Xenharmonic Wiki:Cross-platform dialogue: Difference between revisions

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::::: Hmm... maybe it's a bad example for me because I think tempering 128/125 is unfeasible (maybe [[27edo]] does it well but that uses [[delta-rational chord]]s to justify itself so it's not really the thing temperaments were designed for because the target isn't a fixed point) but I will follow the spirit of the logic of the example. The issue seems to be rather that CTE isn't designed to handle the case where extra generators are independent of the commas tempered if you are valuing p/q over pq (because CTE choosing pure generators makes perfect sense if you want to weight them equally and in this sense it's the logical constraining of [[TE]] which assumes the same). But POTE certainly doesn't seem to be the right fix to prioritising p/q over pq. Rather it seems like (at least in this case) what's wanted is a metric that respects tendency (a desire I've voiced before actually). For example it's noted [[Constrained_tuning#CTE_tuning_vs_CTWE_tuning|here]] that "POTE tuning works as a quick approximation to CTWE" (AKA KE tuning), so maybe CTWE / KE tuning is desired? --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 18:23, 16 March 2024 (UTC)

: Yeah, KE is what you're looking for. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 20:50, 16 March 2024 (UTC)

:::::: Yeah, KE is what you're looking for. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 20:50, 16 March 2024 (UTC)

=== Mike's Response to All This ===

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:: Thanks for expressing your general views tuning theory and tuning optimization. I see you seem to still think there is an open question if you want to "keep" the thing we made which you don't like, or replace it with the thing you made which we don't like. I think I've said my piece about this way of doing things at this point. When you folks figure out what you want to do, if it still involves removing stuff, please ask us on FB first. Thanks. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 20:15, 16 March 2024 (UTC)

::: You said "we generally prefer tunings like POTE, KE, etc."? --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 20:54, 16 March 2024 (UTC)

FloraC has added POTE tuning back to all the temperament pages which used to have it. If there are any pages we missed, please let us know so we can add POTE back to those as well. The consensus in the Discord channel is in favor of displaying multiple tunings on temperament pages, so that's what we're going to do moving forwards. No more removing one in favor of another. --[[User:BudjarnLambeth|Budjarn Lambeth]] ([[User talk:BudjarnLambeth|talk]]) 02:35, 17 March 2024 (UTC)

: Appreciate it. Thank you to Budjarn and Flora.

: OK, now that that is settled, regarding the actual math involved for Godtone, Inthar, Flora and others:

: Yes, it's true that one of the main reasons people liked POTE historically is because it approximates KE. If you want to declare KE some kind of best general-purpose tuning, or whatever, I would probably support that. However, we ought to compute POTE/KE tunings for a huge set of temperaments to see if for any they differ significantly (which would be very surprising to me).

: The bigger picture: all of these tuning optimizations are imperfect because they only measure dyadic error. A 4:5:6 chord, flattened to the "isoharmonic"/"proportional"/"Mt. Meru"/whatever 4:4.98:5.96 chord, or 0-379-690, sounds less far off than something with a similar amount of error which is non-proportional, so we really care about which way the errors are oriented within the triad. If you want, you can look at the Hessian of simple chords in 3-HE, which models this correctly, to build a simple linear model for tuning error of some triad. Then, you can try to optimize the entire "Z-algebroid" of chords, rather than just the Z-module of monzos. In principle it can be done - I've played around with this kind of thing a bit, though don't have any firm results.

: Or: just note empirically that TE seems to magically give pretty good results, even for triads, tetrads, etc. Why? Who knows. Maybe if you did the above thing out all the way you'd derive that TE, or something close enough to it, also happens to be the optimal tuning on the entire algebroid. Similarly, POTE gives good results for this but not CTE. Why? Again, who knows, but one idea is to note that stretching a chord isoharmonically/proportionally in Hz is very close to stretching it in cents, as a first order Taylor approximation. For instance, stretching 4:5:6 both ways so the outer dyad is 720 gives 0-397-720 (isoharmonic) vs 0-396-720 (stretching in cents). So scaling TE to POTE is approximately the same as isoharmonically stretching all chords in the entire tuning.

: So that is the other reason POTE, or any tuning, is useful: empirically, we note it sounds good.

: There are other reasons. Graham has expressed interest in it being the unique pure-octave tuning that minimizes the angle/dot product with the JIP. I don't remember what musical interpretation he gave to this angle; you'd have to ask him why. And there is always this "black magic" element to it where Gene knew a bunch of stuff about all of this, but has sadly passed on and we can't ask him about it. We have the same situation with, for instance, zeta integral and gap tunings - what theoretical justification do these things have, compared with something clear like zeta peak tunings? I don't know, but Gene did. Oh well. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]])

:: I have idiosyncratic reasons to favor CTE or a tuning that doesn't prioritize divisive ratios over multiplicative ratios based on where beating occurs in the frequency spectrum with any harmonic timbre. I documented the details in my essay (→ ''User:FloraC/Hard problems of harmony and psychoacoustically supported optimization''). The essay also contains a design around Hahn distance so you might be interested. Regardless, as I've related to you on FB, I think of CTE as the most straight-forward solution that is most likely to be understood by the widest audience, so the main appeal is its methodological transparency, which is somewhat shared by KE and is in contrast with the "black magic" of POTE.

:: My next plan is to add KE to later temperaments that never had POTE documented (and CTE is also to be added). [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:50, 17 March 2024 (UTC)

::: Thanks, will read when I get a second. It would be great to have all of these things, as I still am not sure if KE and POTE ever give significantly different results. Aren't you writing a Lua module that computes them all at once anyway? [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 18:46, 17 March 2024 (UTC)

:: I appreciate your in-depth response a lot. Sorry if I came across as hostile, it was not my intention. The thing about POTE being the tuning with a unique property is interesting; I hadn't heard it before. If I may offer my own thoughts: I agree that likely the reason POTE seems to be a good approximation is to do with [[delta-rational chord]]s (which from what I understand is the appropriate and nontrivial generalisation of isoharmonic chords, in that delta-rational chords sound like JI without being JI while isoharmonic chords are JI tunings of delta-rational chords); in my mind though it would make more sense to devise a different measure entirely if you wanted to optimise that sort of thing like how you noted that one could devise measures of triadic/tetradic/etc. chords. I have a hypothesis to do with the divide between POTE and CTE, or I think more aptly, between weighting p/q over pq and weighting them the same. It seems to me that the lower accuracy a temperament is, the more we prioritise p/q over pq, so that CTE becomes increasingly worse, while the higher accuracy a temperament is, the more it makes sense to also want to model pq with p/q; maybe this caused an impression here that CTE made more sense. For example, I myself wouldn't usually look at temperaments like tempering [[256/243]] (Blackwood) or [[128/125]] (Augmented) because if I wanted something like that, I would instead investigate a DR (Delta-Rational) chord phenomenon rather than using CTE. Kind regards, --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 20:51, 17 March 2024 (UTC)

[[Category:Xenharmonic Wiki]]

:: Also, if you haven't seen it already, you may want to look at [[Talk:POTE_tuning#Justification]] - it seems relevant to this discussion, as [[User:Sintel]] comments there, although I'm not sure if the comments are outdated. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 21:19, 17 March 2024 (UTC)

wayy back before I understood how the maths worked I always wondered why POTE on the wiki was always given by default. And this confusion was actually quite valid, because nowhere on the wiki is it explained why this is a reasonable choice at all. It seems to me like if you provide one default choice, it should be well-justified.

now, I am quite fond of just providing one default choice, as to not paralyze the reader with too many options, but then the question is which one?

in the past I have compared KE and POTE for like thousands of temperaments, and it seemed like they were always extremely close. so how about just using KE going forward? this way we have something that is both empirically *and* theoretically justified.

[[User:Sintel|Sintel]] ([[User talk:Sintel|talk]]) 22:14, 17 March 2024 (UTC)

: FWIW, that's essentially what I was trying to say in my comment starting with "KE tuning seems acceptable to me" (although I don't understand the specifics enough to argue it more strongly). I don't mind the other solution of listing CTE, POTE and TE together though if that will cause less friction going forwards, although I still think that due to POTE's trivial derivability from TE it seems redundant/unnecessary to list, but I guess dividing the cent values by the ratio between the tempered octave and pure octave (even though trivially easy) is enough of a hassle for anyone who really wants POTE specifically to justify listing it. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 00:40, 18 March 2024 (UTC)

:: So far, my suggestion is to have a single standard optimal tuning displayed in any given temperament data block, and optionally append a collapsible box containing more "optimal tunings" for various optimization methods. These would serve as quick references for people who do not wish to use a calculator, namely if one wants to compare similar temperaments at a glance. These tunings can most likely be computed dynamically if we have the right modules, but they could also just be manually inserted if need be. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 03:01, 18 March 2024 (UTC)

::: Showing a single standard tuning by default has the issue of which though. If they're on board with KE (if we can show that it's practically almost always very close to POTE) then that's not an issue, but otherwise I presume it means that they'd want it to be POTE; I would object to POTE being the standard tuning to show (as opposed to, say, KE) just as they object to CTE. In such a case it seems better to just show a few tunings side-by-side and let the reader make their own judgement. The values given are only meant to be a starting point anyways (for if one doesn't want to use an EDO tuning). --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 03:35, 18 March 2024 (UTC)

:::: My pick for the standard tuning would be TE, with the others (POTE, KE, CTE, anything else) being included in the collapsed box. There seems to be a lot of disagreement about which pure-octaves optimal tuning is acceptable, but most people seem to be okay with TE as the stretched-octaves one, so with TE being the least controversial, it seems to make sense to list it first. --[[User:BudjarnLambeth|Budjarn Lambeth]] ([[User talk:BudjarnLambeth|talk]]) 06:09, 18 March 2024 (UTC)

