Roots, Breaks, etc.

[Carol R. Beigel]

I would suspect, being mathematically challenged, that the reason the two
columns do not have the same number might be related to the Comma of
Pythagoras, discovered about 1500 years ago.  Pythagoris discovered that if
you take a string, pinch it in half - and keep pinching the sections in
half - when you have done this you get X.  An example would be to call the
string Czero, pinch it in half 12 times until you get  to C8.  You have also
arrived at C8 by way of the circle of fifths - 12 of them - and those are
the 12 tones in the octave.  Now, take the same string, start at Czero and
this time pinch the string at one third the speaking length (instead of in
half) and when you get to C8 it is about 30ish-something % higher in pitch,
or X + 33%.
This difference is known as the Comma of Pythagoras.

This difference of about 30ish-some percent is also known as the Wolf
interval.  Piano tuners have had to deal with this "wolf" since piano tuning
became a profession, gradually finding ways to reduce its size.  This is
what tuning in "historical" temperaments is all about.  Since the piano
keyboard (white keys) is laid out in the key of C, most tuning systems have
dealt with the "wolf" on the black keys.  It was once said that one could
tell the key signature of a piece just by listening to it and composers
throughout time have written music using these old tuning systems, taking
advantage of their various harmonies. Only in Equal Temperament are all of
the tones in the octave equidistant and all of the key signatures sound the
same.  We now listen to music in black-and-white instead of color.

Whether we use a Pentium chip, a set of tuning forks, or the wavelength at
NIST, being correct with the numbers is not what piano tuning is all about.
It's about how pretty we can make the music sound - and that includes
voicing!  Inside that window of what is "correct" lies our art.

Many thanks to all of you who have sent me good wishes as they have been
most appreciated.  Kristinn's post about partying in Sweden reminds me that
I
also came home with a healthy supply of that Icelandic Brenniven.  I might
investigate its "healing" properties when mixed with Advil to improve
circulation!  Of course, after reading the above discourse, you guys might
think I've already partaken!

Still not stir crazy,

Carol Beigel
Greenbelt, Maryland