intention behind that?

Also there seems to be a forgotten todo in the description of Category:Intervals. --Arseniiv (talk) 16:06, 7 November 2020 (UTC)

- Good catch! This is caused by the migration procedure (from wikispaces to MediaWiki), categories were retrieved from tags. Tags are much more lightweight and community-driven so there is not much consistency. The important question is how to name it, which has to be wisely decided considering relating (super, sub, sibling) categories. --Xenwolf (talk) 18:21, 7 November 2020 (UTC)

- Yeah I agree. AFAIU, no one here needs ratios by themselves, mathematically, so we would have a simple inclusion
*Just interval*inside*Interval*, taking both existing categories and reshuffling which page belongs where: rational intervals into*Just interval*, and remaining few irrational intervals may reside directly in*Interval*without their own subcategory. (FTR Category:Comma stays as it was.) Now we need more opinions! --Arseniiv (talk) 18:59, 7 November 2020 (UTC)

- Yeah I agree. AFAIU, no one here needs ratios by themselves, mathematically, so we would have a simple inclusion

- I agree. I think Category:Just interval is the best solution here (a more technical term would be something like
`Category:Interval page`

, but I prefer your - more pragmatic - solution). --Xenwolf (talk) 17:41, 8 November 2020 (UTC)

- I agree. I think Category:Just interval is the best solution here (a more technical term would be something like

- I suggest the category "ratio" should remain and "just interval" should go, for there's no consensus what "just" really means. I once talked about the concept of "just" in the FB group. Obviously there are people who argue:

- I guess
*Ratio*may be simply moved to the new one? Ah, but page texts won’t change with that… Looks like work for a bot. But it seems there will be lots of work anyway, as sometimes for example there are several categories applied at the same time. (When I saw that, I didn’t touch it exactly because of undecidedness which ones are suited better.) --Arseniiv (talk) 19:17, 8 November 2020 (UTC)

- I guess

- As we seem to agree about the pragmatical usefulness of "Rational interval", I'd say we could add this without problems to uncategorized pages, we could also replace "interval ratio" with it (this one was introduced by me after the migration to MediaWiki to combine "interval" and "ratio", two tags from the wikispaces era - tags were single words). The same would apply to pages that are categorized as both "interval" and "ratio", or written in a more
- compact form:

- (none) → "Rational interval"
- "Interval ratio" → "Rational interval"
- "Interval" and "Ratio" → "Rational interval"

- But nothing to be done right now. Should we try to get Aura, CritDeathX, IlL, TallKite, and Yourmusic Productions involved? What do you think? --Xenwolf (talk) 19:51, 8 November 2020 (UTC)

- As we seem to agree about the pragmatical usefulness of "Rational interval", I'd say we could add this without problems to uncategorized pages, we could also replace "interval ratio" with it (this one was introduced by me after the migration to MediaWiki to combine "interval" and "ratio", two tags from the wikispaces era - tags were single words). The same would apply to pages that are categorized as both "interval" and "ratio", or written in a more

- @Aura: What you just suggested is already planned: keep Category:Interval and placing Category:Rational interval into it. --Xenwolf (talk) 15:06, 9 November 2020 (UTC)

- I'd incline towards the shortest unambiguous tags possible. The longer they are, the more likely people are to forget or misspell them, resulting in pages falling through the cracks. Yourmusic Productions (talk) 10:30, 9 November 2020 (UTC)

- @Yourmusic Productions: Sorry that I have to correct you about a misconception. There is no
*tag*feature available in MediaWiki. The*category*feature is comparable but not as lightweight and not combinable (see below). Since the term*Just*is disputable and*Interval*and*Ratio*so little significant, we are searching for a*category name*that will do a good job in containing all the pages about individual intervals. MediaWiki unfortunately does not support selecting pages by a logic combination of categories (like`Interval AND Ratio AND Just`

), so single words as category names will not be as usable as you might imagine. --Xenwolf (talk) 11:27, 9 November 2020 (UTC)

- @Yourmusic Productions: Sorry that I have to correct you about a misconception. There is no

- I think it'd be good if we have Interval as a regular category with Rational Interval as a subcategory. Its possible we could include irrational intervals on the wiki, though at the moment it doesn't seem clear when we would need those pages. --CritDeathX (talk) 00:37, 12 November 2020 (UTC)

- I agree with the main ideas for "Rational interval", although I would advise going for "Rational intervals" (plural) instead, since this would be a set category. Considering that the category is still unused at this point, I will take the chance of renaming the category into its plural form, and we can revert if necessary.
- Relatedly, the "Interval" category should probably be called "Intervals", but that category already exists although it is proposed to be merged elsewhere, so I will proceed to freeing that category by completing the current suggested merge.
- I also agree that moving pages to the right categories would be the work for a bot, and I'd be glad to help in this matter if there is anything I can do. --Fredg999 (talk) 16:28, 26 August 2021 (UTC)

- Sure. Now, is it good to add the category to Template:Infobox Interval? Shall we get this started any time? FloraC (talk) 19:52, 20 November 2021 (UTC)

## Templates for wedgies, n-vals?..

How much are they used on the pages? If very so, then if n-vals other than bivals are pretty common too, there can be a reason to make a unified template to rule them all and write as many ⟨ and ] as the user decides, defaulting to two. --Arseniiv (talk) 16:32, 7 November 2020 (UTC)

- Nice to have. So why not simply extend
*Template:Val*and defaulting to one? FloraC (talk) 11:21, 9 November 2020 (UTC)

- @FloraC: You know that Template:Val does nothing but formatting.
- We could do much more if we had scripting on board (see also User talk:Tyler Henthorn #Fwd: Extension request). We maybe should open an own section for this here ... --Xenwolf (talk) 11:44, 9 November 2020 (UTC)

- Still even though that doesn’t do more than syntax, I made a test: User:Arseniiv/Val'. And while scripting is a good boon, what’s expected of it to make better for multival notation? Aside from correctness checks (a
*k*-val should have [math]\binom nk[/math] entries), of course. --Arseniiv (talk) 15:46, 9 November 2020 (UTC)

- Still even though that doesn’t do more than syntax, I made a test: User:Arseniiv/Val'. And while scripting is a good boon, what’s expected of it to make better for multival notation? Aside from correctness checks (a

## Website for listening to intervals

Does someone understand browsers’ API for sound playback? Reading Talk:62/53 gave me an idea. Imagine a website which has a small arsenal of samples of various timbres (maybe sampled in several registers but no need to sample extensively) which it can play to you at intervals you choose. You may compare both how the same interval sounds with different timbres and how do different intervals sound. Maybe also chords, and all of it arpeggiated and instantaneous in any combination you wish. (I have a rough idea how it can all be packed into a comfy UI.) And then we could make links from interval pages to hear or compare them at that site. Surely looks great? If you have more ideas of this sort, please share!

