Re: Intervals enharmony question

[Malte Meyn]

Am 30.04.2018 um 22:11 schrieb Hans Åberg:
> > On 30 Apr 2018, at 21:47, Malte Meyn <address@hidden> wrote:
> >
> > Am 30.04.2018 um 21:32 schrieb Hans Åberg:
> > > One has to adapt the pitch on every note played, and the reference is typically 
> > > the string section, which in turn is tuned in Pythagorean,
> >
> > Many string players tune their perfect fifths a bit small so that they’re near 
> > to equal temperament (700 ct) or even smaller instead of just (702 ct).
>
> So how do they tune their violins?

Tune a fifth perfectly just and then make it a little bit smaller. This 
of course needs experience so that it’s only 2 ct smaller.

> And why would an orchestra do this: it increases the beats in the chords.

It increases beats only in the fifths of open strings. All other fifths 
and other intervals in general can be adjusted by the players. And it’s 
nicer to have a 400 ct third C–E than 408 ct as a starting point for 
such adjustments.

> > > but can adapt into 5-limit Just Intonation if the music played follows the 
> > > Traditional Harmony rules.
> >
> > They could, yes. But I think that most intonation in choir and orchestra is not 
> > just intonation but more or less an approximation; for example leading notes 
> > are often played higher than just because they have more of the leading 
> > character then. And just intonation has other problems that make it impractical.
>
> It is adaptive JI: If pivoting the chord sequence C F Dm G C, it slips a 
> syntonic comma. So the orchestra must slide the pitch somewhere. Sounds 
> terrible on music like organs, though.

That’s one of the problems I had in mind. There are other reasons why 
just intonation, even adaptive JI isn’t really an option and is not what 
orchestras use to play: for example, enharmonic equivalents in 
modulation (like <c e g bes> = <c e g ais>) cannot really be intonated 
perfectly just.

> > > That becomes more difficult in distant keys.
> >
> > Why should it? Just intonation works in every key.
>
> Because there is no reference to the Pythagorean notes.

I’m not sure what you’re talking about here: What are these Pythagorean 
notes? Pythagorean tuning means using only perfect fifths, that’s not 
just intonation.