Beat Rates in music

[Richard Brekne]

Hi Don and thanks for the reply.

This is really interesting and as I, together with another
tech here in Bergen, am drawing up a similar course I would
love to get any advises or information you have from your
technical to help us out.  I suppose I should have written
that request off list, but I wanted to take the opportunity
to throw another twist into this "amount of Stretch"
discussion to include "type of stretch".

One of the things I have noticed in fooling around with a
"perfect 12ths" tuning is that the stretch curves for
different intervals are altered with respect to the basic
shape of these curves. Yet by and large the AMOUNT of
stretch is well within quite usual norms. In an octave
priority stretch (where we insure some smooth transition
from 6:3, to 4:2 to 2:1 octave types or the like) it is the
12th's and 5ths that waver around and not staying on a
smooth 2nd degree like exponential curve. But when you force
the 12ths to stay in a constant relationship as in pure,
then octave types waver a bit back and forth. On the other
hand the harmonics of the 5th and 12th are very strongly
reinforced in this scheme and the effect of this is quite
noticeable to the ear. 

I am not sure what the musicality use of this approach is
(though the tuning does sound very very good), yet from a
tuning pedagogic point of view it demonstrates very clearly
the point I am concerned with here, namely that it seems
clear that we have a lot more decision making power at our
disposal then it seems we often use when it comes to
"colouring" a piano through the tuning.

I also particularly liked what you had to say about
differences in stretch being more noticeable then variations
in temperament. This strikes a familiar note as it were in
my own experience. Thanks muchly.

Cheers !
RicB

Donald Mannino wrote:
> 
> Richard,
> 
> I have taught a technical seminar on this very subject,
> called "The Sound of your Tuning."  I tune 2 matched grand
> pianos with widely different stretches, and demonstrate
> the affect this has on the sound of the tuning overall.
> 
> It is my contention that the octave stretch style used has
> a much larger affect on the sound of the piano than the
> often subtle differences between temperaments.  The
> difference between  sloppy equal temperament and a careful
> equal temperament is rather hard to hear when playing
> music, but the difference between wide octaves and narrow
> ones is quite noticeable.
> 
> I do use different octave tunings depending on the
> situation and use and, to some degree, the tastes of the
> pianist.  I tune for some pianists who like a more
> aggressive sound from the piano that a wide tuning gives,
> while I have had others specifically complement me for the
> "warm" sound of my tuning, after having done my preferred
> narrower tuning style.
> 
> Don Mannino RPT
> 
>