Re: Byzantine chant and microtones

[Hans Aberg]

On 6 Nov 2010, at 03:33, Erich Enke wrote:

> I just happened across a Sept 2010 post on lilypond-devel regarding
> microtones.  It reminded me how I've been wanting to work on Byzantine
> notation support for lilypond.  I would love to have a tool that could
> actually transcribe between western and Byzantine notation, and
> produce midis.  That would be amazing.

LilyPond focuses on staff notation, and may in the future have  
capacities for your needs. For example, there is some support for key- 
signatures beyond major/minor, also microtonal, but it is limited.  
There is an extension by Graham Breed to arbitrary scales, also where  
the diapason is not the octave, but it tied to a specific tuning.

> In Byzantine church music (not sure on other forms of Byzantine
> music), we have the following:
>
> 1) A notation that is completely relative, based on a particular place
> in a scale (roughly analogous to saying "Start on fa").  There is no
> notion of absolute pitch whatsoever.  Just interval.  This allows for
> easy accommodation of the same music to different chanters' voices
> without transposition.  Likewise, there is no necessity for a key
> signature.  Only scale.

It is mostly the interface that is is absolute, but the underlying  
pitch model need not be so, even though one must have some reference  
point. If one outputs a MIDI file, one still needs a tuning note.

> 4) A multitude of standard (within Byzantine chant) scales, which have
> microtonal intervals.  Many Byzantine music theoreticians break down
> an octave into 72 "moria".  6 moria are a Western half step.  But
> different theoreticians differ on the exact spacing.

It seems that the suggest to use E72 (72 equal temperament). In  
Turkish music one is using E53, where the minor second is m = 4, and  
major second M = 9, which in turn is just a very good approximation of  
the Pythagorean tuning. One can in fact move to a more abstract model,  
which does not assign specific values to these defining intervals  
until later when producing an audio file, but currently in LilyPond,  
it is tied to specific tuning.

> 5) To make matters more tricksy, Byzantine music isn't even
> octave-based.  So, when you extend beyond these ranges, there are
> standard expected intervals, but they're predictable on a
> tetrachordal, trichordal, or pentachordal basis, not on octaves.

This happens in Georgian singing and Arab maqam, too. But it seems me  
that the interval ratio 2 still may appear say when letting male and  
female voices or letting a violin play with an oud.