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MilMn

XV 51 AS

^

y

Date Due

e

a crescendo or diminiumh without the risk of the tone

**

breaking

lip U) preserve

;'*

a pure

—" To what extent, and by what were obviated my — as

The question which now means, these defects

arises

in

flute of 18J32?''

will,

I think, be answered by an exact description of the acoustical pro-

mechanism of that instrument.

portions and

Though I was. even

then, x>retty well acquainted with the general

laws of acoustics, I could i^nd scarcely any guide for their special the construction of 3ut^s;

and I was therefore

many merely

empirical exiKjrimenta

application

to

obliged to

have recourse io

before I determined

eolumn

of air as

upon iho following proiwrtions

most suitable

for

my

In English

I.—HsAB Length

of the cylinder

of

In SVcuch

'ixetres-

from the coik ,.

0,4593

..

0.1400

0.0604

. .

0.0184

.

1.1417

.

0,3480

.,

it

II.—MmnLs Length

faet.

Joist.

to the middle joint

Width

of the tube or

purpose.

Joint,

the coce

of

.

.

Width

at the upper

end

,.

..

0.0604

..

0.0184

Width

at the lower

end

.

.

0.0393

,

0.0120

.

.

C.2624

.

0.0800

..

..

0.0420

..

0.0128

0.0361

.e

0.0110

0.1312

.

0.0400

III,—Foot Length

Jonirr.

of its conical part

Width

at the upper

Width

at the lower

cal part

Length

Width

..

of the

end

end ..

of this coni..

..

lower cylindrical part

0.0361

of it

XV.—Whole length of th?. column of air

1

.9947

0.0110

.

.

0.60B0

.

Tlieso proportions being once Citablished, I prepared several tubes, all alike in

thicknesa of wood, 0.0146

ft.,

and

in length,

1

.9947

ft.,

19

The embouchures I made

for producing the fundamental note C.

form

in

them

of

at a distance of 0.0557

embouchure to the cork

till

I obtained

C

ft.,

first

made

of

one of these

I then marked the point of section this operation

Then I bored

octave.

at the points of section

I

from the lower end

off

sharp.

on a second tube, and repeated notes of the

measured from the centre of the

stopper.

After that, I began to cut tubes,

and placed

parallelogram with rounded oornera,

a

till

I had got all the

in the second tube holes

which I had marked before, and these holes which they could be stopped with the

of the largest size at

fingers.

AH the

notes produced in this

way were

too

flat,

on account

of

the holes being smaller than the tube in diameter, therefore 1

moving the holes towards

corrected the tuning on a third tube by

the embouchure.

Though I obtained

way

in this

the

first

aiid

second octaves in correct tune, with equal-sized holes, the third octave

was

still

defective

;

because, to produce the high notes^

it is

necessary to open, together with the hole of the fundamental note,

the

fifth

hole above

it.

as a vent hole

;

and as the

clearness, free

upon the

emission, and correct tuning of the high notes depend position of those vent holes, I

was

obliged to

move

again six of the

upper holes, and to correct the intonation, thus disturbed, by modifying their

At

much

last, I

size.

obtained a tube with fourteen holes, which was very

superior in acoustical proportions to the

as all notes from the fundamental

produced upon

But the

it,

C up

equal, free, certain, jwwerful,

position of the holes being

common

to the highest

now

system of fingering waa wanted, in wliioh

flute tube,

B

could be

and in good tune.

totally changed, a

all

new

holes could be opened

or closed, not only in an ascending or descending series, but also in

every different combination. plish, as

This task was not so easy to accom-

nine fingers have to stop fourteen holes

;

the

thumb

of the

right liaud being indispensable for holding the flute.

The

deficiency

had to be made up by key-mechanism, and I If

a finger-hole bo surrounded by

may be

pressed without touching the

chose ring-keys for this purpose.

a groove, into which a ring

b2

20 and

sides,

be fastened to the axle of an open key, the

this ring

if

finger necessarily presses

One

finger,

down

the key while stopping the hole.

performing in this manner two functions by a single

movement, does the work

of

two

A

fingers.

further difficulty,

that of not being able to reach some holes with the fingers, I obviated by separating the key-handles from the keys, which I could

then bring within reach of the fingers by means of long axles.

With keys, I

these

two

was enabled

D

of their natural position

up to the highest B, with the exception

the right hand, to which I left the

much

in order to retain as is

now no more

and

all

my

mode

(key).

the lowest or

opening the second or

By

opening the third or

It

is

it is all

it

C

is

:

sharp key

D key

D

is

(Fig. 3.)

system, the fingering of the chromatic scale

By

So far

There

being obviated,

holes are closed, the note produced

By opening

of the foot-keys,

as possible Of the old fingering.

formed in the following manner

When

of the little finger of

management

difficulty of the old flute

easy to play in every

According to

from the lower

gliding from one key to another, or to a finger-hole,

immense

this

by which

to establish a system of fingering

move out

the fingers do not

some new combinations of

contrivances, and

is

...

...

m

...

ifcl-i—

...

sharp key

the same as on the

~ i

jfe^-j--

common

flute.

necessar}^ for obtaining a clear and strong tone, that the

holes immediately below the one sounding should remain open, for

the air confined in the lower part of the tube tends to flatten the notes,

and renders them

remains open for

and thus the

less

free

;

therefore the

the whole of the scale,

little finger of

D

sharp key

excepting

'w~^~

the right hand assists at the same time

in holding the flute steadilyc

The next three

holes are encircled by rings, the

are joined to the axle

by the

G

two

first of

natural key, and the third

is

which

com-

n bined with two levers by an asle reaching up as far as to the

Thus the

natural key.

(S )

fourth or

E

TOpr^E

by opening the

which

hole,

J

produced by opening the

is.

.-

B

covered by the third finger, and the

is

¥

fifth or

hole, covered

by the second

by the

first finger, is

finger.

When

the sixth or

F

shai*p hole, covered

opened, the ring-key rises by

we

are opened at once, the note

removed from seventh or

G

¥

its

To

natural

own

spring

obtain

and

;

as thus

two holes

two

half-notes

W

fj

m- ^

is

obtain the preceding

natural hole must remain

closed

~

by the pressure

the

of the

second or third finger upon the ring-key; the second finger, however,

being used only in quick passages, on account of the above-mentioned injurious influence of the lower part of the column of air,

which only ceases when two holes at below the sounding It

win be seen

fingers

on four

that

it

manner

easy in this

is

with three

to play

and that the ring-key prorides a substitute come now to the left hand, by which all holes

holes,

We

one finger.

for

upwards from

least are opened immediately

hole.

G

are closed.

As my system

of fingering is based

throughout on the opening or closing of the holes in regular succession, open keys are, on account of their similarity of motion,

most natural representatives

surely the

of fingers

where the holes

are out of reach.

For

this reason I

except

D

sharp.

have used open keys for

So, too, the key

remains open, untU

it

which

pressed

is

down and

direct action of the little finger of the left

key

by

rises

obtained

its

own

the

spring,

by raising the

little

-m

finger,

notes of the scale,

all

closes the

hand

aJ— as

the

G

sharp hole

closed, as ;

is

if

by the

and as

this

most

naturally

g)

J

is

open

pro-

duced in the same order by raising the third finger from the ninth or

A

hole.

And

as these

two

for half-tones, or together for

fingers,

whether raised separately

whole tones, always have a

similar.

never a contrary movement,

much

little practice,

this action will

G

passage, than that with a shut

The B

flat

which

is

by

own

its

hole following the

fixed to the axle of the spring,

E

therefore, the

To

A hole is E key.

By

hand.

up

for

G

by the

this contrivance it will be seen

and produces

of the lever reaching

first finger of

the right

one more finger

is

made

by a ring-ke37.

