8. The open side of this hemicycle is forty-six feet along the front,
and its curvature inwards is fifteen feet, so that those who are
standing before the magistrates may not be in the way of the business
men in the basilica. Round about, above the columns, are placed the
architraves, consisting of three two-foot timbers fastened together.
These return from the columns which stand third on the inner side to the
antae which project from the pronaos, and which touch the edges of the
hemicycle at right and left.
9. Above the architraves and regularly dispersed on supports directly
over the capitals, piers are placed, three feet high and four feet broad
each way. Above them is placed the projecting cornice round about, made
of two two-foot timbers. The tie-beams and struts, being placed above
them, and directly over the shafts of the columns and the antae and
walls of the pronaos, hold up one gable roof along the entire basilica,
and another from the middle of it, over the pronaos of the temple.
10. Thus the gable tops run in two directions, like the letter T, and
give a beautiful effect to the outside and inside of the main roof.
Further, by the omission of an ornamental entablature and of a line of
screens and a second tier of columns, troublesome labour is saved and
the total cost greatly diminished. On the other hand, the carrying of
the columns themselves in unbroken height directly up to the beams that
support the main roof, seems to add an air of sumptuousness and dignity
to the work.
CHAPTER II
THE TREASURY, PRISON, AND SENATE HOUSE
1. The treasury, prison, and senate house ought to adjoin the forum, but
in such a way that their dimensions may be proportionate to those of the
forum. Particularly, the senate house should be constructed with special
regard to the importance of the town or city. If the building is square,
let its height be fixed at one and one half times its breadth; but if it
is to be oblong, add together its length and breadth and, having got the
total, let half of it be devoted to the height up to the coffered
ceiling.
2. Further, the inside walls should be girdled, at a point halfway up
their height, with coronae made of woodwork or of stucco. Without these,
the voice of men engaged in discussion there will be carried up to the
height above, and so be unintelligible to their listeners. But when the
walls are girdled with coronae, the voice from below, being detained
before rising and becoming lost in the air, will be intelligible to the
ear.
CHAPTER III
THE THEATRE: ITS SITE, FOUNDATIONS AND ACOUSTICS
1. After the forum has been arranged, next, for the purpose of seeing
plays or festivals of the immortal gods, a site as healthy as possible
should be selected for the theatre, in accordance with what has been
written in the first book, on the principles of healthfulness in the
sites of cities. For when plays are given, the spectators, with their
wives and children, sit through them spell-bound, and their bodies,
motionless from enjoyment, have the pores open, into which blowing winds
find their way. If these winds come from marshy districts or from other
unwholesome quarters, they will introduce noxious exhalations into the
system. Hence, such faults will be avoided if the site of the theatre is
somewhat carefully selected.
2. We must also beware that it has not a southern exposure. When the sun
shines full upon the rounded part of it, the air, being shut up in the
curved enclosure and unable to circulate, stays there and becomes
heated; and getting glowing hot it burns up, dries out, and impairs the
fluids of the human body. For these reasons, sites which are unwholesome
in such respects are to be avoided, and healthy sites selected.
3. The foundation walls will be an easier matter if they are on a
hillside; but if they have to be laid on a plain or in a marshy place,
solidity must be assured and substructures built in accordance with what
has been written in the third book, on the foundations of temples. Above
the foundation walls, the ascending rows of seats, from the
substructures up, should be built of stone and marble materials.
4. The curved cross-aisles should be constructed in proportionate
relation, it is thought, to the height of the theatre, but not higher
than the footway of the passage is broad. If they are loftier, they will
throw back the voice and drive it away from the upper portion, thus
preventing the case-endings of words from reaching with distinct meaning
the ears of those who are in the uppermost seats above the cross-aisles.
In short, it should be so contrived that a line drawn from the lowest to
the highest seat will touch the top edges and angles of all the seats.
Thus the voice will meet with no obstruction.
5. The different entrances ought to be numerous and spacious, the upper
not connected with the lower, but built in a continuous straight line
from all parts of the house, without turnings, so that the people may
not be crowded together when let out from shows, but may have separate
exits from all parts without obstructions.
Particular pains must also be taken that the site be not a "deaf" one,
but one through which the voice can range with the greatest clearness.
This can be brought about if a site is selected where there is no
obstruction due to echo.
6. Voice is a flowing breath of air, perceptible to the hearing by
contact. It moves in an endless number of circular rounds, like the
innumerably increasing circular waves which appear when a stone is
thrown into smooth water, and which keep on spreading indefinitely from
the centre unless interrupted by narrow limits, or by some obstruction
which prevents such waves from reaching their end in due formation. When
they are interrupted by obstructions, the first waves, flowing back,
break up the formation of those which follow.
