7 - Limit Just Intonation

[Jason Kanter]

Done. Interesting challenge. Here are the offsets with A at 440:
C +15.64
Db -13.69
D +19.55
Eb +31.28
E +1.96
F -31.17
Gb +5.87
G +17.60
Ab +29.33
A 0.00
Bb -33.13
B +3.91

His tuning instructions start with "First lower the pitch of the 'A' by
approximately one half step" ... e.g. 100 cents south. Unless they are
complete sticklers for his method, I would not do this. I suspect the reason
is to reduce the total strain on the plate. Actually all you need to do for
that purpose is lower A (and all the other offsets) by 4 cents.

With one exception, the ratios are all perfect fifths and perfect thirds, so
I would check your temperament, after setting it with your ETD, following
his instructions. The only non-standard ratio is 7/6 for G minor, where he
wants you to align the 7th partial of G with the 6th partial of Bb.

So the manual tuning sequence that *ought* to be achieved by the above
offsets is this:

Tune A4 and A3. All the following occurs between G3 and G4.
Tune E from A, beatless.
Tune C# from A, beatless M3.
Tune C from E, beatless M3.
Tune G4 and G3 from C, beatless.
Tune D from G, beatless.
Tune Eb from G, beatless M3.
Tune Ab from Eb, beatless.
Tune B from G, beatless M3.
Tune Bb (6th partial) to G (7th partial) beatless.
Tune F to Bb beatless.
Tune F# to D, beatless M3.

Another note from the instructions: "Tacks are to be inserted into each
hammer at the striking point so as to create a pseudo-harpsichord sound.
Either an upright piano or a grand piano may be used." This makes me sad.

As with all just tunings, only certain keys are usable. In this case, the
major keys of C, G, A, Ab and the minor keys of Cmin, Amin, Emin, Bmin are
completely pure (the triads are beatless) ... and almost everything else
will sound horrible.

On 1/18/07, Jason Kanter <jkanter at rollingball.com> wrote:
>
> I have located the tuning instructions online (
> http://www.areditions.com/rr/rra/a031Corrs.pdf) and will calculate the
> cents for you now..
> Jason
>
>
>  On 1/18/07, Jason Kanter <jkanter at rollingball.com> wrote:
> >
> > Send me the tuning instructions and I can convert them to offsets for
> > you. /Jason Kanter
> >
> > On 1/18/07, Thomas Cole <tcole at cruzio.com> wrote:
> > >
> > > Dear historical temperament mavens,
> > >
> > > I've been asked to tune a "tack" piano according to Lou Harrison's
> > > instructions (Cinna, 1955). The schema calls for tuning intervals as
> > > ratios and I'd like to know if there is a way to convert these
> > > fractional numbers to offsets. I have only a short window of time on
> > > stage (Sat, 1/20) and it would be very easy to do if I can use RCT.
> > >
> > > Tom Cole
> > >
> > >
> >
> >
> > --
> > =cell 425 830 1561=
>
>
>
>
> --
> =cell 425 830 1561=




-- 
=cell 425 830 1561=
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