^^^^

The next note double

C

which

hole,

is

opening the key of the

From

^

p

.

produced by opening the key of the

closed

C

^^Em

by the thumb, and

sharp hole, closed by the

repeated, with this difference

is

sharp hole

open for

is

is

^^^zE.

and

S^y^

or fundamental octave must be used

;

into the oetave.

free in tone

and for

G

the

z^^jz

fifth

below, and by opening

This

sharp hole

the

B

is

is

raised

open, for

Hat hole

from the

;

B B

fiat hole.

the

^rlr™

hole opens of

A hole,

owing to

itself,

For

also

Thus, for

^^:r^

but for

is

the notes

it,

and more correct in intonation.

the contrivance of the keys, the

finj^or -D'

the lower

of

opening at the same time

for each note the fifth hole above, as a vent hole.

the hole of the perfect

C

as a vent hole,

For the higher notes which follow, the fingering

"f-^^t^-

finger.

that the

onl}-,

i

by which we pass with more ease and certainty

become

first

by

the fingering of the lower octave or fmida-

--j:

mental notes

second

ring,

key, this rises

note

preceding

by means

closed

as far as the ring-key that is closed

by a

also encircled

Like the

finger is raised,

the

obtain

must be

hole

of

sharp key.

when the second

fei^^

the note

be found, after a

and more convenient in every kind

easier^

when

^ --J'

-

the

i

:^

23 the

G

C and G sharp As

the same time.

g

holes serve in succession as

more

sharp, however, sounding

-^

—f~^—

from

as

as for

natural place and

its

aU these

On

notes.

holes have to be closed

made

by the

vent hole for

serves

C

hole

is

the

;

open at

—

it

must be removed

smaller, in order better to suit

D

lower

E

and

sharp

finger of the right hand,

G

with

stopped by a closed key,

hole,

worked hy the second

finger of

sharp hols being also open) as

(the

T

-g

the

vent holes

sharp hole serving at the same time as

of a long asle is

hand,

!"

;

first

Finally, the last or

vent hole.

the right

rO „

this account the

the fingering of A, the

which by means

if

sharp hole has to serve as vent hole for

the

TVeil

freely

By

it

likewise seven

shakes

may

be

conveniently made.

Besides these keys, I also

made a

lever

by which the C key may

be closed by the third finger of the right hand, and thus this finger

may

be

iised for the

To obtain

movement flute,

which

fiat

with C, and

its

whole weight

B with

restB on the cavity

forefinger of that hand.

arises

pitch, I

B

C.

the left hand, I applied a movable crutch to the

of

by which

thumb and

shakes

a steady hold of the instrument, and a free and easy

upon lengtheniug the

made use

Lastly, to

fiute in order

of several rings, to be used

sliding tube generally adopted

;

fill

in.

between the

up the space to

flatten the

lieu of the

metal

I rejected the latter, on account of

the unequal and disturbed vibration which arises from the close

combination of the metal with the wood, producing, to a disagreeable hardness of "With

thitt

my

my

ear,

lx)ne.

labours terminated.

I found further essential

improvemerits impracticable, without the application of very complicated

mechanism

;

nor did I consider

it

necessary, iuasmach a»

24 the tone and intonation of

flute

were greatly improved, while execution

rendered practicable the

key-mechanism

its

my

every

of.

possible combination of noteSc are, I trust, sufficient to

These explanations invention ripe

of

proofs of

my

persons in

my

not a plagiarism, or

is

meditation and

work

of chance

experience„

practical

were wanted, I can

title to it

Germany and

prove that this

elsewhere, to

whom

cite

;

my

but the result

And many

if

further

respectable

I had communicated

ideas long before their execution.*

improvements (which I leave others to decide),

alterations, or real

I had no part in different

manner.

it

having been,

;

till

1846, occupied in a very

made

Besides, but for the repeated appeals

I should scarcely have considered authenticity of

mere

after the year 1832, be it for

Whatever has been done

my

to

me,

worth while to claim the

it

invention, for all the discussions on this subject

refer merely to the key-mechanism,

which

is

usually judged of by

individual views, each one thinking that the best which best suits I only valued

his taste or fingers,

my own

far as I found in its contrivance the

attairjmsnt of

my

object,

of fingering so

which was the improvement

for the

of the fiute

for this is the chief foundation of

in its acoustical proportions;

higher or lower degree

the

system

most simple means

of

their

mechanism being but

much

easier to construct keys

perfection in

aU instruments,

of secondary importance.

than to improve

It

notes.

is

also

By my

former experience in instrument making, I was fully aware of the causes of the defects of

the most part, on Nevertheless, I

my

wind instruments, and I obviated them,

flute

was

by

still

connected with acoustics, as

the application of mechanical

in obscurity about

my former

for

means.

many phenomena

labours were not founded on

those special theoretical inquiries which I have lately been enabled to

make.

making

;

Last year, however (1846), I recommenced instrument

and I began, for the instruction

of

my

sons,

with a close

inquii-y into the acoustical principles that are involved in the con-

struction of a musical instrument.

* See Dr. ScLifhautl's letter in the

Appendix.—W.

S. B.

25

From

any further

this source only couid

the flute proceed

of

;

science endeavoured to point out

yet

how

essential

improvementB

were made long before

for although flutes

were produced,

their tones

certain that they can never reach their utmost perfection

it is

maker has some knowledge

unless the

of,

and attends

to, nature's

invariaole laws in the matter of proportion and substance.

Wind

instruments, especially those having finger and key-holes,

and depending exceedingly perfection

quality

their

for

mainly upon the accuracy of can only be brought near

complicated proportions,

by a

strict application of

the principles of acoustics in

when

theory and practice go hand in

their construction.

It

is

only

hand, that, by the examination of the causes of the good as well as

bad in existing instruments, the way can be shown

of the

provements which must otherwise be

for

im-

The higher

left to chance.

branches of mathematics have, from time to time, been applied to the investigation of subjects connected with acoustics, and

learned of

that

men have endeavoured

and Lambert, have

D.

science.

columns of

L.

Bernouilli,

and

explained

the

and have given us the

air,

mathematicians

are

much

and many others,

proportions

Tibrating

of

results of various experiments.

Their observations, however, threw but nature of wind instruments.

little light

upon the true

For the conclusions arrived at by general

too

give

to

data practically

In such

applicable to the ccnstruction of our musical instruments. inquiries it is absolutely

most

Lagrange,

Poisson,

Euler,

as well as Biot, Chladni, Savart,

calculated

the

to develop and establish the laws

natural philosopher

necessary that the

should also be both a musician and a mechanist.

This

is

probably

the reason why, as I believe, with the single exception of " The theoiy of covered conical and cylindrical tubes, and published in

Germany by Dr.

Peliisov, in Vol. VIII. of the

German

Schafhautl, under the

name

flutes,"

of C. E.

"Annals of Chemistry and Physics," no

essay on the theory of flute-making has been written, in which the nature, extent,

and combination

our German flute lineal

is

and vibrational proportion.

fife,

phenomena on which

founded, have been explained in

on the above-mentioned the

of the special

In this

little

subject, the theory

or the cylindrical Swiss pipe.

what concerns

extract of a lecture

was simply applied

to

26

A conical laid

down ;

By

security.

by

could not be constructed according to the principles

in this work, unless they were explained in greater

but to an instrument maker already well versed in acoustics, gives a foundation on which he may pursue his way with

detail it

flufce

my own

more

continual attention to Schafhautrs observations, and

experiments, I have obtained, of late especially,

satisfactory results

much

so that at length I have very nearly

;

ascertained the true theory.

As the communication

might be

of these results

less intelligible

without a knowledge of the principles of acoustics upon which they are founded, a simple explanation of them, as far as necessary,

be welcome to those proportions of a

In order

who

German

different

flute.

to obtain the

of air within the tube

from those

may

are not acquainted with the accurate

sound of a wind instrument, the column

must be brought

into certain vibrations,

of strings, tuning-forks, or metallic springs.

These vibrations must re-act upon the body that surrounds the column, and excite

sound can It

is

its

air-

molecular vibrations, without which ao

arise.

therefore necessary, above all things, to gain

with the proportions of these vibrations.

an acquaintance

The simplest means

of

convincing one's-self by ocular demonstration of the pulsatory motion of a

column

of air within a tube or apparatus, is Hopkins's appa-

ratus. (Fig. 4.)

This consists of a glass tube about two feet long

and one and a half inches in diameter, which

is

fixed perpendicularly

into a metal ring lined with cloth, in such a

manner that

beneath the tube, a metal plate or tongue, like the

seoline,

close

may be

screwed, and sounded by means of a violin bow.

There must also be a ring of smaller diameter than the glass tube, covered with a very fine

membrane,

like a

three fine silk threads are fastened, so that

a

it

drum, to which

may

be held like

scale.