::::: I think most users will want a pure-octave tuning to start with and that's why the controversy is on the pure-octave tunings. If there was only one tuning then KE would meet the needs of all parties the best, but at this point it's clear that POTE is to be preserved and CTE is to be added. If we add KE to POTE then they serve the same purpose so it's a waste of space. So I'll add CTE to POTE while leaving the question of replacing POTE with KE to the future. I think additional tunings can be added in the dedicated page for the temperament, properly organized as its own block. (All those additions are low-priority to me so if I'm doing it all alone, it won't happen too quick.) [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:43, 18 March 2024 (UTC)

:::::: Alright, sounds like a good plan to me. Thank you for your hard work on this :) --[[User:BudjarnLambeth|Budjarn Lambeth]] ([[User talk:BudjarnLambeth|talk]]) 09:13, 18 March 2024 (UTC)

=== Table comparing POTE vs KE vs CTE ===

OptimalComparison5Lim.png|Comparison of POTE, KE, CTE tunings for several 5 limit temperaments

OptimalComparison7Lim.png|Comparison of POTE, KE, CTE tunings for several 7 limit temperaments

</gallery>

I made these tables comparing the POTE, KE and CTE tunings for all of the temperaments and microtemperaments listed in Erlich's Middle Path paper, as well as Pelogic, since a comparison like this is something that has been asked for a few times on this page.

I used [[User:Sintel|Sintel]]'s temperament calculator to find the KE and CTE tunings, so a big thank you to Sintel for that :)

--[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 07:08, 19 March 2024 (UTC)

:I wrote some of the headings at the top wrong. I uploaded new versions of the files with this fixed, but it might take a few hours for the file pages to start showing the new versions. Specifically, the columns that say "CTE vs KE" are supposed to say "POTE vs CTE". Sorry for the confusion --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 07:17, 19 March 2024 (UTC)

::As Mike pointed out below, I put the wrong KE generator for 5-limit Porcupine. I have uploaded a new version of the file that fixes this now. The file page has not yet started displaying the changes but hopefully it will soon :) --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 09:44, 19 March 2024 (UTC)

::: I'd just like to note I'm very happy with KE, my feeling is that for low-accuracy temperaments CTE doesn't weight p/q over pq enough but POTE seems to overdo it, so it's very favourable that KE seems to be close to POTE but slightly in the CTE direction. Hopefully KE will continue this trend upon analysis in higher limits with various subgroups. (Not that I don't like CTE, I personally have generally liked the CTE tuning a lot for mid-to-high-accuracy temperaments, EG I think its tuning of meantone as ~2/9-comma (between 1/4 and 1/5) makes sense.) --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 21:08, 19 March 2024 (UTC)

:::: I have made a table comparing some high-limit temperaments (specifically the ones Mike named) as well as some subgroup temperaments in POTE, KE and CTE. The same trend seems to continue, as all the KE tunings are in between POTE and CTE, and most of them lean closer to POTE.

OptimalTuningSubgroupAndHighLim.png|Comparison of POTE, KE, CTE generators for high limit & subgroup temperaments

</gallery>

:::: --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 21:59, 19 March 2024 (UTC)

=== Mike is Done For Now ===

Hi all

This has been fun but I need to be done with this for a while, so I leave it with you all.

So some parting words for POTE vs KE:

# Thanks for putting POTE back and making the charts.

# I've added a bunch of theory, history and Python to the constrained tunings page, so it's easy to compute any arbitrary the CTE/KE/whatever in closed form. Since it looks like you have Lua code for the pseudoinverse you'll be able to use this to easily compute the KE tuning without needing nonlinear optimization.

# When comparing these things it's best to compare the tuning maps, not the generators. It's hard to know how much difference a cent makes just looking at the generator map.

# I would just subtract the two tuning maps and take an RMS of the differences.

# It looks like the biggest differences involve temperaments where the period is some fraction of an octave: Augmented, Diminished, Blackwood, etc.

# The differences should also be pretty small for stuff like magic, porcupine, etc, and also for 5-limit temperaments. It's the things that are a bit further out error-wise and in higher limits that I'm curious about: superpyth, machine, semaphore, pajara, modus, mohajira, etc.

# I think there are some errors - Porcupine doesn't look right; I think it should be 164.0621.

# In general I'm fairly impressed with KE though.

For organizing this stuff:

# I agree having one or two "default" tunings shown prominently is good, and then the rest below it. Maybe one pure-octave and one stretched-octave, if you like.

# Yes, please do put a pure-octave tuning up there. Nobody wants to grab a calculator to derive POTE from TE!

# The above results for POTE vs KE look fairly good to me. If they look this good after checking with higher-limit temperaments and ones a bit less accurate, I'd be alright with making KE the standard and POTE secondary.

# If you like CTE then add it but I don't think it should be standard. It's awful, really.

For the math:

# I don't know how I always end up in this position of defending the "old guard" - I spent the last 15 years arguing with people about changing stuff and now suddenly I'm defending it.

# If you really want my view, I don't really think any of these optimal tunings are ideal. I think log-weighting in general is ridiculous. All of these higher primes end up weighted ridiculously strongly. The "best" EDOs (http://x31eq.com/cgi-bin/more.cgi?r=1&limit=2_3_5_7_11_13_17_19_23_29_31_37_41_43_47_53&error=5) in very high limits with log-weighting are always very strange things like 26, 29, etc, because higher primes just pop up faster than they roll off.

# There is a version of the zeta function which weights things as 1/log(nd) instead of 1/(nd)^s, and the results just seem very silly compared to the real one.

# I came up with the "BOP" and "BE" tunings for this reason, which weight ratios inversely proportional to the exponential of their norm (i.e. 1/(nd)) instead. FWIW I think they're better, the BE tuning in particular. It would not be that hard to figure out some kind of Weil version of this.

# The subgroup version of these is a little bit less easy to do, as you need to check the convex hull of all intervals divided by the exponential of their norm.

# I think this is a much more radical change though and I'd say to go with POTE/KE for now and do this later.

That's it for now, thanks. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 09:27, 19 March 2024 (UTC)

== Working with the Old Guard ==

Hello! I'm glad to see that this page exists. I'm a user on Discord who hasn't had much involvement in the previous conversations on this thread, but I'd like to try and work together with the old guard on some of my ideas- if that's even remotely feasible. To start with, I'd like to get some feedback on some of my ideas that I've worked on here on the wiki over the time I've been here, such as [[Alpharabian tuning]], [[telicity]], [[syntonic-rastmic subchroma notation]] and [[User:Aura/Aura's Ideas on Functional Harmony|my own take on microtonal functional harmony]]. Of these, I think telicity might be of the most interest to the old guard, since it's fairly math-heavy. I hope I'm not being a bother. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:17, 19 March 2024 (UTC)

== Ranking poll for "good" EDOs from 27 to 140 ==

I thought it might be cool to do a poll to see which of these EDOs people subjectively prefer over others. It's far from all EDOs in the 27 to 140 range; I've picked the ones that seem the most significant theoretically as being worth interest, but if you think something's missing there is an option "[your favourite RTT EDO between 27 and 140 not on this list]" at the bottom of the list. The list is in order of number of notes per octave and I hope that each participant takes the time to sort all EDOs they have opinions on to the top and the bottom; if you're not sure that's why I've provided subgroups in up to the 97-prime-limit, although if you just focus on the 43-prime-limit part that's more reliable and probably a lot more intuitive for appraisal purposes.

If you're wondering "why such a high prime limit"? here's details/explainers of the significance of all primes >43 that I've included:

67/64 = 79.31c (close to 1\15 = 4\60, 2\31 = 4\62, 3\46 and practically exactly 8\121; the harmonic 15 EDOstep),

64/61 = 83.12c (close to 1\14 = 5\70 = 6\84 = 10\140, 2\29 = 4\58 = 6\87, 3\43 and 5\72; almost exactly (4/3)^(1/6) (a third of a semifourth)),

64/59 = 140.83c (close to 2\17 = 4\34 = 8\68, 3\26 = 15\130, 5\43, 7\60, 9\77, 11\94 and 13\111; appears in many systems as (3/2)^(1/5)),

71/64 = 179.7c (close to 3\20 = 12\80 = 21\140 but also a harmonic ~10/9),

73/64 = 227.79c (close to 3\16 = 9\48 = 15\80, 4\21 = 12\63, 7\37 = 14\74 = 21\111 and 11\58 but also the harmonic supermajor second),

64/53 = 326.5c (close to 3\11 = 21\77 = 27\99, 10\37 = 20\74 = 30\111, 13\48, 16\59 = 32\118 and 19\70 = 38\140; this corresponds to a very distinctive size of third between minor and supraminor),

79/64 = 364.54c (close to 3\23 = 6\46 and 10\33 = 30\99 but also the harmonic submajor third),

83/64 = 450.05c (practically 3\8 but also the harmonic semisixth),

89/64 = 570.9c (close to 10\21 = 30\63 and 19\40 = 38\80; like a harmonic analogue of 32/23),

47/32 = 665.51c (close to 5\9 = 15\27 = 20\36 = 35\63 = 40\72 = 50\99; the harmonic wolf fifth / 9 EDO fifth),

and 97/64 = 719.9c (practically 3\5; the harmonic 5 EDO fifth).

