# Template talk:Infobox ET

## Parameters

(for better accessibility/readability split into sub headings)

### Prime factorization

IMO usually not that useful, and when it is useful it should be discussed in the theory section of the edo article. I propose it be replaced with number of rings of 5ths (see my proposal below). --TallKite (talk) 22:38, 7 December 2020 (UTC)

- I proposed this, my intention was to show structural properties. Maybe I better suggested
*“d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n”*^{OEIS:A000005}. To me, it feels relevant which cycles (not only of 5ths) are possible at all. --Xenwolf (talk) 12:57, 8 December 2020 (UTC)

- I see your point. On the one hand, 3 is a very important prime, and the template info should be somewhat fifth-centric. On the other hand, we don't want to be too fifth-centric, since lots of microtonalists like omitting lower primes and using higher ones. So I'm in favor of keeping prime factorization. But can there please be a practice of leaving this parameter blank when the edo is prime? Otherwise IMO the template is too cluttered and confusing. --TallKite (talk) 02:45, 9 December 2020 (UTC)

### Subgroup

The criterion for including a subgroup could be <20 cents of dyadic error for each interval, but <10 cents for dyads of integer limit >11 because higher dyads need to be more accurate to be interpreted as that dyad. in the relevant "odd-limit" tonality diamond (and possibly consistency). IlL (talk) 10:35, 3 December 2020 (UTC)

"Subgroup" might be an unnecessarily convoluted way of presenting what can just be presented as harmonic series chords. For example, "18edo approximates 3:7:13:15:17:23:27:29" is more direct than the equivalent "18edo is a temperament on the 2.5.9.21.13/3.17/3.23/3.29/3 subgroup". Arguably the harmonic series chord approximated is the more directly musical property of an edo whereas the subgroup interpretation is a technical tool you use to do temperament computations. IlL (talk) 18:41, 4 December 2020 (UTC)

- I'll be honest, I do think that there should be two sets of criteria for including a subgroup- superb, and passable. I'm thinking the EDO's superb subgroup representation range would be less than 3.5 cents of absolute error for base intervals in a given subgroup- e.g. 12edo and 53edo could both be considered superb at representing both 3/2 and 4/3 because of the differences from just intonation being less than 3.5 cents. Meanwhile, I'm thinking the EDO's passable subgroup representation range would involve differences of less than half of a step for said EDO- e.g. 12edo's representation of 5/4 and 8/5 is passable because the absolute error rates are less than half a step. --Aura (talk) 19:35, 4 December 2020 (UTC)

- This is exact the reason why I'd say only those criteria should go in the infobox that are indisputable and concise. The patent val for instance would be of such kind. I mean, It's obvious that all things in the box will gain higher attention of the reader. But if we try to expand the box to an article of it's own, we loose both, the attraction of the box on one hand and the quality of the surrounding article on the other hand. IOW: keep it short. --Xenwolf (talk) 20:12, 4 December 2020 (UTC)

- I can see why. Still, I can see both the "fifth type" and the "subgroup" parameters being useful if they are refined. The "fifth type" parameter should reflect the nature of the tempered fifth- though we admittedly need to discuss how to do this right- while the "subgroup" parameter (I think) should reflect the portions of the Harmonic Lattice that said EDO approximates to within 3.5 cents of error. I'll tell more about my thoughts concerning the fifth in the section on "fifth type" below. --Aura (talk) 22:47, 4 December 2020 (UTC)

- I totally agree with Xenwolf's "indisputable and concise". There is no indisputable way to decide which primes are tuned accurately enough to be included in this section. The indisputable information about primes is already on every edo page, in the Selected just intervals by error section. The table of errors for each prime, by cents and by % of edostep. This table is not concise enough to fit in the template. So I suggest removing the subgroup parameter from the template altogether. --TallKite (talk) 22:38, 7 December 2020 (UTC)

### Fifth type

Fifth type: not rigorously defined. Perhaps should not be named after temperaments of a mixture of ranks. *Mavila*, *7edo*, *5edo* and *father* are fine, I suppose. What's the boundary between *flattone* and *meantone*, and between *meantone* and *schismic*? Why is 19edo *meantone* and not *flattone*? Why is 12edo *meantone* and not *schismic*? Does it all converge to *schismic* when edos get large enough? FloraC (talk) 07:18, 3 December 2020 (UTC)

