One of the technical areas of piano tuning, the temperament, is
described below. This is more information than some customers want.
However, there are some inquiring minds who love the details.
The Tempered Scale:
The piano temperament is a term in piano tuning that refers to the intervals
between notes on the musical scale. Every pitch can be derived, electronically
or aurally, from a relationship with a chosen fixed pitch source. One of the
first steps in piano tuning is to set one string per note of at least one octave to
the desired relationship with each other. This establishes the temperament
(basis) for tuning the remaining notes on the instrument.
When a piano has been tuned using an equal temperament, the octave
intervals have been divided into smaller steps, each having equal frequency
ratios between the adjacent notes. These are the smallest intervals in the
tempered scale that is commonly used in modern music. Each of these
intervals represent 1/12 the width of the octave and are referred to as a
semitone or half-step. In the modern tempered scale, the frequency between
each interval is perceived as being the same distance apart.
Before learning about the tempered scale, I wondered why classical music
often lists the key. For example "Piano Concerto in A minor" or "Chopin's
Piano Concerto in F minor". Why did these classical composers care what key?
The answer lies in the historical temperaments of that era. There are many
references to the tempered scale, its history, and examples of the historical
temperaments. Importantly, there is no such thing as no temperament (See
Temperament Figure 1) in a piano tuning scale.
To accommodate the imperfections in the scale, some "imperfections" must be
built into the tuning. Various historical temperaments cause a composition to
sound different depending upon what key it is played in. If played in a modern
equal tempered scale, the difference may be undetectable other than the
relative pitch reference. But in the original classical temperaments, the
difference is quite significant.
You can find considerable information on the historical temperaments. If you
want to hear the difference, you can search on-line for "same song in historical
temperaments" and you may be able to listen to recordings for comparison.
Below is a very simple diagram to show why there must be a temperament for
the piano scale. If you search for more information, you will find enough to
keep you reading and listening for a while.