(For me the main block here is that I can’t make heads from tails of browser JavaScript infrastructure and APIs (well, I have some rudimentary outdated knowledge). The server part should be very simple: just fetch pages and sample files. all work will be in the browser. Though I have friends that are in better terms with JS, maybe I’ll could make something with their help later.) --Arseniiv (talk) 13:22, 8 November 2020 (UTC)

- A browser-based solution (JS, WebAudio) would be really great. This included in Interval pages would be superior to most sound examples we uploaded. --Xenwolf (talk) 13:36, 8 November 2020 (UTC)

- Very glad you like it! I also added my view on GUI at User:Arseniiv/Interval player idea. Now I can leave it for a while. --Arseniiv (talk) 13:55, 8 November 2020 (UTC)

- I'm not sure if I didn't saw something like that. Maybe other xenharmonics have a better memory for that. Here is an interesting resource (provided you are not on IE 😉): JavaScript Systems Music --Xenwolf (talk) 14:35, 8 November 2020 (UTC)

- Here is what led me to above page: Making Generative Music in the Browser | by Alex Bainter | Medium --Xenwolf (talk) 15:08, 8 November 2020 (UTC)

## Shorten editing titles

Say what you think about the change proposed (Xenharmonic Wiki:Things to do#Proposal: Shorten editing titles)?

- I'm for it: I have already tried it for three years in another wiki and can say that it proved to be useful there. --Xenwolf (talk)

## New Category?

Would it be possible to have a Kite Guitar category? There's already about a dozen pages about it.

- Definitively. Good idea. I'll do it in a moment. --Xenwolf (talk) 10:37, 22 November 2020 (UTC)

PS: Please, Kite, think of signing your contributions on discussion pages; it's easy, just type`--~~~~`

(2 hyphens and 4 tildes),

the 4 tildes will be replaced automatically (on saving) by your linked user name and the time of saving. --Xenwolf (talk) 10:37, 22 November 2020 (UTC)

- Great :) (I sometimes myself forget to sign). I hope the category:Kite Guitar brings the expected benefits, hopefully I got all the pages you meant. --Xenwolf (talk) 22:06, 22 November 2020 (UTC)

- Double redirects (
*A*→*B*→*C*) are fixed by changing them into normal ones (A → C). Resolving double redirects is no big effort, I check from time to time if there are any to clean up. The Special:DoubleRedirects page helps with that. I'll leave it for a while in case you want to do it yourself. Please let me know if you like me to do it. --Xenwolf (talk) 08:38, 27 November 2020 (UTC)

- Double redirects (

## Naming articles

I'd like to write down our collaborative findings and experience about naming. What do you think? Is it reliable, or even correct? --Xenwolf (talk) 22:10, 27 November 2020 (UTC)

- I'll be adding this:

We follow Wikipedia's style guides Wikipedia: WP:THE, Wikipedia: WP:PLURAL, and Wikipedia: WP:NCCAPS. In summary:

- Case
- Use English sentence case. This means that words inside the title are written in lower case, except for proper names. The very first character is automatically capitalized by the wiki software.
- Plurals
- Use singular nouns, unless it is a collection for different types of things.
- Articles
- Save articles at the initial of the title, unless it is an integral part of the title.

Examples:

- Val (correct)
~~The val~~~~Vals~~- Normal lists (correct)
- Online platforms (correct)

What do you dudes think? FloraC (talk) 15:22, 2 February 2021 (UTC)

- I agree with everything on that topic so far. I also suggest that we follow parts of Wikipedia's style guides for categories, more specifically Wikipedia: WP:TOPICCAT, Wikipedia: WP:SUBCAT and Wikipedia: WP:DIFFUSE.
**Plurals**: Use singular for topic categories and plural for set categories.- Examples:
- Category:Scale (correct: topic category, to include pages like Periodic scale and Hexany)
- Category:Scales (correct: set category, to be diffused in subcategories — see below)
~~Category:Musician~~(unless we have pages that would fit in a "Musician" topic category rather than pages about specific musicians)- Category:Musicians (correct)

**Subcategorization**: If logical membership of one category implies logical membership of a second (an is-a relationship), then the first category should be made a subcategory (directly or indirectly) of the second.- Example:
- Category:Small comma in Category:Comma in Category:Theory (correct)

**Diffusion**: Do not include a page both in a category and its parent category unless the category is a non-diffusing category.- Examples:
- Meantone7 in Category:7-tone scales, but not in Category:Scales (correct)
~~5L 2s in Category:7-tone scales and in Category:Scales~~- 5L 2s in Category:7-tone scales and in Category:MOS scales (correct, because the second category would be non-diffusing)

**Metacategories**: schemes of subcategories can be organized with metacategories.- Example:
- Category:Scales by size (correct, to contain categories such as Category:7-tone scales)

- Aside the fact that there are multiple redundant categories for various topics (which is already noted with Category:Todo:merge categories), it is often the case that pages about a topic and pages in a set are mixed together in one or many of those categories. Category:Scale is a good example of that phenomenon.
- I think there is a way to move and reorganize existing pages and categories efficiently using Cat-a-lot, but I'm not very familiar with it, and I don't know if I even have the user right to use it for that matter. --Fredg999 (talk) 22:38, 1 August 2021 (UTC)

- I agree with these categorization policies. Just a few notes.
*Category:Scales by number of tones*is actually*Category:Scales by size*.*Category:Scale*has been cleared. Most topics are under*Category:Scale theory*. Meanwhile the move from*Category:Musician*to*Category:Musicians*hasn't started yet.

- I agree with these categorization policies. Just a few notes.

- Thank you for the first note in particular. I replaced the example with
*Category:Scales by size*in my previous message for clarity. I hadn't created the category yet at the time of writing that, so it seems I changed my mind afterwards.

- Thank you for the first note in particular. I replaced the example with

- Also, concerning the use of Cat-a-lot, I know there is already a "manual bot" user, User:Keenan Pepper category edits, which can use Cat-a-lot, but I would feel out of place to use that account, since it's associated with Keenan Pepper. Could I create a similar account for myself which I could then use for Cat-a-lot work? --Fredg999 (talk) 00:34, 18 February 2022 (UTC)

- There are only few users in this wiki who have the rights to make this new account a bot (see
`userrights`

in Special:ListGroupRights). And I've currently not the time to wait. --Xenwolf (talk) 18:20, 18 February 2022 (UTC)

- There are only few users in this wiki who have the rights to make this new account a bot (see

- I created the account (User:Fredg999 category edits) anyway. Hope you could spare some time to set it to a bot. Meanwhile I'll get in touch with Mike. FloraC (talk) 13:04, 19 February 2022 (UTC)

## 13-Limit, 17-Limit and 19-Limit Comma Pages

Hey, I was thinking we ought to start reorganizing the 11-limit and 13-limit temperaments, as well as figuring out how to deal with 17-limit temperaments, so far, just leaning on the preview that Flora provided me in a brief discussion on this matter, I'm thinking it should go something like this:

If X is a 3-limit or 5-limit comma, "X family" is for rank-2 temperaments that temper it out. If X is a 7-limit comma, "X family" is for rank-3 temperaments that temper it out, and "X temperaments" is for rank-2 temperaments that temper it out ("X clan" if the comma is a subgroup comma). See: Marvel family, Marvel temperaments. If X is an 11-limit comma, "X family" is for rank-4 temperaments that temper it out, and "X temperaments" is for rank-3 temperaments that temper it out ("X clan" if the comma is a subgroup comma). If the "X family" page isn't there (as it doesn't have many 13-limit branches), in "X temperaments" there is a brief of the rank-4 temperaments. See: Keenanismic family, Valinorsmic temperaments, Kalismic temperaments. We need to figure out how to handle pages like Quartismic family. If X is an 13-limit comma, "X family" is for rank-5 temperaments that temper it out, and "X temperaments" is for rank-4 temperaments that temper it out ("X clan" if the comma is a subgroup comma). If the "X family" page isn't there (as it doesn't have many 17-limit branches), in "X temperaments" there is a brief of the rank-5 temperaments. We need to figure out how to handle pages like the Archipelago, the Biosphere and Marveltwin, which list temperaments of various ranks, as such pages will likely be more common going forward. If X is a 17-limit comma, "X family" is for rank 6-temperaments that temper it out, and "X temperaments" is for rank-5 temperaments that temper it out ("X clan" if the comma is a subgroup comma). If the "X family" page isn't there (as it doesn't have many 19-limit branches), in "X temperaments" there is a brief of the rank-6 temperaments. If X is a 19-limit comma, "X family" is for rank 7-temperaments that temper it out, and "X temperaments" is for rank-6 temperaments that temper it out ("X clan" if the comma is a subgroup comma). If the "X family" page isn't there, in "X temperaments" there is a brief of the rank-7 temperaments.

I hope this idea is at least the start of something feasible. The reason I'm stopping with the 19-limit is because aside from 94edo, none of the EDOs between 1edo and 171edo deal with the 23-limit consistently- at least to my knowledge. --Aura (talk) 17:08, 31 December 2020 (UTC)

I'm hoping for further discussion on how to deal with pages listing temperaments of various ranks that are all connected by the tempering if a single comma, such as the Archipelago, and even the Quartismic family page. Is it possible that these could be analyzed as types of "X family" or "X clan" pages depending on the nature of the comma? From the looks of things, how we handle the page on the Biosphere page in particular will determine how we handle the the current "Quartismic family" page going forward as there seem to be a lot of structural parallels. --Aura (talk) 17:46, 31 December 2020 (UTC)

**[ Start of suggestion/reply by** Godtone (talk) 23:06, 15 January 2021 (UTC)**. ]**

Re: the convention you are proposing, I do not think this is a good way to go about it. Superfamilies of temperaments formed by tempering only a single comma should be described on the page for that comma. Temperaments should get their own page separate from commas only if they temper *at least* 2 commas, but in higher-rank situations, that restriction should be 3 commas. High-rank temperaments tempering 2 or 3 commas should be listed on the page for a certain comma, with the page for that comma being the ultimate "super-family" of those temperaments. This could be justified further by that the temperaments listed for comma X should be ones which prioritise accuracy/idealness of tempering X, and that only temperaments involving at most 3 commas (including X) should be listed, but usually only listing X and 1 other comma. I also think that temperaments should be named based on increasing rank rather than decreasing rank, as it seems unlikely to me (from the perspective of practicality as opposed to theory, and due to various reasons) that someone would want to use (for example) a rank-5 or rank-6 temperament without tempering out any further commas, except as an exercise in exploring the temperings of specific commas or pairs of commas (hence the moving of that information to the main comma being tempered along with 1 or maybe 2 others). On the contrary, there is lots of motivation for using a rank 2 or 3 temperament. I think higher ranks usually serve to contextualise or conceptualise lower ranks, rather than vice versa, hence the lowest ranks should be the "centre of focus" for the most part, except when focusing on specific commas.

Another reason to avoid "single-comma superfamilies" on separate pages is it reduces redundancy/repeated information and it reduces the chaos caused by the fact that reasonably complex temperaments are defined by multiple commas, thus meaning that the position of a comma in a hierarchy of 'super-families' is generally not a necessarily well-defined concept, leading to a mess.

"Temperaments" should therefore refer to rank 2 temperaments, and also rank 3 if the term is interpreted to include "planar temperaments". "Temperament families" should thus be rank 3, and "temperament superfamilies" should be rank 4. (Note that whether a rank 3 temperament is called a "planar temperament" or a "temperament family" should depend on its use in a discussion. If it is being considered as defining a "plane" of tones to choose from, generated by 2 generators with respect to some period, then it is a "planar temperament", but if it is being considered as a larger family uniting multiple rank 2 temperaments (and thus also rank 1 temperaments), it is a "temperament family".)

With that said, here is my alternate proposal which I think would make things less chaotic if applied consistently and broadly. (Note that this is for higher limits/more complex cases, so as the 5- and 7-prime-limits are relatively trivial cases, I will skip past naming them and more generally all temperaments derived from a 3 or 4 dimensional untempered subgroup.)

First, assume that we are dealing with an initial untempered subgroup of at least rank 5. (Lower ranks I'm not too concerned about how they're organised as they're generally pretty simple in comparison.) I'll call this initial untempered subgroup "IUS" for short. Tempering 1 comma leads to a comma-specific temperament, described on the page for the comma. If the IUS is rank 5, tempering 2 commas leads to a family or clan and tempering 3 leads to a temperament. If the IUS is rank 6, tempering 2 commas leads to a superfamily, tempering 3 leads to a family or clan and tempering 4 leads to a temperament. More generally, if the IUS is tempered from rank n to rank k < n through tempering (n - k) commas, then: If the tempered result is rank 1, it is an equal temperament. If the tempered result is rank 2, it is a temperament. If it is rank 3, it is a clan or family, alternatively named a planar temperament if using or considering it with no further tempering is desired. If it is rank 4, it is a superfamily. If it is rank 5, my proposed name is that it is an ultrafamily. Meanwhile, for comma pages, the comma should be described in terms of its arithmetic and musical significance and in terms of the temperaments resulting from tempering it and up to 2 other commas, but generally prioritising the tuning of the comma in question, and providing a spectrum of possible tunings for that comma while showing ranges of possible tunings for other commas to temper with that comma, giving reasons as to why you might want to do so. Furthermore, if the tempering of this comma with 2 other commas results in a temperament of rank 6 or greater, I think the 3 comma combination - if considered significant - should get its own page corresponding to a type of family that I propose to be called a "metafamily". The existence of this "metafamily" should be mentioned on the page for all 3 commas, but no further information should be given (to avoid repetition of information on the page for the metafamily). In the case of tempering 2 commas resulting in rank 6 or greater, the temperament can easily just be named as the combination of the names of the commas, hence it should in that case ''definitely'' be part of the page for the comma(s) in question. If we follow all of these rules, we have a very broad system for dealing with higher rank situations, as: Temperaments of ranks 1 through 5 are given consistent names. (1 through 5 are covered.) Tempering 1 comma is always associated with that comma. Adding only 1 more comma does not change this if the temperament is rank 6 or greater. (+2 ranks covered.) In the extreme case where tempering 3 commas results in a temperament of interest that is rank 6 or greater, this is named a "metafamily", and there can be described derived temperaments of lower ranks. (+2 ranks covered.) This takes us to a complete classification of up to as high as rank 9 temperaments (implying up to a rank 10 IUS, taking us to the 29-prime-limit), and I think this is a very reasonable place to draw a limit. For aiding understanding of what I've stated so far, I'll provide a couple of examples of how the resulting ranks of temperaments would be classified for a couple of different rank IUS's. Rank 9 and lower temperaments would be classified in the following hierarchy (assuming an implied rank 10 IUS): Rank 1 - Equal temperament. Rank 2 - Temperament. Rank 3 - Planar temperament. (Alternatively clan or family.) Rank 4 - Superfamily AKA "[Ultrafamily] temperaments". Rank 5 - Ultrafamily. Rank 6 - Metafamily temperaments. Named as "[Metafamily name] + [comma name] temperaments". As a collective, derived temperaments of a Metafamily are named "[Metafamily name] temperaments". Rank 7 - Metafamily. Rank 8 - 2 comma temperament, derived from a 'main' comma. Named as "[main comma name] + [secondary comma name] temperament". Rank 9 - 1 comma temperament. Named as just "the [comma name] temperament". Rank 10 - the IUS (initial untempered subgroup). If we assume a rank 8 IUS (corresponding to the 19-prime-limit) then the hierarchy looks almost the same except for rank 4 and onwards: Rank 4 - Superfamily AKA an instance of a "[Metafamily] temperament". Rank 5 - Ultrafamily or Metafamily. Which term is preferred depends on if you are looking at it from the perspective of a large (Ultra)family of low rank temperaments or from the perspective of a unique combination of 3 commas being tempered out of the full IUS (thus defining a Metafamily of temperaments). Rank 6 - 2 comma temperament, derived from a 'main' comma. Named as "[main comma name] + [secondary comma name] temperament". Rank 7 - 1 comma temperament. Named as just "the [comma name] temperament". Rank 8 - the IUS (initial untempered subgroup).