- We could just give the size of the best fifth. IlL (talk) 09:33, 3 December 2020 (UTC)
- Or should the order of fifth sizes be mavila, 7edo, hypopent, (just 3/2), hyperpent, 5edo, father? IlL (talk) 09:41, 3 December 2020 (UTC)

- I can right away tell you that 53edo's best fifth is a Mercator/schismic. Truth be told, when the tempered out comma separating a complete chain of fifths from a stack of octaves for a given EDO is smaller than that for other EDOs in the neighborhood, the comma should lend its name to the fifth type, and other EDOs that temper out this same comma should be considered to have this same fifth type. I agree that the idea of fifth type needs more rigorous definition, but hopefully, this a start. --Aura (talk) 15:09, 3 December 2020 (UTC)

Hmm... Perhaps the type tempered fifth- particularly for those EDO fifths that more closely approximate the 3/2 just fifth than their neighbors- should have categories involving the 2.3 comma that's tempered out- e.g. the type of fifth that 53edo has should just be called "Mercator" because Mercator's comma is tempered out. Similarly, the type of fifth that 12edo has should just be called "Pythagorean" because the Pythagorean comma is tempered out. I hope this is at least a start... --Aura (talk) 22:52, 4 December 2020 (UTC)

- "Similarly, the type of fifth that 53edo has should just be called "Pythagorean"" - did you mean 12edo? Every edo tempers out only one 2.3 comma (not counting multiples of this comma). For N-edo, the comma's 3-exponent is ±N/GCD(M,N), where the best 3/2 is M\N. --TallKite (talk) 22:38, 7 December 2020 (UTC)

- Yes, I did mean that the type of fifth that 12edo has should just be called "Pythagorean". I fixed that in the above comment. Thank you. I don't know how I botched that. Unfortunately, I don't see what you're getting at with much of the rest of your comment. --Aura (talk) 08:00, 18 December 2020 (UTC)

I agree with FloraC, fifth type is not rigorously defined. Every comma that contains primes 2 and 3 and only 1 other prime implies a fifth size, or a narrow range of fifth sizes. But the exact range is disputable, and also there are an infinite number of possible commas. There is already a lengthy table of commas on every edo page. By Xenwolf's "indisputable and concise" rule, we should not list the fifth type. I propose there only be fifth size in edosteps and cents, e.g. for 24edo, "14\24 700¢". The shorter the better. We could possibly have IlL's categories of mavila, 7edo, hypopent, (just 3/2), hyperpent, 5edo, father. (BTW these are quite similar to my edo categories superflat, perfect, diatonic, pentatonic and supersharp.) But once you know the fifth size, it's easy to tell what category it's in. The 7edo category is obvious -- the edo must be a smallish (< 50) multiple of 7, and the 5th must be 680-something cents. The 5edo category is even more obvious. Mavila and father are also obvious, the 5th is < 680¢ or > 720¢. It's not like there are edos who's fifths are only a cent or two away from 4\7 or 3\5. Hypopent and hyperpent are mostly easy to tell too, as long as you know how many cents 3/2 is. --TallKite (talk) 22:38, 7 December 2020 (UTC)

### Important MOSes

Important MOSes, common uses: these will be bloated in a later stage. FloraC (talk) 07:18, 3 December 2020 (UTC)

- Right now there's some overlap between MOSes and notable uses, those could use a single parameter. Notable MOSes could be limited to size <=10. (and be described in a temperament-independent manner) IlL (talk) 09:33, 3 December 2020 (UTC)

### Example composition/score

Example composition/score: What kind of one-minute composition can be representative for an edo? Shall we hold a composing contest for this? FloraC (talk) 07:18, 3 December 2020 (UTC)

- I think contests for popular edos is a good idea. What kind of timeline are you thinking of for the contest? As for the kind of composition, I'd think it should showcase some of the special features of the edo. Maybe (like the current 13edo example) short sections in different MOS scales. Or showcase the way that voice leading works differently than in 12edo (e.g., a composition where major triads are dissonances in 17edo). Schrodingasdawg (talk) 18:02, 3 December 2020 (UTC)

