Ulrich Middeldorf
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2013
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THE
NATURAL PRINCIPLES AND ANALOGY OF
THE HARMONY OF FORM. BY
D.
R.
HAY,
DECORATIVE PAINTER TO THE QUEEN, EDINBURGH; HONORARY FELLOW OF THE ROYAL INSTITUTE OF THE ARCHITECTS OF IRELAND, AND AUTHOR OF "THE LAWS OF HARMONIOUS COLOURING," ETC.
"WHEREVER THE BEST TASTE DIFFERS FROM THE WORST, I AM CONVINCED THAT THE UNDERSTANDING OPERATES, AND NOTHING ELSE." Burke on " T!ie Sublime and Iieszutiful."
WILLIAM BLACKWOOD AND SONS,
AND
22
45
GEORGE STREET, EDINBURGH;
PALL-MALL, LONDON. MDCCCXLII.
EDINBURGH: PBINTED BY IiAI-LAXTYNE AND HUGHES. PAL
L S
WORK, CANONGATE.
INTRODUCTION.
It will not be disputed that the effect of forms upon the eye either
is
harmonious or discordant, agreeably to certain modes of arrange-
ment of the
lines
which circumscribe them, or divide their
parts.
All writers on taste, architecture, landscape-gardening, and other subjects
where discussions on the beauty of form are necessarily
introduced, admit this fact.
At
the same time
it is
allowed, that as
yet there has existed no system, or development of fixed principles,
by which forms
may be harmoniously
arranged, but that judgment in
such matters depends upon an abstract idea of beauty not easily defined.
One
of the latest and best writers
upon
taste says
— " In
the greater part of beautiful forms, whether in nature or art, lines of different descriptions unite.
The A
greater part of the forms of
INTRODUCTION.
2
nature and art possess an union, or composition of uniformity and variety, of similarity
combination in
and
itself beautiful, it
every case where
it
mere union of tiful
Mr
And
1
Alison,
and
similarity
or imagine a correspondence
— that
combining
we
different
of the
support of this says
fact,
is
the author in
— " Every one knows
say, that
among
it
is
that the
when we perceive
only
the parts
circumstances with so
—a relation and har-
much
propriety for the
effect."
latest
and most eminent writers on architecture
upon that
asked what standard of beauty there
;
This
result.
dissimilarity does not constitute a beau-
observes, in an excellent essay
be formed
that, in
are enabled to say, " that nature has been kind in
production of one
One
in
who
form;" and proceeds to
mony
would necessarily follow,
was found, beauty would be the
not the case, however." question quotes
But were such a
dissimilarity of forms.
though
it
is
subject, that
in this art
must be obvious, that
—
" It
may
be
on which taste may
like
other children of
the imagination, such as poetry and music, no other can be assigned
than such compositions and modes of arrangement
as,
by their har-
INTRODUCTION.
mony and is
3
simplicity, attract the attention of the rudest
mind, which
pleased without being conscious why, and of the most learned or
practised,
which discovers
in
them those proportions and
peculiarities
of form which always produce the most pleasing impression, and 2 appear to be dictated by nature."
Quotations to a similar
might be given from innumerable works
;
effect
but the above are consi-
dered sufficient to prove, that our general knowledge of the important subject of the fore, it
harmony of form
is
open to improvement.
If,
there-
can be shown, that the impressions made upon the eye by
forms are really founded on natural principles, and that the proportions and peculiarities of form which produce the most pleasing impressions, are in reality, as well as appearance, dictated by nature,
being a response to these principles in the in the arts will
be obtained.
And
human mind,
further, if
it
a desideratum
can be shown that,
agreeably to the boundless analogy by which the sciences and arts are connected, forms are in
all
respects analogous to sounds, and that
consequently a system of linear harmony can be established, similar to that
which regulates the arrangement of musical notes, a know-
INTRODUCTION.
4
ledge of this important branch of art
may
also
become a part of
elementary education.
There can be no doubt that the
effect
produced by the harmony of
sound, colour, and form, are equally the result of a susceptibility of the
human mind, which
renders
it
capable of appreciating an adhe-
rence to certain natural principles by which harmony in every case
produced.
These
principles are clearly understood in regard to the
harmony of sound, from
its
having occupied the attention of the most
eminent natural philosophers discoveries of Sir Isaac
reduced to something left
is
Colours, likewise, since the
in all ages.
Newton, have
like system.
in their
combinations been
But the harmony
of form has been
out of those enquiries, as a matter depending upon opinion alone,
unless in regard to architecture, where the works of the ancients
have in some measure supplied the want of general principles.
As
a knowledge of the natural principles which regulate the
arrangement of musical sounds tends to improve the general understanding and practice of that particular
art,
without producing a
musical ear, or enhancing the pleasure derivable from an intuitive
INTRODUCTION.
5
perception of " the melody of sweet sounds ;" so
may
a knowledge of
form improve our judgment
the natural principles of
harmony
architecture, sculpture,
and painting, without rendering us
in
fit
in
to
follow any of those arts as a profession, or enhancing the pleasure
conveyed to the mind by the visual organ.
A
person
is
said to have an ear for music, in the ratio of the
sensibility of that
sounds
;
and when
organ to the relative gravity and acuteness of this
is
accompanied by an
intuitive appreciation
of the natural principles which regulate their combination, he will,
according to the extent of this talent, have a genius for musical composition.
and
So, likewise, in the ratio of the sensibility of the eye.
intuitive appreciation of the natural principles of form, will an
individual possess a facility in producing harmonious arrangements,
Thus works
independently of any other knowledge of these principles. of art in
all
ages have occasionally displayed the most perfect lv
harmonious combinations of form. occurrence, being the works of
they
may be models
men
These
are,
however, of rare
of great genius
for the careful study of those
;
and although
who
follow such
INTRODUCTION.
6
arts
professionally, they cannot supply the place of natural
ciples in
forming the public
sounds depended,
Had
taste.
like that of forms,
prin-
the arrangement of musical
upon the works of the
ancients,
without a knowledge of the natural principles upon which the excellence of these works depends, music could not have
become a part
of polite education. It
not, therefore,
is
principles of linear
may
be, can
assumed that
harmony, whatever
have any
effect
attempt to develope the
this
its
success in other respects
in raising the standard of excellence,
by improving the practice of professors of genius in the various arts
which owe their excellence to beauty of form.
improvement of the public
Its object is
more the
taste in judging of such productions
;
and
believed the fact will be readily admitted that such an attempt
it
is
is
not uncalled
for.
Neither can a knowledge of these principles
number of
tend, in any way, to add to the
design
:
it
will rather lessen
untalented pretenders in sterling genius will
all
it
;
professors of the arts of
for as the public taste improves,
such professions
meet the encouragement
it
will
be detected, and
alone deserves.
