The problem of tuning a keyboard instrument
The lowest (or highest) note on the scale is called the tonic or key-note. Now it is an easy matter to make a change of key when singing, since the voice can be pitched to any frequency within its natural compass. Also the same principle applies in the case
of stringed instruments, where the length of the vibrating strings can be adjusted by fingering; or with the trombone where the player manipulates the length of the slide.
But with a keyed instrument such as a piano or organ a difficulty arises. The scale represented in Fig. 28.2 begins with c’ (middle C), which is given by a white key near the centre of the keyboard. The rest of the scale is given by the next seven white keys in order. If e’ is taken as the key-note, an ascending scale cannot be played on a succession of white notes, as the intervals do not come in the correct order. For example, the interval between e’ and the next white key f” is only a semitone, whereas the interval between the first and second notes of a diatonic scale must be a major tone. Similar difficulties arise with other intervals, and hence, in order to playa correct diatonic scale beginning with e’, it would be necessary to have four extra keys’. If sufficient extra keys were provided to enable diatonic scales to be played in all other possible keys we should end up with a piano which had so many keys that it would be impossible to play it.
Some compromise is therefore necessary. Space does not allow a detailed discussion of the various attempts which have been made in the past to overcome the difficulty. Suffice it to say that a satisfactory solution of the problem has been effected by substituting the chromatic or equally tempered scale for the diatonic scale. Five black keys, known as sharps (in or flats (~) are added to each octave of white keys, making in all a range of thirteen notes each separated from its predecessor by an interval of 2(, or 1.0595 : 1. This interval is called a chromatic semitone. While ,these notes do not allow true diatonic scales to be played, the differences are so small that only those with extremely sensitive musical ears claim to be able to detect them. The actual frequencies employed in the equally tempered scale are shown in Fig. 28.2.