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204 DEFECTS OF KEYED INSTRUMENTS. [X. § 110.
each Octave. Pure intonation in the 'natural' keys alone, i.e. those whose tonics are white notes on the board, demands, as has been seen, more than twice this number of available sounds; and many more still, if the keys with tonics on the black notes are to be included. Perfect tuning in all the keys being entirely out of the question, a compromise of some kind is the only possible course. Thus we may tune a single key, say C, perfectly; in which case most of the other keys will be so out of tune as to be unbearable. Or again, we may distribute the errors over certain often-used keys, and accumulate them in others which are of less frequent occurrence.
Expedients of this kind are described as modes of 'tempering,' and the system adopted in tuning any particular instrument is called its 'temperament.' A vast number of different methods of tempering have been proposed and tried during the history of the organ and pianoforte.
110. That which has at last been almost universally adopted is the system of equal temperament. It consists in dividing each Octave into twelve precisely equal intervals. Each of these intervals is called a semi-Tone, and any two of them together a Tone or whole Tone.
The Octave of which C, 264, is the lowest note,