h century,
in which the author gives directions for a set of organ pipes. "Take
first," he says, "ten pipes of a proper dimension and of equal length
and size. Divide the first pipe into nine parts; eight of these will
be the length of the second. Dividing the length of this again into
nine parts, eight of these will be the proper length of the third;
dividing the first pipe into four parts, three of them will be the
length of the fourth; taking the first pipe as three parts, two of
them will be the length of the fifth; eight-ninths of this again will
give the proper length of the sixth; eight-ninths of this, the length
of the seventh; one-half the first, the length of the eighth, or
octave." This gives a major scale, with the Pythagorean third,
consisting of two great steps, which was too sharp to be consonant.
The semitone between the third and the fourth is too small, as is also
that between the seventh and eighth. The modern way of making the
pipes of smaller diameter as they become shorter, had evidently not
been thought of. Nevertheless, these directions are very important,
since they throw positive light upon the tuning of the various
intervals, the pipe lengths and proportions affording accurate
determinations of the musical relations intended.

[Illustration: Fig. 44.

PORTABLE ORGAN FROM THE PROCESSION IN HONOR OF MAXIMILIAN I.

(From Praetorius' "_Syntagma Musica_," about 1500 A.D.)]

The early organs were furnished with slides which the organist pulled
out when he wished to make a pipe speak, and pushed back to check its
utterance. The date of the invention of the valve is uncertain, but it
must have been about as soon as the power of the instrument was
increased by the addition of the second or third stop. Before this,
however, and perhaps for some little time after, there were many
organs in use, which were committed to the diaphony of Hucbald, having
in place of the diapason three ranks of pipes, speaking an octave and
the fifth between. Each of these combined sounds was treated in the
same way as simple ones are on other instruments, and if chords were
attempted upon them the effect must have been hideous indeed; but it
is probable that at this time the notes were played singly, and not in
chords, or at most in octaves. We do not know the date at which this
style of organ building ceased, but it is probably before the
thirteenth century. There is a manuscript of the fourteenth century in
the Royal L