To be

able to

is requisite

make an experiment with

given by the glass tube. of the

this

apparatus,

it

that the tongue be tuned to the same sound as that

bow, the

If the tongue be then

air contained in the

tube

is

sounded by means

affected

by the motion

27 of the tongue

and

;

as the

number

not only the

same not«

will he produced

of vibrations

by the tube,

necessarily the same,

must be

but the motion of the column of air will be also communicated to capable of

bodies

all

Thus,

influence.

before, is let

if

down

eimilar

the

as the

fine,

its

dry sand

into the tube while the sound is clear and pure,

the follomng phenomena will result

As soon

and coming within

pulsations,

drum, strewed with

little

drum

is

:—

placed above the border of the sounding

membrane begins to skip, so that part of it is As the dram is gradually let down into the tube,

tube, the sand on the

thrown down.

the height to which the sand until at last,

is

thrown becomes gradually

when we have reached

Beneath that

remains almost motionless.

less,

the middle of the tube, joint the

it

sand begins to

move again more, and this motion increases the more deeply the drum is inserted, until at the lower end of the tube the sand is again thrown off the membrane with the same force as when at the top,

From

(Fig. o.) this simple experiment it is evident the air has not the

same motion in are

different parts cf the tube,

strongest at the

but that the vibrations

two ends, and decrease thence gradually,

xmtil in the middle they are almost at rest,

motion the single particles of towards This

is

air

move

this pulsatory

one another in the direction of the asi« of the tube. called

longitudinal vibration in contradistinction to the

vibrations of a chord or strkig, which

the right and

The

Irj

longitudinally from and

left,

move

sideways, that

isj

to

called trarutverse vibration.

particles of air

move only through a very small

immediately return to their point of rapidly, they oseiliate like a

rest.

But

space,

as they

and

move

pendulum, to equal distances on each

Bide of the point of rest, yet always in the direction of the axis.

Now

if

we

represent to ourselves that these pai-ticles of air advance

and recede again a

little

at the

same time from the openings at where they move in

both ends of the tube,

we

opposite directions, there

must be a part where no movement

lakes place.

If the

shall find that

particles of air

endis at once, they naturally

come

enter the tube

at

all

from both

to a stand in the middle,

and

28 the air at that point contrary, arises

an

expansion

such circumstances

and expansion

is

The

condensation.

where the

where the

in the centre

is,

air

under

an alternate condensation

of the air at those points

—that

was the

motion of a column of

chief

there

rest,

where before there

air,

on the

If,

from the point of

consists, therefore, in

have the least motion

of the tube,

the

of

greatest condensation.

air

in a state of

is

particles of air recede

fche

;

particles of

but at both ends

have the greatest motion, there

particles

neither condensation nor expansion.

All those points where the air rest, are called, in

is

at perfect, or nearly at perfect

the language of acoustics, nodes oi vibration

and

;

the portion of air vibrating between two nodes or points of rest

termed a

is

wave, in contradistinction to the progressive

settled

undulations which transmit the tone through the air outside of the tube,

and.

without which the settled wave within could not be

produced. Further,

we

if

produce the octave of the fundamental note in the

by means of a tongue tuned to the octave, and place the

glass tube

drum strewed with sand about

the mouth of the tube, the sand

will begin to skip as at the first experiment,

thrown down.

But

if

we

motion of the sand will decrease first

experiment

;

and will be

and when

it

when

it

still

If

rest.

has arrived at the middle of the tube, where in the

By

we

more, the sand begins to move again, and

experiment the sand was at perfect motion.

the

the

has reached about the fourth part of

the tube, the sand comes to an almost perfect state of

then sink the drum

partially

drum deeper in the tube, much more rapidly than in

insert the

rest, it

first

dances with the liveliest

proceeding beyond the middle downwards, the motion

of the sand again decreases, until at the last fourth part of the tube it

comes

to the

beyond the

same

state of rest as at the first fourth part

last fourth part,

increases again, until at the lower extremity there violent motion as there in the second octave

was

;

while

and towards the lower end, the motion

at the upper.

two points

From

this

is

the same

we

see that

of rest or nodes are formed, each

distant a quarter of the whole length of the tube from one of its ends.

Between these two nodes there

is,

therefore, a second

and

clearly

defined entire settled "wave, which has its centre or point of greatest

at the middle of the tube

vibration

toward?^ both ends of the tube

between, and

is

;

whilst the

by means

of the

is

first

pressed

new one coming

thus divided into two halves, so that,

in.

the two

if

ends were combined, they would form a settled wave of the same; length as the middle one. If

we

(Fig. 6.)

pursue these experiments

still

further (Fig. 7), three nodes

are formed by the fifth of the octave, the extreme distant

^

two

second, or super-octave, arise four nodes, the

two

distant | of the whole length from either end

;

uncovered organ

pipes,

on which, as

formed in the same manner,

still

is

which are

of

length of the tube from either end

of the

with the

;

farthest being

and upon narrow

well known, the nodes

higher tones

may

are-

be produced,

involving the formation of even 6, 6, 7, and 8 nodes.

Upon

we see of

:

a closer view of the numbers of these vibrational nodes,. (1)

That they appear in the natural arithmetical progression

numbers: and

(2) that this natural progression

numbers

of

expresses the proportions of the vibrations of one note to another

Thus, for instance, vibrations of the

if

1 represents the

column

fundamental note C, with 260

of air in a second,

2 represents the octave,

the condensations and expansions produced being twice as viz.,

520 vibrations

in the

same

The

time.

fifth of

many

—

the octave

requires consequently three times, and the super-octave four times,

as

many

vibrations i^ the

same given time.

We know

also that

the column of air in a sounding tube, according to the laws of equilibrium, only divides itself into portions of equal length.

If,

for instance, four nodes are formed, the undulations are consequently

but half as long as they would be, in the same tube.

And from this

if

again

two nodes only were formed it

follows that the vibrations

are slow or quick in proportion as the undulations are long or short.

An

undulation half the length of another, therefore, vibrates with

exactly twice the rapidity.

The octave

the number of vibrations required for

is its

thus formed by double

fundamental.

however, obtain this octave in another way. the column of

air,

half the length,

We

can,

Instead of dividing

by the force of breath oi wind, into two undulations

and vibrating with double

velocity, suppose

we

30 cut th« tube into two halves at the middle, one undulation only

then produced, shorter by one double the

half,

and vibrating

rajjidity of the original air

By

column.

tlierefore

this

means the

octave obtained before by the whole length of the pipe

number

proceeds again the theoretic law, that the

corresponding to the

pitcii of

becomes

And from

the fundamental note of the pipe half as long.

is

with

this

Wbrations

of

a note varies inversely as the length

of tube.

\Ye

may

also obtain the original

octave lower, without joining

cut

This

off.

In

cover.

done by

fundamental

its

which was an

was

extremity with a

blown in at the labium

the lower end, the undulation

ai

not-e,

to the tube again the half that

closing the pipe at

this case, as the air

cannot escape

bottom

is

on

of the pipe

is rellected

from the

and returns to the upper end; audits vibrations

of the pipe,

becoming thus twice as

3orig

and only half as quick as they were

before the tube was closed, the fundamental note an octave lower is

the result— namely, the same note that

A

the whole length of the unclosed tube. or as

a covered (stopped) tube,

it is called

pitch, equivalent to

to

was

fit

first

is,

an open tube of double

by a certain immber the same for the same

note,

by Caignard dc

la

contrivances

;

or,

more

is

determined

and may be determined exactly by

measurement with the help ;

regard

length.

its

This number always remains

calculations and

Tour

m

therefore,

Purther, the actual pitch of every musical sound of vibrations.

obtained from

tube closed at one end,

of tlie Syren, invented

or by Savait's dented wheels, and other

recently, very securately

tuning-forks, in conjunction

by

il.

Bcheibler's

with the metronome.

According to Soheibler, the jfe^afc- of the Conservatory of Paris

had 868.7, that Yienna 881.74

of

the orchestra in

Berlin 883.25, and that of

oscillations in a second.

lation of this note being determined, the all

The

rapidity of the oscil-

number

of vibrations of

the other notes are easily calculated, the relative proportions of

the intervals of the other notes having long since been fixed.

As

the length of strings decreases in proportion to the increase of the

number

of vibrations,

|-

of the string requisite for the production of

31

C

gives D,

^ E, | G, f A,

?^\ B,

and ^ C gives the octave. For wind and in all keys, the

inBtrumeiits, whicli are used in the orchestra

purely mathematical scale, as

because the notes forming other.

it

is

well known,

cannot

be

used

have proportions different from each

Consequentlv the octave

is

geometrical proportions, of which

divided into twelve inteimediate tlie first is

as the second is to the third, &c., &c.

This

to the second exactly is

called the equally

tempered scale, on account of the conformity of the several parts to

each other.

numbers

for

The following length of

table shows the absolute and relative

string

and number

of vibrations in

chromatic scale of equal temperament, assuming

produced by 880

Lengths

oeciliations.