;
THE
NATUKAL PRINCIPLES OF HARMONY IN FORM, AND
THEIR ANALOGY TO THOSE OF SOUND AND COLOUR.
That
form, in
in its effects
effects
its
upon the
ear, has
There appears to be three or rather, that the different
ways.
intonations
mind
This
still
harmony, by the
through the is
is
artificial
greater degree, by the
analogous to sound
is
different kinds of
of the voice of the It
eye,
been generally admitted.
organ
conveyed by his words. of
is,
upon the
harmony
sound
ear, addressed in three
generally
as
orator, as
it
of the
of
susceptible is
more powerfully tones
in
of the
meaning
affected, in point
vocalist
more powerful, though
the
still
;
and to a
more
artifi-
ON THE ANALOGY OF
8
cial,
effects
produced by the combination of vocal and instrumental
music.
The
first
of these effects
is
a mere auxiliary to the meaning con-
veyed by the oration of the speaker
;
and
it
is
a powerful one
—
the response in the mind to the natural principles which regulate
as
all
sounds accompany the words, which address themselves at the same time to the judgment.
In vocal music, the
effect of
the melody
is
generally fully as powerful as that of the meaning contained in the
words which accompany witli
instrumental music
it
and although the combination of
;
is
perhaps more
artificial, it is
still
this
more
comprehensive, by the variety and power with which such a combination can address the ear.
Forms
are also
made
to address themselves to the eye in three
ways, (mite analogous to those in which sound the ear.
The
made
to address
simple though expressive combinations of form in
architecture, like the
to the
is
harangue of the orator, addresses
judgment than the senses
of the sculptor not only
tell
;
the
more
artistical
a story, but do so in a
itself
more
combinations
way which
is
;
SOUND, COLOUR, AND FORM.
9
capable of exciting the feelings to the highest pitch to which expression,
still
combined with form, can carry them
more
upon the
artificial,
eye,
;
and there are
though more comprehensive,
effects
also the
produced
by the combination of expression, form, and colour,
in
the works of the historical painter. Colours,
when unaccompanied by form,
are
mental music, in which an understood feeling the mind, depending on the
mode
somewhat
like instru-
may be conveyed
to
of combination, which can only be
appreciated by a correct eye in the one case, and a musical ear in the other.
Colour has
its
three effects of
harmony
the effect of the
;
three neutrals, white, grey, and black, which are capable of con-
veying
much meaning
in
the
effects
of light
and shadow, and
thereby addressing their effects more immediately to the judgment the subdued and beautiful effects which accompany the delineation of natural objects in the landscape still
more
sensual,
effects
of
the
;
and the more brilliant
hues
striking,
though
of the
positive
colouring displayed in flowers and the plumage of birds.
Forms
are therefore analogous to sounds B
and colours
in their
ON THE ANALOGY OF
10
effects
upon the
senses,
and through the senses upon the mind.
the proving of this analogy would do intelligible
fect
system of harmony of form
little
:
it
But
in the formation of
must be shown that a per-
analogy also exists in the component parts producing these
effects.
already been observed that the science of acoustics has
It has
engaged the attention of the most eminent natural philosophers all
ages
an
and
;
that,
in
by their experimental enquiries, they have shown
that fixed principles exist in nature which regulate the effects of
sound upon the will
Of the
ear.
result of these enquiries a short account
here be given, as a means of making more clear to the generality
of readers what follows in regard to form.
Sounds are produced by an
elastic
body being put into a
state of
vibration, which thereby puts, within a certain space, the air that
surrounds
it
into a state of agitation or undulation, producing a
corresponding
may be
effect
ear.
This vibratory or
a distended string or wire, a drum, a
other such body. air
upon the
itself
bell,
elastic
body
a gong, or any
Sounds are likewise produced by a portion of the
being put into a state of vibration, and causing a cor-
SOUND, COLOUR, AND FORM.
responding undulation in that which surrounds
ducing the same
effect
upon the
This
ear.
is
11
it,
and thereby pro-
the cause of the sound
produced by an organ-pipe, a trumpet, or by an explosion of
light-
ning or discharge of fire-arms.
The
sensation thus produced
upon the ear
will
be sonorous or
acute, according to the rapidity of the vibration, the greater
producing the more acute sound as the ear
is
audible sound
a second.
;
and
limited in the range of is
has been ascertained, that
it
its
perception, scarcely any
produced until these vibrations reach about 30 in
It has also
been proved, that at the 9th octave of the
musical scale, in which the vibrations are 8192,
human
almost ceases, and scarcely any more acute sound than duced.
Those sounds produced by an
surrounding
number
air, as
elastic
can be pro-
body acting on the
they die away become more acute, while those
produced by the vibration of the
become more grave.
air itself
variety of tones in this wide range of perception,
appear to be equal to 8162 enquiries of those
it
perception
great
;
but
it
is
not
men who have
so.
The
would
at first sight
The
experimental
investigated the subject.
ON THE ANALOGY OF
12
prove that
this science is
extremely simple in
primitive parts
its
indeed that they are the lowest number capable of variety,
harmony, or system
acuteness or pitch
employed
is,
窶馬amely, three
;
and that
uniting
The
first
of these
called the tonic, the medient,
may be any
given sound, and
the other two must bear a certain proportional relation to
when
struck
it
gave 256 vibrations
in a second,
the sound would correspond to the note called middle pianoforte. if it
Sup-
it.
given sound to be produced by a bell or gong 12 inches in
diameter, and that
and,
body
producing them.
in
and the dominant.
this
in
their relative
invertedly, in proportion to the vibratory
These three sounds are respectively
pose
;
Let another
were
bell
C
on the
be struck whose diameter was 6 inches,
in every other respect the
same
as the former,
give 512 vibrations in a second, and the sound
it
it
would
would produce
would correspond to the octave or eighth note above middle C, being, although doubly acute, the
and
the larger bell
;
are as 1 to
The same
2.
this will
same sound
as that
produced by
be the case so long as the relative sizes
result
would occur from an extended
string,
SOUND, COLOUR, AND FORM. or any other elastic body. variety in sound than
This octave occurs
is
when the
There
what
is
13
no greater
can, therefore, exist
found between the tonic and
therefore the
first
its
octave.
homogeneous sound, and always
vibrations are as 2 to
1.
The
next sound of a dis-
tinctive character is called the medient, or third to the tonic,
occurs
when the number
The dominant occurs
when the
is
of vibrations are relatively to
it
and
as 5 to 4.
the third homogeneous or primitive sound, and
vibrations are to those of the tonic as 3 to 2.
These
notes are not, like the octave to the tonic, the same sound, although
more
acute, but are of a distinctive character relatively to
same time combining with
it
in
it
;
at the
harmony, producing together the
most perfect consonance.