- This is a fun idea, but it doesn't belong in the template! How would the contest be judged? Would the winner be indisputable? There's already a section for musical examples. Also, larger edos tend to sound alike. If I wrote something in 5-limit or 7-limit JI and made two recordings, one in 53-edo and the other in 72-edo, I doubt most people could tell which was which. Because all large edos sound like JI. Perhaps instead there could be a sound file, like the ratio template has. For smaller edos, it could be the entire gamut of notes up to an 8ve. For larger edos, perhaps a 5-limit major scale? --TallKite (talk) 22:38, 7 December 2020 (UTC)

- I think a short example composition does belong in the info box. The musical examples linked further down are mostly works of art of varying styles written in the edo, and it's not always obvious to an uninitiated reader to what extent these pieces highlight features of the edo (and which ones). The point of the example composition is to be short (about a minute) and to specifically highlight unique features of the edo, with annotated sheet music to point these features out. (See the example by IIL on the 13edo page.) I think this could be useful for smaller edos (so not really 53edo or 72edo). The problem of course is that even the smaller edos have many features and which are worthy of being highlighted is subjective, and people might disagree about this. That's is why I thought Flora's idea of a competition was a good idea. Schrodingasdawg (talk) 02:09, 8 December 2020 (UTC)

- I think you should consider annotating one of your fugue scores and adding it to the 19edo page as a tuning showcase then! I honestly think having a short piece with an annotated score can help orient a reader who's new to an edo and wants to see and hear in practice how the edo works, with the little details explicitly pointed out to them. Schrodingasdawg (talk) 04:25, 9 December 2020 (UTC)

### Steps or Step count

Steps or Step count: this is the most important parameter, because it lets us calculate the step size and lateron rename the page without loosing information. Also using the page title as table description is not a great idea. --Xenwolf (talk) 09:01, 3 December 2020 (UTC)

### Formatting

Current notation `5*3-2*1`

is confusing. Should be changed to `5L 2s (3-3-1-3-3-3-1)`

or `5L(3)2s(1)`

? IlL (talk) 17:49, 3 December 2020 (UTC)

I'll go with `diatonic (meantone) 5L2s 2221221 (generator = 7\12)`

. For multi-period MOSes, `diminished 4L4s 12121212 (generator = 1\12, period = 3\12)`

IlL (talk) 19:01, 3 December 2020 (UTC)

The formatting could be done with dedicated templates. IlL (talk) 19:07, 3 December 2020 (UTC)

## Template name

I find it not a such great decision to name the template ET where all pages use the EDO abbreviation. --Xenwolf (talk) 08:56, 3 December 2020 (UTC)

I wanted to use it also for nonoctave ETs. But I'm fine with renaming to "edo" and using a different infobox for nonoctave equal temperaments. IlL (talk) 09:15, 3 December 2020 (UTC)

- It's possible to use it for all equal divisions, but this would complicate it. You should have noticed that it's not as easy to cope with all that nested
`{}`

stuff. I'd suggest to discuss the options first. --Xenwolf (talk) 09:25, 3 December 2020 (UTC)

Right now the only parameter that assumes edo is "Fifth type"? IlL (talk) 09:46, 3 December 2020 (UTC)

- I have the feeling you are misinterpreting the current situation. I'm not fighting against "your" template, I try to discuss the best solution of the problem we all have to present properties all EDOs have on EDO pages in a canonical way (that most people will accept as useful). And I'd like to participate all of us in a maximally constructive way. --Xenwolf (talk) 09:52, 3 December 2020 (UTC)

To be clear I was a bit startled. As I stated I have no problem with renaming this template. (I don't consider this template mine.) Feel free to move it and let people give feedback on the way the info is presented. IlL (talk) 10:17, 3 December 2020 (UTC)

