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)
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 53edo 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)
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)
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)