When
an
elastic
body
musical note, which
we
is
put into a state of vibration, producing a
shall
suppose
still
note dies away, the other two notes which
to be middle C, as this
make up
the harmonic
triad are distinctly heard in succession, as the vibrations reach the relative proportional
number already alluded
to.
These three sounds form the groundwork of
all
music
;
and
it
has
—
ON THE ANALOGY OF
14
been satisfactorily proved that the three primary or homogeneous colours, blue, red,
and yellow, are analogous to these sounds
in every
way. It will
now be
show, that harmony of form de-
necessary to
pends upon three homogeneous parts,
and that these parts are
analogous in every respect to the three homogeneous
primitive
sounds, proved by the concurrent testimony of natural philosophers to be the foundation of to actual forms, lines
;
for
it
will
harmony
in music.
But before proceeding
be requisite to make a few observations upon
by these, whether
real or imaginary, all
forms are repre-
sented.
There are only three kinds of
lines
used in producing forms, and
they are
the straight
line,
the crooked line,
All varieties of form, however complex,
and the curved
all
the
line.
similarity
and
——
—
SOUND, COLOUR, AND FORM.
dissimilarity that
combine
in the
15
harmony of forms,
are produced
by these simple elements.
The
straight line has three positions
line
may be
perpendicular,
horizontal,
The crooked
it
:
may
or oblique.
be crooked in three different ways
:
it
may
produce a right angle,
The curved
line has also its varieties
a portion of a circle,
These are capable.
all
The
or an obtuse angle.
an acute angle,
of an
:
it
ellipsis,
may
be or of a volute.
the varieties of which the three kinds of lines are
straight line,
if
not horizontal or perpendicular, must
;
ON THE ANALOGY OF
16
be oblique
two it
for
;
however near
positive positions, so long as
remains
arises
that
is
still
There
oblique.
the right angle
;
of
it
ellipsis
will
The curved
still
is
it will
and
it
line,
when
may have a long
form a portion of an
no part of ellipsis,
only one positive angle, and that
is
and
line,
however near the other two angles
for
one positive curve, and that
its
associates with neither of them,
this in either direction, they still
or obtuse angles.
an
it
or other of
out of the two positive positions of the straight
may approach
for
may approach one
it
it
in
remain simply acute
the same way, has only
forms a segment of a
circle
or a short centre, but every segment
ellipsis.
The same
of the volute
;
for
be found to be a portion of either a circle or an
may
diverge in any degree from
its
centre, but
it
is
a volute.
Lines are, however, merely used to show where a form ends, and
commences, and must now be considered
the space that surrounds
it
mathematically, that
as having length without breadth; at the
is,
same time they must be used
physically,
as
the only
forming the geometrical figures and diagrams that follow.
mode
of
—
SOUND, COLOUR, AND FORM.
As
in
sound and colour, so
primitive,
homogeneous parts
in form, there are only three simple,
;
and they are
the circle,
Of
line
and the square.
the triangle,
these three, the
produced by a single
The
17
line
pre-eminent for simplicity, being
circle is
drawn round a
equilateral triangle
is
single point.
formed of three
lines,
or rather of one
formed into three acute angles, the points of these angles being
equidistant from a single point, and the sides necessarily equal to one
another.
The square
is
composed of a
likewise equidistant
from a
line
formed into four right angles,
single point,
and the
sides of course equal
for they
admit of no change
to one another.
These forms are truly homogeneous, c
ON THE ANALOGY OF
18
The
any of their parts without changing their character.
in
pri-
mitive parts of form are thus analogous to the primitive parts of
sound and colour
in their
number
;
and
it
will
now be shown
that
they arise out of one another in the same relative proportional quantities.
and most homogeneous of these forms be taken as the
If the first
tonic of a series, and forte,
gong will
in the
it
Plate
I.
it
fig.
account given of the laws of acoustics
monic
1.)
There
its
then
;
is
thus an octave formed
quantities,
analogous
to
the
in
bell
its
or
octave
diameter, and consequently
;
order to
musical
2.
— (See
and the other
must occur naturally within
forms
proportional triad,
on the piano-
the relative proportional quantity of 1 to
distinctive
relative
C
was represented by the
be another circle of only half
bearing to
two
to represent middle
same way that
the
in
made
it
make up
consonances
in
their
the
bar-
established
by the experimental enquiries of those great men, whose names are
too
treatise.
well
known
to
require
their
repetition
in
this
simple
SOUND, COLOUR, AND FORM.
It has
been shown that the
ascending from the tonic to this
its
sound, in the number of
the tonic as 5 to
musical consonance that occurs in
first
octave,
its
19
is
the third or medient
vibrations in a second,
is
;
and that
relatively to
In precisely the same proportional quantities to
4.
the length of the line forming the tonic, does the
homogeneous form,
the equilateral triangle, occur invertedly between the two circles. result arises
from dividing the outer
division of twelve,
carrying
it
and drawing a
circle into the
line
—thus producing, between the tonic and is
musical semitonic
from any one of these
across the inner circle three times its
This
— (See Plate
points,
I. fig.
octave, the medient.
2.) It
so in every respect, not only from being in relative proportional
quantity of circumference as 4 to 5, but as dividing the outer circle into three by
its
points,
parts, in touching
it
by
and the inner its sides.
circle into the
same number of
It also, in this capacity of medient,
forms, upon the convex surface of the inner circle, the dominant, the next homogeneous form, which
2 to
3,
and consequently
is
fore, invertedly, its medient.
is
relatively to the outer circle as
to the inner circle as 5 to 4,
This
is
and there-
accomplished simply by repeat-
ON THE ANALOGY OF
20
ing this medient line from each point round the Plate
L
The
circle, as
shown
in
fig. 3.
three kinds of line, the straight, the crooked, and the curved,
are those which combine in producing linear harmony, or the melody of form, as there are no other kinds of lines in nature.
these three kinds of lines
homogeneous forms
arise,
it
Out
has been shown that three equally
and that they likewise occur naturally
musical consonance, in every respect analogous to that of sound. will
now be shown
that
effects
upon one another are
by placing them together
relatively analogous,
of the
their
common chord
of
of the musician, and
its
in
It
also
in the three positions
two
inversions.
— (See
Plates II. and III.)
To show
that these forms, in thus arising naturally out of one
another, proceed inwardly to unlimited minutiae, as they do outwardly to magnitude, there has been given in Plate IV. a diagram contain-
ing four octaves, to which
is
added a scale of the
relative quantities
of line in the tonic, medient, dominant, and octave.
To
those unacquainted with music,
it
may be
here necessary to
SOUND, COLOUR, AND FORM.
mention, that the
common chord
musical note, with
its
is
medient
21
the simultaneous sounding of a
and dominant, generally accom-
panied by the octave of the tonic as a bass
;
that
its
three positions
are simply a change in the arrangement of these three notes, the bass remaining the same, and that
its
inversions produce a change
in its construction, as will be seen in the diagrams, Plates II.
and
III.
