# Talk:Modal UDP Notation/WikispacesArchive

# ARCHIVED WIKISPACES DISCUSSION BELOW

**All discussion below is archived from the Wikispaces export in its original unaltered form.**

Please do not add any new discussion to this archive page.

All new discussion should go on Talk:Modal UDP Notation.

## Agh, editing on top of each other

To Gene: I was just working on a huge edit and I think I may have accidentally overwritten some stuff you did. You can always change it back in the history.

I deliberately stripped the entire thing away and began with a much more basic, bare-bones definition which defines "up" and "down" in terms of generators from the tonic rather than the total ordering on modal shifts of S like we'd talked about before. This is the way I'd originally defined it (or was trying), but I got really confused because I didn't realize you'd interpreted it differently.

If you can agree that this definition is understandable and desirable, then we can get back to things like modal shifts "up" and "down" and "topmost modes," but let's just get on the same wavelength first. I made a larger post on tuning math earlier but maybe it's best to just start here.

- **mbattaglia1** November 18, 2011, 04:50:09 PM UTC-0800

I suggest you wait until I am finished to start your project. I think we may want to split the page into two pages anyway.

- **genewardsmith** November 18, 2011, 04:55:52 PM UTC-0800

I didn't know you were editing when I started editing.

You asked me to clarify UDP notation with a mathematical definition, and the above is it. I'd like to know if you consider it precise and unambiguous, and if not, why not.

- **mbattaglia1** November 18, 2011, 05:01:15 PM UTC-0800

And if we want Lydian to be the "bottom" mode, I suggest we just define "relative bottom" vs "parallel bottom," in a way that generalizes "relative minor" vs "parallel minor." Lydian is the relative bottom mode and the parallel top mode.

- **mbattaglia1** November 18, 2011, 05:02:36 PM UTC-0800

Also, please let me know when you're done, so I can get to editing.

- **mbattaglia1** November 18, 2011, 05:15:44 PM UTC-0800

Alright, are you finished? It's been 3 hours.

- **mbattaglia1** November 18, 2011, 08:00:34 PM UTC-0800

Are you in a rush? I got tired of writing, and thought I'd leave it until tomorrow. If you want to do something, go ahead.

- **genewardsmith** November 18, 2011, 08:08:26 PM UTC-0800

Sorry, it's making me crazy to see you guys take this concept, redefine up so up is down and top is bottom, and then not be allowed to edit it because I'm waiting :)

Can you please tell me if this definition is unambiguous?

"Given a periodic scale S with period S[p], let the tonic be S[0] = 0. If S is MOS, then let the generator S[m] = g such that g is the larger specific interval in its generic interval class.

For any such S, there are two associated values u and d, called the number of generators located "up" and "down" from the tonic. Let u be the maximum integer such that S[m*u] = g*u, and 0 <= u < p. Likewise, let d be the maximum integer such that S[-m*d] = -g*d, and 0 <= d < p.

Let U = uP, and D = dP. The UDP notation for a given mode of an MOS is U|D(P). If P=1 we may omit it and just write U|D."

- **mbattaglia1** November 18, 2011, 08:10:12 PM UTC-0800

Given a periodic MOS scale S, let the generator S[m] = g be such that g >= S[i+m]-S[i] for all i. If L is the period of S, let u be the largest integer such that 0<=u<L and S[m*u] = g*u, and d the largest integer such that 0<=d<L and S[-m*d]=-g*d. If S[P*L] = octave, so that P is the number of periods to an octave, let U = P*u and D = P*d. Then the UDP notation for the given mode is is U|D(P). If P=1 we may omit it and just write U|D.

- **genewardsmith** November 19, 2011, 12:50:44 AM UTC-0800

I think it's clearer, as well as shorter, stripped of the excess verbiage and unneeded concepts.

- **genewardsmith** November 19, 2011, 12:53:08 AM UTC-0800

I don't know if you saw my post on facebook, but I think that's a good definition. I'm not sure how to begin editing the page though.

- **mbattaglia1** November 21, 2011, 04:13:53 AM UTC-0800

OK, I'll start if you like.

- **genewardsmith** November 21, 2011, 09:12:03 AM UTC-0800

I just trimmed a ton of stuff; it's not necessary to include any theorems about how the generator is chosen so that L-s is positive on the lattice. I got rid of an entire section and expanded on the first section a bit. If you think I removed anything useful you can add it back.

I'm still concerned that the information in this page might not be presented clearly to non-mathematicians, mostly because of my own apparent inability to explain this in a simple fashion. But we'll see what people get confused about and then change it.

- **mbattaglia1** November 21, 2011, 05:07:27 PM UTC-0800

Well, we're really smashing away at it at the same time now, you just overwrote my edit. The one I was talking about is here:

http://xenharmonic.wikispaces.com/page/view/Modal+UDP+Notation/277119058

This is the definition:

"Given a periodic scale S with period S[p], let the tonic be S[0] = 0. If S is MOS, then let the generator S[m] = g such that g is the larger specific interval in its generic interval class.

For any such S, there are two associated values u and d, called the number of generators located "up" and "down" from the tonic. Let u be the maximum integer such that S[m*u] = g*u, and 0 <= u < p. Likewise, let d be the maximum integer such that S[-m*d] = -g*d, and 0 <= d < p.

Let U = uP, and D = dP. The UDP notation for a given mode of an MOS is U|D(P). If P=1 we may omit it and just write U|D."

- **mbattaglia1** November 18, 2011, 04:53:50 PM UTC-0800