As for primes > 13, I highly recommend looking at the [[25-odd-limit]] in all its glory if you are unfamiliar with using primes > 13, but as a quick summary, 17 is notable as introducing subminor ([[17/14]]) and supramajor ([[21/17]]) and neogothic minor ([[20/17]]) and neogothic major ([[51/40]]) and a good approximation of the half-octave of [[17/12]]~[[24/17]] but also for its naturalness as the general-purpose semitone in [[srutal archagall]], 19 introduces the harmonic minor third [[19/16]] between [[6/5]] and [[13/11]], and is close to [[32/27]] (and equated with it in [[nestoria]]), 23 introduces [[23/16]] which is what can be thought of as a harmonic augmented fourth in sharp-fifth systems and a harmonic diminished fifth in flat-fifth systems; it also introduces [[23/20]] which is between supermajor ([[8/7]]) and a semifourth ([[15/13]]), plus two new shades of supraminor third at [[23/19]] and [[28/23]], although the latter is more like a subneutral third, [[29/16]] is notable for being basically free in multiples of [[7edo]] (although is also notable as [[29/23]] approximates 400c reasonably well so [[21edo]] (and therefore [[63edo]] and [[84edo]]) has a good 23:29:32:39 chord for example), [[32/31]] is the subharmonic quarter-tone, [[37/32]] is the harmonic semifourth (implying a fourth around that of [[19edo]], so for higher-accuracy systems it works especially well with dual-semifourths; remarkably [[15/13]] and [[37/32]] are made fourth-complements in the miraculous harmonic series autotuner [[311edo]]), [[41/32]] is the harmonic supermajor third and [[43/32]] is the harmonic perfect fourth (as it approximates [[4/3]] significantly better than [[21/16]] and much better than [[11/8]]).

Ranking poll is here: https://strawpoll.com/wAg3A53dMy8

== Reactions to Dirichlet badness ==

Sintel's Dirichlet badness is a TE logflat badness that claims to be able to meaningfully compare temperaments across ranks and subgroups.

Try it on Sintel Microtones's temperament calculator https://sintel.pythonanywhere.com/

Within each rank and subgroup, this badness measure is proportional to Gene Ward Smith's logflat badness (hence it's also a TE logflat badness, only differing by a scaling factor), but the general rule is that a temperament is good if it has Dirichlet badness < 1.

Technically, it normalizes the weight matrix W to U such that det(U) = 1. It can be shown that

U = W/det(W)^(1/d)

where d is the dimensionality of the subgroup.

No other rms-like processes are taken, so the complexity C is

C = ||M(U)||

where || || denotes the standard L2 norm and M(U) means M weighted by U. It can be shown that it equals

C = ||M(W)||/det(W)^(r/d)

where r and d are the rank and dimensionality of the temperament.

The simple badness is likewise given as ||M(U) ^ J(U)|| where J(U) = J(W)/det(W)^(1/d) is the weighted just tuning map. The logflat badness is given as

L = ||M(U) ^ J(U)||||M(U)||^(r/(d - r))/||J(U)||

Notice the extra factor of 1/||J(U)||, which is to say we divide it by the norm of the just tuning map. For comparison, Gene's derivation omits the factor of 1/||J(W)||, whereas with Tenney weights, Graham Breed's derivation should have no effect whether this factor is omitted or not since ||J(W)|| is unity.

Another interesting property it demonstrates is invariability on skew, making TE logflat badness and WE (Weil-Euclidean) logflat badness identical.

I'll be documenting it on the wiki in the next few days, which means I'll be taking over this page https://en.xen.wiki/w/Tenney-Euclidean_temperament_measures.

Some of us in the XA Discord server are fond of this measure and are proposing it as a replacement for Gene's across the wiki.

> I think genes defintion is fine for ranking but if you see a temp with badness 0.0013 it tells you absolutely nothing because that number only makes sense if you know both the dimension and rank

> whats the point of all temperaments having 0.00xxx badness lol

-- Flora Canou, 15 Jul 2024 (imported from Facebook)

: I think the basic idea is good, but the way it scales between subgroups in current form seems to be off. I had played around with something similar in the past, though, and I think this is in the right direction. Although I only had partial results (and I was more focused on generalizing Cangwu badness than logflat badness).

: The way that it's being normalized doesn't seem to make much sense for inter-subgroup temperament comparisons. For instance, you may note that 2.3.5 meantone has a badness of 0.173. On the other hand, here is 2.11/5.13/5 "Petrtri" temperament:

: https://sintel.pythonanywhere.com/result?subgroup=2.11%2F5.13%2F5&reduce=on&weights=weil&target=&edos=&commas=2200%2F2197&submit_comma=submit

: The badness here is 0.018 so it's better than meantone. Here's some random temperament on a hugely complex subgroup

: https://sintel.pythonanywhere.com/result?subgroup=1234.12312.1231&reduce=on&weights=weil&target=&edos=12%2C+31&submit_edo=submit&commas=

: And now the badness is 0.000.

: This is assuming the thing called "badness" on Sintel's temperament finder is the same thing you are talking about.

: -- Mike Battaglia, 17 Jul 2024 (imported from Facebook)

:: I'm actually not sure how it's supposed to work on degenerate subgroups like 2.11/5.13/5 ("degenerate": see my last post about subgroups). My own implementation doesn't support this cuz I'm not sure how complexity is defined on such subgroups.

:: For the next example I reckon it's becuz you're using a very simple mapping for very large primes. I think it's fair to say it makes sense for most practical purposes -- subgroups like 7-limit, 13-limit, 3.5.7, etc.

:: -- Flora Canou, 15 Jul 2024 (imported from Facebook)

::: Are you sure that what's on Sintel's website is the thing you are talking about? Because the results are not making much sense here. For instance, we have

::: 1.496: 2.3.5 mod 256/243

::: 1.234: 2.3.7 mod 256/243

::: 0.818: 2.3.19 mod 256/243

::: 0.701: 2.3.31 mod 256/243

::: So we have the dimension, codimension and kernel all staying the same, but with the subgroup complexity increasing, and the badness gets lower and lower. Shouldn't it be getting higher?

::: For reference, 2.3.5 porcupine is 0.722, so it ranks 2.3.31 mod 256/243 as better than porcupine. And here we have two very similar commas (256/243 and 250/243), but porcupine is much better in terms of error. But, 2.3.31 mod 256/243 is ranked higher because of this weird inverse weighting on subgroup complexity that you seem to be doing.

::: -- Mike Battaglia, 16 Jul 2024 (imported from Facebook)

:::: Why, I've reproduced Sintel's results. I believe the example you're showing here is but an artifact of the Tenney weight.

:::: To be clear it's not the subgroup's complexity that contributes to the badness. It's the temperament's, which decreases as the subgroup's complexity increases. That's what I observed. You're weighting the mapping such that the last prime gets less and less weight. Even tho the weight matrix is normalized the complexity of it still lowers (I'm not sure why but it is what it is).

:::: -- Flora Canou, 16 Jul 2024 (imported from Facebook)

::::: right, and that is the problem. The behavior you are describing is also what happens with just using the naive badness without trying to normalize it. TE weighted error and complexity both decrease as the subgroup gets more complex, so super complex temperaments get ranked very low in badness. This is not usually what you want musically. The goal of a subgroup temperament badness function, or "superbadness" as I was calling it at one point, is to normalize things between subgroups so that this doesn't happen.

::::: -- Mike Battaglia, 16 Jul 2024 (imported from Facebook)

::::: the reason it lowers is very subtle, but a good starting point is to remember that there are two ways to take subgroup complexity: as the norm of a multimonzo K representing the kernel or the multival V representing the subspace of vals supporting the temperament. These are proportional but not equal and in general we have

::::: ||V|| = ||K||/||S||

::::: Where ||S|| should be the determinant of the weighting matrix in *monzo space* (so the inverse of the matrix you have been using, meaning the determinant is the reciprocal of the determinant you have been using). You can see that using ||K|| directly doesn't have the problem with Blackwood above.

::::: I think, though don't remember 100%, that there is a similar thing with the relative error/simple badness. Remember that relative error can also be thought of as ||V||, but with ||...|| now representing a kind of seminorm. There is a kind of dual to that (handwaving a bit about what "dual" means) which, for single commas, is basically the seminorm measuring the span of the comma, and again I think you get a similar kind of equation above. But it's been a while since I looked at it so I don't remember the details.

::::: The point, though, is that if you compute these quantities on the "monzo" side, you get things that already are at least an improvement in that they don't decrease with increasing subgroup complexity! What you have, on the other hand, is the val side, but then divided by a certain fractional power of the val-weighting determinant, which is equivalent to multiplying by some fractional power of ||S|| - but it isn't enough to counteract the implicit division by a much larger power of ||S|| that you get by using the TE version of these metrics to begin with. So, you get something which decreases as subgroup complexity increases.

::::: -- Mike Battaglia, 16 Jul 2024 (imported from Facebook)

:::::: Hmm, alright. Technical parts aside (I'll be experimenting with it some time), I personally don't intuitively insist that this badness figure must be constant or increasing on increasingly complex subgroups, but let me relate your concern to the Discord users and see if they can/will fix it.

:::::: -- Flora Canou, 17 Jul 2024 (imported from Facebook)

: the badness measure is only to be taken seriously on p-limit subgroups otherwise its too easy to game. previously i did 'penalize' weird subgroups but its not very satifying to do so arbitrarily. i personally only care about temperaments that are good in common subgroups and i support weird subgroups only bc some people requested it

: as for the comment on e.g. Petrtri, I *do* think it should have a much lower badness than meantone! look at the mapping matrix: its about the same complexity as something like Dicot, yet its errors are all ~0.05 cents! thats amazing honestly! but of course that only really matters if you take the subgroup seriously (i dont)

: as for the other thing about subgroup complexity with the 256/243 example: that's actually a good point, had not noticed this before. I will investigate the cause!

