D r hay, the natural principles and analogy of the harmony of form by A. Lynn

Ulrich Middeldorf

Digitized by the Internet Archive in

2013

http://archive.org/details/naturalprincipleOOhayd

THE

NATURAL PRINCIPLES AND ANALOGY OF

THE HARMONY OF FORM. BY

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

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

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.

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

â&#x20AC;&#x201D; " 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.

nature and art possess an union, or composition of uniformity and variety, of similarity

combination in

and

itself beautiful, it

every case where

mere union of tiful

And

Alison,

and

similarity

or imagine a correspondence

— that

combining

different

of the

support of this says

fact,

the author in

— " Every one knows

say, that

among

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

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

subject, that

in this art

must be obvious, that

—

" It

may

on which taste may

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

simplicity, attract the attention of the rudest

mind, which

pleased without being conscious why, and of the most learned or

practised,

which discovers

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

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

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.

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

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

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.

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.

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

fit

follow any of those arts as a profession, or enhancing the pleasure

conveyed to the mind by the visual organ.

person

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

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.

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,

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

not uncalled

for.

Neither can a knowledge of these principles

number of

tend, in any way, to add to the

design

will rather lessen

untalented pretenders in sterling genius will

all

;

professors of the arts of

for as the public taste improves,

such professions

meet the encouragement

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

artificial

greater degree, by the

analogous to sound

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

orator, as

of the

susceptible is

more powerfully tones

of the

meaning

affected, in point

vocalist

more powerful, though

the

still

;

and to a

artifi-

ON THE ANALOGY OF

cial,

effects

produced by the combination of vocal and instrumental

music.

The

first

of these effects

a mere auxiliary to the meaning con-

veyed by the oration of the speaker

;

and

a powerful one

â&#x20AC;&#x201D;

the response in the mind to the natural principles which regulate

all

sounds accompany the words, which address themselves at the same time to the judgment.

In vocal music, the

effect of

the melody

generally fully as powerful as that of the meaning contained in the

words which accompany witli

instrumental music

and although the combination of

;

perhaps more

artificial, it is

still

this

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

harangue of the orator, addresses

judgment than the senses

of the sculptor not only

tell

;

the

artistical

a story, but do so in a

itself

combinations

way which

;

SOUND, COLOUR, AND FORM.

capable of exciting the feelings to the highest pitch to which expression,

still

combined with form, can carry them

upon the

artificial,

eye,

;

and there are

though more comprehensive,

effects

also the

produced

by the combination of expression, form, and colour,

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

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

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

sensual,

effects

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

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

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

and

;

that,

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

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.

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

audible sound

a second.

;

and

limited in the range of is

has been ascertained, that

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

perception

great

;

but

not

men who have

so.

The

would

at first sight

The

experimental

investigated the subject.

ON THE ANALOGY OF

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

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.

and the dominant.

this

their relative

invertedly, in proportion to the vibratory

These three sounds are respectively

pose

;

Let another

were

bell

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

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

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

when the

There

what

no greater

can, therefore, exist

found between the tonic and

therefore the

first

its

octave.

homogeneous sound, and always

vibrations are as 2 to

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

of vibrations are relatively to

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

acute, but are of a distinctive character relatively to

same time combining with

;

at the

harmony, producing together the

most perfect consonance.

When

elastic

body

musical note, which

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

has

â&#x20AC;&#x201D;

ON THE ANALOGY OF

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

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

harmony of forms,

are produced

by these simple elements.

The

straight line has three positions

line

may be

perpendicular,

horizontal,

The crooked

may

or oblique.

be crooked in three different ways

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

ellipsis,

may

be or of a volute.

the varieties of which the three kinds of lines are

straight line,

not horizontal or perpendicular, must

;

ON THE ANALOGY OF

be oblique

two it

for

;

however near

positive positions, so long as

remains

arises

that

still

There

oblique.

the right angle

;

ellipsis

will

The curved

still

it will

and

line,

when

may have a long

form a portion of an

no part of ellipsis,

only one positive angle, and that

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.

or other of

out of the two positive positions of the straight

may approach

for

may approach one

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

a volute.

