Eight foot pitch

Eight-foot pitch is a term common to the organ and the harpsichord. An organ pipe, or a harpsichord string, designated as eight-foot pitch is sounded at standard, ordinary pitch. For example, the A above middle C in eight-foot pitch would be sounded at 440 Hz. (or at some similar value, depending on how concert pitch was set at the time and place the organ or harpsichord was made).

Eight-foot pitch may be contrasted with four-foot pitch (one octave above the standard), two-foot pitch (two octaves above the standard), and sixteen foot pitch (one octave below the standard). The latter three pitches were often sounded (by extra pipes or strings) along with an eight-foot pitch pipe or string, as a way of enriching the tonal quality.

The origin of all these terms is based on the fact that, all else being equal, a pipe or string that is half the length of another will vibrate at a pitch one octave higher.

Why eight feet?

The particular length "eight feet" is based on the approximate length of an organ pipe sounding the pitch two octaves below middle C, the bottom note on an organ keyboard. This may be calculated as follows.

Physics tells us that if a pipe is open at one end, as is true of organ pipes, its fundamental frequency "F" will be:

$F=frac\{V\}\{2L\}$

If "V" is assumed to be 1130 feet per second (the speed of sound at sea level, with temperature 70 degrees Fahrenheit), and the pipe length "L" is assumed to be eight feet, then the formula yields the value of 70.6 hertz (Hz; cycles per second). This is not far from the pitch of the C two octaves below 440 Hz, which (when concert pitch is set at A = 440 Hz) is 65.4 Hz. The discrepancy may be related to historical differing definitions of the length of the foot as well as variations in tuning prior to the setting of A = 440 Hz as standard pitch in the 20th Century.

ee also

*Pipe organ
*Harpsichord