7. In the same manner the voice executes its movements in concentric
circles; but while in the case of water the circles move horizontally on
a plane surface, the voice not only proceeds horizontally, but also
ascends vertically by regular stages. Therefore, as in the case of the
waves formed in the water, so it is in the case of the voice: the first
wave, when there is no obstruction to interrupt it, does not break up
the second or the following waves, but they all reach the ears of the
lowest and highest spectators without an echo.
8. Hence the ancient architects, following in the footsteps of nature,
perfected the ascending rows of seats in theatres from their
investigations of the ascending voice, and, by means of the canonical
theory of the mathematicians and that of the musicians, endeavoured to
make every voice uttered on the stage come with greater clearness and
sweetness to the ears of the audience. For just as musical instruments
are brought to perfection of clearness in the sound of their strings by
means of bronze plates or horn [Greek: êcheia], so the ancients devised
methods of increasing the power of the voice in theatres through the
application of harmonics.
CHAPTER IV
HARMONICS
1. Harmonics is an obscure and difficult branch of musical science,
especially for those who do not know Greek. If we desire to treat of it,
we must use Greek words, because some of them have no Latin equivalents.
Hence, I will explain it as clearly as I can from the writings of
Aristoxenus, append his scheme, and define the boundaries of the notes,
so that with somewhat careful attention anybody may be able to
understand it pretty easily.
2. The voice, in its changes of position when shifting pitch, becomes
sometimes high, sometimes low, and its movements are of two kinds, in
one of which its progress is continuous, in the other by intervals. The
continuous voice does not become stationary at the "boundaries" or at
any definite place, and so the extremities of its progress are not
apparent, but the fact that there are differences of pitch is apparent,
as in our ordinary speech in _sol_, _lux_, _flos_, _vox_; for in these
cases we cannot tell at what pitch the voice begins, nor at what pitch
it leaves off, but the fact that it becomes low from high and high from
low is apparent to the ear. In its progress by intervals the opposite is
the case. For here, when the pitch shifts, the voice, by change of
position, stations itself on one pitch, then on another, and, as it
frequently repeats this alternating process, it appears to the senses to
become stationary, as happens in singing when we produce a variation of
the mode by changing the pitch of the voice. And so, since it moves by
intervals, the points at which it begins and where it leaves off are
obviously apparent in the boundaries of the notes, but the intermediate
points escape notice and are obscure, owing to the intervals.
3. There are three classes of modes: first, that which the Greeks term
the enharmonic; second, the chromatic; third, the diatonic. The
enharmonic mode is an artistic conception, and therefore execution in it
has a specially severe dignity and distinction. The chromatic, with its
delicate subtlety and with the "crowding" of its notes, gives a sweeter
kind of pleasure. In the diatonic, the distance between the intervals is
easier to understand, because it is natural. These three classes differ
in their arrangement of the tetrachord. In the enharmonic, the
tetrachord consists of two tones and two "dieses." A diesis is a quarter
tone; hence in a semitone there are included two dieses. In the
chromatic there are two semitones arranged in succession, and the third
interval is a tone and a half. In the diatonic, there are two
consecutive tones, and the third interval of a semitone completes the
tetrachord. Hence, in the three classes, the tetrachords are equally
composed of two tones and a semitone, but when they are regarded
separately according to the terms of each class, they differ in the
arrangement of their intervals.
4. Now then, these intervals of tones and semitones of the tetrachord
are a division introduced by nature in the case of the voice, and she
has defined their limits by measures according to the magnitude of the
intervals, and determined their characteristics in certain different
ways. These natural laws are followed by the skilled workmen who fashion
musical instruments, in bringing them to the perfection of their proper
concords.
5. In each class there are eighteen notes, termed in Greek [Greek:
phthongoi], of which eight in all the three classes are constant and
fixed, while the other ten, not being tuned to the same pitch, are
variable. The fixed notes are those which, being placed between the
moveable, make up the unity of the tetrachord, and remain unaltered in
their boundaries according to the different classes. Their names are
proslambanomenos, hypate hypaton, hypate meson, mese, nete synhemmenon,
paramese, nete diezeugmenon, nete hyperbolaeon. The moveable notes are
those which, being arranged in the tetrachord between the immoveable,
change from place to place according to the different classes. They are
called parhypate hypaton, lichanos hypaton, parhypate meson, lichanos
meson, trite synhemmenon, paranete synhemmenon, trite diezeugmenon,
paranete diezeugmenon, trite hyperbolaeon, paranete hyperbolaeon.
6. These notes, from being moveable, take on different qualities; for
they may stand at different intervals and increasing distances. Thus,
parhypate, which in the enharmonic is at the interval of half a semitone
from hypate, has a semitone interval when transferred to the chromatic.
What is called lichanos in the enharmonic is at the interval of a
semitone from hypate; but when shifted to the chromatic, it goes two