Note: A partial reason I chose "Metafamilies" to correspond to 3 commas (and thus "Metafamily temperaments" to 4) is to suggest focusing on tempering at least 3 or 4 commas in high rank situations so that we don't just get a whole bunch of 1 or 2 comma temperaments which are comparatively uninteresting and of which, at that scale, there will inevitably be (perhaps far too) many. This also has the neat property of meaning that Metafamily temperaments in the 19-prime-limit are "cubic" in analogy to how rank 3 temperaments are "planar", and that Metafamily temperaments in the 17-prime-limit are "planar temperaments". Plus I like the fact that "Metafamily temperaments" are either equated or closely connected to Superfamilies and/or Ultrafamilies depending on how high of a rank your IUS is, further justifying the aesthetic choice of "meta" (at least IMO).

**[ End of suggestion/reply by** Godtone (talk) 23:06, 15 January 2021 (UTC)**. ]**

In hindsight this suggestion of mine is suggesting to redefine the word "temperament" but considering terms such as "planar temperament" and "linear temperament" I think the confusion is understandable, plus I still think the spirit of the suggestion is still relevant and if anything more relevant than before considering temperaments describing complete or near-complete harmonic series maps for the purpose of making constant structure harmonic series scales will be very high limit by default. Also I think the most important/least aged insight here is merging the information for temperaments that are dependent strongly on a single comma into the page for that comma, where it should logically belong; why talk of a comma if you don't talk of tempering it? If you don't temper it, then temperaments are either irrelevant, or you can suggest other commas to equate it with and thereby link to corresponding temperaments. In other words, every interesting small comma should ideally have some information on consequences and relation to temperaments in a standard "Temperaments" subsection. Information about how it relates to other intervals (the structure of JI) would **not** go under the Temperaments subsection.

For example, for 676/675 it is notable that it is a square superparticular (its numerator is 26^{2} and its denominator one less) and also a ratio of the square superparticulars S13 = 169/168 and S15 = 225/224 which gives a mathematical explanation of why tempering 676/675 means tempering (4/3)/(15/13)^{2}. (For an explanation of why check the "semiparticular" section of square superparticulars.) It suggests that tempering {S13, S15} is an efficient simple temperament that tempers S26. If we then notice another pattern explained on that page, we can temper {S25, S26, S27} which implies tempering both S13 and S15 by multiple coincidences. Specifically, S25*S26*S27 = S15 (a 1/3-square-particular; guaranteed to be superparticular in this case but a coincidence that it is also a square superparticular) and S25*S26*S26*S27 = S13 (note that 26/2 = 13 which is how this general pattern works). This all together suggests that the no-11's 13-limit catakleismic temperament **2.3.5.7.13[19 & 53] = {S13, S15, S25, S26, S27}** is very efficient because many of the commas imply each-other and thus this description's multiple redundancieds shows how naturally these commas pair together.

**[ End of comment/refinement by** Godtone (talk) 21:41, 29 September 2022 (UTC)**. ]**

- Allow me to open a giant can of worms. :) I feel pretty strongly that a rank-2 "family" should only apply to strong extensions (meaning the pergen doesn't change), and weak extensions should not be part of a family. For example, tempering out both 81/80 and 243/242 from 2.3.5.11 gives you a temperament that I wouldn't call a member of the meantone family, because it has a fundamentally different structure. In pergen terms, it's (P8, P5/2) not (P8, P5). I would call this temperament a member of the Neutral/Lulu family instead. In other words, 243/242 is the comma that identifies/defines the family, not 81/80, even though the latter is 5-limit and the former is 11-limit. This suits my personal preference not to elevate prime 5 too much above primes 7, 11, etc. Now this is *not* how family has been used in the past, and much of the xenwiki is based on including weak extensions, and having the comma with the lowest prime limit be the one to identify the family. So maybe this is a futile request. But think about it -- you usually can't translate a piece in Neutral to Meantone. Half the notes simply aren't there. Thoughts?

- BTW Godtone, linear/planar temperament means a rank-2/rank-3 temperament with a period of an octave, as opposed to some fraction of an octave. Did you mean to make that distinction, or are you talking about all rank-2/rank-3 temperaments?

- Other ideas: It seems counter-intuitive that the Semaphore/Zozo family is rank-3 and the Semaphore/Zozo clan is rank-2. I'd actually like to see "clan" repurposed to refer to collections of rank-3 temperaments, and "family" be only rank-2 temperaments. Temperaments above rank-3 just aren't used that much. There could be a third term for rank-4 and higher, perhaps "tribe"? --TallKite (talk) 23:14, 24 January 2021 (UTC)

- We might wanna consult the inventor of the scheme for their logical basis, but I reckon it important to point out that "family" and "clan"/"temperaments" seem to be defined by nullity instead of rank in the first place. I don't know why it's the case, but by the fact that I can word it this way, it's not utterly broken. I'm not one of the experts who may disagree though, but I hope to be sure whether redefining by rank is really an improvement. FloraC (talk) 09:04, 25 January 2021 (UTC)

- Well, at least I now have an idea at to how to deal with pages like The Archipelago, and that is for such pages to serve as a hub for accessing the different clans and families and stuff such that are defined by tempering out the comma in question. --Aura (talk) 15:33, 18 April 2021 (UTC)

## Comma tables in EDO pages

If unsure, or in case of disputes, please add suggestions, thoughts about Xenharmonic Wiki: Things to do #Comma tables in EDO pages here, thanks!

