Re: Diatonic notation system

[Graham Breed]

2008/12/9 Hans Aberg <address@hidden>:
> On 9 Dec 2008, at 03:13, Graham Breed wrote:

>> Lilypond code is already semantic markup for music.  Your intermediate
>> file would end up looking a lot like the original.
>
> If that would be the case, it would be not point, right?

Right.

> The format should be such that it can be sued by sound generating programs.

Do you have a patch?

>> 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.

> 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.

> But it is obviously a matter of notational taste.

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

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

It is.

>> No, your system will not always work, as I've said, because diesis
>> shifts introduce more equivalences.  What example do you have where
>> Lilypond's transpositions don't work?
>
> Then you will to give a reference what intervals are produced by a say a two
> generator system.

You know about M and m.  Why do you need a reference?

>>> One example is Just intonation. The major seconds between C-D and D-E.
>>> But
>>> here the tradition is to just forget about it, temper the difference out.
>>> -
>>> I do not know about any specifically Just intonation music.
>>
>> You what????????? 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.

>> 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.

>> Okay, I know how to transpose.  What I'm asking is why it doesn't work
>> for you in Lilypond.  The way Lilypond does it looks fine to me.
>
> If it now can produce other than multiple of 12.

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

>>> Right, But I think that is the limitation of the Western notation system.
>>> And normally, I think one tempers it out, performing in a diatonic
>>> system.
>>
>> That's what Lilypond does.  You should be quite happy with Lilypond as it
>> is.
>
> It did not work when I tried it - see the file I attached. I was quite
> unhappy - I gave up.

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

>>>> And there are plenty of cases where the same pitch can be
>>>> written different ways for a rank 2 tuning.  Like a meantone notation
>>>> with a new symbol for "diesis" shifts (1 step of 31, 50, 43, etc).
>>>> You could write Db as the diesis above C# and you want it to stay like
>>>> that.
>>>
>>> Those are E31 enharmonic equivalents. A true meantone might use M =
>>> sqrt(5/4).
>>
>> They're equivalents in either E19, E31, E43, E50, and so on.  The
>> tuning doesn't matter.
>
> If know LilyPond can handle it. But ET's are just tuning intermediates for
> the music, not describing the musical intent.

That's right.

>>> If you introduce enharmonic equivalents, or specific symbols for
>>> tonesteps,
>>> then it is tied to that tuning, and it cannot be retuned without lifting
>>> it
>>> to the diatonic structure.
>>
>> No.  In this case the equivalents (call them enharmonic if you like)
>> are not tied to the tuning.  The current Lilypond system allows them
>> to be distinguished but an abstract M m wouldn't.
>
> 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?

>> 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 don't know that "the Turks" are of a single mind on this.  Last I
>>>> heard Ozan was looking at 41-equal because the 79 from whatever system
>>>> was too complicated.
>>>
>>> It is a mess. So I think a system like Farhat's or the Arab would be
>>> best,
>>> and then indicate details as intonations or choice of tunings.
>>
>> Maybe the actual system they're notating is a mess when you try to fit
>> it into your theories, because it wasn't developed according to those
>> theories.
>
> Ozan Yarman and Nail Yavuzoğlu mentions the problems they perceive.

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

> 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?

>>>>> So that illustrates the problem of having notation tied to a specific
>>>>> tuning.
>>>>
>>>> Does it?  What notation could possibly have handled these makams
>>>> without tying itself to the tuning?
>>>
>>> The Arab, Persian or the older system with letters, as here
>>>  http://en.wikipedia.org/wiki/Makam#Intervals
>>
>> No, those specify a division of the whole tone into 9 commas.  They're
>> tied to the tuning of a comma.
>
> My impression was that those letter existed before, and an E53 translation
> was done afterwards, resulting in A's of different sizes.

So they started out notating a tuning.

> 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.

>>>>> But when playing this, I think two M's of different sizes in succession
>>>>> sounds weird. So it does not bother me, too much. :-)
>>>>
>>>> It's a problem that's bound to arise with a 53 note system.
>>>
>>> E53 does not have this problem.
>>
>> 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.


                         Graham