The
scale of the musician, however, contains, besides those three
elementary parts, other four of a secondary or intermediate kind,
making
in all seven.
These are
called the supertonic, the
subdomi-
nant, the submedient, and the subtonic, and act in melody as links to
unite the elementary parts
;
and they are suitable to
this purpose,
by
the relation they bear, in quantity or pitch, to the notes between
which they are placed.
In the scale of the colourist,
also,
there are
the intermediate or secondary hues, orange, green, purple, and neutral gray.
It will
be requisite, therefore, to the completion of this analogy,
that forms be found corresponding to these secondary notes and colours.
—
ON THE ANALOGY OF
22
The forms adopted The
for this purpose are
the rhombus,
parallelogram,
These secondaries
differ
from the primaries, because they admit
of being altered either in their length or width, while their other
dimensions remain the same, and they
still
retain the
same name and
character of form.
The
first
medient
of these, the parallelogram,
lines as
run
produced by such of the
one another, and those that form a
parallel to
hexagon within the outer
is
circle.
— (Plate
V.
fig.
properly the secondary to the square, although tity, as well as origin,
cannot lose
places
its distinctive
it
between the
character until
its
its
1.)
This form
is
proportional quan-
circle
and
triangle.
length be equal to
It
its
SOUND, COLOUR, AND FORM.
width
—the proportions of the
seem not to have given any particular figure, in
forming
it
23
homogeneous square.
Geometricians
fixed rules for the proportions of this
and consequently various modes have been adopted
—such
drawing a
as
line
from the opposite angles of a
square, and fixing that as the proper length of a figure of this kind,
whose breadth was equal to one of the
sides of such a square.
But
the parallelogram found in the natural key of the circle, by the means
way
preferable to this or any other propor-
same
relative quantity to the tonic, that the
explained, seems in every tion.
It stands in the
supertonic does in the scale of the musician.
The second
of these heterogeneous forms
is
the rhombus.
found naturally in the intersections of the medient Plate V.
It
fig. 2.
is
lines, as
It
is
shown
in
the secondary to the triangle, and consequently
holds the place of a fourth, or that of the subdominant, in the natural scale of the musician. differs
shown.
from that It
is
Its proportional relative quantity to the tonic
scale
by about a semitone, as
truly heterogeneous, by having
obtuse angles, and
it
can only lose
its
will
be afterwards
two acute and two
distinctive character
when
it is
ON THE ANALOGY OF
24
shortened until these become right angles, which will not be, as in the case of the parallelogram, until they produce the homogeneous square.
These two secondary forms should probably therefore, series,
in a general
be placed on each side of the dominant primary, or square, into
But the
which they resolve themselves. parallelogram gives
it
relative
the place of the supertonic.
quantity in the It
may
here be
observed, that the rhombus, thus occurring in the natural or general series,
has the same proportion of an acute angle that belongs to the
equilateral triangle.
The
third of the secondaries
is
the only form in the seven that does
not arise naturally between the circular tonic and the
which, although
ellipsis,
it
must have a place
as secondary to the circle, could not in
and
its
producing
all
figure
entirely will
had
its
octave.
It
is
in the general series
any way occur between that
octave by the lines drawn from the semitonic division the other forms.
this series of
be afterwards shown.
It might,
however, have been
left
out
forms been confined to a particular key, as Its
being formed upon two points renders
SOUND, COLOUR, AND FORM.
it
heterogeneous, and these points
creasing
its
relative length or breadth to
whatever these proportions ellipsis.
may be
— (Plate V.
may
placed near or apart, in-
any given proportions
be, the figure thus
It has
fig. 3.)
25
formed
is still
left
unoccupied by forms arising
out of the angles produced by the intersections of the straight
an archeus or key to the Indeed
well as tertiary forms.
it
this situation
neral principles be correct, this, like
many
The hexagon, although
in
secondary as
scientific
;
and should the ge-
other questions arising out
of the present enquiry, will be settled by those
more
series of
line.
would appear that these curvilinear
forms have a prescriptive right to
attention to, and employ
an
been placed in the situation of the
submedient, being the only situation
It will be next used as
but
;
who can devote more
knowledge upon, the
subject.
some measure the most heterogeneous
of all forms, being composed of oblique and perpendicular lines arranged circularly
round one point,
is
likewise,
from the same cause, a nearer
approximation to the homogeneous than any of the other forms the multiplication of
its
parts by
homogeneous form, that
two brings
at a little distance
D
it
it
;
for
so near the pre-eminent
can scarcely be distin-
—
ON THE ANALOGY OF
26
guished from
This form arises naturally out of the intersec-
it.
tions of the medient line,
and
it
is
in
some measure
like the neutral
colour of the chromatist, composed of portions of the three primaries.
— (Plate V.
fig.
4.)
These seven parts are adopted, as a general all
series
embracing
the requisite varieties of form, and not as those belonging parti-
cularly to the circle.
A
scale
of
forms belonging exclusively to the
produced by dividing lines 1 to
3 and
1
it
into twelve parts,
circle
will
be
and drawing the two
to 5, thus
and by repeating them from each division of the Plate VI. will be formed.
circle,
the diagram
SOUND, COLOUR, AND FORM.
The
intersections of these
two
lines,
27
thus repeated, will produce a
series of forms, which, together with the circle itself, will
These are given
seven.
amount
to
in detail in Plate VII., with a scale of their
relative quantities of circumference.
By
this scale
it
be seen,
will
that, leaving out the 7th, or dodecagon, all these forms increase
gradually, in the same relative quantities that are termed in the
arrangement of musical notes
full
tones
;
but that this 7th form
seems to stand halfway between the hexagon and therefore, differs
from that of the musician,
in
circle.
This
scale,
regard to the two
semitones that occur in a major key between the third and fourth,
and seventh and eighth degrees. ever,
The
scale of the musician,
was not always known or adopted
in its present
how-
state,
but
appears, in the earlier stages of the art, to have consisted of those notes
only which are
separated by complete intervals,
or whole
tones. It will
directly
be observed that the 2d, 3d, and 4th forms proceed
from the outer
circle,
the 2d from four points,
from three points, and the 4th from two
points.
the 3d
— (Plate
VII.
—
ON THE ANALOGY OF
28
fig. 1.)
While the other
three, the 5th, 6th,
upon the surface of the inner points,
the
(Plate VII.
6th at fig. 8.)
six
It
by touching the outer
circle
points,
may
also
;
the 5th touching
and the 7th
its
twelve
and the inner
octave at six points.
medient or 3d, by touching each of the well as the 4th,
at
at four
it
points
be worthy of remark, that the 2d,
circle at four points
connected with the tonic and
and 7th, are formed
which touches the outer
So
at two, also
is
is
the
circles at three points, as
circle at two,
and the inner
at four.
