Re: Diatonic notation system

[Graham Breed]

2008/12/9 Hans Aberg <address@hidden>:
> On 9 Dec 2008, at 13:42, Graham Breed wrote:
>>>>>
>>>>> 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.
>
> Not using key signatures will not solve that problem.

I didn't say anything about not using them -- although, as it happens,
they are trouble in microtonal music.  What I said is that they lead
to confusion.  The main point is that learning contradictory meanings
for existing symbols has a higher cognitive load than learning new
symbols.

>>>> 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?
>
> Rather which accidentals do you use?

It depends on what system you use, doesn't it?

Incidentally, JI notations won't usually work with the Lilypond model
because it only allows a single glyph for each alteration.  Pure
sagittal can still go a long way though.

> If transposition calls for say a comma below an m, and that m is computed
> not against E53, but E12, I think there might be an error. I leave it to you
> figure out. By contrast, if it is in E53, then I know it is right, and I do
> not have to do that exercise.

Transpositions aren't "computed against" any equal temperament.  If
you transpose by a comma, then a comma will be added or subtracted
from the previous alterations.  The resulting alterations will be
calculated according to the grid you specified.  If you defined
accidentals for them, those accidentals will be shown.  Maybe there's
an error -- if you find it, report it as a bug.

The difficult case is the most common one where a transposition moves
from one scale degree to another.  In this case it can be separated
into a "microtonal transposition" -- specified according to the
alterations -- and a "diatonic transposition" -- where Lilypond will
use chromatic scale steps.  A diatonic transposition will only lead to
a change of alteration of M-m.  (I hope this is obvious.)  Lilypond
will identify this interval as a "half step" and add or subtract 1/2
from the alterations.  As long as you defined your alterations so that
M-m=1/2 then all will be well.

>>> 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.
>
> Since the name diesis has many uses, you will have to elaborate.

Since even the name "enharmonic diesis" has more then one use even in
a meantone context, I did elaborate.  I got the definition wrong
though, because I said it was 1 step from 50.  It should be 2 steps so
maybe that's what confused you.  It's 1 step from 19, 31, 43, 55, and
so on adding 12 each time.  In M and m it would be 2m-M I think.

>> 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.
>
> In E31m these are 4 tonesteps, so the difference with M is one E31 tonestep.

Yes, but I wasn't talking about E31, and the interval I was talking
about is 3 steps from E31.

>> 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?
>
> If you want to have the tonestep between Db and D, that is a neutral second,
> generating a symbol for an intermediate pitch.

That's true, but nothing to do with what I was talking about.

>>> 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.
>
> So that would then work with the method I gave.

I didn't say it wouldn't.  But, in fact, it wouldn't.  Your
Pythagorean notation would make the comma below E indistinguishable
from Fb.


                          Graham