Talk:Val

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IIL's Recent Edit

IIL suggested we also talk about subgroup vals and tempered vals on this page. Some material on these have already been written (Gene called these "svals" and "tvals"). I revamped these two sections and linked to the relevant pages. Also, there is already a fairly universal notation everyone has been using on the various social media groups, where a subgroup val is notated "2.3.7 ⟨12 19 34]", for instance, so I put that there instead.

Tempered monzos and vals are something that I, in particular, have worked with very frequently (I think I made the original "Tmonzo and Tval" page). The notation we have been using is the same as the subgroup val notation, but with "tempered interval names," e.g. for meantone we'd have "P8.P5 ⟨12 7]" for 12-EDO (where P8 means 2/1 * (81/80)^n and P5 means 3/2 * (81/80)^n). For arbitrary temperaments without names we would typically do basically the same thing you said, i.e. just pick the best JI interval in the preimage and call it that. I adjusted the notation slightly to match the subgroup val one but your basic idea is good.

It would be really nice to get some notification about these suggestions before sweeping changes are made; if Flora Canou hadn't posted on FB I wouldn't have seen this. The mathematical pages have always been a collaborative effort and, for better or worse, every one of the heavy math folks are on Facebook. It would be great if you could join us there: https://www.facebook.com/groups/xenharmonicmath/ Mike Battaglia (talk) 10:20, 12 April 2021 (UTC)

Hi Mike! I remember you from seeing you on the FB Xenharmonic group approximately 10 years ago and learning RTT. I ideally don't want to join the group because I don't wish to associate my IRL name with my online handle. We can still talk on the wiki, though. Inthar (talk) 11:31, 12 April 2021 (UTC)

Hi Inthar, good to meet you... Could you at least make a new pseudonymous FB account then with a different name? There is currently some talk on Facebook about how we all feel the edits on here are impossible to keep up with; sometimes there are errors, etc. It would also be much better if we could talk about proposals for notation directly, rather than having you edit a page and then us edit only after, if we see it... There are plenty of users on the FB groups not using their real names... Thank you! Mike Battaglia (talk) 18:25, 12 April 2021 (UTC)

Consider delete the current page of "Val" and move this page to "Val"

@Xenwolf

Like Monzo and Monzos and Interval Space. FloraC (talk) 05:56, 25 June 2020 (UTC)

Done. --Xenwolf (talk) 06:38, 25 June 2020 (UTC)

Some specific problems in the last two edits

> Intervals a.k.a. frequency ratios

Intervals can be represented by frequency ratios but intervals aren't frequency ratios!

From the page, we have the definition "An interval is the difference in pitch between two notes. Human pitch perception is logarithmic, therefore an interval can be described with a frequency ratio or a logarithmic measure of that ratio, such as cents". The frequency ratio is the rational number, which is what goes into the mapping function, so seems more accurate than "interval", no? --Godtone (talk) 22:02, 7 May 2026 (UTC)

No? It's the monzo. But whatever it is, we're essentially mapping the thing and not a representation of the thing. —FloraC (talk) 08:39, 8 May 2026 (UTC)

Hmm, I still genuinely estimate that adding "(aka. frequency ratios)" would be helpful for a beginner and do no harm to the state of the page, cuz "frequency ratio" is essentially the beginner word for "interval" if someone isn't accustomed to the meaning of "interval", EG isn't a musician as many new to xen aren't. I also say this coming from the perspective of concern about negative intervals being unintuitive/potentially confusing to get right in technical speech and consideration while a ratio (a rational number) is extremely straightforward. Also, there was some discussion on Discord that "val" actually comes from "p-adic valuation", which suggests that the preimage is a rational number, not a monzo. In light of this, I'm really curious what you think of [this https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_7525.html#7532] which was linked to me by sintel, as it (apparently) concerns the origin of the term "val". --Godtone (talk) 09:46, 8 May 2026 (UTC)

Quite the opposite, interval is the beginner word for frequency ratio. All musicians know about intervals, but only the small group of musicians who study JI like us know about frequency ratios. Non-musicians might not know about either, but if they do know about one, it's 99% interval.

I don't see how negative intervals pose a problem at all. If anything they pose a problem as much as less-than-one ratios do.