: [[User:Sintel|Sintel]] ([[User talk:Sintel|talk]]) 21:06, 17 July 2024 (UTC) [copypasta from facebook]

:: Why not just penalize it so that [subgroup].p has increasing badness for increasing complexity of p? Or if that leads to a strange normalizer for whatever reason, why not just have all [subgroup].p have equivalent badness assuming that p is unconstrained in all of them? I don't think "the exact normalizer expression that would make all extensions equal badness assuming everything else stays the same" is arbitrary. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 18:38, 3 October 2024 (UTC)

::: I attached another piece of information below. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 18:46, 3 October 2024 (UTC)

: Sintel Microtones Why don't you try your metric on the "monzo" version of logflat badness? Just use the L2 norm on the multimonzo for complexity and simple badness, and this problem may partly solve itself. I think it'll be the same thing you have, but times the subgroup determinant raised to some slightly different power than what you are currently doing.

: When you say that you are mainly trying to compare p-limit subgroups, are you also trying to compare subgroup temperaments of different ranks, or different codimensions, or what? Or just like, 5-limit vs 7-limit meantone, for instance? Because I noticed some weirdness also with p-limit subgroup temperaments - it rates 7-limit meantone as much worse than 5-limit meantone, which is another thing I'm not sure I agree with, as 5-limit meantone practically gives you all of these ratios of 7 for free, with barely no added error!

: -- Mike Battaglia, 18 Jul 2024 (imported from Facebook)

:: Regarding meantone, since septimal meantone is about twice as complex as 5-limit meantone with virtually the same avg error, it should be normal that septimal meantone has about twice the badness.

:: -- Flora Canou, 20 Jul 2024 (imported from Facebook)

:: I noticed if instead of

:: U = W/det(W)^(1/d)

:: you go for

:: U = W/det(W)^(1/r)

:: and thus

:: C = ||M(W)||/det(W)

:: you get invariant complexities and therefore invariant badnesses on the same kernel in arbitrary subgroups. However comparison of temps across ranks/dimensionalities no longer make sense now, so some other factor needs to be introduced.

:: -- Flora Canou, 20 Jul 2024 (imported from Facebook)

::: right, this is the metric I was talking about above regarding the "monzo" version of logflat badness. This is a pretty good start already, but now we have this issue of normalizing things of different rank.

::: The starting point is: how can one meaningfully assign a complexity to two arbitrary JI *subgroups* of different rank? This is useful not just for ranking subgroups themselves to derive temperaments from, but also ranking kernels, which are also just JI subgroups. We could use the Tenney norm of the multimonzo of the subgroup - this is the weighting matrix determinant you have been using - but now we're comparing lengths to areas to volumes, etc, so how do we do that?

::: This is something I put together many years ago but just haven't put on the Wiki, although I never put it all together into any combined metric. But basically the way I did it is to start with what's called the "theta function" or "theta series" of the subgroup as a lattice, but using the L1 norm instead of the L2 norm. We instead just look at the subgroup as a set of intervals, rather than as any kind of geomeric object. The theta function associated to any lattice is all points of the form Sum 1/(n*d)^s on all n/d in the subgroup, where s is a free parameter determining how much we care about more complex intervals. The s is a free parameter that determines how fast complex intervals should roll off, similar to with the zeta function. This can be thought of as representing a kind of "strength" for the subgroup, so that its inverse is a kind of complexity.

::: We do a bunch of analysis with rational approximations at s -> 0 and derive the "lambda function" for the subgroup, which is basically the multimonzo norm/subgroup determinant, but normalized in a certain magic way that makes it all work out. There is one free parameter that simultaneously measures how fast complex intervals should roll off, how much you care about rank, how much you care about larger chords, how simple a new JI interval should be for it to be worth it if you go up a rank and add it, and even the base of the logarithm. There is a closed-form expression relating all of these things and I had some recommended values for this one parameter.

::: Anyway, if you're interested I can write this all up at some point, but if you want to start playing around, you can do so right now just by taking what you already have but changing the base of the logarithm.

::: -- Mike Battaglia, 20 Jul 2024 (imported from Facebook)

== Proposal to promote more admins ==

Over the past few months, the prospect of adding more admins to the wiki has been heavily discussed in the #wiki channel of the Xenharmonic Alliance Discord server.

Several people (myself included) have said they would like to see this happen, and no one on the Discord was against it. However, we do also recognise that many wiki editors do not have access to Discord, including those who actually have the authority to make such a decision, and we think it's essential that everyone be included in such an important discussion as this, not just people on Discord. So that's why I'm writing this, to post on Facebook and on the cross-platform collaboration page on the wiki itself.

The main reason why we would like to see more admins, is that many of the current admins are not online on the wiki very often. No one blames them for this, as they are unpaid volunteers and have lives outside the wiki. However the result of this is that all of the burden of the wiki's day to day administrative tasks falls on the shoulders of the one or two active admins, which isn't really fair on them. They need more hands on deck to help them out.

At the moment, a lot of low-priority admin tasks (like some of the ones in the admin Todo category) just sit gathering dust for years because the few active admins have to spend all their time keeping on top of day-to-day maintenance and don't have the breathing room to get to those. This does harm the overall quality of the wiki. It also has the potential to lead to admin burnout, which would be an existential risk to the wiki given how few active admins we currently have.

There has been a lot of discussion on the Discord about who these new admins should be. Several names were floated of experienced editors who we think would be up to the task. We asked each of those experienced editors whether they would be happy to volunteer as admins, and three of them said yes: Fredg999, Lériendil, and ArrowHead294.

For each of these people, several others commented in favour of their nomination, and no one commented against. I will outline the reasons why we nominated each of these people.

We believe Fredg999 would make a good admin because he has many years' experience as an active editor on the wiki. He has made extensive contributions towards making the wiki more accessible by consolidating existing work into a more navigable structure, and by quality-checking new work and ensuring it meets the wiki's existing standards and conventions. He has made extensive improvements to the category system, merging duplicate categories, categorising uncategorised articles and other improvements along those lines. In short, he has consistently demonstrated the attention to detail, the willingness to do repetitive maintenance work, and the calm, cautious and diplomatic demeanour which are the hallmarks of a great admin. Our existing admin tean exhibits all those qualities, so I think Fredg999 is a very natural addition.

We believe Lériendil would make a good admin because of their dedication to improving existing articles, especially neglected articles like individual temperament pages, and edonoi (nonoctave equal tuning) pages. Lériendil created, and maintains, the temperament infobox, which helps elevate temperament pages to the same level of importance and navigability as EDO pages, a very welcome addition for RTT fans. Lériendil is the founder of, and a highly active contributor to, WikiProject TempClean, which has been doing great work expanding and beautifying pages on individual regular temperaments to give them the quality and depth of coverage they deserve, for such an important component of regular temperament theory (the temperaments themselves!) In WikiProject TempClean, Lériendil has demonstrated the ability to unite, inspire, and organise fellow editors to carry out coordinated maintenance work on neglected pages. This ability is something very valuable to have on an admin team. I think that Lériendil could breathe a lot of life and goodwill into the wiki.

We believe ArrowHead294 would make a good admin because of his extensive maintenance work. He has written documentation for dozens of templates on the wiki, helping other editors to understand how to utilise those templates, and how to debug them. He has also done the painstaking word of renaming dozens of articles to use the correct capitalisation, the correct hyphenation, etc. to match the wiki's conventions, which makes the wiki much easier to search for readers (they don't have to try to remember what capitalisation or what symbol to type into the search box). ArrowHead294 has also worked to locate several instances of wanted pages (lots of red links to the same place), which are actually just different names for existing pages, and has created the necessary redirects to make them worj. It goes without saying how much that has helped improve navigability. ArrowHead294 has also coded, drafted, published and maintained several modules and several templates, which have been a big help in automating the more monotonous parts of page creation, so that editors can be freed up to spend more time writing the main body of the page. This has allowed the relatively small wiki community to punch above its weight in terms of the scale of its ambition amd comprehensiveness. As with Fredg999 and Lériendil, ArrowHead294's willingness to do the mundane, often uncelebrated, but essential day-to-day maintenance work that elevates the wiki to the next level, makes him an excellent candidate for admin.

So, our proposal (the wiki editors on Discord), is that Fredg999, Lériendil and ArrowHead294 should be promoted to admin. For the reasons stated above, we believe they would make great additions to the admin team. Would you be in favour of this too?

