RE: microtonal notation

[Bodo]

Dear Han,

I've looked at the documents at plainsound.de, in particular at
http://www.plainsound.de/research/notation.pdf. This seems quite complicated
but seems well thought-out at first glance.

> Unfortunately, noone has come up with a sensible idea for 
> linking both concepts, and I'm not familiar enough with 
> microtones to judge what is right.
> 
> What do you think of this idea:
> 
>   * each pitch may be adjusted with a 'cents property (which 
> is used in MIDI as well.)
> 
>   * each note is compared to the tonic of the scale
> 
>   * this difference, together with the microtonal adjustment 
> is used to select which microtonal accidental should be printed.
> 

That sounds reasonable. The cents property would be relative to the nearest
equal-tempered tone, right? That gives a maximum difference of + or - 50
cents. I have some software that calculates this exact cent value, but I can
imagine that this notation, while very precise, would be hard to enter for
many people.
An easier approach (for me, anyway), would be not to indicate the cent
number, but the harmonic number relative to a given fundamental tone.

Here is the harmonic series of the equal-tempered c in current lilypond
notation. It shows the nearest tempered tone, the cent difference to this
tone at the top, and the harmonic number at the bottom.

\version "2.6.0"
\score{
<<
\new Staff {
       \set Score.timing = ##f
       \override Staff.Stem #'transparent = ##t
  \clef treble
    s1 s1 g'1_"3"^"+2" c''1_"4" e''1_"5"^"-14" g''1_"6"^"+2"
ais''1_"7"^"-31" c'''1_"8" 
    d'''1_"9"^"+4" e'''1_"10"^"-14" fis'''1_"11"^"-49" g'''1_"12"^"+2"
gis'''1_"13"^"+41" 
    ais'''1_"14"^"-31" b'''1_"15"^"-12" c''''1_"16"
}  
\new Staff {
  \clef bass
    c1_"1" c'1_"2"  
  }
>>
}

Now it would be much easier to write something like this:

\harmonic-relative c { 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 }

Of course, the fundamental itself may not be well tempered, so this too may
have to be written as an interval to some other reference tone.

I guess the harmonic-relative notation would be very convenient for people
that specifically deal with overtone music. I'm not sure how useful it would
be to others. The general cent notation would be able to solve everybody's
needs, but be a pain to work with manually.

So far I have only talked about entering the notes. The other aspect of this
is of course the output. For my purposes it would be enough to simply use up
or down arrows to indicate a large deviation from the nearest tempered tone
(for example more than 20 cents). A more advanced project would be something
like the Helmholtz-Ellis notation, but that can be implemented later, as it
is independent of the method of note input.

 Bodo