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Re: Diatonic notation system

From: Hans Aberg
Subject: Re: Diatonic notation system
Date: Tue, 9 Dec 2008 13:15:13 +0100

On 9 Dec 2008, at 11:57, Graham Breed wrote:
The format should be such that it can be sued by sound generating programs.

Do you have a patch?

Then I would not need to mention it here as an idea, would I.

When a musician's reading the notation, they're not looking above or
before the key signature. They're looking at the notes. So the notes
should look different to remind the musician that they should sound
different.  Otherwise it can get confusing as you switch between

That is not how it is done in current Western musical notation with respect to tuning, which has been in use from around 1600. But you can always invent
something new.

No Western musical notation I know of includes a specification of the tuning.

Right, the notes look the same, though performed differently.

And key signatures make the notes sound different.

Yes, and it's a classic cause of errors in performance, despite the
key being reinforced by the music.

If you don't know how to read them.

But it is obviously a matter of notational taste.

No.  Some systems really are easier to learn and use than others.

Well, the Western notation system is not an easy to learn system.

Then I am not sure what a two generator system is: is it not just the
generated Abelian group?

It is.

OK. Thanks.

 Elsie Hamilton, Harry Partch, Lou Harrison, Terry
Riley, La Monte Young, Kraig Grady, Toby Twining, Greg Schiemer, all
passed you by?  You don't know about the hexachords Willaert
supposedly used to get just intonation performances?  And yet you're
happy to tell the Lilypond developers how they should implement their
microtonal support!

So how do they notate if a say piece in C major modulates to D major?

They always, or even generally, write in major keys.  Willaert, in
particular, was writing before major keys were defined.  But let's
assume they'd notate it as just intonation.

But the question is how to notate a change a key from C to D.

Yes.  Hence Sagittal, HEWM, Extended Helmholtz-Ellis, and Johnston's
notation.  They won't work with your system. They will work for
printing with the current Lilypond system and third-party fonts. They would work for MIDI if Lilypond allowed the tuning of the nominals to
be specified ... and MIDI didn't suck quite so much.

What do you mean here. In Sagittal
The Sagittal notation uses a conventional staff on which the natural notes
are in a
single series of fifths, with sharps and flats (and doubles thereof)
indicating tones that
are members of that same series, regardless of the particular tonal system
notated2. Therefore, if the notation is used for just intonation, these
notes will indicate a Pythagorean tuning.

That is what my system does.

No, your system, at least as you describe it, only has two generators.
 Sagittal allows for systems with any number of generators.

No, the first two m M are used generate the staff system and sharps and flats.

Then one add a suitable number of neutrals n_1, ..., n_k to get the intermediate pitches.

For example, putting n = M3 - M gives an accidental suitable for Just relative Pythagorean.

If it now can produce other than multiple of 12.

Do you have evidence that it ever didn't work?

I attached file, you can try to tweak it into proper E53 if you like.

That file plainly isn't for a western notation system.

It is for Arab music.

Abstract m M surely does.

How can it possibly do so?  Tell me!  C to Db is M.  C to the diesis
above C# is M.  How does abstract m and M distinguish M from M?

C to C# is M - m, C to Db is m.

C to an E31 above C#, can be described as a double flat. double sharp, or by adding a neutral second, all having different musical function.

So, Lilypond being a notation program, you aren't worried about the
pitch fine-tuning?  It already does what you want.

I wasn't able to get E53.

You said you weren't worried about pitch fine-tuning.

I want to be able to produce the right output with narrow m's.

Ozan Yarman and Nail YavuzogĖ†lu mentions the problems they perceive.

And Ozan plainly does not say that somebody else's system would be better.

One a of the paper makes a comparison of three different system.

Otherwise, I know roughly how new translations can be done. And it is very hard to translate E53 back to intervals letters, especially in the presence
of variable scale degrees.

What does this have to do with Lilypond?

It would then be easy to typeset.

But anyway, such a letter system can be used for notating without tying to a tuning like E53. But translation back is difficult - try that on those that
Scala lists.

So the model doesn't describe the right tuning.  The goal is to notate
the correct tuning.

Which fails, because one can use different tunings.

Of course it does! C-D is 9 steps, D-E is 8 steps, if C-E is to be a
pure major third.

E53, in Scala is the Pythagorean notation system. The one you indicate would
have to be given a different name.

It doesn't matter how you notate it.  The music will have two
semitones of different sizes.

But i want to find out how you want to notate it: as E53 with intermediate pitches or a system where the note names have different interval values.


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