I don't care about the origin of val. Gene is but one who liked computing RTT in terms of ratios but it's not the most common way to do RTT today. I for one have been thinking of val as the dual of interval lately and haven't run into any issue.

In any case, I don't mind replacing interval with frequency ratio tho I also don't think it adds anything. I'm against equating them.

—FloraC (talk) 13:21, 8 May 2026 (UTC)

> Tunings of interest

Not necessary, subjective, and annoyingly uninclusive. Composers approach JI approximation differently. We should not assume the interesting edos are usually 5-odd-limit consistent.

—FloraC (talk) 20:36, 7 May 2026 (UTC)

The general problem of the motivation section

It focuses too much on how to make inconsistency workable and doesn't touch on how and why to think of the intervals the interval space/lattice way. I'll be giving it a major rewrite to address that. (Update: done.) —FloraC (talk) 20:36, 7 May 2026 (UTC) (Updated FloraC (talk) 21:05, 7 May 2026 (UTC))

Ditch wart notation?

Why don't we ditch wart notation? Sintel has demonstrated a much clearer notation on his temperament finder. For example, if you want 13edo mapped with its flat fifth, that would be 13b in wart notation and 13[-3] in Sintel's notation. Which is clearer?

To further complicate things, let's say you wanted 26b-edo. Based on what I just said about 13b, one might assume that 26b means 26 with the fifth flattened by 1 edostep. That's not the case, so Sintel swoops in to save the day by using the notation 26[+3] to refer to 26b. In fact, if you want 26 with the fifth flattened by 1 edostep, that would be 26bb. What. The. F. Double. Sharp. Just call it 26[-3] like Sintel does, for goodness sakes!

I hope my point is clear (unlike wart notation): Wart notation is bad. I hope this discussion will be able to continue and result in the END of wart notation.

G-d bless you all! MisterShafXen (talk) 15:47, 9 May 2026 (UTC)

I'd be happy to include sintel's wart notation but I'd prefer to avoid complicating the page, so I'm wondering if the "Sparse Offset Val notation" really needs to be there as I'm not aware of anyone who uses it, but then I'm also not on Facebook so... point being, wart notation is, at least for now, a consistent standard in how ppl specify non-patent vals, with everything else essentially being less standard, so it seems to deserve mention, though maybe it'd be better to link to a separate page explaining all the different wart notations, but that kinda goes back to my point about using letters as in practice it's rare that you need more than two warts for a prime, and if you're interested in an equal temperament you usually know which primes are worst and in what directions. --Godtone (talk) 16:14, 9 May 2026 (UTC)

I also want to point out that on pages containing temperament data, one will often find tunings like 80bbcccef in the optimal ET sequences for tedmperaments. If we used Sintel's notation, 80bbcccef becomes 80[+3, --5, -11, +13]. That's a whole lot clearer!

So, based off what I just said, is there any chance we can go through all the temperament data and at least put Sintel's notation alongside the regular wart notation?

G-d bless! MisterShafXen (talk) 17:18, 9 May 2026 (UTC)

The "optimal ET sequences" is its own standard format. I personally am not a fan of it and would prefer some different standard or nonstandard optimal sequence to go alongside it or replace it which could implement what you're talking about while including more notable EDO tunings in the list as the optimal ET sequences can miss crucial patent val tunings. I tried to do this myself some time ago by listing custom lists of notable EDOs, so I'd need some support from others. (In that regards, are you on Discord? I'm osmium (@osmiumic) on Discord.) Other than that, no feedback on what I said? --Godtone (talk) 15:30, 10 May 2026 (UTC)

Hi Godtone, how are you? Sadly, I used to be on Discord but my school WiFi blocks it.

Is there any chance we can work on lists of notable EDOs, maybe on one of our userspaces? Also, yes, I do see why completely ditching wart letters wouldn't work (yet).

Btw I just wonder what happens when you want to wart a "formal prime" such as 9 in the 2.9.5.7 subgroup. Sintel makes it easy: just put the alteration (+ or -) in [] brackets, followed by the number 9 (within the brackets).

Have a great day! G-d bless! MisterShafXen (talk) 16:01, 10 May 2026 (UTC)