By
drawing a
4th, thus
line
from the
1st to the 2d,
and from the
1st to the
—
and repeating these two and square
are
lines
from
formed within
it
all
the divisions, a dodecagon
from these
points,
as
shown
SOUND, COLOUR, AND FORM.
in the diagram. will
outer
be
—(Plate
found
circle,
in
VIII.
fig.
By
1.)
arrange
the
same order
that
these lines the forms
on
themselves
to
29
the
they are
inside
formed
of
the
by the
other two lines on the outside of the inner circle, by the intersections of the medient lines.
It will
be seen from Plate VIII.
that the square thus formed meets the dominant square, by sides touching the outer angles of that form.
gives these It
two
series
six distinctive
this, as well as
forms arising out of
tones, that they
this
circle;
inner
lines.
from the circumstance of the diagram being divided by
may be numbered from
from the inner to the outer
full
the outer to the inner, or
for the medient will take the
place of the dominant, and the dominant that of the medient, thus
s
2,
Fig. 3 of Plate VIII.
connected by the medient
would appear from
its
fig.
:
Dominant.
Medient
There
is
another very striking musical analogy in the situations of
ON THE ANALOGY OF
30
the intersections, which produce those forms within the diagram of the circles.
If the space between the circles be divided into the
semitonic or musical division of twelve parts, by circular lines formed
round the same point, the seventh of these will pass
lines
from the outer
through the intersections of the medient
the dominant.
At
lines that
drawn from the
1st to the 4th,
produced a dodecagon, the most consonant form to the
The same
produce
this point, also, the intersections of the larger
square, formed by the lines
series.
circle
have
circle in the
takes place on the third line from the outer circle,
corresponding to the minor third of the musician
:
and
exactly where the oblong intersects the medient lines.
this occurs
It will also
be observed from the diagram, Plate IX., that the lines being drawn
from twenty-four points, the equilateral triangles or medients
inter-
from the outer
circle.
sect themselves at the fourth circular division
The consonances
thus occurring amongst these forms
are
quite
apparent in the diagram.
The now
scale arising out of the secondary
claims attention.
The
ellipsis
forms in the general series
must take the place of the
circle,
SOUND, COLOUR, AND FORM.
31
the rhombus that of the triangle, and the parallelogram must
the dominant. is
of a
its
of
harmony produced by
this class of
forms
more subdued and pleasing kind than that produced by the
primaries. like
The kind
become
The
ellipsis
being a compound form, and not occurring,
the other two secondaries, in the original diagram of the circle,
proportions should be those of the parallelogram, which neces-
sarily inscribes
it,
as dominant.
In adopting this form as a tonic, (Plate X. that,
by drawing medient
lines
between
it
and
medient and dominant are formed, (Plate X. latter is in relative proportional quantity
from the outer ellipsis,
ellipsis,
fig. 1,) it will
its
be found
octave, the proper
figs. 2,
3
;)
but that the
about a semitone further
and therefore about as much nearer the inner
than in the series of the
circle
ascent of the forms in the ratio of the
duce sounds, instead of the
;
consequently, in counting the
number
of vibrations that pro-
size of the bodies that vibrate, this
would hold the situation of a minor
third, or medient.
as the other trifling discrepancies noticed,
reconciled in this elementary treatise
;
it is
is
form
This, as well
not attempted to be
enough
in it to
show that
ON THE ANALOGY OF
32
these secondary forms have the elements of harmony, although that
harmony be of a
different kind
nation of the primary forms.
may be
forms, which
from what
is
produced by the combi-
In Plate XI. there
is
given the four
called the secondaries in this series.
diagram of the secondaries, the intersections of the
lines
In
this
drawn from
the 1st to the 3d and 5th divisions produce a perfect square, and the lines
from the
sides a
1st to the 4th,
two perfect
rhombus and hexagon of the same proportions
circular diagram, in addition to those forms
to
equilateral triangles, be-
itself.
figs. 2, 3,
The manner and
Thus the
in
more
which these occur
is
peculiarly belonging
shown
in Plate
XL
5.
primaries seem to accompany the secondaries in their
formation, as the secondaries did the primaries.
No
of ellipsis would produce this result, as will be
shown
of the third class of forms.
correct in
as those in the
its
It
other proportion in the
diagram
may, therefore, be assumed to be
proportional relation to the circle, the pre-eminently
homogeneous form. In Plate XII. the secondary forms arranged as the
common
chord,
SOUND, COLOUR, AND FORM.
with
its
and inversions, are given.
positions
corresponding to these, reference as
it is
may
be
made
33
For the musical notes to Plates II.
and
III.,
not intended to go into the subtleties of musical transposition.
In the primary series of forms arising from the intersections of the lines drawn between the circles, from the 1st to the 3d and 5th,
the parallelogram, or second of the series,
is
that which gives the pro-
portions of the curvilinear form, which produces the secondary series. So, likewise, in this secondary series, there occurs another parallelo-
gram, (Plate XI.
fig. 1,)
which
used in proportioning an
is
which acts as tonic to give a third
class of
forms of a
dued and pleasing kind, as in the general character of
still
more sub-
their horizontal
Of these forms
curves and angles they approach nearer that of nature.
a general diagram, with the medient and dominant,
ellipsis,
is
given in Plate
XIII., without going into further details, as they are regulated by similar laws to those which govern the primaries It will
now be
necessary to notice the
melody of form. In music the simple
and
is,
of course, regulated
and secondaries.
harmony of
air to
succession, or the
be performed
is
the melody,
by the relation which musical notes have E
ON THE ANALOGY OF
34
when produced
to one another, as in the
singly to the ear
harmony of combination.
;
not simultaneously,
Colours have also a somewhat
similar relation in succession, as noticed by Field in his excellent
and truly philosophical works on chromatics.
The melody defined.
It
of form, or
is
line,
may
be termed linear harmony,
simply the general outline
straight line in either of
angular
it
its
and the curved
—the
two positive line, follow
manner
in
is
easily
which the
positions, the crooked or
one another.
This
is
very
important in architecture and sculpture; the compositions of those arts being in
most cases
liable to
be viewed against a light sky, in
which situation the melody of form alone
is
appreciable.
In music, the rules of melody are quite correlative to those of
harmony, the general outline of an of the
common
ever filling-up
the
is
chord in some of
air
its
being the component parts
positions or inversions
produced upon the
ear.
