The Ten Books on Architecture
semitones away; and in the 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: synêmmenon]; fourth, the disjunct, named
[Greek: diezeugmenon]; the fifth, which is the highest, is termed in
Greek [Greek: hyperbolaion]. The concords, termed in Greek [Greek:
symphôniai], 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 should be placed, may be described as follows. If the theatre
be of no great size, mark out a horizontal range halfway up, and in it
construct thirteen arched niches with twelve equal spaces between them,
so that of the above mentioned "echea" those which give the note nete
hyperbolaeon may be placed first on each side, in the niches which are
at the extreme ends; next to the ends and a fourth below in pitch, the
note nete diezeugmenon; third, paramese, a fourth below; fourth, nete
synhemmenon; fifth, mese, a fourth below; sixth, hypate meson, a fourth
below; and in the middle and another fourth below, one vessel giving the
note hypate hypaton.
3. On this principle of arrangement, the voice, uttered from the stage
as from a centre, and spreading and striking against the cavities of the
different vessels, as it comes in contact with them, will be increased
in clearness of sound, and will wake an harmonious note in unison with
itself.
But if the theatre be rather large, let its height be divided into four
parts, so that three horizontal ranges of niches may be marked out and
constructed: one for the enharmonic, another for the chromatic, and the
third for the diatonic system. Beginning with the bottom range, let the
arrangement be as described above in the case of a smaller theatre, but
on the enharmonic system.
4. In the middle range, place first at the extreme ends the vessels
which give the note of the chromatic hyperbolaeon; next to them, those
which give the chromatic diezeugmenon, a fourth below; third, the
chromatic synhemmenon; fourth, the chromatic meson, a fourth below;
fifth, the chromatic hypaton, a fourth below; sixth, the paramese, for
this is both the concord of the fifth to the chromatic hyperbolaeon, and
the concord[8] of the chromatic synhemmenon.
[Note 8: Codd. _diatessaron_, which is impossible, paramese being
the concord of the fourth to the chromatic meson, and identical with the
chromatic synhemmenon.]
5. No vessel is to be placed in the middle, for the reason that there is
no other note in the chromatic system that forms a natural concord of
sound.
In the highest division and range of niches, place at the extreme ends
vessels fashioned so as to give the note of the diatonic hyperbolaeon;
next, the diatonic diezeugmenon, a fourth below; third, the diatonic
synhemmenon; fourth, the diatonic meson, a fourth below; fifth, the
diatonic hypaton, a fourth below; sixth, the proslambanomenos, a fourth
below; in the middle, the note mese, for this is both the octave to
proslambanomenos, and the concord of the fifth to the diatonic hypaton.
6. Whoever wishes to carry out these principles with ease, has only to
consult the scheme at the end of this book, drawn up in accordance with
the laws of music. It was left by Aristoxenus, who with great ability
and labour classified and arranged in it the different modes. In
accordance with it, and by giving heed to these theories, one can easily
bring a theatre to perfection, from the point of view of the nature of
the voice, so as to give pleasure to the audience.
7. Somebody will perhaps say that many theatres are built every year in
Rome, and that in them no attention at all is paid to these principles;
but he will be in error, from the fact that all our public theatres made
of wood contain a great deal of boarding, which must be resonant. This
may be observed from the behaviour of those who sing to the lyre, who,
when they wish to sing in a higher key, turn towards the folding doors
on the stage, and thus by their aid are reinforced with a sound in
harmony with the voice. But when theatres are built of solid materials
like masonry, stone, or marble, which cannot be resonant, then the
principles of the "echea" must be applied.
8. If, however, it is asked in what theatre these vessels have been
employed, we cannot point to any in Rome itself, but only to those in
the districts of Italy and in a good many Greek states. We have also the
evidence of Lucius Mummius, who, after destroying the theatre in
Corinth, brought its bronze vessels to Rome, and made a dedicatory
offering at the temple of Luna with the money obtained from the sale of
them. Besides, many skilful architects, in constructing theatres in
small towns, have, for lack of means, taken large jars made of clay, but
similarly resonant, and have produced very advantageous results by
arranging them on the principles described.
