PIANO TUNING - Page 3

What Does Tuning a Piano Mean ?

The relationship between two pitches, called an interval, is the ratio of their absolute frequencies. Two different intervals are percieved to be the same when the pairs of pitches involved share the same frequency ratio. The easiest intervals to tune are those that are just, which have a simple whole-number ratio. The term temperament refers to a tuning system which tempers the just perfect fifth (which has the ratio 3:2) in order to satisfy some other mathematical property; to temper a fifth, in this case, is to slightly narrow the interval by flattening its upper pitch slightly.

Tempering an interval produces a beating, which is a fluctuation of the intensity of sound heard when an interval is played. The rate of beating is determined by the difference of their absolute frequencies, and is heard clearly when two pitches are close enough together that this difference is small (less than 20Hz). Because the actual tone of a vibrating piano string is not just one pitch, but a complex of tones arranged in a harmonic series, two strings which are close to a simple harmonic ratio such as a perfect fifth will produce a beating at a higher pitch due to an interaction between their harmonic series'. In the case of an interval that is close to a perfect fifth, the strongest beating will be heard at 3 times the fundamental frequency of the lower string (known to musicians as an octave plus a perfect fifth up), and 2 times the frequency of the higher string (an octave up). Where these frequencies can be calculated, a temperament may be tuned aurally by timing the beatings of tempered intervals. One practical method of tuning the piano begins with tuning a set of strings in the middle range of the piano to a temperament octave. Once these strings are tuned, the tuner may proceed to tune all other pitches by comparing octave intervals against this temperament octave. This is convenient, because the octave is the most easy interval to tune (having the simplest ratio of 2:1) after the unison (1:1). (These octaves are tuned to have no beating.) The following table lists the beat frequencies between notes in an equal temperament octave. The top row indicates absolute frequencies of the pitches; usually only A440 is determined aurally. Every other number indicates the beat rate between any two tones (which share the row and column with that number) in the temperament octave. Begin by tuning one note to the other so that the beating disappears, temper that interval in the appropriate direction (either making the interval wider or narrower, see further below) until the desired beat rate is achieved. Slower beat rates can be carefully timed with a metronome, or other such device. For the thirds in the temperament octave, it is difficult to tune so many beats per second, but after setting the temperament and duplicating it one octave below, all of these beat frequencies are present at half the indicated rate in this lower octave, which are excellent for verification that the temperament is correct. One of the easiest tests of equal temperament is to play a succession of major thirds, each one a semitone higher than the last. If equal temperament has been achieved, the beat rate of these thirds should increase evenly over the range of the piano.