So
also
what-
will
be regulated by
effect
intended to be
used to connect those parts,
nature of the subject and consequent
;
must the three kinds of
lines or
forms which they inscribe, be employed in the outline of every
SOUND, COLOUR, AND FORM.
composition of architecture, in eye
;
and the
which
it
effect will
all
cases
where
it
35
alone
may meet
the
be doubly enhanced when the combinations
inscribes are apparent
and equally harmonious.
may be
In combined harmony, notes at considerable intervals
produced simultaneously, and a perfect consonance of sounds produced
;
but in melody the passage from one part to another, must
in general be gradual
and connected.
This
is
precisely the case in
regard to form, and appears to have been a rule observed in best architectural productions of the ancients.
Indeed
it
all
the
appears very
evident, that something like the musical arrangement of sounds
had
been adhered to in the linear harmony of those great works.
The melody
of an edifice
may
enter into combination with sur-
rounding objects, or the ground upon which
form an independent melody of Architecture, in
its
its
original productions,
its
effect.
placed, or
it
may
own. is
sculpture or painting, and must therefore natural principles for
it is
The
five
not an imitative
art, like
depend exclusively on
orders evidently
owe the
varied excellence of their proportions, and indeed their existence, to
ON THE ANALOGY OF
36
an adherence, intuitively or by acquirement, to those principles on the part of their originators, otherwise they could not have afforded
models of study to
all
But
succeeding ages.
an immeasurable degree
as nature surpasses in
works of imitative
art, so
do natural
principles, in the inexhaustible variety they present, the
works that
all
mankind have formed upon them.
The most exists,
is,
since
its
perfectly harmonious production in architecture that
by the concurrent opinion of the best judges in production,
structure owes
its
the Parthenon
at
Athens.
all
ages
Whether
this
perfection to an acquaintance with a particular
system of applying the natural principles of form to architecture, lost to
alone,
is
succeeding ages, or to the natural genius of the designer a matter of doubt, and
may
ever remain so.
But whether
the knowledge of the artist was acquired or intuitive,
it
must be
admitted that the elements of harmony are transcendently displayed in this great
work.
The melody
or general outline of the temple itself seems to enter
into combination with the hill
upon which
it
stands,
and thus to make
;
SOUND, COLOUR, AND FORM.
up the harmonic triad of the third to be
shown
in Plate
XIV.
class of forms.
37
This
strong
component parts of the temple occur,
line.
endeavoured
In the centre of the diagram formed by the
repetition of the line 1st to 5th, within the ellipsis,
that the
is
it will
as
be observed
marked by the
These being removed from the harmony of combination
to that of succession, the curve of the ellipsis
mental bass, and the temple
itself supplies
becomes
its
funda-
the other two component
parts of a melody.
This melody
is
only appreciable at such a distance as allows the
general outline of the temple, in combination with the
which
it
hill
upon
was placed, to be encompassed by the eye of the spectator
consequently when he ascended the Acropolis, the curvilinear forms,
which at a distance
made up the harmonic
triad,
disappeared.
Instead of which, however, the most beautiful harmony of combination was presented to his view, accompanied, as has been proved
by late investigations, with an equally perfect harmony of colour.
The
curvilinear
form, so amply supplied in the distance, which,
like cool colours in nature,
always predominate in the most pleasing
ON THE ANALOGY OF
38
combinations, he
now
in the horizontal
and perpendicular
exquisite
The
taste
bas-reliefs
finds in equal proportionate quantity, not only
which
lines of the
embellish
and knowledge of the
the
artist
is
columns, but in the
frieze
and tympanum.
further displayed
;
for
that there might be no harsh or sudden transition from the curved to
the
perfectly straight line,
the architrave, frieze,
and cornice
approach the tympanum by an almost imperceptible curve. 3 In thus gliding, by an imperceptible gradation, from one component part of harmony into another, a
facility easily
form, but which can only be attained in music by the is
made
The
attainable in
human
voice,
available.
portico or front elevation of this temple, from the base of the
columns to the extreme point of the pediment,
is
inscribed by the
parallelogram, adopted in this treatise as the second of the general series of forms.
It
has been already observed, that geometricians
have given no definite rules for the proportions of
form
;
remark
this particular
but that in question has peculiarities which are worthy of in this place.
—
SOUND, COLOUR, AND FORM.
It
the only rectilinear form that
is
of the circle, therefore requiring in
which
is
drawn from the
not produced by the inter-
is
drawn from the
section of the medient line,
first
39
first
to the fifth division
formation the second
its
to the third division.
equilateral triangle, the square, nor the
line,
Neither the
rhombus, can be reproduced
by any smaller number of forms of a similar kind and proportion to themselves than four
;
and
it
takes the
same number of parts to
reproduce a parallelogram of any other proportions
reproduced by three, and also by four. the semitonic division of twelve, divisions
;
larly, their
consequently,
its
Plate
it
shortest dimension
XV. The
be seven of those
are placed together perpendicu-
seems in the present case to be employed, is
therefore divided, as
shown
in the scale
subdivision of the parts of this unequalled structure
are, agreeably to this scale, as follows
The
will
length will be collectively twenty-one of those divisions.
In this triple capacity
and
when three
but this can be
If its length be divided into
breadth
its
;
.
perpendicular and obviously curvilinear portion ends, and the
horizontal or rectilinear portion begins, on the
seventh semitonic
ON THE ANALOGY OF
40
dominant of the
division of the parallelogram, the perfect 5th or
present scale of the musician. linear part ends,
The
horizontal or apparently recti-
and the oblique or angular part commences, on the
next musical consonance, the 6th or submedient of the same scale.
—(Plate XV.) Taking the dimensions from the elevation of the portico in Stuart's
column
is
Athens, the minute groove cut below the capital of the
one of these semitonic divisions.
From
centre to centre
of the columns, on each side of the middle space, divisions,
and
this is continued,
includes the columns
is
three of those
The
till
the last
space which
exactly the proportion of the second paral-
lelogram produced within the
ellipsis,
as the first
was within the
If this be divided into twelve parts, the capital will be
circle.
to be
is
with a slight deviation,
which must include the outer column.
division,
as given
found
one of these in height, and the triglyphs one of the same
breadth.
But
architect,
whose education enables him to enter
in
these matters can only be properly investigated by the into details with
which the unprofessional are necessarily unacquainted.
;
SOUND, COLOUR, AND FORM.
Amongst
the architectural remains of ancient
41
Rome,
the Pantheon
perhaps one of the most perfect specimens of harmony
is
interior, in
its
ment of
which there appears an evidently musical arrange-
parts, ascending in full tones agreeably to the series of forms
that belong to the circle.
From
— (Plate XVI.)
the peculiar construction of the interior, there seems to
have occurred some
difficulty in
ever, has been obviated
of the
especially
;
dome
harmonizing
its
outline, which,
how-
by the angular work which unites the curve
to the perpendicular line of the exterior wall.
This
angular form acts as a medient, and completes the harmonic triad.