Here's my experiment: User:FloraC/Sandbox. Does it look better? FloraC (talk) 12:18, 11 January 2021 (UTC)

- @Flora Your version
**looks better**(BTW: "Name(s)" should be "Name" and "Comments" could be dropped) but that's not important. We should ask**what purpose**these tables are supposed to serve.*I think*the practical use of these tables is negligible, but we should let the people who actually get value from them have their say. --Xenwolf (talk) 14:10, 11 January 2021 (UTC)

- Is the discussion about whether to remove these tables of commas? I don't think they should be removed because they often list lots of commas that
*aren't*given under the "Theory" section of a rank one temperament; in other words they're usually a lot more complete. I find them interesting to look at and I don't think they're entirely useless. If anything I'd argue that we should remove the list of commas under "Theory" and just talk about what temperaments (ones which temper more than one comma) a rank one temperament is good for. Then have a comprehensive list of commas sorted by prime limit as a table, kind of like how we have tables of intervals for some large EDOs. Also, IMO, comments on the commas shouldn't be included, instead, there should be many more comma-specific pages explaining both what exactly a comma allows you to do and listing various temperaments that support tempering it. Godtone (talk) 19:52, 11 January 2021 (UTC)

- Is the discussion about whether to remove these tables of commas? I don't think they should be removed because they often list lots of commas that

- I'm in favor of monzos for every comma. I don't like having to factor e.g. 352/351 into component primes. Hurts my head :). There should be a ratio column too, but for large ratios, it should be blank or else just say e.g. "9 digits". I also really like having the color name in there, but I'm biased :) The cents is useful too. Don't see the point of deleting all this info. I think if a comma needs a comment, that comma should be discussed in the theory section of the edo page. That will avoid a mostly empty column that takes up lots of room horizontally. I agree with Godtone (cool name BTW) that the theory section shouldn't merely list commas, since the table does that. The prime limit column can be dropped if for each prime limit we have a gray header row that is one big merged cell going clear across the table. The first row says "3-limit commas", next row is the one 3-limit comma, next row says "5-limit commas", next come all the 5-limit commas, etc. This makes the table narrower. That's good because there's always more room vertically, but not horizontally. --TallKite (talk) 02:50, 12 January 2021 (UTC)

- Slightly off topic, but I would rather patent vals be octave reduced, so that ⟨41 65 95 115 142...] becomes ⟨41 24 13 33 19...]. Less mathematician-friendly, but more musician-friendly. --TallKite (talk) 03:11, 12 January 2021 (UTC)

- Hmm, IMO, reducing patent vals wouldn't help. It seems your problem is the general idea of monzos being "musician-unfriendly", in which case maybe you'd prefer "musician-friendly monzos" where primes are octave-reduced and octave-complemented to be in the 0c to 600c range, and where all ratios written in the form of these "musician-friendly monzos" are octave-agnostic, with a "number of octaves" specified only if needed but otherwise deduced to be the right amount for the context. --Godtone (talk) 22:39, 18 January 2021 (UTC)

- I never said monzos are musician-unfriendly, only vals aka edomappings. I think octave-complemented monzos would be too confusing. I agree you can omit the first number of a monzo if you know the cents are below 1200¢. I do this myself sometimes, especially for commas, but I'm not suggesting the xenwiki do that. --TallKite (talk) 03:57, 19 January 2021 (UTC)

- Duplication of information is a severe problem we discussed. The tendency to copy&past from table to table raises the danger of spreading errors and making much more work... That's the problem I have with all that information. I had much hope in your comments, @Kite, but to be honest, I still don't see in how far this information will be helpful for you. Just saying I like it is not enough in my opinion. Can you please explain your personal use of comma information? --Xenwolf (talk) 06:31, 12 January 2021 (UTC)

- If I understand you correctly, you want the cents for say 81/80 to only appear on the 81/80 page, and nowhere else? Same for say 5/4 and 3/2?

- You asked about the practical purpose of these tables. Many microtonalists are locked into a specific edo because of the nature of their instrument (e.g. guitarists). The comma table tells them what commas they can pump, very important for a composer to know. They are also useful when deciding which guitar to get, and which edo it will be in.

- The disadvantage of not duplicating the info is that you have to go to another page and wait for it to load to see the info you need. For example, say I'm looking for a smallish comma that 41-edo tempers out. Without the cents column, I have to do a lot of clicking to find one. With the cents column, it's all right there. I actually did that recently. We're planning a series of videos about the Kite guitar, and in one we discuss how 81/80 pumps cause pitch shifts. I wanted to include an example of a comma pump that not only doesn't require pitch shifts, but in fact would require them on a 12-edo guitar. I knew I wanted one with a small cents for this example, so that a short pump would still be well-tuned. So I went to the 41edo page and ran down the list and quickly found Latrizo. And now that pump is added to the video script. Incidentally, the color names really made my search much easier. Because I can never keep straight the 800 (literally! I counted them!) non-color comma names. This is of course merely my personal preference.

- Now if the xenwiki had the hover feature that wikipedia has, then not duplicating info would make more sense. I'm referring to how you hover over a wikipedia link and the first paragraph of the article pops up on your screen. I think it only works on non-touchscreens, i.e. laptops not phones or tablets. Another possibility is for each edo page's table to somehow directly link to the comma page, so that changing the comma page's data affects all the other tables. And maybe even have the comma page calculate the cents internally from the actual ratio and/or monzo? Just suggesting possibilities here. If we could automate everything, there would be no danger of errors creeping in.

- I'd also like to point out that wikipedia has tons of duplication. To pick a random example, the page for Barack Obama has a lengthy section on his presidency. It has an even longer page solely about his presidency. Plus another page solely about his first 100 days. Lots and lots of duplication. I mention this because I figure wikipedia knows what they're doing, and obviously they have decided that duplication is not a problem. I also question your use of "severe" to describe the issue. How many actual reduplicated errors have you seen recently? --TallKite (talk) 01:01, 15 January 2021 (UTC)

- In terms of the risk of errors due to duplication of information in tables, this shouldn't be a problem if the tables are computer-generated or at least computer-checked. I kind of presumed they were at least in part (either generated or checked, or both)... I have some (quite unpolished) Python 3 code that could be relatively easily used to verify commas' ratios, monzos and cent sizes, but I have yet to figure out a good general-purpose way to
*find*the commas that a rank one temperament tempers, mainly because I can't think of a good general-purpose way of thinking of what commas are meaningful/interesting, as there are many very complex commas that might be considered of interest, such as the tolerma, which is interesting mainly because of the variety of commas it can combine with and the unique resulting tempered arithmetics/rank one temperaments. The only thing is the tables would have to list information in a predictable way so that code could be made that accepts text input and spits out any inconsistencies, but I presume they are mostly already in that format? Removing the "comments" column could help with this. As for "hovering", maybe we could just show the patent val and the cents and the hover can give the ratio if needed? I've seen the ratio appear as a hover in other parts of the xen wiki already, and it'd remove one of the columns, the only problem is some commas may be more easily identifiable by their ratios than their vals, and hovering doesn't (necessarily?) work on phones (and probably some other devices). Removing the "prime limit" column in favour of having rows that separate the prime limits is something I can get behind, especially if it means we can instead list commas by JI subgroup interpretations of a rank one temperament rather than just by the rather restricted (but not unuseful) "prime limits" construct. This would also be very beneficial to rank one temperaments with multiple valid JI subgroup interpretations, such as 9edo. The only thing is the rows that separate different comma subgroups should be bolded or made easy to spot in some way. (Oh and BTW, my name is based on my nickname for my favourite JI interval, 23/20, which is just about 2 cents sharp of 1 step of 5 EDO. I was gonna mention it on my user page at some point later but I wanna get a bulk of my thoughts/theories about microtonal music written first before I talk about it.) --Godtone (talk) 22:39, 18 January 2021 (UTC)

