Disklavier

This post will try to explain why the tuning on your piano may not perfectly 
match the tone-generated ensemble sounds.  However, if the piano is properly 
tuned, the differences should be barely noticeable.  Piano tuning theory 
differs from reality because piano wire has actual stiffness.  Harmony is a 
system of compromises, and many musical schemes  have been used over time, 
i.e.  Meantone, Well-Temperament and Equal Temperament just to name a few.

The great mystery discovered by Pythagoras over 1500 years ago was that you 
can\ufffdt tune  strings by the numbers.  If you take a string and pluck it, you 
get a Fundamental tone.  If you pinch it in half you get a tone that is one 
octave higher; pluck that segment in half and you get another octave higher, 
etc.  Do that 8 times and the value of the frequency for  that highest tone 
equals \ufffdx\ufffd.  Now take the same string and this time pinch it in thirds 
(instead of halves).  Do that 12 times and you get the Circle of Fifths, 
which are the 12 tones that make up the octave.  However, the great mystery 
is that when you get to \ufffdx\ufffd it is now 33% higher!  This significant 
deviation was known throughout musical history as the \ufffdwolf\ufffd and threw any 
tuning of stringed instruments into a tizzy until about 1918.

Where to start was a big problem.  No matter what key you picked to start 
the tuning, only half the tones were musically useable.  Keyboard 
instruments were finally laid out in the key of C and are still that way 
today.  All the tuning compromises were done on the black keys, or the \ufffdhalf 
tones\ufffd.  There was a huge difference between the color and mood  of each key 
signature, and you could only play music written for the way your piano was 
tuned.

As time went by, musicians wanted more out of their music.  Everytime the 
\ufffdwolf\ufffd could be reduced, more keys became musically available for 
composition.  Bach wrote his 26 Inventions because there were only 26 ways 
he could play with the harmony.  During his lifetime, a new tuning system 
appeared called Well Temperament, so he wrote music for it called the 
Well-tempered Clavichord. Mozart had more tones to work with, and Beethoven 
had even more harmony at his disposal because tuning systems had found a way 
to further reduce this \ufffdwolf\ufffd.  However, no tuning system was \ufffdall purpose\ufffd 
until the early 20th century with the use of Equal Temperament.  By this 
time calculus had been invented, and a system for making each tone on the 
keyboard equidistant was in place.  Today, this tonal distance is 1/12th the 
square root of 2.  However, now that we use a one-size-fits-all temperament, 
our music has lost the color that individual key signatures once gave it.  
No matter what key signature the music is written in, they all sound the 
same today in Equal Temperament so we only hear our music in 
black-and-white.

Because piano wire has stiffness, the numbers will never match the 
theoretical values.  For instance, the A above middle C is set to a standard 
pitch of 440 hertz.  In theory, the A an octave below it would be tuned to 
220 hertz.  A very clean stringing scale might have this lower A tuned to 
222 hertz before the octave is \ufffdbeatless\ufffd.  A tuner would then need to 
spread out this 2 hertz difference over the 12 tones in the octave.  There 
can be as much as a 15 hertz difference among different piano brands and 
models.  A graph of a well-tuned piano that is pleasing to the ears does not 
look like a perfect horizontal line.  The line would be at an angle, with 
the bass tones starting about 30 cents flat and the high treble tones 
gradually increasing to 30 cents sharp.  Each piano will have its own 
anomalies.

Tone generators are pretty much bound by the mathematical values assigned by 
MIDI.  It probably makes a difference if the \ufffdsampling\ufffd was done on a 
Steinway or a Yamaha piano for the bass and high treble notes.  Yamaha 
pianos have a very clean tone with very little stretch in the octaves; 
Steinways have a large amount of stretch with a very verve sound.  However, 
XG tone generators were sampled on Yamaha pianos!

A piano tuner sets the pitch of the piano \ufffd the standard international pitch 
being A=440 hertz.  If your piano sits in a humid room, and measures out at 
A=442 in the middle of the summer, it might be prudent to leave the pitch 
alone knowing that it will probably drop to A440 as soon as the heating 
season starts.  Often in the middle of the winter, pianos can be 25 cents 
flat.  This is why piano technicians recommend climate control for the 
piano.  Tuning forks can change their pitch if they are dropped or get 
bumped by the other tools in the tool kit.  They also change their pitch 
with the temperature.  The dial tone on the telephone is close to A440.  You 
can always use the M tune feature on the Disklavier to help compensate for 
the pitch fluctuations of the piano.

Using a computer to tune a piano lets you see what you are hearing.  You can 
instantly see what is going on with the piano pitch; calculate the perfect 
tuning for that particular instrument and can show the piano owner how the 
pitch is affected by the humidity or lack of it.  But the most wonderful 
thing a good tuning program will do is calculate the historic temperaments 
we almost lost so we can hear the music the way the composers heard it!

Piano tuning is still an art \ufffd even when using a computer.  There is a large 
window of what is considered \ufffdcorrect\ufffd.  Not only does all this theory come 
into play when tuning, but also the physical adjusting of the tuning pins 
and the rendering of the strings.  No two tuners work alike, so you may have 
to try a few before you find one that makes your piano sound the way you 
want.


Carol Beigel
crbrpt@...


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