Pitch Raise

[Don]

Hi Marshall

Here are some things to memorize and then gestalt.

Ratios (mostly approximate but useable):

Unison 1:1
Octave 2:1  
Fifth 3:2
Fourth 4:3
Major third 5:4
Minor third 6:5

http://hyperphysics.phy-astr.gsu.edu/hbase/music/mussca.html

The reason ratios are good to know is that they "give" the lowest common
partial. For example the fifth between d4 and a4 will have a common partial
at a5. If one knows where to listen it really does make life a lot easier.
In the case of the fifth again for example there is a strong second set of
coincident partials at the 6:4 level (or a6). If one tunes the a6 partial
the fifth will not be the "width" intended.

The other reason ratios are so important is that they, when used in
contiguous interval ladders, will tell us how fast the beat rates need to
be. For example in a "ladder" which has f3:a3 and a3:c#4 the lower third
will beat 4 times in any time period and the upper third will beat 5 times
in that identical time period. This allows the piano to determine the beat
rates rather than the tuner "forcing" an arbitrary number on it. Have a
look here for a very nice "self correcting" temperament (and many other
"goodies" as well):

http://www.accu-tuner.com/SATIIImanual/sat3manual.html

It will be very useful to be able to quickly "parse" the partial structure
of any note. Here is an example:

C1:c2:g2:c3:e3:g3:b3:c4

As we can see these correspond to some musical intervals. As we get higher
and higher the intervals drift farther and farther away from the tempered
scale used on keyboards. Musically speaking the "leaps" are (approximately):

C1
Octave
C2
Fifth
G2
Fourth
C3
Third (large)
E3
Third (small)
G3
Third (very small)
B3
Second (large)
C4

Octaves:

Octaves have many coincident partials besides the "base pair" of 2:1.They
become larger as the coincident partials increase. It is rare in "real
life" tuning to use an octave that is as "narrow" as 2:1. Here are some
examples of octaves and their coincident partials and where to "listen" (or
ghost them)

2:1 = C1:C2 listen at c2
4:2 = c1:c2 listen at c3
6:3 = c1:c2 listen at g3
8:4 = c1:c2 listen at c4
10:5 = c1:c2 listen at e4
12:6 = c1:c2 listen at g4

It would be rare to use the extremes at either end of this chart.

Using coincident partials it is possible to "design" aural tests for all
sorts of intervals using a "third" note-just as is done when "setting" a4
to a fork (or other pitch source).

Remarks:

Some tuners seem to be able to do a wonderful job of tuning without any of
the above information, and some may consider this "path" limiting in some
ways. (for example listening to the "whole sound") But on the whole if this
information is used then learning tuning becomes much easier for we mere
mortals.

At 07:42 AM 1/8/2006 -0500, you wrote:
>Hi Don,
> I understand the note placement, such as a1 or c4 etc.  I understand some 
>about partials etc, but when I'm tuning, I just let my ear tell me quiite a 
>bit as well.  They're pretty keen.  It is intereesting how the partials 
>work.
>Marshall

Regards,
Don Rose, B.Mus., A.M.U.S., A.MUS., R.P.T.
Non calor sed umor est qui nobis incommodat

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