- In terms of the risk of errors due to duplication of information in tables, this shouldn't be a problem if the tables are computer-generated or at least computer-checked. I kind of presumed they were at least in part (either generated or checked, or both)... I have some (quite unpolished) Python 3 code that could be relatively easily used to verify commas' ratios, monzos and cent sizes, but I have yet to figure out a good general-purpose way to

- I like removing the comments column. To judge a comma meaningful/interesting, why not just use some sort of taxicab distance? Commas_by_taxicab_distance. Or maybe just limit the absolute value of the numbers in the monzo. Perhaps the 2-exponent is unlimited, 3-exponent is <= 12, 5-exponent is <= 8, 7-exponent <= 6, etc. That should get all important commas. If hovering doesn't work on touchscreens, we probably shouldn't implement it. I sort of like your idea of header rows for each prime subgroup, but I fear it might be too cluttered. I imagine ordering the 7-limit prime subgroups as 2.3, 2.5, 3.5, 2.3.5, 2.7, 3.7, 5.7, 2.3.7, 2.5.7, 3.5.7, 2.3.5.7. We've gone from 3 categories to 11. And the 6 two-prime subgroups have only 1 comma in them. 11-limit adds 15 more categories, 4 with only one comma. In general, N categories expands to 2^N - N - 1 categories. That's a lot of header rows! --TallKite (talk) 03:57, 19 January 2021 (UTC)

- This kind of argumentation does not convince me at all. We don't need to redefine a well-known concept to justify a non-zero cell in a table. If we have the tables about prime intervals (and we have and will have even more of it) all that information will be obvious. I'm planning a layout which has two separate rows (original values and octave-reduced ones i.e.
`v % edo`

), it's somewhat like the table in User:Xenwolf/Fifthspan#Separate mod steps (without the*fifthspan explained*rows). It's possible to produce tables like this automatically. The only thing (after implementing fifthspan calculation in Lua, after having it done in Python) is to figure out appropriate coloring or border styles for better orientation in the then bigger table. IOW: let the patent vals be as they are: we will have a more obvious presentation of the information you wish. --Xenwolf (talk) 07:32, 15 January 2021 (UTC)

- This kind of argumentation does not convince me at all. We don't need to redefine a well-known concept to justify a non-zero cell in a table. If we have the tables about prime intervals (and we have and will have even more of it) all that information will be obvious. I'm planning a layout which has two separate rows (original values and octave-reduced ones i.e.

- Wow, your user page is quite impressive! Did you do it manually or by computer? I like the format you have with two separate rows for unreduced and reduced vals. Prime 2 being reduced to zero is absolutely no problem in this format. You might want to change the row label from "mapping" to "nearest mapping". I do think fifthspans should be allowed to be negative, just like the errors are. --TallKite (talk) 03:57, 19 January 2021 (UTC)

## Improve accessibility of wiki and present info in a non-technical way

In my and Adam's experience many newcomers to xen are daunted by the math-heavy presentation of tunings and basic MOS/temperament ideas on this wiki. I propose we section off or subpage all the math-heavy parts of articles (for example I'd prefer all of this to go in Fokker block/Math). Introductory articles and sections should only assume high-school algebra and shouldn't use linear algebra terms, perhaps except for the most common RTT terms like rank. Inthar (talk) 21:41, 15 January 2021 (UTC)

- Full agreement from my side. Having university knowledge in mathematics unfortunately too often does not go hand in hand with the ability to communicate this to others. I myself - despite high motivation - too often feel locked out when trying to follow the explanation of an abstract concept based on more than one other abstract (and unknown to me) concept. Looking for a possible entry point, I usually suffer a stack overflow. --Xenwolf (talk) 11:47, 16 January 2021 (UTC)

- I highly appreciate that. At least for Fokker block I'm sure it's better presented in graphical method to average users, and I hope we have the capacity to write about it. FloraC (talk) 15:57, 16 January 2021 (UTC)

Made some more proposals.

Let me explain my decision to single out MOS sizes from 5 to 10 and why I believe scales of these sizes should be given extra attention on the wiki. There's something called the trill threshold in human psychoacoustics which is about 23/20 (close to 1\5) according to the linked paper. It's where rapidly alternating between two notes stops sounding like a trill or a vibrato and starts sounding like two disconnected notes and is a natural boundary between "steps" and "leaps", or "seconds" and "thirds".

In a scale for writing melodies in, though not all steps has to sound like seconds (it's not true for meantone[5]), at least one step should. Since a 5-note scale has average step size close to the trill threshold, 5 is a good lower bound. Since a 10-note scale, on average, will have two steps on the trill threshold, 10 notes is the size where two consecutive notes in scale will start sounding like chromatic alterations of the same note. (These arguments will hold more for MOSes for other scale types because of the regularity of MOSes.) I think we should include 10-note scales anyway, since some like blackwood[10] are commonly used in the community.

MOSes of larger size such as meantone[12] would probably be used as gamuts to choose notes for melodic scales and choose notes for MODMOSes of smaller MOSes from. They could still have Scale Workshop links but given less focus on. Inthar (talk) 17:31, 16 January 2021 (UTC)

### Reorganize temperament pages

IMO there are too many rank-2 temperaments on this wiki that are just variants of each other (have similar optimal tunings) and only differ in some high complexity interpretation for an extra harmonic. Ideally the most important (low-complexity) approximations and subgroups should be given first, and one way we can pin those down is look at what intervals are approximated in small EDO tunings (<=36edo) for the rank 2 temperament. I'm not proposing deleting any material, just reorganizing the data presented.

This suggests a scale-tree based format for temperament pages; each page would focus on a fixed MOS structure and possible temperaments for the generator chain that generates that MOS. The temperaments are ordered in increasing generator size, and more complex temperaments (i.e. approximating additional JI intervals with intervals further out in the generator chain) would be children of simpler temperaments. See proposed format for rank-2 temperament pages. The new scale tree temperament pages need not replace current temperament pages, but I believe that this is the most intuitive format and should be what newcomers to RTT-based tunings should be directed to. Inthar (talk) 07:11, 27 January 2021 (UTC)

- You have a fair point, but the premise yet to be discussed is what purposes these temperament pages serve. In the end, most temperaments may be augmented with their own pages and even subpages just like those edo pages, where much more detailed information can be presented, so that novices can get practical help to the full extent. We've got some of them (such as
*Meantone family*vs*Meantone*), so why not most of them? Apart from that, this wiki must reserve the capacity to technically precisely document the temperaments.

- The structure you illustrated looks like a catalog by MOS scales, but we've got pages for MOS scales such as
*5L 2s*, which you might feel like working on instead (they're indeed in need of an overhaul). The reason I'm saying this is, the scale structure is a function of generator set, not temperament. Meantone and garibaldi are temperaments which, despite having the same generator chain, require vastly different approaches to harmony due to tempering out different commas. All temperaments in meantone family takes +4 steps (or a multiple thereof if the generator is split) for harmonic 5, whereas all temperaments in schismatic family takes -8. So if you're interested in scale structure, there are such pages; if you're interested in temperaments, I think meantone, garibaldi and superpyth are too different to be temperament-wise reasonably listed in the same page.