- Renaming is no problem at all. To me it's the question which option will be better. We really should discuss pros and cons first. Admittedly starting with a general solution is not my way to do things that have to be done fast. You told that you were in need for such a template, as turns out seemingly only for EDO pages. If seen in this context, the decision to name it ET is just questionable, that's why I started this discussion topic. --Xenwolf (talk) 10:28, 3 December 2020 (UTC)

## Related project

We already started a project about a template of this kind but maybe too hidden Xenharmonic Wiki:Things to do#Infobox for EDO pages, Xenharmonic Wiki talk:Things to do#Infobox for EDO pages. In any case, it would be good to also let the thoughts there flow into the discussion here or vice versa. --Xenwolf (talk) 09:17, 3 December 2020 (UTC)

## Styling

I tried to reduce the color. Of course this is a matter of taste but I suggest that we use colors sparingly in the design, which involves many pages. Personally, I would prefer a shade of grey. --Xenwolf (talk) 10:18, 3 December 2020 (UTC)

## Normalize parameter names

It's not a good idea to start a template with alternative names for the same parameter. So I suggest to normalize the names to "Lemma case", that is, only first letter is uppercase, except for the MOS abbreviation. Category:Todo:normalize EDO parameters collects use cases of the template with parameter names that should therefore be changed. --Xenwolf (talk) 21:35, 3 December 2020 (UTC)

## Kite's proposed format for the edo template

I propose step size, fifth in edosteps and cents, number of rings, and pythagorean major 2nd and minor 2nd in edosteps and cents. Indisputable and concise. If the fifth is M\N, the number of rings is GCD (M,N). This number tells us which smaller edos have the same fifth. For example, 72-edo has 6 rings. Divide 72 by 6 to get 12, therefore 12-edo has the same 5th. As do multiples of 12 like 24, 36, 48 and 60. If there are N rings, there are N-1 smaller edos with the same fifth. I'm tempted to add the sharpness/flatness parameter (# of edosteps per sharp sign), but this is just the # of edosteps in the pythagorean A1, and that's easily calculated as M2 - m2. 31edo example: Step size = 38.710¢, Fifth = 13\31 = 696.77¢, Rings = 1, Major 2nd = 5\31 = 193.55¢, Minor 2nd = 3\31 = 116.13¢. --TallKite (talk) 22:41, 7 December 2020 (UTC)

- I also propose putting the patent val in the table of primes that has the error in cents, error as % of edostep, and fifthspan. This is the obvious place for it, I should have done this when I first started making those tables. Since this table is so important, I propose moving it up to the theory section (the first section) where it is easier to find. --TallKite (talk) 22:47, 7 December 2020 (UTC)

- Most people will value an EDO for some "classical" or "just" qualities. So it's understandable that the 5th is given a prominent role for characterizing an EDO, but I'd like to be more neutral in this aspect. That's why I suggested a formula for the 5th lovers which I'd now like to call the
(an optional parameter) which is**tone ratio**`1:1`

in 12edo and`2:1`

in 19edo. The name is derived from tone and inspired by the Golden ratio (BTW, the*tone ratio*of Golden meantone is`φ:1`

). I'd like to omit cent values here; for EDOs it can be calculated easily with every pocket/phone calculator. --Xenwolf (talk) 13:28, 8 December 2020 (UTC)

- Most people will value an EDO for some "classical" or "just" qualities. So it's understandable that the 5th is given a prominent role for characterizing an EDO, but I'd like to be more neutral in this aspect. That's why I suggested a formula for the 5th lovers which I'd now like to call the

- It must be m2 to A1. But let's get down to the details. (1) Should the term be
*semitone ratio*since it's of two semitones? (2) Should we ever reduce the ratio? (I guess not.) (3) A1 to m2, or m2 to A1? Btw, the just value is 1.26001... or 0.79364..., respectively. A new page is necessary if we use this neologism. FloraC (talk) 07:02, 9 December 2020 (UTC)

- It must be m2 to A1. But let's get down to the details. (1) Should the term be

- I added M2, m2 and A1 to the template. (Hopefully I did it right, I'm new at editing templates.) I saw that for multi-ring edos, the fifth field should include any lower edo with the same fifth. For example 24edo has "12edo" in the fifth parameter. This makes the Rings parameter unnecessary, so I no longer think it should be included. Rather than seeing 24edo and 2 rings and deducing that 24-edo's fifth is 12-edo's fifth, you can see it directly, much better. Related, I now think prime factorization should be included.

