Tuning a Keyboard Instrument
The lowest or highest note on a scale is called the tonic or key note. It is an easy matter to make a change of key when singing, since the human voice can quickly be pitched to any frequency within its natural range. Some string instruments – the violin and cello – can also have the frequency of vibration of a string changed very quickly by changing the position of the finger on the string and some wind instruments – the trombone and recorder have frequencies changed by changing the length of the pipe. In the case of the trombone the length of the slide is manipulated and with the recorder the player changes the length of the pipe by moving their fingers between the holes.
With keyed instruments such as a piano or organ there is a difficulty. The diagram below shows a middle C, given by a white key near the centre of the keyboard. The rest of the scale (to the right of middle C) is given by the next seven white keys, which have relative frequencies 9/8 (major), 10/9 (minor), 16/15 (semi), 9/8 (major), 10/9 (minor), 9/8 (major) and 16/15 (semi). If middle E is taken as the key note, an ascending scale cannot be played on a succession of white keys as the intervals do not come in the correct order.
The interval between middle E and the next white key middle F is only a semitone, but the interval between the first and second notes of a diatonic scale must be a major tone. Similar difficulties arise with other intervals, so in order to play a correct diatonic scale beginning with middle E, it would be necessary to have four extra keys. If enough extra keys were provided to enable diatonic scales to be played in all possible keys, the piano would have a GREAT MANY KEYS!
For this reason keyed instruments use a modified 'chromatic' scale, with the frequency ratio between successive white keys at 2 12 :1 or 1.0595:1. This interval is called a chromatic semitone. The difference between the chromatic and diatonic scale are to small to be noticed by all but the most musical ears.