Lines are, however, merely used to show where a form ends, and

commences, and must now be considered

the space that surrounds

mathematically, that

as having length without breadth; at the

is,

same time they must be used

physically,

the only

forming the geometrical figures and diagrams that follow.

mode

â&#x20AC;&#x201D;

SOUND, COLOUR, AND FORM.

sound and colour, so

primitive,

homogeneous parts

in form, there are only three simple,

;

and they are

the circle,

line

and the square.

the triangle,

these three, the

produced by a single

The

line

pre-eminent for simplicity, being

circle is

drawn round a

equilateral triangle

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

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

The

any of their parts without changing their character.

pri-

mitive parts of form are thus analogous to the primitive parts of

sound and colour

in their

number

;

and

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

Plate

fig.

account given of the laws of acoustics

monic

1.)

There

its

then

;

thus an octave formed

quantities,

analogous

the

bell

its

octave

diameter, and consequently

;

order to

musical

â&#x20AC;&#x201D; (See

and the other

must occur naturally within

forms

proportional triad,

on the piano-

the relative proportional quantity of 1 to

distinctive

relative

was represented by the

be another circle of only half

bearing to

two

to represent middle

same way that

the

made

make up

consonances

their

the

bar-

established

by the experimental enquiries of those great men, whose names are

too

treatise.

well

known

require

their

repetition

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

the third or medient

vibrations in a second,

;

and that

relatively to

In precisely the same proportional quantities to

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

and drawing a

circle into the

line

â&#x20AC;&#x201D;thus producing, between the tonic and is

musical semitonic

from any one of these

across the inner circle three times its

This

â&#x20AC;&#x201D; (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

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

and consequently

fore, invertedly, its medient.

relatively to the outer circle as

to the inner circle as 5 to 4,

This

and there-

accomplished simply by repeat-

ON THE ANALOGY OF

ing this medient line from each point round the Plate

The

circle, as

shown

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,

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 the musician, and

its

also

in the three positions

two

inversions.

â&#x20AC;&#x201D; (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

added a scale of the

relative quantities

of line in the tonic, medient, dominant, and octave.

those unacquainted with music,

may be

here necessary to

SOUND, COLOUR, AND FORM.

mention, that the

common chord

musical note, with

its

medient

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,

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.

â&#x20AC;&#x201D;

ON THE ANALOGY OF

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

circle.

â&#x20AC;&#x201D; (Plate

fig.

properly the secondary to the square, although tity, as well as origin,

cannot lose

places

its distinctive

between the

character until

its

1.)

This form

proportional quan-

circle

and

triangle.

length be equal to

its

SOUND, COLOUR, AND FORM.

width

â&#x20AC;&#x201D;the proportions of the

seem not to have given any particular figure, in

forming

homogeneous square.

Geometricians

fixed rules for the proportions of this

and consequently various modes have been adopted

â&#x20AC;&#x201D;such

drawing a

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

the rhombus.

found naturally in the intersections of the medient Plate V.

fig. 2.

lines, as

shown

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

Its proportional relative quantity to the tonic

scale

by about a semitone, as

truly heterogeneous, by having

obtuse angles, and

can only lose

its

will

be afterwards

two acute and two

distinctive character

when

it is

ON THE ANALOGY OF

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

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

the only form in the seven that does

not arise naturally between the circular tonic and the

which, although

ellipsis,

must have a place

as secondary to the circle, could not in

and

its

producing

all

figure

entirely will

had

its

octave.

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.

heterogeneous, and these points

creasing

its

relative length or breadth to

whatever these proportions ellipsis.

may be

â&#x20AC;&#x201D; (Plate V.

may

placed near or apart, in-

any given proportions

be, the figure thus

It has

fig. 3.)

