Xenharmonic Wiki:Things to do

Hello there! This page is a place for various projects and minute things to do on this wiki. Please be welcome to help with any of them you like!

If you think something essential was forgotten and should be here, don’t be shy to add a new section here! If you don’t know if a project would be interesting to others, write at the talk page and let’s decide it together.

When the technical help is needed, please aid volunteers with a tool or two for being sure the details are easy to make right. For example, a template, a converter etc..

See also Conventions, Wikifuture, Migration FAQ as well as Category:Todo and its subcategories.

Details to fill out in articles

• Interval pages like 3/2
  • <Please write what may still be desired>

• <Other kinds of pages>

Archiving outdated discussions

Discussion pages tend to become confusing over time. The sections at the beginning are often long since finished. This tendency is easy to observe, but hardly anyone knows how to archive outdated articles.

We probably need some templates to support archiving. Moving old sections to subpage(s) is not as hard, but a bit of automatic decoration/guidance/navigation would help people to do this.

Automated archiving would be nice, but not essential in the first place.

Infobox for EDO pages

In EDO pages (see for example 23edo, 74edo, 167edo), core information is currently still given in prose, which makes it difficult to get this information together. Adding another infobox template would help to present and manage the formal information.

At the moment, we tend to include of these core characteristics

• step count
• step size
• patent val

Join our discussion: Xenharmonic Wiki talk:Things to do #Infobox for EDO pages

Categories of interval pages

There are lots of interval pages in the wiki, for example 3/2, 8/7, 25/24, 11/8... We developed an info box that brings the core features together. Still open is the question which category name would fit best for all of them. We currently observe a seemingly random mix of

• Category:Interval
• Category:Ratio
• Category:Interval ratio
• Category:Just interval

At present, it appears that we will replace most of them with Category:Rational interval" in the future.

Please join our discussion in Xenharmonic Wiki talk:Things to do #Relations of various interval categories! Thanks 🙂

Proposal: Shorten editing titles

When using tabbed browsing, long identical prefixes (like Editing ) in titles make it hard to differentiate tabs of wiki pages currently being edited.

system message	predefined text	suggested text
MediaWiki:Editingcomment	Editing $1 (new section)	✎ $1 (new section)
MediaWiki:Editing	Editing $1	✎ $1
MediaWiki:Editingsection	Editing $1 (section)	✎ $1 (section)

What do you think about the proposed change?

Join the discussion at Xenharmonic Wiki talk:Things to do #Shorten editing titles

Get rid of "alternative pages"

There are some pages that were mostly started out of frustration of on particular user not any more active in this wiki. The problem with diverging pages about the same topic is that linking to it tends to break or at least dissipate the consistency of the entire wiki. As normally would be the case with pages targeting the same topic but created by chance, the content should be merged into the (mostly obvious) main page. If there is noting valuable on it, the pages should be deleted. The pages are currently in the Category:Alternative pages. For discussing deletion etc, we should refrain from doing that on the respective discussion pages, because deletion will remove these as well. We'd better open an own page for discussion deletion.

I took a look at these. The edo pages are a relic of a discussion on facebook about the proper format for edo pages. Sort of useful. I suggest deleting all but the 15edo-a page and Gareth's page. The 94-edo page might have some good stuff, but since it's 94edo and 15edo jumbled together, it's also really confusing. This is what I suggest, but I don't feel I have the authority to actually delete someone's page. --TallKite (talk) 03:05, 12 January 2021 (UTC)

Place to discuss deletion requests

Sometimes it's not easy to decide if a page should be deleted or not, it has to be discussed first. The problem with discussing deletion requests on the discussion page of the page being questioned is that they both have the same future. If the deletion happens, normal users have no access to the reasoning any more. Most wikis use an extra page for this purpose.

The so-called project namespace (in this wiki it's indicated by the prefix Xenharmonic Wiki:) is dedicated to that purpose, see pages currently in the project namespace.

Disambiguation project

There is a project Xenharmonix Wiki:Disambiguation that aims to build the tools we need. Please join the work and discuss related issues.

Naming articles

To reflect our current efforts, a #Naming articles section should be added to Xenharmonic Wiki:Conventions. Please review, rework, and/or discuss following draft:

---

Wiki pages should follow the usual English capitalization rules, except for the very first character, which is automatically capitalized by the wiki software. This means that words inside the title are written in lower case, except for proper names.

