![]() The system allows music in all keys, but at a price: all intervals other than octaves are slightly out of tune. Thus, by advancing a full octave, the frequency is doubled. With 12 semitones in an octave, this ratio is the 12th root of two. Western music is based predominantly on a tuning system called equal temperament, where the ratio of frequencies of neighbouring notes is constant. The amplitude gives the loudness of the wave, whereas the frequency – the number of pressure oscillations per second – gives the pitch or tone. They may be analysed into wave- like components, each being a pure sine wave with fixed amplitude and frequency. All sounds travel at the same speed, but they have many different patterns of pressure. Sound is a series of variations of air pressure. In the context of piano tuning, entropy measures disharmony or discord: the aim is to make it as small as possible. It measures disorder.Īround 1948, Claude Shannon developed a mathematical theory of communications and used entropy to indicate information content. Entropy was first recognised in the mid-19th century in thermodynamics and later in statistical mechanics. An ingenious method of tuning pianos based on the concept of entropy was recently devised by Haye Hinrichsen of Würzburg University. ![]()
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