Re: Diatonic notation system

[Graham Breed]

2008/12/9 Hans Aberg <address@hidden>:
> 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.

Fine, you've mentioned it.

>>> 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.

Even if you know how to read them you are likely to make mistakes.

>> 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.

Write different notes?

>> 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.

Sorry, I was wrong.  You do have more generators.

>>> 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.

What does E53 have to with anything?  We were talking about correct
transposition.

>> 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?
[corrected]
>
> 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.

No, not an E31.  An enharmonic diesis.  m is not a double flat.
2(m-M) would be a double flat.  m is not a double sharp.  2(M-m) would
be a double sharp.  Adding a neutral second to what?  m is not a
neutral second.  m is, in fact, m.  How does abstract m and M
distinguish it 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 want to be able to produce the right output with narrow m's.

Then are you or are you not worried about pitch fine-tuning?

>>> 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.

Typeset what?  How does Lilypond make it difficult to typeset anything?

>>>> 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.

I'm not writing it.  If I did I'd probably use Pythagorean notation
with a comma accidental.  But I might use Erv Wilson's duodecimally
positive notation.


                                   Graham