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= ARCHIVED WIKISPACES DISCUSSION BELOW =
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'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
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== "h12" ==
== IIL's Recent Edit ==
Go get consensus on the new shorthand notation on tuning before changing this page. There are at least 4-5 people who have been using the wart notation specifically as described and we've been doing it this way for months now. It makes no sense to change the whole thing up on a whim.
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 {{val|12 19 34}}", for instance, so I put that there instead.


And besides, this "h12" thing makes no sense. I like Gene's proposal of just using "12" better.
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 {{val|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.


- '''mbattaglia1''' December 27, 2011, 11:03:52 PM UTC-0800
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/ [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 10:20, 12 April 2021 (UTC)
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Change it on a whim to what? What, exactly, are we talking about?


- '''genewardsmith''' December 27, 2011, 11:21:48 PM UTC-0800
: 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. [[User:IlL|Inthar]] ([[User talk:IlL|talk]]) 11:31, 12 April 2021 (UTC)
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Carl edited this page and the "Keenan's explanation of Vals" page to remove all instances of the "12p" notation where the "p" wart is taken to represent the patent val, and replaced them with "h12." So instead of 7p & 12p being meantone it's now h7 & h12.


The discussion about all of this took place back on tuning-math in April, including the use of "p" for "patent." Since then, the system has been, a patent val can be specified by a number itself, e.g. 12 & 19, or it can be specified by a number plus "p", e.g. 12p & 19p. Some people have preferred to leave the "p" off and others have preferred to use it. There are a few of us who have chosen to use it. For my part I've been posting to tuning-math with that notation, and teaching people on XA that notation, and using it in XA chat that way for months now, and heard no objections about it.
:: 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! [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 18:25, 12 April 2021 (UTC)


If we now want to bar the use of "p" for "patent," which may be a good idea, then let's come up with a sensible alternative before just putting something random up. For example, Carl's proposed alternative of "h12," which I assume you invented years ago to stand for "homomorphism 12," may not be ideal if we're going to also use Herman's postfix letter notation. A better alternative to "12p" would be your proposal of just using "12." Another good alternative is Herman's "12a," which was in his original scheme before Graham made it 12p.
== Consider delete the current page of "Val" and move this page to "Val" ==


- '''mbattaglia1''' December 27, 2011, 11:54:33 PM UTC-0800
@Xenwolf
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My suggestion is not to use "p" unless it is needed, and since so far as I can see it never is needed, we could let it fade quietly away. Then, if someone wanted to talk about the 53-limit, they could.


- '''genewardsmith''' December 28, 2011, 11:50:13 AM UTC-0800
Like [[Monzo]] and [[Monzos and Interval Space]]. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 05:56, 25 June 2020 (UTC)
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: Done. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:38, 25 June 2020 (UTC)
The only reason I think something like "p" is useful is because sometimes people just throw the bare number around to mean the best val. So for those people, it's useful to be able to say "7p" and know unambiguously that you're talking about the patent val.


If we could get people to stop making the bare number mean the best val, that would be nice. I've never liked it and doubly so because it's dependent on an assumed error metric, and should we ever come up with something besides TE to use then all of the "best vals" might change.
== Some specific problems in the last two edits ==
> Intervals a.k.a. frequency ratios


- '''mbattaglia1''' December 28, 2011, 11:56:02 AM UTC-0800
Intervals can be represented by frequency ratios but intervals aren't frequency ratios!
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I think we should just ignore it to death. What the hell is someone going to do if they want to talk about the 71-limit, do you know? I think 101 is a safer place to stop than 53.


- '''genewardsmith''' December 28, 2011, 12:08:50 PM UTC-0800
: From [[interval|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? --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:02, 7 May 2026 (UTC)
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== Silly vals ==
:: No? It's the monzo. But whatever it is, we're essentially mapping the thing and not a representation of the thing. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:39, 8 May 2026 (UTC)
I'd be careful labeling a val "silly", which suggests you know no possible use could ever be found for it. Your example <12 19 28 33| is the sharptone val for 12edo, and if you find the corresponding dwarf scale, it's quite different from the one for the patent val. That's two uses right there.


- '''genewardsmith''' September 28, 2011, 09:36:43 AM UTC-0700
::: Hmm, I still genuinely estimate that adding "(aka. [[frequency ratio]]s)" 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". --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 09:46, 8 May 2026 (UTC)
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OK, I changed it.


- '''mbattaglia1''' September 28, 2011, 10:23:50 AM UTC-0700
:::: 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''.
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== Definition of a val ==
:::: 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.  
My problem with your approach is that you start by saying "A val is a map representing how the intervals in an equal temperament..." and as you very well know, this is wrong. Vals do not need to be about equal temperaments at all.


- '''genewardsmith''' September 04, 2011, 06:08:38 AM UTC-0700
:::: 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.  
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Sorry, I meant to change that but forgot. This is a much shorter version of what I originally wrote. I spent so much time on this article and went through so many iterations of it that at like 4 AM I finally gave up and just posted what I had.  


I changed it to link to an article called "generator" that hasn't been written. Does this look better?
:::: 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.  


- '''mbattaglia1''' September 04, 2011, 05:01:06 PM UTC-0700
:::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 13:21, 8 May 2026 (UTC)
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> 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.
 
—[[User:FloraC|FloraC]] ([[User talk: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.) —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 20:36, 7 May 2026 (UTC) (Updated [[User:FloraC|FloraC]] ([[User talk: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! [[User:MisterShafXen|MisterShafXen]] ([[User talk: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. --[[User:Godtone|Godtone]] ([[User talk: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! [[User:MisterShafXen|MisterShafXen]] ([[User talk: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? --[[User:Godtone|Godtone]] ([[User talk: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! [[User:MisterShafXen|MisterShafXen]] ([[User talk:MisterShafXen|talk]]) 16:01, 10 May 2026 (UTC)
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