Tempering. The basis for tuning, dividing the octave into whole and half-tones. The tempering in tuning the organ is done on the Prestant, covering a twelfth, from F to the second C above. The tempering is done by tuning the octaves just, and the fifths first just, then diminished, so the beats are below. [1]

The basis for tempering is the pitch of a one-foot pipe, to which middle C on the keyboard is tuned in unison. This pitch is two octaves above the musicians’ standard pitch, which is the pitch of a four-foot open pipe. After tuning C to the pitch of C , all the pitches comprising the tempered scale are tuned as shown in [Plate XI] fig. 68 . The half-notes in this figure are the pitches to which tuning is done, and the quarter-notes are the pitches being tuned. Thus, starting with C , the C an octave above is tuned just. Next returning to the first C , tune the G above. This is a fifth, which must be lowered a little after it has been tuned just. All the fifths that are tuned above the note to which they are tuned, like G in the present example, must be lowered slightly below the just fifth, which produces a rather noticeable beat in the trebles , and less pronounced in the basses . When the fifths are tuned below, for example the fifth F C , the F being tuned must be raised slightly above a just fifth below C , in each case diminishing the interval between the notes, a tempering required by the fifths in the tempered diatonic system, used for tuning organs and harpsichords. After the G is tuned and tempered suitably, the G an octave above it is tuned; then to this G the D a fifth above is tuned; it must beat likewise.

Next take the C an octave higher and tune the F a fifth below; this fifth must beat, being narrow. The fifths are correctly tempered if the major third, F A , in the fifth, F C , is just. This major third is sounded with the note being tuned, with which the F must be just. The fifth below, Bb , is tuned, beating narrow; this fifth has for proof the major third, Bb G ; then return to the A tuned a fifth above D , and tune the octave below. To the last A tuned, tune the fifth, A E , which beats narrow; then for proof the major third, E C , above this E natural. This fifth, which must beat narrow, is proved by the major third, B G ; then the B natural an octave below is tuned, which like all the other octaves must be just. To the lower B natural the fifth above, B F# , is tuned, then the F# an octave below is tuned to it, then the fifth above, F# C# , is proved by the major third, C# A , with the narrow beat. To C# the fifth, C# G# , is tuned, again with the narrow beat, and for proof the major third, E G# ; to G# the G# an octave above is tuned, and that completes the tempering .

Next the trebles and basses are tuned by octaves to the notes of the tempering ; the treble notes, AC [Plate XI] fig. 68 , are tuned to the octave of notes B , which are half-notes. The bass notes , ED , are tuned an octave above notes A , which are those of the tempering ; they are half-notes to distinguish them from the quarter-notes, FD , which are the ones to be tuned.

Usually keyboards have a note below the four octaves, which is tuned an octave below the lowest G , or three octaves below tenor G ; the C# key of the lowest octave [is tuned] an octave below low A , as shown in the figure at letter D . To bring the pipes to pitch, tuning cones ABC, abc [Plate IX] fig. 49 are used, the first of which are for large pipes, and the second, with handles, for small pipes that cannot be reached with the hand; three sizes are sufficient. To lower the pitch of a pipe, a hollow cone is placed on the pipe and pressed down, narrowing the top of the pipe and lowering the pitch; to raise the pitch, the tip of the cone is inserted, spreading the pipe and raising the pitch. See Tuning cones and [Plate IX] fig. 49 ; No. 1 of fig. 6 shows the hollow cone for lowering pitch, and No. 2 the pointed cone for raising it.

1. That is, “the beats result from narrowing the interval” (Translator’s note).