octave test?

[Jim Coleman, Sr.]

Hi John:

When we listen to an octave, it is difficult to tell when a certain type
of octave match is at exactly zero beat (for ex. the 4-2 relationship). 
This is why we use the M3rd-10th test such as you cite below:
C4-E4 compared to C4-E5. With the faster beating intervals we can tell
quicker whether we need to raise or lower the E5. We would have to wait
for 8 seconds to tell if we had a 1/8 bps whereas if we listen to the
M3rd-10th test, we can tell immediately if the E5 needs to be raised or
lowered. BTW listening to the octave alone, we can't tell if it needs to
be raised or lowered, just that there is a very slow beat. So, now you can
see the distinct advantage of using the higher partials. You have no doubt
been hearing them all along, but were not conscious of them.

It is of course necessary as foundational information to know that the
following intervals when properly tempered all beat on the wide side of
zero:  M3rd, M10ths, 4ths, M6ths, minor 7ths. These next intervals normally
beat on the narrow side: minor 3rds, perfect 5ths, and minor 6ths. The 
tricky part comes when you have to consider that if you are tuning the
upper note of a M3rd and the coincident partials are beating too slow, then
you must raise that note. Conversely, if you are tuning the lower note of
a M 3rd and it is beating too slowly, then you must lower that note. This
is often confusing to the novice at first. The simple rule is: Think of
the interval as being expanded or contracted; if it needs to be expanded
more, raise the upper note or lower the lower note of expanded intervals,
and do the opposite for the normally narrowed intervals.

Jim Coleman, Sr.


On Mon, 19 Apr 1999, John M. Formsma wrote:

> Dr. Coleman,
> 
> Thanks for this information. I noticed that when I tuned the octave they
> sounded OK. But I know that an octave must be tested because the ear can
> deceive, especially with the octave. I did hear a slight "waver" when tuning
> the octave, but the beat was more perceptible when C4-E4-E5 were all played
> together. The beat was probably there all along, and my ear/brain will
> develop better discernment with practice.
> 
> Thanks,
> 
> John Formsma
> 
> -----Original Message-----
> From: Jim Coleman, Sr. [mailto:pianotoo@imap2.asu.edu]
> Sent: Sunday, April 18, 1999 10:45 PM
> To: John M. Formsma
> Cc: PianoTech
> Subject: Re: octave test?
> 
> 
> Hi John:
> 
> The slow beat comes from the 2:1 and 4:2 relationships of the Octave you
> are checking.
> 
> Jim Coleman, Sr.
> 
>