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.

this situation

neral principles be correct, this, like

many

The hexagon, although

secondary as

scientific

;

and should the ge-

other questions arising out

of the present enquiry, will be settled by those

series of

line.

would appear that these curvilinear

forms have a prescriptive right to

attention to, and employ

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,

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

;

for

so near the pre-eminent

can scarcely be distin-

â&#x20AC;&#x201D;

ON THE ANALOGY OF

guished from

This form arises naturally out of the intersec-

it.

tions of the medient line,

and

some measure

like the neutral

colour of the chromatist, composed of portions of the three primaries.

â&#x20AC;&#x201D; (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.

scale

forms belonging exclusively to the

produced by dividing lines 1 to

3 and

into twelve parts,

circle

will

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,

thus repeated, will produce a

series of forms, which, together with the circle itself, will

These are given

seven.

amount

in detail in Plate VII., with a scale of their

relative quantities of circumference.

this scale

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,

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

â&#x20AC;&#x201D; (Plate

VII.

â&#x20AC;&#x201D;

ON THE ANALOGY OF

fig. 1.)

While the other

three, the 5th, 6th,

upon the surface of the inner points,

the

(Plate VII.

6th at fig. 8.)

six

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 four

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

at two, also

the

circles at three points, as

circle at two,

and the inner

at four.

drawing a

4th, thus

line

from the

1st to the 2d,

and from the

1st to the

â&#x20AC;&#x201D;

and repeating these two and square

are

lines

from

formed within

all

the divisions, a dodecagon

from these

points,

shown

SOUND, COLOUR, AND FORM.

in the diagram. will

outer

â&#x20AC;&#x201D;(Plate

found

circle,

VIII.

fig.

1.)

arrange

the

same order

that

these lines the forms

themselves

the

they are

inside

formed

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

Fig. 3 of Plate VIII.

connected by the medient

would appear from

its

fig.

Dominant.

Medient

There

another very striking musical analogy in the situations of

ON THE ANALOGY OF

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.

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.

the rhombus that of the triangle, and the parallelogram must

the dominant. is

of a

its

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

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,

;)

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

form

This, as well

not attempted to be

enough

in it to

show that

ON THE ANALOGY OF

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

produced by the combi-

In Plate XI. there

given the four

called the secondaries in this series.

diagram of the secondaries, the intersections of the

lines

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

equilateral triangles, be-

itself.

figs. 2, 3,

The manner and

Thus the

which these occur

peculiarly belonging

shown

in Plate

primaries seem to accompany the secondaries in their

formation, as the secondaries did the primaries.

of ellipsis would produce this result, as will be

shown

of the third class of forms.

correct in

as those in the

its

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

made

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,

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

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,

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

the melody,

by the relation which musical notes have E

ON THE ANALOGY OF

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.

of form, or

line,

may

be termed linear harmony,

simply the general outline

straight line in either of

angular

its

and the curved

â&#x20AC;&#x201D;the

two positive line, follow

manner

easily

which the

positions, the crooked or

one another.

This

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

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

chord in some of

air

its

being the component parts

positions or inversions

produced upon the

ear.

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

effect will

all

cases

where

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

precisely the case in

regard to form, and appears to have been a rule observed in best architectural productions of the ancients.

Indeed

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

original productions,

its

effect.

placed, or

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

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

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,

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,

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

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.

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

it will

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

only appreciable at such a distance as allows the

general outline of the temple, in combination with the

which

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

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

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,

inscribed by the

parallelogram, adopted in this treatise as the second of the general series of forms.

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.

â&#x20AC;&#x201D;

SOUND, COLOUR, AND FORM.

the only rectilinear form that

of the circle, therefore requiring in

which

drawn from the

not produced by the inter-

drawn from the

section of the medient line,

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

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

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

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.

