[NewMusic] microtones

[Chris Broderick]

In the book Temperment by Stuart Isacoff (which is a
good historical overview of the rise of equal
temperment, if not terribly clear on the technical
aspects of intonation) the author claims that outside
of a harmonic framework that underpins what they do,
singers will tend to go towards the pythagorean 5th
rather than the equal tempered one.  I dunno if I buy
it, but that's what he sez...

The best part of the book IMHO, are the pictures of
the weird keyboards that were created with extra or
other keys to have both pythagorean 3rds & 5ths as
well as well-tempered ones.

-Chris


--- David Slusser <slusser at pixar.com> wrote:

> Anybody look at where singers place the third?
> 
> On Jan 12, 2007, at 7:18 AM, Jon Raskin wrote:
> 
> > an in tuned third feels way better than a theory.
> >
> >
> > ----- Original Message ----
> > From: Amar <amar at ptank.com>
> > To: Bay Area New Music Discussion Group
> <newmusic at music.mills.edu>
> > Sent: Thursday, January 11, 2007 8:56:06 PM
> > Subject: Re: [NewMusic] microtones
> >
> >
> >> Perhaps it turns the whole history of tuning
> theory on it's head. . .
> >> or perhaps not. . .
> >
> > Or perhaps perfectly consonant 5:4 thirds are not
> that important,  
> > compared
> > to fifths and octaves...
> >
> >   -Amar
> > (who believes that major 3rds ruined music theory)
> >
> >
> >
> >
> >
> >
> >> On Jan 11, 2007, at 2:50 PM, Jon Raskin wrote:
> >>
> >>> How is a just third derived?
> >>
> >> It's two frequencies that have a 5:4 ratio: for
> example the lower  
> >> note
> >> is 500 Hz, the upper note is 400 Hz.  It is
> comparable to the 5th
> >> partial in the overtone series.
> >>
> >> This is why what is often called "just" tuning is
> really a 5-limit
> >> tuning, based on Perfect 5ths (3:2) and Major
> 3rds (5:4). A typical
> >> 5-limit tuning for a C-Maj scale would take F
> from a 3:2 below C, G a
> >> 3:2 above C, and D a 3:2 above G. E would be a
> 5:4 above C, A a 5:4
> >> above F, and B a 5:4 above G: you therefore end
> up with in tune  
> >> tonic,
> >> dom, subdom, mediant, and submediant chords: the
> scale in ratios  
> >> would
> >> work out 1/1, 9/8, 5/4, 4/3, 3/2, 8/5, 15/8.
> >>
> >> The point of mean-tone tuning was to temper the
> 5ths slightly so that
> >> you could get a bunch of in-tune Maj. 3rds,
> "in-tune" being the 5:4
> >> ratio. That's why I find it fascinating that in
> practice players tend
> >> toward the Pythagorean 3rd (at least according
> the book The  
> >> Acoustical
> >> Foundations of Music), since in theory they
> should tend toward the  
> >> 5:4.
> >> Perhaps it turns the whole history of tuning
> theory on it's head. . .
> >> or perhaps not. . .
> >>
> >> _______________________________________________
> >> Bay Area New Music Discussion Group
> >> NewMusic at music.mills.edu
> >> http://music.mills.edu/mailman/listinfo/newmusic
> >>
> >
> >
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> > NewMusic at music.mills.edu
> > http://music.mills.edu/mailman/listinfo/newmusic
> > _______________________________________________
> > Bay Area New Music Discussion Group
> > NewMusic at music.mills.edu
> > http://music.mills.edu/mailman/listinfo/newmusic
> _______________________________________________
> Bay Area New Music Discussion Group
> NewMusic at music.mills.edu
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