The
geometrical elevation of the wall
the portico
is
composed of this and the
is
the
first
parallelogram, and
rhombus.
This structure being upon a level base independently of situation, having within
first
— (Plate XVII.)
perfect in
is
itself
its
outline,
the three elements
of harmony.
In the street architecture of Rome, perhaps the most perfect specimen
is
the Farnese Palace.
Here no general
but the combination and arrangement of F
its
outline
is
required
parts display a perfect
ON THE ANALOGY OF SOUND, COLOUR, AND FORM.
42
and most beautiful arrangement of the three component parts of linear
harmony,
in the judicious
admixture of the curve, the angle,
and the straight line— (Plate XVIII.) In conclusion, the scale of forms adopted in this treatise as the elements of harmony, and the lines by which they are produced, are, in the
same
plate,
brought into comparison with the scales of
the musician and colourist, in order to like
sound and colour, has
its
make
three primaries
it
;
more
clear that form,
and that consequently
there can be no perfectly harmonious combination of forms in which
one of these
is
wanted
;
and that the distinctions of harmony,
like
those of sound and colour, depend upon a predominance of one, and
a subordination of the other two, in the composition.
—
—
; :
NOTES AND APPENDIX. NOTE An
1.— Page
Essay on Taste by Sir Thomas
2.
Dick
Lauder,
accompanying the
Third Edition of " Sir Uvedale Price on the Picturesque," 8vo.
Edinburgh
1842.
NOTE
A
2.— Page
3.
on Architecture by William Hoskins, F.S.A., Architect,
Treatise
4to.
Edinburgh: 1835.
There are many excellent observations on the harmony of form of
which the following are a few
in this treatise,
:
" Simplicity and harmony are the elements of beauty in architecture plicity in the general
collocation
"
in architecture
is
parts, as in the relation of a
its
various parts."
that agreement
column
part of a composition with another.
and
exist, too,
These
between the
facts the
tectural details,
and concludes
solids
and
*
*
which
exists
;
between
and
its
various
stylobatc, in the
crowns, and in the coherence of one
and
which
it is
*
exists in the
that
*
*
vacuities of
an
enrichment and decoration."
circular in
must
it
It is that
lines of a structure
*
to its entablature
accordance of a cornice with the elevation
dency of the leading
sim-
form and arrangement of a subject, and harmony in the
and combination of
Harmony
;
common
which blends the
"A degree
of
ten-
straight
harmony
edifice."
author in question exemplifies by referring to various archi-
which must be of great value
to students in that particular art
:
" Thus, harmony has reference to comparative magnitude, strength, decoration, disposition,
and proportion.
produce a worthy
result,
To
acquire a knowledge of
all
these sufficient to
a long course of study and careful observation are
44
NOTES.
necessary
:
but such can only be necessary to the architect
general student to be able to appreciate them
The Author
absence."
natural principles of
when
;
present,
it is
and
enough
for the
to detect their
of the present Treatise, in attempting to point out the
harmony
in form,
and
aims
their application to architecture,
at the latter result alone.
Mr
Hoskins
also gives
some
chitectural Composition," in
excellent observations
which he shows
that,
rent in the widely differing species of horizontal
the elements of architectural beauty
on the " Principles of Ar-
although these must be
and
diffe-
vertical architecture,
must be the same
in
all.
still
This will be
found to be precisely the case with the forms produced between the curvilinear tonic
the
and
its
octave.
The
depressed obtuse-angled triangle, produced by mixing
rhombus with the parallelogram
horizontally,
is,
when
the parallelogram
stands vertically, replaced by an acute-angled triangle, from the necessarily
mixed with
it
in a vertical position.
NOTE Colonel
Mure
rhombus being
3.— Page
38.
of Caldwell, in a note to his excellent " Journal of a
Tour
in
Greece," mentions that, during his residence at Athens, a Bavarian architect, by a series of observations carried on with great nicety through every portion of the
Parthenon, had ascertained that there was not a straight line of any considerable length in the whole extent, with the exception of those of the pediments. horizontal lines of the basement, architrave, frieze,
and
cornice,
he found
The to
be
curved upwards, but in so slight a degree as not to be perceptible unless on very accurate inspection several other
that in
a
;
and
members
letter
that these observations
of the
same
from Athens, read by
Society of Literature, on the 13th of liarity is also
Colonel
profession.
W.
be verified by
Mure
also mentions,
Hamilton, Esq., to the Royal
March 1840,
observable in the Theseum.
to
were said
it is
stated that the
same pecu-
—
—
—
APPENDIX. In the progress of
this
enquiry
many
observations of apparent interest suggested
themselves, the introduction of which into the body of the treatise might have
rendered
it
more tedious and obscure than add them
therefore has been thought better to
Combinations of
lines
seem
to
straight line placed perpendicularly
is
in
is
its
present state, and
it
in this form.
have their discords as well as concords.
upon an oblique
line,
A
thus
discordant, for the former will appear to lean towards the
latter.
upper end of the
Therefore no vertical form ought to be placed upon an inclined base,
without the intervention of a horizontal upon, and in contact with, a curved
is
it
likewise discordant, as
Oblique
lines
it
will
line.
line,
A straight line placed horizontally
thus
appear curved, but in the opposite direction.
can only produce pleasing forms where their obliquity
is
in the
same degree, thus
or any other such combination of the oblique
and
straight line,
is
inharmonious.
—
;
APPENDIX.
46
Curved meet them
lines
can only combine harmoniously with straight lines
at right angles
are harmonious
when they
thus
:
while such combinations as
;
are discordant.
The
circle, as
being the most simple of the primary forms, has been adopted
key or tonic
as a
more
fitted to
having,
to
what may be termed the natural
hold this
when made
situation from
to represent
scale of forms.
being the form of the eye
its
It is the itself,
an octave of form, by inscribing another
and
circle
of the relative proportion of 1 to 2, a peculiarity exclusively belonging to that organ.
The
inner
circle,
agreeably to the analogy attempted to be established,
cannot be increased beyond
this relative
diminished in the ratio of
1
shown
to 2, until
in the diagram, Plate IV.
the eye cannot approach the
iris
It
to this
In
it
like
;
but
it
may
arrives at inappreciable minutia, as
manner, the pupil or inner
it
seems
to
circle of
have the power of contraction to
diagram.
has been observed that the series of forms in which the
place of the circle, exercises a softer influence on the eye tions of those forms are
continue to be
or outer circle nearer than a certain distance
while in viewing minute objects
an extent similar
proportion
more
natural,
;
ellipsis
takes the
and that the combina-
and the harmonies they produce more
pleasing, than those arising out of the combinations of the forms
which have the
APPENDIX. This would,
circle for their key. it
must be taken
eyes,
whose rays
at first sight,
into consideration that
we
47
are
made
traverse or cross each other horizontally
to
—
earth, air,
that, consequently,
encompassed by
easily
The
more primary or homogeneous forms.
in this double capacity associates
three elements
view nature with two
and
;
any object of a horizontally elongated kind can be more the visual rays than any of the
But
appear quite paradoxical.
eye
rays at once with the forms in which the
its
—
and water
are generally presented to our view,
and
in which, consequently, the landscape-painter generally transfers their effects to his canvass.