- A lot of problems in this wiki can be fixed by linking improvement. The navigation will be much more friendly to novices if there are straightforward, logical links between scala files, scale structure pages, and temperaments. FloraC (talk) 09:34, 27 January 2021 (UTC)

- I hadn't seen this before.

- I'm sure I've written this several times, but the "right" answer to this is to complete organizing things into "subgroup families," which is a nontrivial problem. Originally, the theory involved only prime limits, and after we started looking at subgroup temperaments, Gene Smith tried a variety of different naming systems for the other ones, all of which are incompatible and for which the consensus is that these are suboptimal. For instance, The Archipelago is one early naming system which was subsequently abandoned, followed by some work algorithmically naming them after dyadic chords and ultimately the Chromatic pairs page. The idea on the latter page was to see subgroup temperaments as being derived from full-limit temperaments and then give it like a weird, variant/misspelled name. But, it is clearly not great for us to have a thousand different versions of "Porcupine" named "Porkypine" or whatever, or "Mohaha" and "Mohoho" as subgroup versions of Mohajira.

- The correct answer would be to generalize the way "families" are laid out, so that instead of 2.3.5.7 temperaments being "extensions" of 2.3.5 temperaments, we have 2.3.5.7 temperaments "extending" both 2.3.5, 2.3.7, 2.5.7, or even 2.3.7/5, etc. Then we can look for just the "best" "root" temperaments which start a tree of extensions and focus on those. These would become the "main" temperaments of the theory, and everything else would be different extensions. For instance, "meantone" is a "main" temperament, and we know there are many meantone extensions ("meantone", "meanpop", "flattone", "meanenneadecal", etc), but these are all grouped in the "meantone" family. Similarly, the 2.3.11 243/242 temperament (called "neutral") is a *VERY* important subgroup temperament of which mohajira, suhajira, migration, "mohoho" and "mohaha" and *all* of these related temperaments are extensions of.

- This is a very interesting and nontrivial problem. Not every "good" comma leads to a "good" rank-2 temperament, for instance. 36/35 is simpler than 49/48, for instance, but 49/48 is "better" for rank-2 temperaments because it is supported on a simple rank-3 subgroup (2.3.7) whereas 36/35 doesn't have any good rank-3 subgroup that it is part of. Similarly, 225/224 is not as "good" as 1029/1024 for the same reason.

- There is quite a bit of partially developed theory on this and a few missing puzzle pieces. I don't know how mathematical you Discord folks are, but perhaps someone sees something that I'm missing on how to put it all together. But it would be *great* to get this done, as we could then just "close the book" on this subgroup temperament problem and then move onto whatever the next part of the theory is.

- Lastly, the consensus we came to on Facebook was, rather than just arbitrarily organizing them into families, we ought to be somewhat methodical in figuring out which ones really matter, by ranking them the same way we do temperaments and etc. So I hope that any proposed reorganizational scheme will either be compatible with this structure, or leave us adequate room to do this properly later. Mike Battaglia (talk) 02:41, 13 April 2021 (UTC)

- It
*is*a nontrivial problem. The question is which root temperament is the best. For one, I most recently moved*guiron*from*schismatic family*to*gamelismic clan*not only because it's a strong extension (i.e. the pergen remains unchanged) of slendric and a weak extension (i.e. the pergen changes) of helmholtz, but also because the mapping of 2.3.7 is much simpler than that of 5, resulting in more abundant septimal intervals in a small scale. Such moves are currently based on my intuition and can be explained thru reasons like above but I don't have a rigorous approach yet. I feel the same that temperament*families*and*clans*are the more prioritized categories and*collections*such as*marvel temperaments*are less of a concern. I'll post on the FB group when I got more ideas. FloraC (talk) 09:41, 13 April 2021 (UTC)

- It

### New format for temperament entries

I'm not fond of external links to Scale Workshop. We've got pages for Scala text. Plus, you're using way too much **bold**.

See my example. FloraC (talk) 07:23, 19 January 2021 (UTC)

- Ok, but the Scala files should preferably in POTE tuning. Inthar (talk) 08:07, 19 January 2021 (UTC)

## Categorizing edos as subgroups

We need a criterion that's as objective as possible for when an EDO should be said to be good for JI subgroups. Some possibilities:

- absolute error

- [Inthar: arbitrary since different people accept different amounts of error]

- consistent

- [Inthar: semi-objective, but breaks for small edos; actual accuracy depends too much on the size of the edo]

- consistent to distance 1?

- [Inthar: see new definition in Consistent page), The justification is that some small piece of the JI subgroup lattice (maybe to distance one of the "fundamental chord") should map "consistently" in the edo, in addition to the chord itself being consistent. May be too strong for large EDOs.]

- [Inthar: Subgroup information might be considered technical data IMO.]

**Proposal**: for nEDk (meaning n equal divisions of the interval k/1, so k=2 is an octave/ditave, k=3 is a tritave, k=5 a pentave, etc.), consider the step errors, defined as err(x) = round(n*log_k(x)) - n*log_k(x), of the first L positive integers AKA of the first L harmonics. Specifically, let X be the set of the errors, meaning for all x in X, we have x in the range [-1/2, 1/2] so that |x| does not exceed 1/2. Then, to determine the error of a subgroup, pick a subset S of X (it does not have to include any powers of 2), and look at the statistical variance (AKA the square of the standard deviation) of the set of error values, however, weight the contributions of harmonics according to their expected frequency of use in factorisations of JI intervals intended to be approximated. This is taken to be the "expected error" (note that the (weighted) mean of the (signed) errors in S is the reference by which error is judged, as this provides a sort of "agnosticism" to the subgroup).

To use this to find a reasonably objective measurement of what subgroups are best, we can add a few logical restrictions on this rather general definition:

- Consider the monzos of the harmonics in any S as r-dimensional vectors (AKA, interpreted as members of N^r), corresponding to the p_r-prime-limit with p_r the r'th prime, and with p_r not exceeding L. These vectors must be linearly independent, so as to not represent a "pathological" subgroup which can have multiple mappings for the same positive integer.
- Then, if we assume that all harmonics in the subgroup are harmonics we want to approximate, we can think about the logarithmic size of each harmonic as the amount of information it generates, because smaller harmonics generate more of the harmonic series, especially when combined with other small harmonics, hence leading to prime limits as the most efficient subgroup representations of the harmonic series, with "efficient" being defined as "generates the most harmonics considering the number of generators". This leads to about the most natural formulation I can currently think of which is relatively straightforward and (as a sanity check) which is used on the page for The Riemann Zeta Function and Tuning, which is weighting each generator by the reciprocal of the log of its size. To then make the definition invariant to the number of generators, you can make the weightings sum to 1 by multiplying by an appropriate scalar.
- Then, to find the subgroups that nEDk best approximates relative to its step size, simply look at all choices for subsets of L where all harmonics are linearly independent and where the error is low enough to guarantee a good level of consistency, and sort results by increasing errors. Note that this becomes very computationally intensive for large L, so L=30, L=42, L=58, L=96 and at most L=126 are all good restrictions, depending on what is computationally feasible in a reasonable amount of time.

