diatonic it is at an interval of three
semitones from hypate. Hence the ten notes produce three different kinds
of modes on account of their changes of position in the classes.

7. There are five tetrachords: first, the lowest, termed in Greek
[Greek: hypaton]; second, the middle, called [Greek: meson]; third, the
conjunct, termed [Greek: synemmenon]; fourth, the disjunct, named
[Greek: diezeugmenon]; the fifth, which is the highest, is termed in
Greek [Greek: hyperbolaion]. The concords, termed in Greek [Greek:
symphoniai], of which human modulation will naturally admit, are six in
number: the fourth, the fifth, the octave, the octave and fourth, the
octave and fifth, and the double octave.

8. Their names are therefore due to numerical value; for when the voice
becomes stationary on some one note, and then, shifting its pitch,
changes its position and passes to the limit of the fourth note from
that one, we use the term "fourth"; when it passes to the fifth, the
term is "fifth."[7]

[Note 7: The remainder of this section is omitted from the
translation as being an obvious interpolation.]

9. For there can be no consonances either in the case of the notes of
stringed instruments or of the singing voice, between two intervals or
between three or six or seven; but, as written above, it is only the
harmonies of the fourth, the fifth, and so on up to the double octave,
that have boundaries naturally corresponding to those of the voice: and
these concords are produced by the union of the notes.

CHAPTER V

SOUNDING VESSELS IN THE THEATRE

1. In accordance with the foregoing investigations on mathematical
principles, let bronze vessels be made, proportionate to the size of the
theatre, and let them be so fashioned that, when touched, they may
produce with one another the notes of the fourth, the fifth, and so on
up to the double octave. Then, having constructed niches in between the
seats of the theatre, let the vessels be arranged in them, in accordance
with musical laws, in such a way that they nowhere touch the wall, but
have a clear space all round them and room over their tops. They should
be set upside down, and be supported on the side facing the stage by
wedges not less than half a foot high. Opposite each niche, apertures
should be left in the surface of the seat next below, two feet long and
half a foot deep.

2. The arrangement of these vessels, with reference to the situations in
which they sho