^

tf~z

the

to be

As

in the works of natural philosophy

volume of the column essential influence

it

assumed that the

is

has in musical wind instruments no

of air

on the pitch, the lengths

of

strings indicated

ought to correspond to the lengths of the columns of * to obtain the same notes

From colnmn

examinations lately

a series of

Schafhiiutl

in

regard to the

of air, it

is

entered

established tliat evei'y pipe

the eifect

From

is

remaining unchanged while as

if

by

Prof.

which

is

the

shoi-tened

abridgment according

its

to the calculation for strings, but a lower one of the tube

into

the diameter of

influence of

does not give the sound corresix>nding to

air requisite

because the diameter

;

length

its

is

diminished,

the diameter of the tube had been increased.

the same experiments

it

appeared that,

if

a tube closed at

one end be used, the divergence from the calculations which hold true for strings will be

ends were employed

;

greater than

still

that

is,

if

a tube open at both

the sound obtained will be flatter

in proportion to the diminution of length.

Though the proportionate

vibrations of a

column

of air, partly

or entirely surrounded by a conical tube, are based on the same principles, the

cone gives

Of these the theory

rise to

some remarkable modifications.

of covered tubes, very. much enriched

by the

investigations of Dr. Schafhautl, gives a full explanation.

It is

known

that a cylindrical tube,

will give a sound lower

when

covered at one end,

by an octave than that given by a

precisely

similar tube open at both ends.

If in the cover of this cylindrical tube a small aperture be made,

and gradually enlarged,

it

will be found that the sound given

by

the tube rises in direct proportion to the enlargement of the aperture

and thus

it

may be shown

from the cover of the cylindrical tube size

;

that the reflection or the column of air

of the aperture in the cover.

is

in an inverse ratio to the

The same author has

stated

that a cylindrical tube terminating towards one end by a cone

may

* I conld, however, never persuade myself of the truth of the above-mentioned all wrnd instrument makers know very well that the pitch of a

statement, since

—

wind mstmment depends partly upon the diameter of its tube. T. Bohm. [This ha« since been proved and demonstrattjd by A. Cavaill^-Coll, the organ builder, with regard to organ pipes.— See Nature^ Aug. 7, 1879.]

33 be considered as u cylindrical tubo covered at one eud, and having ill

which bears the same

cover an aperture, the diamet/er of

its

end

]»roportion to tliat of the tube as the aperture at the smaller

does

that

to

of

the larger f-nd of

the cylindro-conical tube.

(Fig. 8.)

As

witli conical

columns of

air,

a lesser volume has to be put in

than with cylindrical ones

vibration

of

follows that conical pipes emit the sound

same time that the tone

;

softr- sounding

It is further, known,

easily,

it

but at the

loses in strength in the proportion in

the dfameter of the pipe diminishes

only ones used for the

the same diameter,

more

which

wherefore conical pipes are the registers of the organ.

from Dr. Schafhautrs experiments, that the

part of a column of air in a wind instrument below a lateral or finger-hole exercises

length

;

an influence only partially proportionate to

and must therefore be considered and calculated

column, and shorter in the

]»roi»ortion

finger-hole bears to that of the tube

which the diameter

and

its

as a shorter of the

to the length of the air

column.

From

the

same experiments

be considered as

little

it results

tubes of

that the finger-holes

the same length

the wood, and also that the embouchure of a flute

may

as a finger-hole, the quantity of tone remaining the

be considered

same whether

be played at the embouchure or at the finger-hole.*

tlie flute

must

as the thickness of

The

portion of tube from the centre of the embouchure to the cork,

when

rightly pieced,

covered pipe,

must be reckoned double, because

it

forms a

and counteracts the sharpening influence exercised by

the embouchure on the pitch, which thus remains the

obtained by blowing into the orifice

same

as that

of the tubo when without cork

or embouchure.

Thus

far

theories, I

in

supjKirted

by the general acoustic laws and

recommenced the investigation

special

of acoustical proportions

wind instruments, and made a great many experiments, the

results of

which I

will

communicate

concisely, as far as they relate

to the flute.

Buhm's words me here ^iven without

alteration.

34

As the

acoustical proportions of a cylindrical

he the basis of

a

I

flute,

all

made a number

first

different lengths

which

and diametersj

from blowing

arise

column

must

of air

the calculations requisit-e for the construction oi of

wooden tubes

cylindrical

ot'

in order to find out the modifications

laterally into the

embouchure.

But on

account of the instability of wood, I never succeeded in obtaining reliable results

;

make

to

trials?

many

wherefore I resolved, after all

the models necessary for

my

For the investigations of the proportions

metal.

the quality of sound

is

was

proportions

able to perceive the ;

my

hence

of length,

where

not an essential point, thin hard-drawn

tubes of brass of various diameters did that I

unsatisfactory

experiments of

me

such excellent service,

most minute deviations in

their

experiments attained great exactness.

After I had provided

all

my tubes with embouchures and stoppers,

I sought the lengths corresponding to the diameters, by cutting

off

portions, until the fundamental note sounded with ease, certainty,

And

from 0.0328

ft,

to

(iO to 30 millimetres), and the lengths from 0.82

ft,

to

and clearness. 0.0984 4.92

ft.

ft.

as the diameters increased

(|-1| metre), I found

compass of two octaves,

C

of

up

an organ pipe 4

^^^

to

vis.,

many fundamental

from

feet long*

notes within the

Sh!^^ down

Ths sound, however,

was weak and hollow

;

and

all

Droceeding from the aliquot parts of the column of

^^^^

J^F''^—'

to

the lower

of these notes

the higher notes air

were too

fiat,

^^^^^ defects were less perceptible, because the

embouchure, which would have been too large for playing upon

made

of a size corresponding to the diameter of the long tubes,

of the

right

size

for shorter

and narrower

tubes,

so

if

was

that the

vibrations could be completely excited.

Ck)nvinced that tubes entirely cylindrical could not be used for

German fiut^swith the fundamental note ^^^^»

b^i^ that, in

order

to obtain a free tone and correctly tuned octaves, the conical form

must be made use cone.

of,

I began to examine the proportions of the

I changed or lengthened alternately the base or the apex of

the cone, which brought advaistr^es ot disadvantages

;

but,

upon

the whole the results of these experiments, although highly in-

35 «truotive,

were not important enough to be more particularly men-

tioned here.

Now,

was very

as there

little

to be improved in the conical sliape

employed towards the lower end years, I reversed the projiortions

part of the tube, and executing

of the flute for

more than 100

by putting the cone in the upper

it

in very different dimensions.

I

had made a few similar experiments thirty years before without sucAfter several fruitless

cess.

trials,

with wooden and then

first

with metal tubes, I thought I should have been obliged to give up, this

time

also, the realization of

made my

discarded since I

understand while

ail

at the

why

an idea which I had never entirely

was always

I

fiute.

first

at a loss to

the flute alone should be played at the wide end,

other wind instruments of conical proportions are played

narrower end, especially as the

latter

method seems more

in accordance with Nature ; for while the sections of the air-column

decrease in length as the pitch rises, so they also

diameter.

The reverse

which the cone

is

of this is the case

now

in

flute, in

continued beyond the lower holes.

Ab the fundamental note of cone, as

decrease

with the conical

those tubes sounded best in

which the

applied by me, reached from the stopper nearly to the

uppermost hole, and

as,

on the contrary, the highest notes were im-

proved by shortening the cone and lengthening the cylinder, there

was naturally a medium best

And

further,

suited to these opposite requirements.

as according to theory a curbed line

for the gradual contraction or

at the upper end of

my

is

most suitable

enlargement of an instrument, I made

tube shorter or longer contractions, which

in the outline of their form approached the " parabola/' and which

terminated

in,

or converged to, a hemisphereo

At length I obtained a cylindrical tube 0.0787

ft.

appeared that

all

also be produced

of which,

on a

(24 millimetres) in width, and without

side holes, I could produce the

the stopper was moved a

means

head-piece, by

low

little,

all

E

of the clarinet,

the

harmonics

;

and when

whence

it

the natural tones of the horn and trumpet can

on a flute-tube,

if it is

long and narrow enough for

the division of the column of air into the requisite aliquot parts.