—[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 01:19, 5 February 2025 (UTC)

== Request: make Legacy Xen Wiki visually distinguishable ==

I would like to request the implementation of at least one change in the visual aspect of the Legacy Xen Wiki to help visitors distinguish it from the regular Xen Wiki and ensure they are actually browsing the version of the wiki they think they are browsing. For instance, the logo could be made slightly different by adding a "LEGACY" text over the original logo (e.g. at the top or at the bottom), The [[Legacy:Main Page]] could also be edited to make it more obvious that it is on the legacy version, ideally with a link back to the regular version, for example by adding a [[Template:Mbox|message box]]. I don't plan on creating an account on the legacy wiki, so this is why I am requesting the change here. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 05:51, 18 February 2025 (UTC)

@@ Line 114: / Line 114: @@
 ::::: Hmm... maybe it's a bad example for me because I think tempering 128/125 is unfeasible (maybe [[27edo]] does it well but that uses [[delta-rational chord]]s to justify itself so it's not really the thing temperaments were designed for because the target isn't a fixed point) but I will follow the spirit of the logic of the example. The issue seems to be rather that CTE isn't designed to handle the case where extra generators are independent of the commas tempered if you are valuing p/q over pq (because CTE choosing pure generators makes perfect sense if you want to weight them equally and in this sense it's the logical constraining of [[TE]] which assumes the same). But POTE certainly doesn't seem to be the right fix to prioritising p/q over pq. Rather it seems like (at least in this case) what's wanted is a metric that respects tendency (a desire I've voiced before actually). For example it's noted [[Constrained_tuning#CTE_tuning_vs_CTWE_tuning|here]] that "POTE tuning works as a quick approximation to CTWE" (AKA KE tuning), so maybe CTWE / KE tuning is desired? --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 18:23, 16 March 2024 (UTC)
-: Yeah, KE is what you're looking for. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 20:50, 16 March 2024 (UTC)
+:::::: Yeah, KE is what you're looking for. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 20:50, 16 March 2024 (UTC)
 === Mike's Response to All This ===
@@ Line 142: / Line 142: @@
 :: Thanks for expressing your general views tuning theory and tuning optimization. I see you seem to still think there is an open question if you want to "keep" the thing we made which you don't like, or replace it with the thing you made which we don't like. I think I've said my piece about this way of doing things at this point. When you folks figure out what you want to do, if it still involves removing stuff, please ask us on FB first. Thanks. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 20:15, 16 March 2024 (UTC)
+::: You said "we generally prefer tunings like POTE, KE, etc."? --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 20:54, 16 March 2024 (UTC)
+FloraC has added POTE tuning back to all the temperament pages which used to have it. If there are any pages we missed, please let us know so we can add POTE back to those as well. The consensus in the Discord channel is in favor of displaying multiple tunings on temperament pages, so that's what we're going to do moving forwards. No more removing one in favor of another. --[[User:BudjarnLambeth|Budjarn Lambeth]] ([[User talk:BudjarnLambeth|talk]]) 02:35, 17 March 2024 (UTC)
+: Appreciate it. Thank you to Budjarn and Flora.
+: OK, now that that is settled, regarding the actual math involved for Godtone, Inthar, Flora and others:
+: Yes, it's true that one of the main reasons people liked POTE historically is because it approximates KE. If you want to declare KE some kind of best general-purpose tuning, or whatever, I would probably support that. However, we ought to compute POTE/KE tunings for a huge set of temperaments to see if for any they differ significantly (which would be very surprising to me).
+: The bigger picture: all of these tuning optimizations are imperfect because they only measure dyadic error. A 4:5:6 chord, flattened to the "isoharmonic"/"proportional"/"Mt. Meru"/whatever 4:4.98:5.96 chord, or 0-379-690, sounds less far off than something with a similar amount of error which is non-proportional, so we really care about which way the errors are oriented within the triad. If you want, you can look at the Hessian of simple chords in 3-HE, which models this correctly, to build a simple linear model for tuning error of some triad. Then, you can try to optimize the entire "Z-algebroid" of chords, rather than just the Z-module of monzos. In principle it can be done - I've played around with this kind of thing a bit, though don't have any firm results.
+: Or: just note empirically that TE seems to magically give pretty good results, even for triads, tetrads, etc. Why? Who knows. Maybe if you did the above thing out all the way you'd derive that TE, or something close enough to it, also happens to be the optimal tuning on the entire algebroid. Similarly, POTE gives good results for this but not CTE. Why? Again, who knows, but one idea is to note that stretching a chord isoharmonically/proportionally in Hz is very close to stretching it in cents, as a first order Taylor approximation. For instance, stretching 4:5:6 both ways so the outer dyad is 720 gives 0-397-720 (isoharmonic) vs 0-396-720 (stretching in cents). So scaling TE to POTE is approximately the same as isoharmonically stretching all chords in the entire tuning.
+: So that is the other reason POTE, or any tuning, is useful: empirically, we note it sounds good.
+: There are other reasons. Graham has expressed interest in it being the unique pure-octave tuning that minimizes the angle/dot product with the JIP. I don't remember what musical interpretation he gave to this angle; you'd have to ask him why. And there is always this "black magic" element to it where Gene knew a bunch of stuff about all of this, but has sadly passed on and we can't ask him about it. We have the same situation with, for instance, zeta integral and gap tunings - what theoretical justification do these things have, compared with something clear like zeta peak tunings? I don't know, but Gene did. Oh well. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]])
+:: I have idiosyncratic reasons to favor CTE or a tuning that doesn't prioritize divisive ratios over multiplicative ratios based on where beating occurs in the frequency spectrum with any harmonic timbre. I documented the details in my essay (→ ''User:FloraC/Hard problems of harmony and psychoacoustically supported optimization''). The essay also contains a design around Hahn distance so you might be interested. Regardless, as I've related to you on FB, I think of CTE as the most straight-forward solution that is most likely to be understood by the widest audience, so the main appeal is its methodological transparency, which is somewhat shared by KE and is in contrast with the "black magic" of POTE.
+:: My next plan is to add KE to later temperaments that never had POTE documented (and CTE is also to be added). [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:50, 17 March 2024 (UTC)
+::: Thanks, will read when I get a second. It would be great to have all of these things, as I still am not sure if KE and POTE ever give significantly different results. Aren't you writing a Lua module that computes them all at once anyway? [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 18:46, 17 March 2024 (UTC)
+:: I appreciate your in-depth response a lot. Sorry if I came across as hostile, it was not my intention. The thing about POTE being the tuning with a unique property is interesting; I hadn't heard it before. If I may offer my own thoughts: I agree that likely the reason POTE seems to be a good approximation is to do with [[delta-rational chord]]s (which from what I understand is the appropriate and nontrivial generalisation of isoharmonic chords, in that delta-rational chords sound like JI without being JI while isoharmonic chords are JI tunings of delta-rational chords); in my mind though it would make more sense to devise a different measure entirely if you wanted to optimise that sort of thing like how you noted that one could devise measures of triadic/tetradic/etc. chords. I have a hypothesis to do with the divide between POTE and CTE, or I think more aptly, between weighting p/q over pq and weighting them the same. It seems to me that the lower accuracy a temperament is, the more we prioritise p/q over pq, so that CTE becomes increasingly worse, while the higher accuracy a temperament is, the more it makes sense to also want to model pq with p/q; maybe this caused an impression here that CTE made more sense. For example, I myself wouldn't usually look at temperaments like tempering [[256/243]] (Blackwood) or [[128/125]] (Augmented) because if I wanted something like that, I would instead investigate a DR (Delta-Rational) chord phenomenon rather than using CTE. Kind regards, --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 20:51, 17 March 2024 (UTC)
 [[Category:Xenharmonic Wiki]]
+:: Also, if you haven't seen it already, you may want to look at [[Talk:POTE_tuning#Justification]] - it seems relevant to this discussion, as [[User:Sintel]] comments there, although I'm not sure if the comments are outdated. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 21:19, 17 March 2024 (UTC)
+wayy back before I understood how the maths worked I always wondered why POTE on the wiki was always given by default. And this confusion was actually quite valid, because nowhere on the wiki is it explained why this is a reasonable choice at all. It seems to me like if you provide one default choice, it should be well-justified.
+now, I am quite fond of just providing one default choice, as to not paralyze the reader with too many options, but then the question is which one?
+in the past I have compared KE and POTE for like thousands of temperaments, and it seemed like they were always extremely close. so how about just using KE going forward? this way we have something that is both empirically *and* theoretically justified.
+[[User:Sintel|Sintel]] ([[User talk:Sintel|talk]]) 22:14, 17 March 2024 (UTC)
+: FWIW, that's essentially what I was trying to say in my comment starting with "KE tuning seems acceptable to me" (although I don't understand the specifics enough to argue it more strongly). I don't mind the other solution of listing CTE, POTE and TE together though if that will cause less friction going forwards, although I still think that due to POTE's trivial derivability from TE it seems redundant/unnecessary to list, but I guess dividing the cent values by the ratio between the tempered octave and pure octave (even though trivially easy) is enough of a hassle for anyone who really wants POTE specifically to justify listing it. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 00:40, 18 March 2024 (UTC)
