Re: Diatonic notation system

[Hans Aberg]

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
> > > systems.
> >
> > 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
> > being
> > 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 Yavuzoğlu 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.

  Hans