Sut

as the

low E, though

easily sounded,

was weak

in

c 2

tone, I

36 shortened the tube until the sound became powerful and perfectlr clear,

F

by which I obtained

fundamental note.

as the

After

having applied these proportions to different lengths, always placing the stopper at about the -^th part of the whole length of the

column

of

I

air,

-4—^—-^J-^z:

With of the

at

the

fundamental

my

investigation of the proportions

air best suited for the

development of the funda-

mental notes ; and from the experiments made thus far (1.)

notes

^^}i a ygiy perfect tone.

these results I ended

column of

obtained

last

That the strength, as well as the

fundamental notes,

is

full

appeared

it

:

and clear tone of the

proportional to the volume of air put in

motion. (2.)

That simple vibrations can be most perfectly excited in large

tubes having a contraction at the embouchure. (3,)

That every modification in diameter or length

traction has a great influence

of this con-

on the emission and

intonation, of the

must not be made

in straight lines^

aliquot parts. (4.)

That

this contraction

but in curves. (5.)

That J moreover, the divisions of the columns of

— —

aliquot parts, or the formation of vibrational nodes

phenomena which appear

in a vibrating

column of

air

is

in short, all

are exhibited

manner

in a cylindrical tube in the most perfect and easy

quently that a cylindrical tube

air into

;

conse-

that best adapted for the con-

struction of a flute. (6.)

That

upper end

cylindrical tubes

may

with the cone, as applied by m€», at the

be considered as entirely cylindrical

fluence of the cone on the pitch

with the fundamental note C length of 0.00492

ft.

it

is

;

since the in-

so insignificant, that in a tube

scarcely occasions a difference in

(1| miUimetres).

As, then, the dimensions that correspond best to the formation of

the fundamental note are also the most nearly in conformity with theor}% a flute constructed according to such proportions,

and with

a compass of two octaves, woul^ certainly be the most perfect in

regard to fulness, purity, and freedom of tone;

but in order to

37 extend the compass to three octaves, as day, I

was

use narrower tubes, and thus again to injure, in some

notes, t^

measure, the finest notes of the

me

obstacle which obliged

the embouchure proportional air,

two

octaves.

A

from theory was

of the stopper

second the im-

from the centre of

to the lengths of the several undulations

by mechanism, the making

unless

almost insuperable

A

first

to deviate

making the distance

possibility of

of

required at the preseiit

is

obliged, for the sake of freedom of tone in the upper

of

which would

j>re8ent

difficulty.

me(3ium place for the stopper must therefore be found, by

means

of

which the vibrational nodes

of the

upper notes

may

be

prevented coming too near the embouchure, so that the development

may

of these notes

liy several trials,

still

be secured.

made

as accurately as possible, I found that the

proportions most suitable for obtaining good and pure tone through-

out the compass of a flute with the fundamental note

were

as follows

(1.)

Length

:—

of the tube

The

Metre.

..

.

.

=-

1.984

0.606

=

0.002

0.019

=

0.0065

0.002

=

0.055

0.017

l-'32nd part of this length, as best

suited for a

medium diameter

of the

cylijider

(3.)

Foot.

from the stopper to

the eiid of the flute (2.)

ffiErEi^

Reduction of conical

that

contraction,

width

by the

beginning

at

the upper sixth part of the whole length of the tube, and being at the middle of the embouchure (4.)

Medium

distance

of

.

the middle of

the embouchure from the stopper. Further, I

form and air

size

.

made some experiments

.

as to the embouchure,

being of the greatest importance.

by which the tone

is

The current

its

of

produced must always be blown at an

angle proportionate to the height of the note towards the uj)per

38 border of the embouchure, which breaks, or rather divides

it,

ao

that part of the current of air passes over the hole ; but the greater

—

part

—produces

the column

tone, exciting

with a good embouchure

especially

and putting

of air enclosed in the tube,

lating vibrations,

much in the same way

it

undu-

into

as the string of the violin

put into transverse vibrations by the passing over it of the bow By the undulations of air the molecular vibrations at right angles.

is

surrounding tube are also excited, and the result

of the

which

lasts as

long as the supply of vibrating air

The strength

of the

tone will be proportionate to the quantity of

within the tube

air set in vibration

and as the aperture between

;

the lips through which the air passes into the embouchure

form

a

of

slit,

tone,

is

maintained.

is

in the

is

a long-shaped quadrangular embouchure,

with

rounded corners, which presents a wide edge to the broad pencil

must be

of air,

in a large quantity of

to take

better adapted

For the same

breath than an oval or round hole of equal size.

reason a larger embouchure will produce a stionger tone than a

A

smaller one.

space beneath the

becomes

which

difficult to direct

lips,

is

also their quality

breath

embouchure;

is

;

requires

unsupported, and

therefore

intonation

downwards

directed

the

greater

leaves a hollow

it

the

of

the tone becomes flatter, more

towards

and more hollow

sharper

directed towards

because

it

the current of air at the proper angle.

this depends not only the

Upon the

lip,

however,

embouchure,

large

strength in the muscles of the

circumference.

when

centre of the

tlie

when

notes^ but

conjSned,

the

Consequently

breath the

is

angle

formed by the sides of the embouchure, as well as the height of these sides, has great influence on the freedom of tone. In

my

opinion an angle of

7*"

is

that best suited to the whole

compass of notes, the sides having a height of 0.0137 ft. (i*2 and the size of the embouchure l^eing 0.0393 ft.

millimetres),

(12 millimetres) in length to 0.028

ft.

ia breadth.

Theae proportions I think best adapted to most

On

a flute-tube

sounded with the

made

after these designs the

sliglitcFl

was removed from iH

flute players.

fundamental note C

breath, notwithstanding that the stopper

theoretiv-ally cor?-ect place

;

it

admitted also

39 being very strongly blown without rising in pitch,

of

me

Berved to prove to

tube and

that,

o^ng

the fine tone of

therefore, to

And out the

shortest and moat simple

until the

my

Hence, as wt

friction.

as

11

from

the aliquot parts, I concluded that the tube I

all

had now obtained was the one best adapted

is

This

to the accuratje dimensions of

very smooth inner surface, the undulations of air were

its

formed without any noticeable

octave

and the

was not heard.

hissing noise so perceptible on other flutes

divisions of the

mode of obtaining

for a flute.

coiumn of

all

I began,

The

air.

the notes of the

flrst

naturally thai of cutting from the lower end of the tube,

new fundamental

note produced hy each section answers

and shown by tuning-pipes,

to the pitch of the note sought for

tuning-forks, or a well-tuned piano

;

then the ear decides as to

tJie

accuracy oi the result.

Theory indicates a much surer, but also more troublesome method. Schafhautl has shown, the stopper

If J as

is

so placed

fundamental note given by the whole length of the

that

flute

the

appears

perfectly correct, the tubal sections for the remaining notes follow

the same laws as those which determine lengths of strings. therefore easy to ^iid by ealculation the notes of the either in their natural or their

first

tempered proportions.

It is

octave,

As the

fluence of the contraction of the upper part of the tube is the

upon

all

in-

same

the notes, and need not therefore be taken into account,

made

this calc^ilation is

in the

most simple manner, and

mth

an

accuracy suSicient for the practical construction of instruments, in the following

end

lowe^

way

:

—The

constant length of the tube from the

to the centre of the

embouchure being 1.9324

millimetres), and the distance of 0.0771

the stopper (when in tlic

its

ft, (*^'3.5

ft.

(589

millimetres) from

theoretically correct place) to the centre of

embouchure being counted double (because that part

is

con-

sidered as a covered pipe), the whole length of the assumed column

1.9324

of air is then:

(23.5

The

X

2) =-

+ (0.0771x2)

=. 2,0866

ft.

= 589

+

636 miilimetrea.

fieotioiiB of

this assumi as good solo players

all

as your

London

like very

much,

one who,

till

But

As

Mr. Wehner

lately,

At

of wood.

played on a silver flute

good player on

Dome

to fine taste, 1 consider

now he

;

many

we remember

said to

"

:

flutea,

and De Yroye as

De Vroye

;

as to tone,

De Yroye had

little

fine

As

promises to get on very well.

now

I have

taste.

to playing in a

a pupil

grand

never more heard anything like Nicholson and Tiilou.

now much

S.

style,

I

German.

the

—

S. B.)

JI1

20, 1867.

Broadwood.

wind instruments

It results from the laws of acoustics that all

with a wide bore are

fuller in the

lower notes, while, on the other

those with a narrower bore are freer in the upper notes.

The only

question, therefore, is

wooden

therefore one

flutes

which you

prefer.