+:: So far, my suggestion is to have a single standard optimal tuning displayed in any given temperament data block, and optionally append a collapsible box containing more "optimal tunings" for various optimization methods. These would serve as quick references for people who do not wish to use a calculator, namely if one wants to compare similar temperaments at a glance. These tunings can most likely be computed dynamically if we have the right modules, but they could also just be manually inserted if need be. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 03:01, 18 March 2024 (UTC)
+::: Showing a single standard tuning by default has the issue of which though. If they're on board with KE (if we can show that it's practically almost always very close to POTE) then that's not an issue, but otherwise I presume it means that they'd want it to be POTE; I would object to POTE being the standard tuning to show (as opposed to, say, KE) just as they object to CTE. In such a case it seems better to just show a few tunings side-by-side and let the reader make their own judgement. The values given are only meant to be a starting point anyways (for if one doesn't want to use an EDO tuning). --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 03:35, 18 March 2024 (UTC)
+:::: My pick for the standard tuning would be TE, with the others (POTE, KE, CTE, anything else) being included in the collapsed box. There seems to be a lot of disagreement about which pure-octaves optimal tuning is acceptable, but most people seem to be okay with TE as the stretched-octaves one, so with TE being the least controversial, it seems to make sense to list it first. --[[User:BudjarnLambeth|Budjarn Lambeth]] ([[User talk:BudjarnLambeth|talk]]) 06:09, 18 March 2024 (UTC)
+::::: I think most users will want a pure-octave tuning to start with and that's why the controversy is on the pure-octave tunings. If there was only one tuning then KE would meet the needs of all parties the best, but at this point it's clear that POTE is to be preserved and CTE is to be added. If we add KE to POTE then they serve the same purpose so it's a waste of space. So I'll add CTE to POTE while leaving the question of replacing POTE with KE to the future. I think additional tunings can be added in the dedicated page for the temperament, properly organized as its own block. (All those additions are low-priority to me so if I'm doing it all alone, it won't happen too quick.) [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:43, 18 March 2024 (UTC)
+:::::: Alright, sounds like a good plan to me. Thank you for your hard work on this :) --[[User:BudjarnLambeth|Budjarn Lambeth]] ([[User talk:BudjarnLambeth|talk]]) 09:13, 18 March 2024 (UTC)
+=== Table comparing POTE vs KE vs CTE ===
+<gallery>
+OptimalComparison5Lim.png|Comparison of POTE, KE, CTE tunings for several 5 limit temperaments
+OptimalComparison7Lim.png|Comparison of POTE, KE, CTE tunings for several 7 limit temperaments
+</gallery>
+I made these tables comparing the POTE, KE and CTE tunings for all of the temperaments and microtemperaments listed in Erlich's Middle Path paper, as well as Pelogic, since a comparison like this is something that has been asked for a few times on this page.
+I used [[User:Sintel|Sintel]]'s temperament calculator to find the KE and CTE tunings, so a big thank you to Sintel for that :)
+--[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 07:08, 19 March 2024 (UTC)
+:I wrote some of the headings at the top wrong. I uploaded new versions of the files with this fixed, but it might take a few hours for the file pages to start showing the new versions. Specifically, the columns that say "CTE vs KE" are supposed to say "POTE vs CTE". Sorry for the confusion --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 07:17, 19 March 2024 (UTC)
+::As Mike pointed out below, I put the wrong KE generator for 5-limit Porcupine. I have uploaded a new version of the file that fixes this now. The file page has not yet started displaying the changes but hopefully it will soon :) --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 09:44, 19 March 2024 (UTC)
+::: I'd just like to note I'm very happy with KE, my feeling is that for low-accuracy temperaments CTE doesn't weight p/q over pq enough but POTE seems to overdo it, so it's very favourable that KE seems to be close to POTE but slightly in the CTE direction. Hopefully KE will continue this trend upon analysis in higher limits with various subgroups. (Not that I don't like CTE, I personally have generally liked the CTE tuning a lot for mid-to-high-accuracy temperaments, EG I think its tuning of meantone as ~2/9-comma (between 1/4 and 1/5) makes sense.) --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 21:08, 19 March 2024 (UTC)
+:::: I have made a table comparing some high-limit temperaments (specifically the ones Mike named) as well as some subgroup temperaments in POTE, KE and CTE. The same trend seems to continue, as all the KE tunings are in between POTE and CTE, and most of them lean closer to POTE.
+<gallery>
+OptimalTuningSubgroupAndHighLim.png|Comparison of POTE, KE, CTE generators for high limit & subgroup temperaments
+</gallery>
+:::: --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 21:59, 19 March 2024 (UTC)
+=== Mike is Done For Now ===
+Hi all
+This has been fun but I need to be done with this for a while, so I leave it with you all.
+So some parting words for POTE vs KE:
+# Thanks for putting POTE back and making the charts.
+# I've added a bunch of theory, history and Python to the constrained tunings page, so it's easy to compute any arbitrary the CTE/KE/whatever in closed form. Since it looks like you have Lua code for the pseudoinverse you'll be able to use this to easily compute the KE tuning without needing nonlinear optimization.
+# When comparing these things it's best to compare the tuning maps, not the generators. It's hard to know how much difference a cent makes just looking at the generator map.
+# I would just subtract the two tuning maps and take an RMS of the differences.
+# It looks like the biggest differences involve temperaments where the period is some fraction of an octave: Augmented, Diminished, Blackwood, etc.
+# The differences should also be pretty small for stuff like magic, porcupine, etc, and also for 5-limit temperaments. It's the things that are a bit further out error-wise and in higher limits that I'm curious about: superpyth, machine, semaphore, pajara, modus, mohajira, etc.
+# I think there are some errors - Porcupine doesn't look right; I think it should be 164.0621.
+# In general I'm fairly impressed with KE though.
+For organizing this stuff:
+# I agree having one or two "default" tunings shown prominently is good, and then the rest below it. Maybe one pure-octave and one stretched-octave, if you like.
+# Yes, please do put a pure-octave tuning up there. Nobody wants to grab a calculator to derive POTE from TE!
+# The above results for POTE vs KE look fairly good to me. If they look this good after checking with higher-limit temperaments and ones a bit less accurate, I'd be alright with making KE the standard and POTE secondary.
+# If you like CTE then add it but I don't think it should be standard. It's awful, really.
+For the math:
+# I don't know how I always end up in this position of defending the "old guard" - I spent the last 15 years arguing with people about changing stuff and now suddenly I'm defending it.
+# If you really want my view, I don't really think any of these optimal tunings are ideal. I think log-weighting in general is ridiculous. All of these higher primes end up weighted ridiculously strongly. The "best" EDOs (http://x31eq.com/cgi-bin/more.cgi?r=1&limit=2_3_5_7_11_13_17_19_23_29_31_37_41_43_47_53&error=5) in very high limits with log-weighting are always very strange things like 26, 29, etc, because higher primes just pop up faster than they roll off.
+# There is a version of the zeta function which weights things as 1/log(nd) instead of 1/(nd)^s, and the results just seem very silly compared to the real one.
+# I came up with the "BOP" and "BE" tunings for this reason, which weight ratios inversely proportional to the exponential of their norm (i.e. 1/(nd)) instead. FWIW I think they're better, the BE tuning in particular. It would not be that hard to figure out some kind of Weil version of this.
+# The subgroup version of these is a little bit less easy to do, as you need to check the convex hull of all intervals divided by the exponential of their norm.
+# I think this is a much more radical change though and I'd say to go with POTE/KE for now and do this later.
+That's it for now, thanks. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 09:27, 19 March 2024 (UTC)
+== Working with the Old Guard ==
+Hello!  I'm glad to see that this page exists.  I'm a user on Discord who hasn't had much involvement in the previous conversations on this thread, but I'd like to try and work together with the old guard on some of my ideas- if that's even remotely feasible.  To start with, I'd like to get some feedback on some of my ideas that I've worked on here on the wiki over the time I've been here, such as [[Alpharabian tuning]], [[telicity]], [[syntonic-rastmic subchroma notation]] and [[User:Aura/Aura's Ideas on Functional Harmony|my own take on microtonal functional harmony]].  Of these, I think telicity might be of the most interest to the old guard, since it's fairly math-heavy.  I hope I'm not being a bother. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:17, 19 March 2024 (UTC)
+== Ranking poll for "good" EDOs from 27 to 140 ==
+I thought it might be cool to do a poll to see which of these EDOs people subjectively prefer over others. It's far from all EDOs in the 27 to 140 range; I've picked the ones that seem the most significant theoretically as being worth interest, but if you think something's missing there is an option "[your favourite RTT EDO between 27 and 140 not on this list]" at the bottom of the list. The list is in order of number of notes per octave and I hope that each participant takes the time to sort all EDOs they have opinions on to the top and the bottom; if you're not sure that's why I've provided subgroups in up to the 97-prime-limit, although if you just focus on the 43-prime-limit part that's more reliable and probably a lot more intuitive for appraisal purposes.
+If you're wondering "why such a high prime limit"? here's details/explainers of the significance of all primes >43 that I've included:
+/64 = 79.31c (close to 1\15 = 4\60, 2\31 = 4\62, 3\46 and practically exactly 8\121; the harmonic 15 EDOstep),
+/61 = 83.12c (close to 1\14 = 5\70 = 6\84 = 10\140, 2\29 = 4\58 = 6\87, 3\43 and 5\72; almost exactly (4/3)^(1/6) (a third of a semifourth)),
+/59 = 140.83c (close to 2\17 = 4\34 = 8\68, 3\26 = 15\130, 5\43, 7\60, 9\77, 11\94 and 13\111; appears in many systems as (3/2)^(1/5)),
+/64 = 179.7c (close to 3\20 = 12\80 = 21\140 but also a harmonic ~10/9),
+/64 = 227.79c (close to 3\16 = 9\48 = 15\80, 4\21 = 12\63, 7\37 = 14\74 = 21\111 and 11\58 but also the harmonic supermajor second),
+/53 = 326.5c (close to 3\11 = 21\77 = 27\99, 10\37 = 20\74 = 30\111, 13\48, 16\59 = 32\118 and 19\70 = 38\140; this corresponds to a very distinctive size of third between minor and supraminor),
+/64 = 364.54c (close to 3\23 = 6\46 and 10\33 = 30\99 but also the harmonic submajor third),
+/64 = 450.05c (practically 3\8 but also the harmonic semisixth),
