Music, mathematics, philosophy and tuning:
Harmonic theory pages
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See also, on piano tuning
on
falseness and paradigms for
the nature of piano tuning
why are pianos tuned to Equal Temperament
what makes a piano string vibrate ?
what is the theory of piano tuning ?
the place of piano tuning theory
for piano tuners
The piano tuner-technicians' area
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See also, on music and mathematics
music, mathematics and philosophy
background to the musical scale
natural correspondence and esoteric symbolism
on music, mathematics and tuning
on scales, tone, pitch (and piano tuning) with interactive media |
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Piano tuning - the essential idea Brian Capleton PhD
Updated 27th May 2007 © copyright Brian Capleton 2006, 2007
Page 4 go to page 1 here
Sound recipes affect both pitch and tone. A change in pitch usually requires a change in the recipe. (Not always, because, remember, pitch is also determined by the ear and the brain, so it is possible to have a change in pitch, while the recipe remains the same. For example, some people hear two different pitches, one in each ear, for the same sound).
If we change the pitches of the notes in a musical interval, even slightly, then we change the recipe for the musical interval. We therefore change the tone of the musical interval.
When we hear a musical interval that sounds "out of tune", there are at least two audible reasons it can sound "out of tune". The first is that the notes sound at the wrong pitches. The second is that the tone of the interval sounds wrong, or unpleasant.
One of the main factors affecting the tone of an interval is that its recipe may contain ingredients that beat, that is, the ingredients fluctuate relatively rapidly. This can have an effect on tone that we may find unpleasant. If you explore the rest of this site, you will find many sound examples of this.
This is why explanations of piano tuning invariably tackle the subject through the theory of beating, which involves the idea of beat rates. As I have already said, this theory is a nineteenth century theory based on the nineteenth century model of vibrating strings.
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