The musical scale, consisting of 12 semitones or 8 tones to an octave, may at first sight be considered to be divided equally; ie., the musical interval between each adjacent note might be thought to be equal.
In fact this is not the case. The most ‘natural’ interval to the human ear is the octave (notes an octave apart sound ‘alike’); the next most natural interval is the fifth (notes five tones apart). However, in order for the octaves to be tuned exactly, the fifths have to be flattened slightly.Whilst a fifth on the keyboard spans seven semi-tones, an acoustically correct ‘pure’ fifth spans 7.019550008654 semitones. The problem would not be so apparent except that modern music can be played in many keys, and a scale tuned to be correct for C would sound incorrect when a scale of F (for example) was played on the same instrument (a phenomenon known as the ‘Wolf’). Modern musical styles both classical and popular – the compositions of Jerome Kern are an excellent example – often change key within the piece (‘enharmonic changes’).
In order to overcome this problem, tuners adopt a system of very slightly flattening fifths. Such a system is known as ‘temperament’ – the most usual one adopted is Equal Temperament. Many other temperaments (‘unequal’) have been devised; some work extremely well in some keys, but poorly in others.They may however be better suited (for example) for early music.
The phenomenon was known to Pythagorus, and J.S. Bach issued very specific instructions regarding temperament as well as composing preludes and fugues demonstrating in all twelve keys whether an instrument was ‘Well-Tempered’ or not.
As late as 1860, the organ in the Temple church in London was equipped with separate notes for G sharp and A flat, and for D sharp and E flat. The keys were split so that the forward portion played one note and the rearward portion the other.
The subject of temperament is a very wide one and deeply researched. ‘The Well-Tempered Organ’ by Charles Padgham (Positif Press, ISBN 0 906894 13 1) contains much information on the subject.