+/64 = 570.9c (close to 10\21 = 30\63 and 19\40 = 38\80; like a harmonic analogue of 32/23),
+/32 = 665.51c (close to 5\9 = 15\27 = 20\36 = 35\63 = 40\72 = 50\99; the harmonic wolf fifth / 9 EDO fifth),
+and 97/64 = 719.9c (practically 3\5; the harmonic 5 EDO fifth).
+As for primes > 13, I highly recommend looking at the [[25-odd-limit]] in all its glory if you are unfamiliar with using primes > 13, but as a quick summary, 17 is notable as introducing subminor ([[17/14]]) and supramajor ([[21/17]]) and neogothic minor ([[20/17]]) and neogothic major ([[51/40]]) and a good approximation of the half-octave of [[17/12]]~[[24/17]] but also for its naturalness as the general-purpose semitone in [[srutal archagall]], 19 introduces the harmonic minor third [[19/16]] between [[6/5]] and [[13/11]], and is close to [[32/27]] (and equated with it in [[nestoria]]), 23 introduces [[23/16]] which is what can be thought of as a harmonic augmented fourth in sharp-fifth systems and a harmonic diminished fifth in flat-fifth systems; it also introduces [[23/20]] which is between supermajor ([[8/7]]) and a semifourth ([[15/13]]), plus two new shades of supraminor third at [[23/19]] and [[28/23]], although the latter is more like a subneutral third, [[29/16]] is notable for being basically free in multiples of [[7edo]] (although is also notable as [[29/23]] approximates 400c reasonably well so [[21edo]] (and therefore [[63edo]] and [[84edo]]) has a good 23:29:32:39 chord for example), [[32/31]] is the subharmonic quarter-tone, [[37/32]] is the harmonic semifourth (implying a fourth around that of [[19edo]], so for higher-accuracy systems it works especially well with dual-semifourths; remarkably [[15/13]] and [[37/32]] are made fourth-complements in the miraculous harmonic series autotuner [[311edo]]), [[41/32]] is the harmonic supermajor third and [[43/32]] is the harmonic perfect fourth (as it approximates [[4/3]] significantly better than [[21/16]] and much better than [[11/8]]).
+Ranking poll is here: https://strawpoll.com/wAg3A53dMy8
+== Reactions to Dirichlet badness ==
+Sintel's Dirichlet badness is a TE logflat badness that claims to be able to meaningfully compare temperaments across ranks and subgroups.
+Try it on Sintel Microtones's temperament calculator https://sintel.pythonanywhere.com/
+Within each rank and subgroup, this badness measure is proportional to Gene Ward Smith's logflat badness (hence it's also a TE logflat badness, only differing by a scaling factor), but the general rule is that a temperament is good if it has Dirichlet badness < 1.
+Technically, it normalizes the weight matrix W to U such that det(U) = 1. It can be shown that
+U = W/det(W)^(1/d)
+where d is the dimensionality of the subgroup.
+No other rms-like processes are taken, so the complexity C is
+C = ||M(U)||
+where || || denotes the standard L2 norm and M(U) means M weighted by U. It can be shown that it equals
+C = ||M(W)||/det(W)^(r/d)
+where r and d are the rank and dimensionality of the temperament.
+The simple badness is likewise given as ||M(U) ^ J(U)|| where J(U) = J(W)/det(W)^(1/d) is the weighted just tuning map. The logflat badness is given as
+L = ||M(U) ^ J(U)||||M(U)||^(r/(d - r))/||J(U)||
+Notice the extra factor of 1/||J(U)||, which is to say we divide it by the norm of the just tuning map. For comparison, Gene's derivation omits the factor of 1/||J(W)||, whereas with Tenney weights, Graham Breed's derivation should have no effect whether this factor is omitted or not since ||J(W)|| is unity.
+Another interesting property it demonstrates is invariability on skew, making TE logflat badness and WE (Weil-Euclidean) logflat badness identical.
+I'll be documenting it on the wiki in the next few days, which means I'll be taking over this page https://en.xen.wiki/w/Tenney-Euclidean_temperament_measures.
+Some of us in the XA Discord server are fond of this measure and are proposing it as a replacement for Gene's across the wiki.
+> I think genes defintion is fine for ranking but if you see a temp with badness 0.0013 it tells you absolutely nothing because that number only makes sense if you know both the dimension and rank
+> whats the point of all temperaments having 0.00xxx badness lol
+-- Flora Canou, 15 Jul 2024 (imported from Facebook)
+: I think the basic idea is good, but the way it scales between subgroups in current form seems to be off. I had played around with something similar in the past, though, and I think this is in the right direction. Although I only had partial results (and I was more focused on generalizing Cangwu badness than logflat badness).
+: The way that it's being normalized doesn't seem to make much sense for inter-subgroup temperament comparisons. For instance, you may note that 2.3.5 meantone has a badness of 0.173. On the other hand, here is 2.11/5.13/5 "Petrtri" temperament:
+: https://sintel.pythonanywhere.com/result?subgroup=2.11%2F5.13%2F5&reduce=on&weights=weil&target=&edos=&commas=2200%2F2197&submit_comma=submit
+: The badness here is 0.018 so it's better than meantone. Here's some random temperament on a hugely complex subgroup
+: https://sintel.pythonanywhere.com/result?subgroup=1234.12312.1231&reduce=on&weights=weil&target=&edos=12%2C+31&submit_edo=submit&commas=
+: And now the badness is 0.000.
+: This is assuming the thing called "badness" on Sintel's temperament finder is the same thing you are talking about.
+: -- Mike Battaglia, 17 Jul 2024 (imported from Facebook)
+:: I'm actually not sure how it's supposed to work on degenerate subgroups like 2.11/5.13/5 ("degenerate": see my last post about subgroups). My own implementation doesn't support this cuz I'm not sure how complexity is defined on such subgroups.
+:: For the next example I reckon it's becuz you're using a very simple mapping for very large primes. I think it's fair to say it makes sense for most practical purposes -- subgroups like 7-limit, 13-limit, 3.5.7, etc.
+:: -- Flora Canou, 15 Jul 2024 (imported from Facebook)
+::: Are you sure that what's on Sintel's website is the thing you are talking about? Because the results are not making much sense here. For instance, we have
+::: 1.496: 2.3.5 mod 256/243
+::: 1.234: 2.3.7 mod 256/243
+::: 0.818: 2.3.19 mod 256/243
+::: 0.701: 2.3.31 mod 256/243
+::: So we have the dimension, codimension and kernel all staying the same, but with the subgroup complexity increasing, and the badness gets lower and lower. Shouldn't it be getting higher?
+::: For reference, 2.3.5 porcupine is 0.722, so it ranks 2.3.31 mod 256/243 as better than porcupine. And here we have two very similar commas (256/243 and 250/243), but porcupine is much better in terms of error. But, 2.3.31 mod 256/243 is ranked higher because of this weird inverse weighting on subgroup complexity that you seem to be doing.
+::: -- Mike Battaglia, 16 Jul 2024 (imported from Facebook)
+:::: Why, I've reproduced Sintel's results. I believe the example you're showing here is but an artifact of the Tenney weight.
+:::: To be clear it's not the subgroup's complexity that contributes to the badness. It's the temperament's, which decreases as the subgroup's complexity increases. That's what I observed. You're weighting the mapping such that the last prime gets less and less weight. Even tho the weight matrix is normalized the complexity of it still lowers (I'm not sure why but it is what it is).
+:::: -- Flora Canou, 16 Jul 2024 (imported from Facebook)
+::::: right, and that is the problem. The behavior you are describing is also what happens with just using the naive badness without trying to normalize it. TE weighted error and complexity both decrease as the subgroup gets more complex, so super complex temperaments get ranked very low in badness. This is not usually what you want musically. The goal of a subgroup temperament badness function, or "superbadness" as I was calling it at one point, is to normalize things between subgroups so that this doesn't happen.
+::::: -- Mike Battaglia, 16 Jul 2024 (imported from Facebook)
+::::: the reason it lowers is very subtle, but a good starting point is to remember that there are two ways to take subgroup complexity: as the norm of a multimonzo K representing the kernel or the multival V representing the subspace of vals supporting the temperament. These are proportional but not equal and in general we have
+::::: ||V|| = ||K||/||S||
+::::: Where ||S|| should be the determinant of the weighting matrix in *monzo space* (so the inverse of the matrix you have been using, meaning the determinant is the reciprocal of the determinant you have been using). You can see that using ||K|| directly doesn't have the problem with Blackwood above.
+::::: I think, though don't remember 100%, that there is a similar thing with the relative error/simple badness. Remember that relative error can also be thought of as ||V||, but with ||...|| now representing a kind of seminorm. There is a kind of dual to that (handwaving a bit about what "dual" means) which, for single commas, is basically the seminorm measuring the span of the comma, and again I think you get a similar kind of equation above. But it's been a while since I looked at it so I don't remember the details.
+::::: The point, though, is that if you compute these quantities on the "monzo" side, you get things that already are at least an improvement in that they don't decrease with increasing subgroup complexity! What you have, on the other hand, is the val side, but then divided by a certain fractional power of the val-weighting determinant, which is equivalent to multiplying by some fractional power of ||S|| - but it isn't enough to counteract the implicit division by a much larger power of ||S|| that you get by using the TE version of these metrics to begin with. So, you get something which decreases as subgroup complexity increases.
+::::: -- Mike Battaglia, 16 Jul 2024 (imported from Facebook)
+:::::: Hmm, alright. Technical parts aside (I'll be experimenting with it some time), I personally don't intuitively insist that this badness figure must be constant or increasing on increasingly complex subgroups, but let me relate your concern to the Discord users and see if they can/will fix it.
+:::::: -- Flora Canou, 17 Jul 2024 (imported from Facebook)
+: the badness measure is only to be taken seriously on p-limit subgroups otherwise its too easy to game. previously i did 'penalize' weird subgroups but its not very satifying to do so arbitrarily. i personally only care about temperaments that are good in common subgroups and i support weird subgroups only bc some people requested it
+: as for the comment on e.g. Petrtri, I *do* think it should have a much lower badness than meantone! look at the mapping matrix: its about the same complexity as something like Dicot, yet its errors are all ~0.05 cents! thats amazing honestly! but of course that only really matters if you take the subgroup seriously (i dont)
+: as for the other thing about subgroup complexity with the 256/243 example: that's actually a good point, had not noticed this before. I will investigate the cause!
+: [[User:Sintel|Sintel]] ([[User talk:Sintel|talk]]) 21:06, 17 July 2024 (UTC) [copypasta from facebook]