- But ye gods, people, it took a lot of self-control when editing not to delete the parameters about Important MOSes and Common Uses and Compositions on the spot. These things belong on the edo page, but there's already a place for them. Further down the page, where there's room to list ALL the MOSes and ALL the uses and ALL the compositions. Same for the type of fifth as schismic/meantone/superpyth etc. There's already a table that lists ALL the temperaments the edo supports, without having to single out one as "the" defining temperament. Having these parameters in the template invites endless debate.

- The subgroup is also problematic, since any criteria for including a borderline prime or not is by necessity somewhat arbitrary. This one isn't as bad as the others, but moving the prime errors table to the top of the page is a much better solution. Because the table gives the complete picture in a way the template parameter can't. For example, you can look at the percentage error and decide for yourself if the edo accurately represents that prime. BTW this also makes it unnecessary to add the prime-3 error in the template's fifth parameter (e.g. -1.955¢ for 12-edo).

- Can we all agree that the template should only be for those things that are indisputable facts? Or if we can't all agree, can we at least agree that we won't reach consensus on including those parameters, and the right course of action is to delete them? --TallKite (talk) 02:45, 9 December 2020 (UTC)

- In editing all the EDO pages, I came to realize that the cents for the m2 and A1 are very handy. Yes, you can do the math and calculate the cents, but it's really handy to see at a glance how many cents a sharp sign is. Also for large edos, doing the math is too much work. So on second thought, I would only like this proposed format if it also included the cents. Also, this is a bit of a quibble, but "semitone" means half a tone. And in a lot of these edos, it's nowhere near half. So the term semitone is a bit misleading, and IMO better avoided. --TallKite (talk) 08:48, 18 December 2020 (UTC)

- Update: see #Reduce parameters. FloraC (talk) 12:56, 7 October 2021 (UTC)

I just removed all the disputable parameters. I carefully moved all the data entries to a better spot on the EDO page. Example compositions got moved to "Introductory Materials". Important MOSes got moved to "Rank Two Temperaments". Common uses and subgroups got deleted. I considered working the common uses into the theory section, but they just seemed so arbitrary. Every edo has a thousand uses. I didn't do anything with the intro section. --TallKite (talk) 07:41, 18 December 2020 (UTC)

## Intro sentence on EDO pages

Slightly off-topic, but related in a way. IMO it would be good if this sentence were standardized. Not good to put important info here, too easy to miss. So something short like "N-EDO or N-ET divides the octave into N equal steps." No need to say what the step size is, since the template covers that now. The phrase "equal steps" could link back to the main EDO page, which would be handy when comparing EDOs. --TallKite (talk) 23:05, 16 December 2020 (UTC)

- I think the introduction (a section with a few sentences) is invaluable. We learn that from the silent but effective Wikipedia-Google collaboration: The question "What is <Random Xen Lemma>?" typed in the input line of Google or any other search engine should not only give results from the XenWiki in the first matches but the XenWiki result should also give the short answer. This is what the introduction is for. This is the reason why it has to start the article directly under the H1 (=lemma) header. The introduction should be readable, informative, and short. I know this is sometimes not easy but it's good to invest time here. Look into Wikipedia to find good examples: they have definitely a higher ratio of great introductions than we have. Standardization may not be a bad thing but an introduction that can be written by a bot is not an introduction a human reader wants to read (and the best search engines have increasingly good algorithms for distinguishing readable - and worth-to read - text from pseudo text). BTW: this is true for all articles. --Xenwolf (talk) 23:42, 16 December 2020 (UTC)

## Reduce parameters

I think it's enough to specify the *fifth* since the parameters *M2*, *m2*, and *A1* are not independent (see diatonic range). Also the sizes could be calculated by the template or a module. What do you think? --Xenwolf (talk) 22:12, 11 June 2021 (UTC)

- Yes, especially as they don't make sense for nondiatonic edos such as 13 or 16. Maybe specify the other parameters for diatonic edos but not for nondiatonic edos. Yes, they could be computed. Inthar (talk) 22:17, 11 June 2021 (UTC)