I could indeed

millimetre wider than usual

still

were sounded with

I have

;

the

play up

tx)

difficulty,

C^ ; but from and

if

my

lip

E*?*'^

first

was not

is

all.

solo playing, is treated

as the next highest instrument after the piccolo

bore of 19 m. m. diameter

so good.

did not happen to be in

whether in the orchestra or in

especially do not hesitate to write for it

and second

upwards, the notes

good order, I could not sound the higher notes, piano^ at fiute,

made

with a bore 20 millimetres in diameter^

octaves were better, but of course the third octave

The

much who

I^hry play

May To Mr. W.

several

but

more, but less in quality.

{From

hand,

;

and weak in

player has more tone, and as

first fiute

execution, but not the

flutes.

Mr. Kesewitz.

a very fine artist

is

I

the only

also has a fluto

first

A\Tien

your tone and playing, he seems

Ou?

comparison."

me

is

on the old

still

my

Ott, Krijger, aiid several others are superior.

if

He

at St. Petersburg.

i^

Berlin and Vienna they play

at Frankfort is also a

played here,

whom

players, with the exception of Mr. Pratten,

up

;

modern composers

to C-% therefore the

certainly the best for general purposes.

Large holes are always better than small ones, for with them the sections of the air-column are

better and

more

freely.

more perfect,

ai^d the tone is

developed

Probably, no flautist or instrument maker

51

made

ever

many

so

esperiments of

all sorts as

Having

I have.

been a professional musician, I was competent to give an opinion on

what

related to art

;

and as I was never

satisfied until

I had

myself thoroughly acquainted with the theoretical side

may

question, I think I of

my

whom

colleagues,

know more than any

venture to say that I I have

known

made every

of

either personally, or through

their work.

In

my pamphlet,

"Ueber denFiotenbau und dessenneueste Verbes-

serungen " (Schott, Mayence, 1848), I have stated that even at that time I had already made experiments of

and narrow, thick and silver,

brass,

copper,

vibrating tone,

kinds with metal tubes, wide

But

tin.

:

German

o! silver,

an

to get

easily sounding,

the material of the whole flute

;

know

I

in this respect,

recommend thick

and

all

hard or soft-drawn

not enough that the head-joint should be thin

it is

end hard-drawn

thin,

quite well

silver tubes.

It

is

why

must be

similar

the instrument makers

because the difficulty of draw-

ing the tubes increases in proportion to their thinness Isfeither

the English nor the French makers draw their tubes

they have not the necessary machinery,

themselves;

can procure them ready made cheaper and with

made

everything myself

happened that at the very

it frequently bui'st,

and

;

despite all

my

it

many

I must have

best.

For fourteen years I had as assistant a

whom

honest as he

Our fina

skilful.

is

ideas, this,

Your ,vili

will soon be

and no

object

known

watchmaker,

He

is

*'

as

Bohm and Mendler." For if my death, according to my

after

man.

with two head-joints, one

(^IJameter;

skilled

workshop.

as

be ready in a month at farthest.

19 m.m,

my

quality rather than quantity.

other, is the right

silver flute

If I

for

is

on the business

to carry

making

I never allow him to employ more than

two workmen, because the any one

my

four years since I gave over is

a tube would

things pass which were not of the

living,

to

I

precautions,

oould not be used.

pension, and depended wholly on flute let

all

moment

last

or became crooked or oval, so that

had not

care and

and they

less trouble.

silver,

the other wood,

I have kept to the bore of

but the holes will be one millimetre wider,

with such an opening as will admit

of the freest

development of D 2

52

The mechanism

tone.

so arranged that the

is

of the holes also will

is

closes

be the same, as in the

you wished) be

will (as

the same as before, only that the

C key always

with

last fiute,

head out about 2 m.m., and

still

play in tune.

the workmanship

and

solid as possible.

me

tell

is

as good

Bb key position

but the pitch

This will be effected by the in-

sliarper.

may draw

creased width (1 m.m.) of the holes, so that you

You

The

it.

the

I will take care that

that Mr. P. has two middle joints, one for normal,

the other for sharp pitch, but only one foot-joint, used for both.

But the intonation can only be

correct for one of

whole

The

flute

put together).

is

from

positions of tlie holes

Those who made the

flute

they themselves understood

The

difference

E down

to

C

is

them (when the

of

the calculated

more than 5 m.m.

ought to have explained

this, if

when

head-joint can only be used for either pitch equally,

has been specially of this in

made with a view

making the head

of your present flute, so that

pitch,

if,

as

doubtless will

eventually adopted in England.

would be useful

for calculating

you can at it

at the

be the case, that pitch

In that case

new

my

also

scales for pianos.

it

I took care

to that purpose.

any time have a middle joint and foot-joint made to normal

indeed

it.

is

diagram

On

it

you

will find all the proportionate lengths given with mathematical

accuracy.

Note.— The

fiute

above described, made for

head-joints, was, I believe, the first silver flute joint.

Bohm was much

at a later date

have

flat silver

pleased with the remilt of the experimeDt, and flutes very etrorgly,

lately flute.

G

flute (alto).

had this wooden head fitted—as Bohm foretold—to a The silver head and middle piece and foot are in the

possession of Mr. T. Jones, of Ludlow.

To W.

S.

In a

with two

a wooden head-

recommended wooden heads for silver

especially for the silver

I

me by Bohm

made with

—W.

S. B.

Broadwoob. letter dated

Munich, June, 1867, replying to some

questions respecting the origin of certain improved processes in the

manufacture of pianoforte

strings,

and that of the system of

53 diagonal (crossed) stringing, both

Bohm, but "If

carried out

apparently

and even patented by

suggested by

others, he says

were desirable and possible to analyse

it

first

all

the inventions that

have from time to time been brought forward, we should scarcely in any instance single

individual, but

:—

find that

were they the offspring of the brain of a

that

all

progress

gradual only

is

each

;

worker follows in the track of his predecessor, and eventually perhaps advances a step beyond him. for it

an

depends frequently on some mere

man's mind at the right moment.

Note.

I

was myself never

—Bohm

fertile in expedients,

time he was engaged.

which may not occur

trifle,

in th^

He

steel.

North of England an im-

always showed himself very

whatever might be the pursuit in which for the

— \V. S. B.

Teobbnsee,

The is

S.

Sept. 23, 1868.

Broad WOOD.

difference caused

by embouchure

many

so considerable that in

quarter, in

to a

..."

and sold

also devised

proved method of manufacturing

To W.

at a loss

and have often helped others onwards towards success

idea,

some even

cases

to half a tone

;

(viz.,

it

method

amounts

therefore, in

me

to

of blowing)

more than a

making a

know

flute

to any given pitch,

it is

not enough

must

also

have some knowledge of the player's em-

vibrations

bouchure.

;

I

for

to

For instance, I have never yet met with a

played as sharp as myself on the same

was celebrated

flute,

size of the

tone a large mouth -hole ftmall oval

flautist

of

who who

Dorus would have

flute.

mouth-hole, as well as that of the finger-holes,

also materially influences the

with

number

excepting Tulou,

for the largeness of his tone.

played a quarter of a tone flatter on the same

The

the

is

volume

necessary.

mouth-holes.

of the tone.

For a large

full

I could never play properly

54 (From

German.)

the

Munich, Nov. h% 180)8. To W. S. Broadwood. Your letter gave me mueii pleasure, for the approTal of one who understands the subject is always a satisfaction.

You

my

see that, although nearly

endeavours to render

my

75 years

old, I

have not relaxed in

instruments as perfect as possible

and when you read

my

you

have not made, or subsequently

will see that I

treatise

upon the

jSute

and

its

treat-meut,

altered,

any-

thing without good and sufficient reason.

Thank

goodness, I have at length finished

There ought properly to

a publisher.

English translation

You wish As the holes

on

and

will see alxjut

both a French and an

but I cannot myself undertake them.*

;

know

to

bt-

it,

the effect of shortening the head- joint.

proportions which det^ernjine the position of the finger-

anj!-

fiute

can only be quite accurate

when based upon

one

particular measurenieni of distance from the cork,

it

every diminution

must influence

,

or addition

of,

that the proportions are quite accurate

3 m.m,

much

therefore you

may

distance

to, this

Your new

the intAjnation prejudicially.

follows that

silver flute is so

when

the head

is

arranged

diawn out

also sliorten the air-column

by that

(thus sharpening the pitch), without very perceptibly

aif ecting

;

the intonation.

