Equal temperament is most widely used today, and the one most familiar
to us.  Temperament within an octave must be established before any
tuning is considered.  Temperament is the mathematical relationship
between notes within an octave (the spacing).

Few people are familiar with other exotic temperaments such as
Werkmeister or Meantone.  Equal means just that: equal spacing between
the notes of an octave.

Other temperaments are not equal and contain fractional and uneven
spacing.  These non-standard temperaments can give the impression that
something is wrong, to those who are used to hearing equal temperament
in the majority of musical instruments in the modern world.

Pitch is the level at which a tone is raised or lowered.  For a
reference, the use of A=440 Hz is a good starting point.  This means
that there are 440 vibrations per second in the sound of A above middle
C on a piano (or above middle C at an 8' pitch on an organ).  I am not
sure about the date, but early pianos were tuned at A=435 pitch, and
some even lower.  These pianos were not designed to be raised upward
to A=440; although some tuners do this, I have refrained from doing
so, because of the increased tension upon the frame and/or the cast
iron plate.

The interesting part about piano tuning is that the tuning is not
precise, and differs from one piano to another.  As one progresses
up the scale, octaves require stretching, which is increasing the pitch
a very small amount.  Theoretically, if A equals 440 Hz, the A in the
octave above should equal 880 Hz, however this is not necessarily true
-- it depends upon the piano.  It is definitely expanded to 881 and
upward or more as one ascends the scale.  It all depends upon how well
it sounds to the tuner.

It is my feeling that some of the modern programs for electronic visual
and computerized tunings have built-in octave stretching based on a
formula taken from a sample from a variety of pianos.  It is an
estimate, and comes close to being acceptable.  Some programs may not
include this stretching.

In regard to band organs, I have only tuned a few (many years ago),
but these band organs that I tuned contained a glockenspiel.  If my
memory is correct, I believe that the bar on the glockenspiel was
printed A=440.  Since a glockenspiel does not go too far out-of-tune,
it led me to believe that the entire organ was meant to be tuned at
A=440.  Interestingly, one band organ owner had the bars of the
glockenspiel nickel plated!  The plating destroyed the tuning, which
required having the glockenspiel re-tuned.

I recall some pipe organs containing a harp or chimes marked A=435.
It is important to check these percussive instruments before starting
the tuning.  There is nothing worse than an organ tuned at A=440, and
the chimes or harp tuned at A=435.

All in all, the majority of people haven't a clue whether an instrument
is in tune or not.  Recently I was having dinner in a fine restaurant
which had a pianist.  The music was excellent, but the piano was a
horror.  There were bass notes at least a quarter tone flat!  (Also
four or five dampers were missing.)  I spoke to the pianist, who told
me that she dreaded playing on such a poorly-tuned piano, but the
management thought that it sounded just fine.  Not one patron in over
two years ever made a comment that the piano was out of tune!

To me, the music was being ruined by all the sour notes.  It was
actually painful for me to hear.  For her Christmas gift, I spent a
great deal of time tuning and adjusting this piano.  I am convinced
that she and I will be the only ones who will notice any difference.
Sad but true.

Bruce Clark