+:: Why not just penalize it so that [subgroup].p has increasing badness for increasing complexity of p? Or if that leads to a strange normalizer for whatever reason, why not just have all [subgroup].p have equivalent badness assuming that p is unconstrained in all of them? I don't think "the exact normalizer expression that would make all extensions equal badness assuming everything else stays the same" is arbitrary. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 18:38, 3 October 2024 (UTC)
+::: I attached another piece of information below. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 18:46, 3 October 2024 (UTC)
+: Sintel Microtones Why don't you try your metric on the "monzo" version of logflat badness? Just use the L2 norm on the multimonzo for complexity and simple badness, and this problem may partly solve itself. I think it'll be the same thing you have, but times the subgroup determinant raised to some slightly different power than what you are currently doing.
+: When you say that you are mainly trying to compare p-limit subgroups, are you also trying to compare subgroup temperaments of different ranks, or different codimensions, or what? Or just like, 5-limit vs 7-limit meantone, for instance? Because I noticed some weirdness also with p-limit subgroup temperaments - it rates 7-limit meantone as much worse than 5-limit meantone, which is another thing I'm not sure I agree with, as 5-limit meantone practically gives you all of these ratios of 7 for free, with barely no added error!
+: -- Mike Battaglia, 18 Jul 2024 (imported from Facebook)
+:: Regarding meantone, since septimal meantone is about twice as complex as 5-limit meantone with virtually the same avg error, it should be normal that septimal meantone has about twice the badness.
+:: -- Flora Canou, 20 Jul 2024 (imported from Facebook)
+:: I noticed if instead of
+:: U = W/det(W)^(1/d)
+:: you go for
+:: U = W/det(W)^(1/r)
+:: and thus
+:: C = ||M(W)||/det(W)
+:: you get invariant complexities and therefore invariant badnesses on the same kernel in arbitrary subgroups. However comparison of temps across ranks/dimensionalities no longer make sense now, so some other factor needs to be introduced.
+:: -- Flora Canou, 20 Jul 2024 (imported from Facebook)
+::: right, this is the metric I was talking about above regarding the "monzo" version of logflat badness. This is a pretty good start already, but now we have this issue of normalizing things of different rank.
+::: The starting point is: how can one meaningfully assign a complexity to two arbitrary JI *subgroups* of different rank? This is useful not just for ranking subgroups themselves to derive temperaments from, but also ranking kernels, which are also just JI subgroups. We could use the Tenney norm of the multimonzo of the subgroup - this is the weighting matrix determinant you have been using - but now we're comparing lengths to areas to volumes, etc, so how do we do that?
+::: This is something I put together many years ago but just haven't put on the Wiki, although I never put it all together into any combined metric. But basically the way I did it is to start with what's called the "theta function" or "theta series" of the subgroup as a lattice, but using the L1 norm instead of the L2 norm. We instead just look at the subgroup as a set of intervals, rather than as any kind of geomeric object. The theta function associated to any lattice is all points of the form Sum 1/(n*d)^s on all n/d in the subgroup, where s is a free parameter determining how much we care about more complex intervals. The s is a free parameter that determines how fast complex intervals should roll off, similar to with the zeta function. This can be thought of as representing a kind of "strength" for the subgroup, so that its inverse is a kind of complexity.
+::: We do a bunch of analysis with rational approximations at s -> 0 and derive the "lambda function" for the subgroup, which is basically the multimonzo norm/subgroup determinant, but normalized in a certain magic way that makes it all work out. There is one free parameter that simultaneously measures how fast complex intervals should roll off, how much you care about rank, how much you care about larger chords, how simple a new JI interval should be for it to be worth it if you go up a rank and add it, and even the base of the logarithm. There is a closed-form expression relating all of these things and I had some recommended values for this one parameter.
+::: Anyway, if you're interested I can write this all up at some point, but if you want to start playing around, you can do so right now just by taking what you already have but changing the base of the logarithm.
+::: -- Mike Battaglia, 20 Jul 2024 (imported from Facebook)
+== Proposal to promote more admins ==
+Over the past few months, the prospect of adding more admins to the wiki has been heavily discussed in the #wiki channel of the Xenharmonic Alliance Discord server.
+Several people (myself included) have said they would like to see this happen, and no one on the Discord was against it. However, we do also recognise that many wiki editors do not have access to Discord, including those who actually have the authority to make such a decision, and we think it's essential that everyone be included in such an important discussion as this, not just people on Discord. So that's why I'm writing this, to post on Facebook and on the cross-platform collaboration page on the wiki itself.
+The main reason why we would like to see more admins, is that many of the current admins are not online on the wiki very often. No one blames them for this, as they are unpaid volunteers and have lives outside the wiki. However the result of this is that all of the burden of the wiki's day to day administrative tasks falls on the shoulders of the one or two active admins, which isn't really fair on them. They need more hands on deck to help them out.
+At the moment, a lot of low-priority admin tasks (like some of the ones in the admin Todo category) just sit gathering dust for years because the few active admins have to spend all their time keeping on top of day-to-day maintenance and don't have the breathing room to get to those. This does harm the overall quality of the wiki. It also has the potential to lead to admin burnout, which would be an existential risk to the wiki given how few active admins we currently have.
+There has been a lot of discussion on the Discord about who these new admins should be. Several names were floated of experienced editors who we think would be up to the task. We asked each of those experienced editors whether they would be happy to volunteer as admins, and three of them said yes: Fredg999, Lériendil, and ArrowHead294.
+For each of these people, several others commented in favour of their nomination, and no one commented against. I will outline the reasons why we nominated each of these people.
+We believe Fredg999 would make a good admin because he has many years' experience as an active editor on the wiki. He has made extensive contributions towards making the wiki more accessible by consolidating existing work into a more navigable structure, and by quality-checking new work and ensuring it meets the wiki's existing standards and conventions. He has made extensive improvements to the category system, merging duplicate categories, categorising uncategorised articles and other improvements along those lines. In short, he has consistently demonstrated the attention to detail, the willingness to do repetitive maintenance work, and the calm, cautious and diplomatic demeanour which are the hallmarks of a great admin. Our existing admin tean exhibits all those qualities, so I think Fredg999 is a very natural addition.
+We believe Lériendil would make a good admin because of their dedication to improving existing articles, especially neglected articles like individual temperament pages, and edonoi (nonoctave equal tuning) pages. Lériendil created, and maintains, the temperament infobox, which helps elevate temperament pages to the same level of importance and navigability as EDO pages, a very welcome addition for RTT fans. Lériendil is the founder of, and a highly active contributor to, WikiProject TempClean, which has been doing great work expanding and beautifying pages on individual regular temperaments to give them the quality and depth of coverage they deserve, for such an important component of regular temperament theory (the temperaments themselves!) In WikiProject TempClean, Lériendil has demonstrated the ability to unite, inspire, and organise fellow editors to carry out coordinated maintenance work on neglected pages. This ability is something very valuable to have on an admin team. I think that Lériendil could breathe a lot of life and goodwill into the wiki.
+We believe ArrowHead294 would make a good admin because of his extensive maintenance work. He has written documentation for dozens of templates on the wiki, helping other editors to understand how to utilise those templates, and how to debug them. He has also done the painstaking word of renaming dozens of articles to use the correct capitalisation, the correct hyphenation, etc. to match the wiki's conventions, which makes the wiki much easier to search for readers (they don't have to try to remember what capitalisation or what symbol to type into the search box). ArrowHead294 has also worked to locate several instances of wanted pages (lots of red links to the same place), which are actually just different names for existing pages, and has created the necessary redirects to make them worj. It goes without saying how much that has helped improve navigability. ArrowHead294 has also coded, drafted, published and maintained several modules and several templates, which have been a big help in automating the more monotonous parts of page creation, so that editors can be freed up to spend more time writing the main body of the page. This has allowed the relatively small wiki community to punch above its weight in terms of the scale of its ambition amd comprehensiveness. As with Fredg999 and Lériendil, ArrowHead294's willingness to do the mundane, often uncelebrated, but essential day-to-day maintenance work that elevates the wiki to the next level, makes him an excellent candidate for admin.
+So, our proposal (the wiki editors on Discord), is that Fredg999, Lériendil and ArrowHead294 should be promoted to admin. For the reasons stated above, we believe they would make great additions to the admin team. Would you be in favour of this too?
+—[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 01:19, 5 February 2025 (UTC)
+== Request: make Legacy Xen Wiki visually distinguishable ==
+I would like to request the implementation of at least one change in the visual aspect of the Legacy Xen Wiki to help visitors distinguish it from the regular Xen Wiki and ensure they are actually browsing the version of the wiki they think they are browsing. For instance, the logo could be made slightly different by adding a "LEGACY" text over the original logo (e.g. at the top or at the bottom), The [[Legacy:Main Page]] could also be edited to make it more obvious that it is on the legacy version, ideally with a link back to the regular version, for example by adding a [[Template:Mbox|message box]]. I don't plan on creating an account on the legacy wiki, so this is why I am requesting the change here. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 05:51, 18 February 2025 (UTC)