Talk:Keenan's explanation of vals/WikispacesArchive
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12p and 19p?
First, this notation isn't introduced on this otherwise elementary page (nor hardly anywhere on the wiki).
Second, I don't see how 12p has any meaning in terms of "5-limit meantone"...
- clumma December 26, 2011, 05:39:12 PM UTC-0800
"...he may be assuming something other than patent vals as the base from which to add warts..."
No, he's definitely not. The base is always the patent val.
I'm not sure what happens if you want to talk about 53-limit temperaments. I guess the letter "p" might be skipped over and 53 would be assigned to "q" instead? The practical importance of this is limited, of course, but we should agree on a standard.
- keenanpepper December 26, 2011, 08:25:09 PM UTC-0800
"I don't see how 12p has any meaning in terms of "5-limit meantone"..."
No idea what you mean by this. Does the definition 12p = <12 19 28| eliminate the confusion?
- keenanpepper December 26, 2011, 08:26:44 PM UTC-0800
If we ever start exploring 53-limit temperaments, we could just pick a different, non-alphanumeric symbol to use to specify the patent val. 53* or something would do.
It isn't just Graham's idea but Herman's as well.
- mbattaglia1 December 27, 2011, 03:17:37 AM UTC-0800
Also, if you guys don't like the use of "p" for patent val because it conflicts with the 53-limit, you're going to hate the use of q, r, s, etc to denote non-prime elements in the val, listed by the order in which they appear in the basis. For example, 184.108.40.206/7 17-EDO is <17 27 39 11|, and if I want to specify <17 27 39 12| that's 17q.
- mbattaglia1 December 27, 2011, 03:47:51 AM UTC-0800
I added a definition here
- mbattaglia1 December 27, 2011, 03:59:51 AM UTC-0800
Oh yeah, there's that q, r, s thing. So only the letters a...o (representing primes 2...47) are guaranteed to follow the pattern.
- keenanpepper December 27, 2011, 06:55:16 AM UTC-0800
p is for patent? That's really really really dumb.
We used patent vals for years without this wart notation. You get the first two reallys for trying to change that, and the third for conflicting with your own idea (16th prime)! I would say I'm surprised but then again, I'm talking to the people who put a hundred redirects into the wiki namespace for no reason...
Graham just said on tuning that it stands for "prime", so now I have no idea what's going on. He must have been talking about something else.
- clumma December 27, 2011, 12:30:55 PM UTC-0800
Graham's the one to talk to about this, not me. I'm just used to it because I use his super helpful website all the time.
Do you think this page would be clearer if it always spelled out vals, like <12 19 29|, or used some other notation?
- keenanpepper December 27, 2011, 12:45:09 PM UTC-0800
The vals can easily be written out, or referred to as, e.g. the "12-tone patent val" or "12-ET patent val" or "12-EDO patent val" or "patent val with 12 notes/oct" etc. If you really want a shorthand, Gene has precedence with "h".
- clumma December 27, 2011, 01:17:14 PM UTC-0800
Sorry, no square brackets there, just "h12".
- clumma December 27, 2011, 01:20:33 PM UTC-0800
You guys should post all of these complaints to the tuning list where Graham and Herman can see them. No good talking about it over here.
- mbattaglia1 December 27, 2011, 02:03:40 PM UTC-0800
I use no wart to default to the patent val. Why does that not suffice?
- genewardsmith December 27, 2011, 06:07:11 PM UTC-0800
12p and 19p are Graham's idea; I don't know why they would be need on the Xenwiki. I dislike it because in theory, "12p" means something else and is redundant if you assume patent vals unless otherwise stated, but Graham seems unwilling to default assume patent vals for some reason I don't understand.
- genewardsmith December 26, 2011, 05:47:44 PM UTC-0800
Come to think of it, he may be assuming something other than patent vals as the base from which to add warts, which would be why the "p", perhaps.
- genewardsmith December 26, 2011, 05:48:58 PM UTC-0800
It seems to me the "mathematical name for this" is homomorphism.
- genewardsmith December 23, 2011, 01:18:25 PM UTC-0800
It is a homomorphism, but how is this not also a linear function?
- mbattaglia1 December 24, 2011, 12:46:33 AM UTC-0800
Mathematicans would always call it a homomorphism, but it's also a linear functional which is important if you want to embed it in tuning space.
- genewardsmith December 24, 2011, 09:04:12 AM UTC-0800
But a functional is a certain kind of function, right? Every functional is a function. So, if something is a linear functional, then it is a linear function.
Using a term other than the most specific possible term is not incorrect.
- keenanpepper December 24, 2011, 09:27:25 AM UTC-0800
Using a name mathematicians would almost never use in such a context and then calling it the "mathematical name" is highly misleading.
- genewardsmith December 24, 2011, 09:36:18 AM UTC-0800
Alright, but just to make sure my understanding is correct, homomorphisms and linear functionals are also technically linear functions, right? Or linear maps, or linear operators, or linear transformations or what not.
- mbattaglia1 December 25, 2011, 12:29:56 AM UTC-0800
A homomorphism of abelian groups has the property h(a+b) = h(a) + h(b). However, it isn't necessarily an embedding into a field nor a map from a field, and fields are generally what you have in mind for linear functions. A linear functional L maps into a field, mapping from a vector space over that field, with L(a+b) = L(a) + L(b). In both cases h(0)=0, L(0)=0 with the appropriate definitions of "0". This is also true of a linear map or linear operator, but sometimes "linear function" is taken in a broader sense than that, as an affine map.
Why the hell not just call a homomorphism a homomorphism and be done with it? Particularly since the article is using multiplicative notation for the abelian group of rationals.
- genewardsmith December 25, 2011, 01:07:15 AM UTC-0800