- The sharpness is an important piece of information that I find really handy. That's why I've always argued for
*semitones (A1:m2)*. It saves a line. Semitones are also helpful in that they are the basic building blocks for 12edo users. Chromatic semitone and diatonic semitone are established terms long before xen practice. And cent values still can be shown along with step numbers. FloraC (talk) 12:56, 7 October 2021 (UTC)

- The sharpness is an important piece of information that I find really handy. That's why I've always argued for

- As discussed in the Discord server, I'm adding
*sharp fifth*and*flat fifth*for dual-fifth edos. I define a dual fifth edo as those whose error of the fifth is greater than 1/3 edostep, since it is the point where the approximation of the major second (9/8) becomes better than the fifth (3/2) itself, and where doubling the edo guarantees a better fifth. For dual-fifth edos, I'd like to reflect their two typical interpretations as 2.3-.3+ and 2.9, so we'll use*sharp fifth*,*flat fifth*, and*major 2nd*. For other edos,*fifth*and*semitones*. FloraC (talk) 18:32, 19 August 2022 (UTC)

- I have a strong preference for M2, m2 and A1 all spelled out like they used to be, like this:
- M2: 4\22 (218¢)
- m2: 1\22 (55¢)
- A1: 3\22 (164¢)
- There's almost always room on the page, since the infobox sits opposite the table of contents. The various L/s ratios can be read quite easily. Diatonic is 4:1, chromatic is 3:1. Heck, you can even figure out that 2L3s[5] is 5:4 pretty easily. -- TallKite (talk) 00:08, 8 October 2022 (UTC)

- The only thing I can think of as a use for a modified version of the M3 line is as the representation for 5/4 for systems that have a consistent representation of it- and this merely because 5/4 is such a common reference point for major thirds. I wouldn't bother with those systems where 5/4 can reasonably be mapped to one of two possible EDO-steps. Other than that, I do indeed think that adding the M3 line is questionable. --Aura (talk) 15:31, 25 May 2023 (UTC)

- There's the prime harmonics table for that, and assuming the diatonic major third to be consistent with 5/4 is very meantone-centric anyway. The semitone ratio is already plenty of information. I agree that the M3 field should be removed, because it adds more clutter for no new significant information. --Fredg999 (talk) 22:11, 25 May 2023 (UTC)

## Consistency level

I'd like this to be present in the infobox because it quickly captures how the edo is likely to be used (in an RTT way or in an JI agnostic way). It's present in the theory section of basically every edo, often for the purpose I just mentioned. FloraC (talk) 21:40, 5 October 2021 (UTC)

Added diamond consistency and diamond monotonicity. FloraC (talk) 12:56, 7 October 2021 (UTC)

- Deprecating monotonicity. It wasn't a considerate decision. FloraC (talk) 12:27, 26 March 2022 (UTC)

## Highly composite sequence past 5040

The template shows 9240edo as highly composite, yet it's not a member of the highly composite sequence, it's only largely composite. Also, past 5040 the sequences split into highly composite and superabundant so it would be worthy to get this noted. Eliora (talk) 23:17, 17 March 2023 (UTC)

← 3ed4 | 5ed4 | 7ed4 → |

(convergent)

At the moment, if you are on a page for an ed4, say for example 5ed4, then the the "**<--**" and "**-->**" links will link to **4ed4** and **6ed4**, both of which will immediately redirect you to the relevant edo page (2edo or 3edo):

I think this is a bit of a hinderance for navigation. It would be more helpful, I think, for "**<--**" and "**-->**" to link to **3ed4** and **7ed4**, instead of 4ed4 and 6ed4.

Similar problems may also occur with other non-prime EDs (ed6, ed8, ed9, ed10, etc.), I haven't checked.

--BudjarnLambeth (talk) 07:29, 24 June 2023 (UTC)

## Automatic link to xen-calc?

Would it be hard to add an automatic to xen-calc like the template for intervals has? (Something like "Open this temperament in xen-calc".) Lucius Chiaraviglio (talk) 22:15, 7 October 2024 (UTC)