â&#x20AC;&#x201D;(Plate XV.) Taking the dimensions from the elevation of the portico in Stuart's

column

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

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

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

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

Rome,

the Pantheon

perhaps one of the most perfect specimens of harmony

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

â&#x20AC;&#x201D; (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

composed of this and the

the

first

parallelogram, and

rhombus.

This structure being upon a level base independently of situation, having within

first

â&#x20AC;&#x201D; (Plate XVII.)

perfect in

itself

its

outline,

the three elements

of harmony.

In the street architecture of Rome, perhaps the most perfect specimen

the Farnese Palace.

Here no general

but the combination and arrangement of F

its

outline

required

parts display a perfect

ON THE ANALOGY OF SOUND, COLOUR, AND FORM.

and most beautiful arrangement of the three component parts of linear

harmony,

in the judicious

admixture of the curve, the angle,

and the straight lineâ&#x20AC;&#x201D; (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

;

clear that form,

and that consequently

there can be no perfectly harmonious combination of forms in which

one of these

wanted

;

and that the distinctions of harmony,

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

Dick

Lauder,

accompanying the

Third Edition of " Sir Uvedale Price on the Picturesque," 8vo.

Edinburgh

1842.

NOTE

2.— Page

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

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

enrichment and decoration."

circular in

must

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

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,

acquire a knowledge of

all

these sufficient to

a long course of study and careful observation are

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.

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

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

in a vertical position.

NOTE Colonel

Mure

rhombus being

3.â&#x20AC;&#x201D; Page

38.

of Caldwell, in a note to his excellent " Journal of a

Tour

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

curved upwards, but in so slight a degree as not to be perceptible unless on very accurate inspection several other

that in

;

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.

be verified by

Mure

also mentions,

Hamilton, Esq., to the Royal

March 1840,

observable in the Theseum.

were said

it is

stated that the

same pecu-

â&#x20AC;&#x201D;

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

more tedious and obscure than add them

therefore has been thought better to

Combinations of

lines

seem

straight line placed perpendicularly

its

present state, and

in this form.

have their discords as well as concords.

upon an oblique

line,

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

likewise discordant, as

Oblique

lines

will

line.

line,

A straight line placed horizontally

thus

appear curved, but in the opposite direction.

can only produce pleasing forms where their obliquity

in the

same degree, thus

or any other such combination of the oblique

and

straight line,

inharmonious.

â&#x20AC;&#x201D;

;

APPENDIX.

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

fitted to

having,

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

shown

to 2, until

in the diagram, Plate IV.

the eye cannot approach the

iris

to this

;

but

may

arrives at inappreciable minutia, as

manner, the pupil or inner

seems

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

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

are

made

traverse or cross each other horizontally

—

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

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

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

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.

;

exists,

the key or tonic adopted, the square

and

When

equilateral triangle will

—

APPENDIX.

When

be the leading features of the forms introduced into the composition. the ellipsis

the tonic, their leading features will be the parallelogram

rhombus, whether the composition be horizontal or

doubt

men

kind

But

not attended

men

Indeed

genius.

to.

knowledge

to such, a

rules are requisite to enable the generality of

appreciate judiciously the works of

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

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

has done so in

appears.

But

—

all 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

which

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

Real genius

In like manner will pretension and mediocrity in the

In investigating the in

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.

It is a well-established

to us quite colourless, are

composed

—which, by

refraction,

blue, red,

and yellow

APPENDIX. are

made

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

worthy of some attention.

which the variety

in the elements that

rent to the eye,

made by such means

refraction to

;

and

The

only means,

compose white

believed,

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

â&#x20AC;&#x201D;

would appear that these mediums of communication between external and the senses correspond

nature

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.

him

that a certain

number

apart from the object of this

however, remark, that

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.

APPENDIX.

horizontally lengthened,

and in the same

ratio vertically shortened, thus bring-

ing distant objects more distinctly into view, and conveying distant sounds

distinctly to the ear.

But

this supposition

advanced with much

dence.

Erratum

â&#x20AC;&#x201D;

for Medient, read

Mediant.

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