The C^

Vvdii

now become

proportion to the A^; and

6 m.m, in

flat.

if

and the C^ sharper, in the same

you puli out 8 m.m. more (therefore

beyond the central

all)

then, conversely, the too

ilatter,

In the

C

first

(theoretioallj^ accurate) point,

will be as mucii too sharp at the

two octaves

in the third octave a little different,

for instance,

Ei

is

influenced only by

fluenced in addition

You

will

my

will be

by the opening

on account of the vent-holes

its

special finger-hole,

of the hole of

understand this perfectly

explanation of

C2

this influence will be equal, but

if

diagram attentively. t

A^ the

E^

fifth

is

;

in-

above.

you read the enclosed I drew out this diagram

in order that instrument makers might form an accurate idea of the

geometrical progression in which the position of the holes must bo * Die Flote und daa Fioteuspiel.

AiU, Munich.

f See page

^li.

55 This diagram could only be designed

varied to suit different pitches.

by one who was at once musician, instrument naker, and

At the

acoustics.

skilled in

Paris Exhibition, unfortunately, the jurors, being

unfamiliar with the subject, declined to go into

it

;

wherefore, at

the request of the Committee of the Bavarian Polytechnic Society,

I had

my

diagram published in their " Kunst-und Gewcrbeblatt,"

much time and

This work cost

penny

of profit

;

trouble, without bringing

my

nor did I receive anj^^hing for

me

one

pamphlet on

the CoQstniction of the Elute, of which Mr. Carte took possesaion.*

My

treatise will contain chapters as follows

The various kinds

(1) Introduction, (2) of the Eiute Tube, (4)

The

(G) Description of the

Key-Mechanism,

of the

Material, (5)

:

of Flutes, (3) Description

The System

of Eingering,

(7) Repairs, (8)

Treatment

Mecbaaism, (9) The Pads, (10) The Spiings, (11) The Cork,

(12) Troai-meut of the Elute, (13)

The

Tone^Seasoninrf of

New

Flutes (das J'^inblasen), (14) Study of Tone (Embouchure), (15)

The

Moveme!it of the Fingers, (16) Exorcises, (17) Style, (18) Table of Fingering, (19) Prejiminaiy Exercisps,

(2f))

Examples

illustrative of

Style.

If to this

were appended the explanations of theory formerly

given (pamphlet 1847), and also the diagram, the history of

work and

all

my

contained in one it

out in

experience, during a period of

Perhaps

little ])ook.

two separate

pai-ts

i

it

60

years,

all

my

would be

would be better to bring

(1) Theory, (2) Practice.

Very few

people understand anything about theory, and might not care to

pay the additional to

What

pric^.

do you think ?

1 should be glad

know, because I value your opinion highly.

NoTF.— Tiie

" pamphlet " alluded to is that now published with these Mr. Carte tells me that it was given not to him, but to Mr. Kudall. The " Treatise " is published in German, but has not yet been printed in Eoglish. Boliui wished me to translate it. W. S. B. (1882.)

letters.

—

MUiViCH, May, 1S70.

To W. S. Bp-OAiiiwooD. Aa you have already so many flutes, I should not like to make one moro for you without being sure of everything. Therefore

you must allow

mo

* This

t^>

ia

be somewhat particular in

the pamphlet

now

published.

my

requeate,

56 and I

will try to be as precise as possible, if

trouble to atten(5 to them.

length of a millimetre

you will take the a good ruler of the

is

a compass, and a measure with miilimetres.

flute,

is

All you require

now

universally used, as it

the

is

small parts, and the easiest for calculations in decimals.

do not like such things, I will

The question

way.

trj'

But

if

you

to be as clear as possible in another

hoiv long

is,

The

measuring

fittest for

must be the tube

from

of a flute

the corh in the head to the end of the foot, in order to obtain the

Ci exactly in tune with 529 vibrations?

If the

A^ must make 889.67. whatever tone you design by the number

C^ makes 529

vibrations per second, the alike,

all

I find

the rest, and also

all

columns

of air, in

my

all

diagram

measures on the enclosed

You

and

C^

for the

I send you

They

slip of paper. is

shut

oS.

length, in case the foot

m.m. is

made

it is

down

these

by the cork in the

=

The number 593.92 to go

now

are all taken from

A^

will find the length for the

= 598

me,

to

the corresponding lengths of the directly.

the point where the column of air

head- joint.

As

of vibrations, as

to BiJ.

332.28 m.m., indicates the

In that case

the centre of the G^ hole would be bored at the indicated point.

Now

a

flute

made

to

these

measurements would be

pitch you require with most flute players as I always played

much

and open embouchure. Paris,

who

but

it

would not stiit me,

sharper than others, on account of

There was in

my

flutes

my free

time only old Tulou at

must always be longer from the cork

the A^ by about 3 m.m., and

you write to

me

all

is,

Now,

the rest in proportion.

;

to

as

that you, too, play with an open embouchure, to get

a fuller tone you also will require a longer measurement question

the

played at as high a pitch as myself on any given flute

my own

therefore

;

in

;

and the

how much ?

This must be ascertained precisely, or you will get a

fl.ute

not

perfectly to your wishes.

You

say in your letter, " I have put the head- joint No. 2 into

the lower part of the normal diapason flute," and afterwards, **

Well, this brings the flute to the pitch I require, or nearly so ; '*

and then you any other

say, "

flute I

But I

find the C* too sharp, just as

draw out the head-joint a good

when on

deal, I find the

57

C

lower

My

too sharp."

dear Sir, you 8ay here what

and quite impossible

dictory,

drawing out and drawing in

&a

;

A

!

more than a couple

must become

of millimetres

5

10

|nii|rnij

(

=

If

twice as groat as on the

in proportion to C^,

of

air,

\

but

=

C\ which

The natural consequence

instead of 5.

if

Now

10 m.m.).

you puU out the head 5 m.m.

drawing. the C*

correct

,

|||

is

mn

the effect on

i

|

requires 10 m.m.,

that the

C Ms

and your remark on drawing out

you draw

in,

above where the holes begin,

proportion.

Therefore

it

perfectly

flat in

the

cannot be the fact that the C^ gets

too sharp in proportion to the 0^,

when

a shorter head

is

AU

used.

Therefore you must

must be accurately examined.

take your fiute with the head which you prefer,

j

and draw in or out

is

putting on a shorter head-

b}^

same

details

too sharp

or shorten the upper part of the column

the effect must be contrary, and the C^ gets too

proceed as follows

look at the

5

joint,

such

you draw

If

the intonation

defective, because all the holes should be regulated in

geometrical progression

is

contra-

effect to

can only be perfectly in tune

flute

in the diapason corresjwnding to its measurements.

out or in

is

you ascribe the same

till

you get the A^ at the required

you are quite sure that

it is

right—taking

When

pitch.

into account all such

infiuencos, as for instance, the temperature of the room, &c., &c.

then lay your

flute

down, and place

my

drawing over

it,

so that

the rim of the embouchure in the drawing corresponds exactly

with the rim of the embouchure of your

flute

;

then, by stretching

out the drawing, you will at once see whether there

what

so,

difference in length

centre of the

Mark

A^

is

any, and

hole^

this difference

the end of the flute

you have measui'ed

on the drawing, and

if

you do the same

the

Now

as

you wish

new middle and what

me

to use the head-joint No.

foot-joints, I

remember) whether there at

for

much the better. It will show whether correctly. You will notice that I have marked also, so

on the drawing the two measurements which you sent me on of paper.

if

from the rim of the embouchure to the

is

distance from the

want

to

know

slips

2 with

(for I

and

cannot

on this head-joint a ring

;

end?

have always

Of

late years I

if

so,

58

made

that ring in two separate pieces

the " box

that

**

on the middle

(Biichse)

when

the flute

—one

of

them

soldered to

the other to the head

joint,

;

so

put together, both parts form the complete

is

ring.

As

the head ought to go into the "

joint) till the

to

know it

extremity.

its

tiie

Mark

this also

In

way

in your next letter.

meet your wishes

A thread

rely.

box" (upper

reaches the tube of

it

part of middle

middle

;

this

want

joint, I

nng on

the length of that part which extends from the

head-piece to

return

end of

I hope

I shall

be able to

but I must have measurements on which 1

which will

the

on th« drawing, ?nd

cati

stretch will not do.

All the rest I know, and your middle and foot-joint sbail be

made

I wish I could carry out orders more

as well as possible.

quickly

but since

;

my

former pupil, Heindi, travelled through iho

United States, I have had more orders than I can execute from

America

;

and though I

offered to procure flutes

Lot, at Paris, people prefer to wait for those

Begging your excuses for

my

from

my

friend

made by myself. I do what I eaji

bad writing

—

—

remain, &c.