(The choices of L that I listed here are based on prime limits (specifically, record prime gaps, and 30 is 2*3*5 so its significant) with the exception of 58 which is based on the 53-prime-limit being the highest limit available on x31eq. Note that larger L can be used for small ETs if we restrict accuracy sufficiently or consider only lower-prime-limit subsets of L.) - As for making the search more computationally feasible, there is an easy way to eliminate possibilities, which is by adding harmonics in order of increasing error relative to the error of some starting harmonic until there are none left in L or none left that wouldn't introduce too much error. This provides an easy way to define "families of subgroup interpretations" by increasing error and through superset/subset relationships as well as compatibility relations, which could be an interesting direction to take this in of itself.

(I wonder how related it'd be to families of temperaments? Seems like it'd be strongly related, and better yet, suggest potential ways of organising relatively unknown temperaments.)

A few notes on the mathematics:

- I pick the variance over the standard deviation because squaring the error leads to a "least-squares" optimisation, which is then much more "compatible" with the tuning optimisations represented by the Riemann Zeta function.
- We can take an alternative strategy to tuning a subgroup less focused on the regular temperament theory interpretation and more focused on what consonant chords and intervals are approximated that you want to use. In such a case, you pick
*any*subset of X corresponding to*any*subset of L, which is to say that the r-dimensional vectors*are not*required (or even recommended) to be linearly independent. Then the subset of L represents a generalisation of odd limits, where odd limits are specific to where your subset of L is only odd harmonics due to the discarding of 2's in the prime factorisations due to being specific to ED2s. This interpretation/use fits very nicely with the notion of consistency to distance d, with the standard deviation being an "expected overall consistency" which is less discrete/rigid. The only potential problem with this is it seems like a very large number of possibilities can result with different subsets being preferable for subjective reasons.

--Godtone (talk) 04:01, 22 January 2021 (UTC)

- @Godtone your proposal looks like a measure of absolute error very similar to TE error (weighted RMS error of primes). I suggest you check that if you have not. FloraC (talk) 11:54, 22 January 2021 (UTC)

- I don't think it's our place as wiki editors to pass judgement on what an edo can do. Our job is just to report the facts. But any rating or metric will have some arbitrariness. We have the absolute and relative errors of each prime right there at the top of the edo's page. This lets people make their own decisions. Not to say that what you're doing isn't a worthwhile endeavor. I just don't think it belongs on the edo pages. Perhaps it could be a separate page on the xenwiki called "Godtone's analysis of EDO subgroups" or some such, that the main EDO page links to. --TallKite (talk) 07:59, 24 January 2021 (UTC)

- I've amended my proposal to "Xenharmonic Wiki talk:Things to do# Odd harmonics table instead of prime harmonics for edos". It's better to report odd harmonics so they're immediately visible. Better yet, Tom Price suggested we use a circular diagram to plot the error of odd harmonics mod edo steps. Which allows seeing at a glance which ratios between odds are in tune. Inthar (talk) 20:31, 24 July 2021 (UTC)

## Accessibility formatting guidelines for presenting RTT in general-audience pages

It seems the proposal for making the temperament material more accessible has failed. It might be better for pages intended for a general audience to be as isolated as possible from the temperament pages and for us to be especially careful to try not to obligate newcomers to learn it at all.

**Proposal:** On a page intended to be read by a general audience and those unfamiliar with RTT, such as pages about MOS patterns,

- A temperament should not be mentioned at all, unless the temperament has been used in at least 20 compositions (for example, a 1L6s MOS in a porcupine tuning, or pumps the porcupine comma). Pages on which this temperament restriction policy is active should be clearly marked for editors.
- When linking to a temperament name, it should link to a page describing the temperament for a general audience, not a technical temperament entry.
~~The same threshold should apply for creating a temperament page.~~

Inthar (talk) 08:37, 27 March 2021 (UTC)

- > The same threshold should apply for creating a temperament page.

- A temperament page documents whatever important about the temperament: notation, interval chain, chords, scales, history, music examples, etc. It's with the page will come compositions, not the other way around. Therefore, there should be no barrier for creating a temperament page so that its use can be facilitated.

## Category: Pages with internal sound examples

I made a new category called "Pages with internal sound examples". This category is similar to the "Listen" category, but it only lists pages with embedded audio files AKA internal sound examples. I believe this is a useful category to have for cases in which someone on the xen wiki wants to listen to a sound example without having to go to an external website. So far I have looked through the list of all pages to find and categorize pages that have internal sound examples, but for me alone to fully complete this process would take at least a week or so, provided I have enough spare time to edit the xen wiki on a regular basis. Because of this, I would like to know if anyone else on this wiki would be willing to help me add pages to the "Pages with internal sound examples" category. --Userminusone (talk) 03:25, 28 March 2021 (UTC)

- I've already partially guessed this intention, so good to read this. This category definitely wouldn't hurt, let's see if it's of any use. I'm happy to join your efforts and will add sites to this category as I come across them (though probably not systematically). --Xenwolf (talk) 08:43, 31 March 2021 (UTC)

- Thanks, Xenwolf. Now that you're on board, can I put this on "Xenharmonic Wiki:Things to do" so that other people can see it and contribute? --Userminusone (talk) 19:01, 2 April 2021 (UTC)

## Odd harmonics table instead of prime harmonics for edos

Suggestion: use User:Inthar/Template:Harmonics in edo (for odd harmonics) instead of Template:Primes in edo (for prime harmonics).

- I saw that this has been done to a number of edo pages. The way I use this table is to find the error of a JI ratio in an edo. For 5/3, I subtract prime 3's error from prime 5's error. For 15/14, I add 3 and 5 and subtract 7. Because I'm used to doing all this, I don't need that redundant 9 column. For 9/8, I simply double 3's error. So this table which already is rather wide on the screen now has redundant columns for 9, 15, 21, 25 and 27. So personally I would prefer the old way, prime harmonics only. --TallKite (talk) 05:37, 6 September 2021 (UTC)

- One of the points of using odd tables is to ease inconsistent edos. With some edos with like a really off 3 but accurate 9, the odd table is likely to be helpful. With others the odd table is redundant. It depends on the edo. I propose a general guide: if error of prime 3 < 25%, show the prime table, otherwise odd table, or we may examine it case-by-case. FloraC (talk) 08:53, 6 September 2021 (UTC)

- Re: inconsistent edos, that is indeed one reason why I made the odds table. My humble proposal: if there's no inconsistency in the odds table, use the prime table (showing primes up to 31). Otherwise use the odds table.
- Imo even when there's no inconsistency, I can still see the odds table being useful for showing at a glance how e.g. 31edo's 11/9 is really good. And, lack of inconsistency is in itself a piece of information about an edo. Inthar (talk) 09:09, 6 September 2021 (UTC)

- 18edo is an example of an edo that has a good 21/16 (-4.1c error) which is inconsistent with the best 3/2 and the best 7/4. And it's nice to to be able to gauge the error for, say, 21/17 in an edo just by looking at the direct errors of the best 21 and the best 17. The table is meant to be a quick reference. Besides, aren't 15/8 and 21/16 both important JI ratios in the 5-limit and the 7-limit? Inthar (talk) 01:36, 7 September 2021 (UTC)