Real-Life Math
"The job for a piano tuner is to equally space the notes apart from
one another, so that any music can be played and sound harmonious," says Paul
Brown, a registered piano repair technician.
There are two ways of
spacing the notes: using a device, and not using a device.
"If one
uses an electronic device, it will mathematically space the notes apart and
be very rigid in its placement. The human brain can mathematically space notes
equally apart, but also takes into account imperfections in the music wire,"
explains Brown.
"This difference is small, but audible to the human
ear. I prefer tuning 'aurally' with my ears over an electronic device for
most of the piano. I'll only use an electronic device in the high octaves
of the piano, where hearing is a little difficult because of the high frequencies
involved."
Brown counts "beat rates" when he tunes a piano. "I listen
to intervals: 4ths, 5ths and octaves.
"This means that a tuner has
to be able to count from 1 to 10 beats per second. When you're first learning,
you would probably use a watch to make sure you were accurate in your counting.
After a while, however, you get so used to counting that you actually stop!
You eventually tune by simply 'feeling' the beats."
A tuner also has
to understand the physics and math of harmonics -- especially when using an
electronic tuner.
Each note has a particular frequency -- cycles per
second -- which is the result of the oscillation of the piano wire. For example,
the note A440 has a frequency of 440 cycles per second. The higher the note,
the higher the frequency.
You can calculate the frequency of a note
by multiplying the frequency of the previous note by 1.059.
If the
note B7 is measured at 3,951.066 cycles per second, what is the frequency
of the next note higher, the C8?
If you would like to try this again,
determine the frequency of C sharp 1, if C1 is 32.703 cycles per second.
If
the frequency of C5 is 523.251, what is the frequency of C sharp 5?