CHAPTER VI
PLAN OF THE THEATRE
1. The plan of the theatre itself is to be constructed as follows.
Having fixed upon the principal centre, draw a line of circumference
equivalent to what is to be the perimeter at the bottom, and in it
inscribe four equilateral triangles, at equal distances apart and
touching the boundary line of the circle, as the astrologers do in a
figure of the twelve signs of the zodiac, when they are making
computations from the musical harmony of the stars. Taking that one of
these triangles whose side is nearest to the scaena, let the front of
the scaena be determined by the line where that side cuts off a segment
of the circle (A-B), and draw, through the centre, a parallel line (C-D)
set off from that position, to separate the platform of the stage from
the space of the orchestra.
2. The platform has to be made deeper than that of the Greeks, because
all our artists perform on the stage, while the orchestra contains the
places reserved for the seats of senators. The height of this platform
must be not more than five feet, in order that those who sit in the
orchestra may be able to see the performances of all the actors. The
sections (cunei) for spectators in the theatre should be so divided,
that the angles of the triangles which run about the circumference of
the circle may give the direction for the flights of steps between the
sections, as far as up to the first curved cross-aisle. Above this, the
upper sections are to be laid out, midway between (the lower sections),
with alternating passage-ways.
3. The angles at the bottom, which give the directions for the flights
of steps, will be seven in number (C, E, F, G, H, I, D); the other five
angles will determine the arrangement of the scene: thus, the angle in
the middle ought to have the "royal door" (K) opposite to it; the angles
to the right and left (L, M) will designate the position of the doors
for guest chambers; and the two outermost angles (A, B) will point to
the passages in the wings. The steps for the spectators' places, where
the seats are arranged, should be not less than a foot and a palm in
height, nor more than a foot and six fingers; their depth should be
fixed at not more than two and a half feet, nor less than two feet.
4. The roof of the colonnade to be built at the top of the rows of
seats, should lie level with the top of the "scaena," for the reason
that the voice will then rise with equal power until it reaches the
highest rows of seats and the roof. If the roof is not so high, in
proportion as it is lower, it will check the voice at the point which
the sound first reaches.
5. Take one sixth of the diameter of the orchestra between the lowest
steps, and let the lower seats at the ends on both sides be cut away to
a height of that dimension so as to leave entrances (O, P). At the point
where this cutting away occurs, fix the soffits of the passages. Thus
their vaulting will be sufficiently high.
6. The length of the "scaena" ought to be double the diameter of the
orchestra. The height of the podium, starting from the level of the
stage, is, including the corona and cymatium, one twelfth of the
diameter of the orchestra. Above the podium, the columns, including
their capitals and bases, should have a height of one quarter of the
same diameter, and the architraves and ornaments of the columns should
be one fifth of their height. The parapet above, including its cyma and
corona, is one half the height of the parapet below. Let the columns
above this parapet be one fourth less in height than the columns below,
and the architraves and ornaments of these columns one fifth of their
height. If the "scaena" is to have three stories, let the uppermost
parapet be half the height of the intermediate one, the columns at the
top one fourth less high than the intermediate, and the architraves and
coronae of these columns one fifth of their height as before.
7. It is not possible, however, that in all theatres these rules of
symmetry should answer all conditions and purposes, but the architect
ought to consider to what extent he must follow the principle of
symmetry, and to what extent it may be modified to suit the nature of
the site or the size of the work. There are, of course, some things
which, for utility's sake, must be made of the same size in a small
theatre, and a large one: such as the steps, curved cross-aisles, their
parapets, the passages, stairways, stages, tribunals, and any other
things which occur that make it necessary to give up symmetry so as not
to interfere with utility. Again, if in the course of the work any of
the material fall short, such as marble, timber, or anything else that
is provided, it will not be amiss to make a slight reduction or