Landscape composition has ture, or historical painting
;
its
and
linear
it
In
this, as
as well as architecture, sculp-
likewise consists in the judicious arrangement
of the three elementary parts of form
the curved line.
harmony
—the
in every case
straight line, the angular line,
and
where various forms are combined,
But
there can be no perfect composition, unless the harmonic triad be present.
the parts of this triad must not be jumbled promiscuously together, however irregular the general character of the subject
there
must be system in
it,
may be
for if linear
;
as there is in every other
system must consist in certain geometrical
rules.
to be developed in the foregoing treatise
and
;
harmony
kind of harmony
Such a system it
is
assumed that
leading features of a natural theory in the extreme simplicity of parts,
and the endless variety of combination of which they are
The harmony a
strict
forms
—
of forms depends
much on
the circle, the triangle, and the square
The
tertiary forms
positions
first,
— have
attempted it
is
has the
elementary
and
three primary
each only one proper
indeed, can take no position but one, while the secondary and
strictly
adhered to
;
vertical.
These
for obliquity in this case is inadmissible,
and, as already shown, can only be employed to produce angular forms. the circle
this
susceptible.
The
have two proper positions, the horizontal and
must be
its
and
the propriety of their position,
adherence to the key or tonic in a composition.
position.
is
;
exists,
the key or tonic adopted, the square
and
When
equilateral triangle will
—
APPENDIX.
48
When
be the leading features of the forms introduced into the composition. the ellipsis
is
the tonic, their leading features will be the parallelogram
rhombus, whether the composition be horizontal or
No
doubt
men
kind
But
not attended
is
men
of
Indeed
genius.
to.
knowledge
to such, a
rules are requisite to enable the generality of
appreciate judiciously the works of
to
and
of great genius can do this intuitively,
of rules is superfluous.
There can be no
vertical.
properly harmonious composition in which this classification
and
manit
is
presumed, that the dissemination of a general knowledge of the fundamental
would in
principles of art,
this
way do more
of tuition directed immediately to the
cannot
lie
dormant
it
has done so in
it
appears.
But
—
all it
it
improvement of
ages,
It is well
weed it.
known
and only requires
its
known and encouraged when The
greater the
in the
advancement of
art, if
not strictly
be the mischief
in the cultivation of the fruits of the earth, that
and
it
is
which
it
upon the
were
would soon choke and
extingiiish the efforts of real genius,
arts, if
by withdrawing
alone has a right to receive.
effects of vibratory
bodies upon the
air,
and the manner
ear, it
appeared to the author very probable
composed of three
different kinds or forms of particles,
effects act
that atmospheric air
quite unappreciable to the senses in any other
way than by
suppose this requires no great stretch of the imagination. fact, that
and academics
to its legitimate object, the greater will
roots that nourishment
which these
be
Real genius
In like manner will pretension and mediocrity in the
In investigating the in
to
fostered along with the useful plant,
equally fostered, choke
from
students.
never can be properly fostered while the public arc unable
and judiciously confined
extinguish
its
will shine forth independently of schools
amount of money expended nominally
the useless
advancement than any system
from mere pretension or humble mediocrity.
to distinguish it
done.
to its
the rays of the sun,
which appear
of three distinctly different colours
—
these effects.
To
It is a well-established
to us quite colourless, are
composed
—which, by
refraction,
blue, red,
and yellow
APPENDIX. are
made
to
49
appear distinctly visible to the eye, accompanied by other four
intermediate hues.
If,
therefore, a substance so subtle
and impalpable
as light
has been proved to be composed of three primary parts, the supposition here
advanced
is
worthy of some attention.
which the variety
in the elements that
rent to the eye,
by
is
made by such means
refraction to
;
and
The
only means,
compose white
is
it
believed,
by
be made appa-
light can
that these primitive elements can never be
appear unaccompanied by the other two in combination,
because (as the Author has elsewhere stated*) they seem to have an affinity to
When,
one another that prevents their actual analyzation. that there are only three primary sounds produced as the three colours are produced
sounds have,
by the
;
it is
found
by the agitation of the
refraction of light
corresponding secondaries
too, their
therefore,
;
air,
that these three
and that no sound can be thus
produced unaccompanied by the other two which make up the triad of harmony
—
it
would appear that these mediums of communication between external and the senses correspond
nature
in
their
component
parts.
The
author
has been confirmed in this supposition by such experiments as he has had an opportunity of performing, and which he thinks
He may,
treatise at present to publish.
to
him
that a certain
number
it
apart from the object of this
however, remark, that
it
appeared clear
of vibrations in a second affected a certain class
of those particles particularly, while the other two were affected subordinately,
producing the harmonics, and that the secondary or intermediate notes were
produced by two of these classes of particles being simultaneously and equally affected.
near,
and
These to
particles
may
be supposed to be circular, angular, and
rectili-
correspond to one another in the relative proportional musical
quantities or intervals.
They may
also
be subject to horizontal compression in
proportion to the density of the atmosphere, in which case they would become
*
Laws
of Harmonious Colouring, 4th edition.
G
APPENDIX.
50
horizontally lengthened,
and in the same
ratio vertically shortened, thus bring-
ing distant objects more distinctly into view, and conveying distant sounds
more
distinctly to the ear.
But
this supposition
is
advanced with much
dence.
Erratum
—
for Medient, read
Mediant.
EDINBURGH: MINTED BY BALLANTYNH AND HUGHES. PAUL'S WORK, CANONGATE
diffi-
PLATE Fit/. 1.
I.
PLATE
II
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PLATE Fig.
III.
1
Original rhoril
Fig.
2.
I? Inversion
A
a
^ :
Fig.
.3.
'J? hirrrsion
m—
PLATE
IV.
PLATE
V.
PLATE
Diagram cvrUawzng
all
ftic
VI.
forms thai arise within an octave of the
circle.
r ATE I.
ML
Tig.1.
:
*s
PLATE VUL
PLATE
IX
PLATE
Diagram, ccntjunmg
the
X.
farms that arise within an
Figl.
octave,
of
the,
ellipsis
PLATE
XL
PLATE
XH.
plate xnr.
PLAT E XIV
Mi'/mhi
nt
/J/,- Pii/Y/'/ii
Hi'' r]i,
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Pu/fhuwu
PLATE XV
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PLATE Wl
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PLATE
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PLATE XVin.
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