tuning octaves using partials

[Don]

Hi Gary,

The partial series for A3 is:

1           2       3     4     5    6 
A3          A4      E5    A5    C#7  E6

The partial Series for A4 is:

             1            2          3      
             A4           A5         E6

So an Octave that is "beat free" at the 6:3 level would have the coincident
partial at E6. These partials are only "around" that pitch not necessarily
*exactly* at that pitch.

Make yourself a Coleman Slide rule with two pieces of cardboard marking the
first 8 partials and it will be very easy to see where the partials "line up".

As to when to use them, that is a matter of taste. Generally speaking the
middle of the piano will be 4:2 and the bass on most instruments 6:3.
Ideally there should be a smooth progression from 6:3 to 2:1 I.E. 6:3 to
(smaller than 6:3 but larger than 4:2) to 4:2 to (smaller than 4:2 but
larger than 2:1). On some lovely pianos the 6:3 in the low tenor is beat
free at the same time the 4:2 is beat free. This makes the transition very
easy, but most often we are not that lucky. Particularly at the extreme
ends these suggestions become increasingly a matter of taste. On larger
pianos 12:6 or even 14:7 might be used in the very low bass. Few tuners in
the real world use 2:1 even at the very top octave.

One tuner suggested listening to the intervals. I think he means you should
try playing the octave "broken" I.E. play c7 and then play c8. This is
sometimes called "melodic" tuning. Of course partials are nearly useless
for that style of tuning. It is generally accepted that a "melodic" octave
may often be wider than the theory of "unison played" octaves using
partials to tune.

I do think a good understanding of partials is worth learning and it is not
rocket science.

One of the HT tuners on this list does tune C8 about 75 cents sharp--which
would be unlikely to be a 2:1 from C7. His clients like it. 

At 08:07 AM 12/3/01 -0800, you wrote:
>     How do I know when to  use which one?   I just don't know when to use
>one in place of  another. (I may know this, but I just don't know if I know
> it!) Thanks for any advice Gary McCormick 

Regards,
Don Rose, B.Mus., A.M.U.S., A.MUS., R.M.T., R.P.T.

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