Currently, there is still a mixture of styles that has historical reasons: In the beginning, titles were started in WikiCase because the Wikispaces software used at that time automatically linked such words. Later, the configuration was adjusted so that links were only created if this was specified by appropriate markup. Here, the titles started to look like titles, but to a large extent also with the usual capitalization of all meaningful words for titles (book titles). Then came the switch to MediaWiki with new features that were only slowly adapted (redirects, categories, etc.). Meanwhile, we have moved on to making full use of the wiki software's support. Thus a) pages are always linked regardless of the upper and lower case of the first character (e.g. [[Cent]] == [[cent]] → Cent == cent) and b) characters that are appended after the link markup are included in the link label (e.g. [[cent]]s == [[cent|cents]] → cents == cents). This way, links can usually be embedded in the text without much effort.

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

todo

A project to reorganize 11-limit and 13-limit temperaments. That is still discussed.

Join the discussion Xenharmonic Wiki talk:Things to do#13-Limit, 17-Limit and 19-Limit Comma Pages!

Comma tables in EDO pages

We found (on User talk:FloraC #Fractions vs. names in interval lemmas) that the comma tables on EDO pages are overloaded with information already given elsewhere. This self-evolving "convention" makes it hard to provide consistent and correct information about, (alternative) names, corrections etc. The original information should eventually find place in a dedicated page for each comma; the overview pages about commas (Large comma, Medium comma, Small comma, Unnoticeable comma) should be seen as secondary source then. Currently we tend to reduce the comma tables on EDO pages to at most three columns:

• p-Limit
• linked name or fraction (depending) on the lemma of the link target
• Comments ← only if there really are useful comments

This can be discussed in Xenharmonic Wiki talk:Things to do#Comma tables in EDO pages

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

(shortcut(s): Xenwiki:Accessibility, XenWiki:Accessibility)

Many newcomers to xen are daunted by the math-heavy presentation of tunings and basic MOS/temperament ideas on this wiki. Therefore we propose the following:

• Section off or subpage all the math-heavy parts of articles (for example to move Fokker block#Mathematical description to Fokker block/Math).
• Introductory articles and sections should assume at most high school algebra and should focus on practical knowledge for musicians and composers, such as musical examples, how to build a scale in Scala, or what intervals and chords 17edo has.
• EDO pages should follow the above rule too. They should present general information in a standardized format, like an encyclopedia article (Not making any particular suggestion on the format now).
  • Subpage more theoretical data such as RTT data (such as the comma table) and Zheanist data (such as nejis and higher harmonic series chords approximated)?
• Explanations of abstract concepts should use visualizations and examples where possible (They help even in more mathy contexts).
• Scales of size 5 to 10 should be given extra attention on the wiki.
• Collaborative work on the Practical RTT series for teaching regular temperament theory (RTT) while using linear algebra terms as little as possible. While Mike's lectures were no doubt valuable to some people, they would have effectively involved teaching a whole course on theoretical linear algebra.
  • Maybe there's no need to even teach people to use x31eq or read mapping matrices; see newer proposals above.

Further proposals coming.

Please join the discussion in Xenharmonic Wiki talk:Things to do#Improve accessibility of wiki and present info in a non-technical way!

New format for temperament entries

Present regular temperament tunings on temperament pages in a new concrete, easy-to-read format.

• Have dropdown tables of intervals in an appropriate MOS, alongside clear JI interpretations each interval has if any. Maybe we can have a script to automatically generate tables like that, given a temperament's mapping matrix. Then there would be no need to teach people to read mapping matrices.
  • The MOS should be the first MOS size that contains the "fundamental consonance" of the subgroup of the temperament (the lowest odd-limit chord that contains all of the basis elements; for example, 4:5:6 for 2.3.5, 4:9:21 for 2.9.7/6).
• Linear algebra data such as mapping matrix and badness should be hidden under a dropdown view.
• Have ScaleWorkshop links for MOSes. MOSes with 5 to 10 notes should be bolded.

Sample entries here.

Please join the discussion in Xenharmonic Wiki talk:Things to do#New format for temperament entries!

Terminology proposals

Reformulate use of special terms to make them more obviously musically meaningful.

• Re-formulate "consistent": Use the formulations "all-odd harmonic series chord C is consistent in N-edo" to mean that:

1. every instance of an interval in C is mapped to the same size in its approximation C' (for example, 4:6:9 is approximated using two fifths of the same size), and
2. no interval within the chord is off by more than 50% of an edo step.

I think the formulation "1:3:5:7:9:11 is consistent in 31edo" is more obviously meaningful than "31edo is consistent in the 11-odd limit". A set of odd numbers such as an odd limit corresponds to a harmonic series chord independent of voicing.

Set a semi-objective standard for classifying edos as subgroup temperaments

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:

1. absolute error? (arbitrary since different people accept different amounts of error)
2. consistent? (semi-objective, but breaks for small edos; actual accuracy depends too much on the size of the edo)
3. consistent to distance 1? (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.

Whatever criterion is used, we should state that that criterion was used, in the interest of transparency.

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)