Re: accidentals for just intonation

[David Kastrup]

"Phil Holmes" <address@hidden> writes:

> I have quite an interest in intonation, and my degree dissertation was
> based on the study of musician's reaction to just and equal tempered
> music, and was created using LilyPond.  However, I'm not clear why you
> believe that accidentals in non-equal temperaments require different
> signs (I think that's what you're proposing here).  It's said that
> early music was based on one or other form of just temperament, and
> used normal accidental signs.  To me, they indicate that the music is
> altered to the next higher or lower semitone in the key and
> temperament being employed: so why are other signs needed?

Well, Urs' printing of the cents does have educational purpose.  For
example, I can spell out the tuning of a guitar done by pure harmonics
(the highest-sounding two strings in relation to harmonics of the
lowest-sounding one):

e, as a, * 3/4 (e, +2)
a, as a,       (a, +0)
d as a, * 4/3  (d  -2)
g as d * 4/3   (g  -4)
b as e, * 3    (b  +4)
e' as e, * 4   (e' +2)

And if that kind of information is spelled in a scale, it becomes
obvious why G major and E minor chords have a problem sounding good out
of the box if you tune to perfect harmonics.  Because the interval g-b
should end up as -14 (!) in order to be a pure third, but actually ends
up as +8, a discrepancy of 22 cent.

Which explains why my default manner of tuning a guitar, namely just
tuning each string to sound as I think it should in relation to the
sequence of previous strings, has a good chance to end up more playable
than the followup work of a "serious" guitar player believing in tuning
by using harmonics.

In the scheme of talking about tunings or ad-hoc modifications, a scheme
like Urs' that can accommodate basically a continuity of values
certainly has some merit.  As a continuous notation for the sake of
playing, I think it would end up a nuisance.

-- 
David Kastrup