—

Note. The above may interest flute players as showing how minutely and painstaking Bohm was, and how thoroughly he understood

caref\ii

his business.

—W.

S. B.

{Frmn

the

German.)

MiJNCHEN,

To

I

am

Your notions about tone

glad that you like the flute.

quite agree with mine. it

AltffUSt^ 1871.

Broadwood.

"W. S.

A silver flute is from

ever will be, whereas a wooden

improving continually.

For

tube quite dry, and to clean

flute, if

that, it is

it

most

each time

it

and a

old

cocoa-nut

silk or linen

flute

handkerchief

which has

ideal of tone, large, sonorous,

an

first

as good as

essential to

wipe the

has been played upon.

when the drawn through.

This, however, can only be properly done out,

the

properly treated, goes on

excellent

cork

tone

is

taken

I have an ;

but

mj^

and powerful, admitting of every

59

up

gradation from pianissimo

The

silver flute in G.

playing

it

.

although I

,

,

to fortissimo, is

am now

an old

man

With a

the tone

very brilliant, and no room

is

make

this flute

and a gold emhouchure,

silver head- joint

with a wooden embouchure on the

and use

of 78J,

falae teeth, is such that I only regret that I did not

forty years ago.

my

the tone of

still

I have repeatedly produced, Avhen

effect

too large for

is

it

;

while

silver head-joint, the tone gains

in richness without losing power.

Compared

to tho

G

flute, it is like

the voice of a fine powerful

Once when I played

soprano in contrast to that of a child.

church on this

flute j

My

French horn.

I receive proofs for correction every week.

the press.

De Vroye where

in a

accompanying a soprano, it was mistaken for a. work, " Die Elote und das Flotenspiel," is in

a first-rate artist, but his tone

is

iS'ichoIson is still

remembered,

is

too small for London,

I did as well as any Conti-

nental flautist in London in 1831, but I could not match l^icholson in

power

Had

of tone,

wherefore I set to work to remodel

I not heard him, probably the

For

my

flute.

would never have

flute

of all other flautists, not

oven excepting Tulou in

no one could do more than I could, so

far as tone is concerned.

been made. Paris,

Bohm

Ail Nicholson's immediate successors had, more or tone, but they

made

a trumpet of the flute.

enough, but loudness alone

is

not what

less,

wanted

is

a powerful

Their tone was loud for singiw}.

J

always prefer quality to quantity.

Munich, Nov.

To Mr. W.

made myself an exact drawing

I have

of the position of

the holes, according to the paper slip you hud sent

being correct

8, 1873.

r. Mills.

:

so there can be

Next week your

flute will

unexpected hindering,

it

be commenced, and

will be finished in

the octave key, which makes

me

back as

no mistake as regards the pitch.

much

less

if

there comes no

December.

I ordered

complication than the

ahake lever, and which will never come out of order, as the hole, about as large as

f^,

is

shut so very

easily.

I find that

little little

60 "key very useful,

the player wants to be always perfect in tune in

if

the following notes .

j^

jt

«

»

always a tendency to get a if

yon open the

rect,

(

i

"^

T

i

T"

little flat if

i

These tones have

~F"b

played in pianissimo

easily.

The key can easily be opened with

a very small motion of the thumb, and you will get used to least trouble.

When not wanted,

in rapid passages, it will not hinder

to execute

^^

.

without that

^

^-^J

little

and

octave key, they are not only perfectly cor-

little

but sound also very

and by without the

;

key.

by

your execution. Thus, if you wish

you

\

it

as, for instance,

will hardly play

it

perfectly

j

Now

in regard to a second middle joint,

I advise you not to have one, as the difference in pitch

is

much

was

in

your

greater in comparison with the normal pitch than

You

first flute.

it

will never be able to play in tune

if

the foot

not conformed, in the position of the holes, with the middle

The

Not only the lower

difference is too great.

will be

much

notes,

is

joint.

C\ C^4|,D\D%

too sharp, but also several tones in the third octave

will not be in tune, nor sound easily.

It

is

just

as

half a note higher,

if

you had three

You cannot do without having of a head

is

very

little in

you will do much better

A

strings

on

a violin tuned

and leave the lower one half a note too also another foot,

comparison with the two other

to get

middle joint without foot to

a second

it is

flat

and as the price

flute at the

joints,

normal pitch.

throwing away money

61

Munich,

To Mb. W. p. Mills. As to the preference never be solved

have said about best for after I

many had

bouchure.

it

in

wood

of

my

some front

Silver

If

you could read what I

book, you would find that I myself played

years on silver flutes

lost

or silver, tbat question will

a matter of taste.

it is

;

1878.

teeth,

;

but took to wooden flutes

my

and with them

sound more readily, and

flutes

adapted for modulating tone

;

but those

who have

good emare

better

not the right

sense and feeling generally produce a hard tone, and therefore do better to play silver

on wooden

I could produce

flutes,

effects

on

my

which I could never afterwards produce on wooden

flute

flutes,

I think Mr. Broadwood,

who always endeavoured

to get the

best tone, will tell you the same.

My

eyes get

now

so

weak

that I must end.

Munich, JWy,

To W. P. Mills. The head-joints

of

our wooden flutes must be

never the middle or the foot-joint.

best

is

oil

fectly dry,

of Provence)

with a

the evening, that the

the oil»before the morning. before playing. is

If

you

oil

oiled,

You can apply a litble oil feather, when the head is

and when you have taken out the cork.

is to oil it in

1878.

The

wood may have time

Then you wipe

it

but (the

per-

best time to absorb

dry with some linen

the head once a fortnight at

first it

quite enough, and afterwards only every month.

I

am

quite well in

eyes are very bad.

my

old age of eighty-five years, only

my

62

BOHM'S DIAGKAM The GermaJi

text of Bohm's description and explanation of his

Diagram was

first

published in a special

number

Tmd Gewerbeblatt," Munich, October, 186S. sent

o{ the

Bohm had

" Kunst-

previously

with a model of his G fiute to the Paris Exhibition, 1867, it was " mis hors de co-ucquts " by the musical jury,

it

where, however,

who

were not competent to decide upon the merits

said they

duction which

have

was

scientific rather

said, published it at

than

He

artistic.

Munich, and sent

me

the copy (of which

I have made, I fear, but an indifferent translation), by

He

way

of reply

had asked.

to certain questions I

subsequently published

different

of a pro-

then, as Z

it

in a somewhit, but not materially,

form in his "Die Plote und das Flotenspiei."

I believe the

date of this latter pamphlet vas 1873, and the pablisher, Joseph Aibl,

In

Munich.

of

also

it

he has re-written in German, nearly word

for word, several passages of the earlier English pamphlet,

the

first

now

for

time printed,

Bohm was

very anxious that the German (1873) pamphlet should

be translated and published, with the earlier one, in England. " Then," he wrote to me, " ail that I have done in 60 years will be

known " must be Mayy

On

the

He repeatedly urged me to undertake the task, and this my excuse for the present imperfect attempt, W. S. B.

1882.

Method

holes of BoHiu',

to he

Wind

adoj>ted in determini'nxf the position of the Note-

Instrumrmts for

(Bavarian

The manufacture

of

''^

everi/

given Pitch.

Kun^t-und Gewerbeblatt"

wind instruments having

By TEEOJSiXD

October, 1868.)

note-holes, ajid

their adaptation to the various musical pitohes, necessitates, for the

most

part,

and money.

new

calculations or models,

which cosb time, trouble,

63

To avoid such

inconveniences, I

the basis of calculation

measurement.

Thus,

is

in

drew out a diagram, on which

represented and

the

following

marked out table,

the

in linear

reciprocal

numerical proportions of vibration to length of string, in the equally

tempered

scale, are

represented by horizontal or by vertical lines

while diagonal lines indicate the geometrical progression in which the longitudinal measurements

may

be varied without disturbing

the proportion which they bear to the vibrations.

64 I have founded help,

my

determined

my

wind instruments constructed on

holes on all ;

With

diagram on these considerations.

and without resorting to calculation, the centres

its

of the note-

system

may be

as also the position of the so-called " frets " of guitars,

mandolines, zithers, &c., &c.

To do

this,

of

course, the

numbers must be converted and

positive longitudinal

assumed

into absolute

numbers

As the French normal

my

of

vibrations

measurements. pitch

(A^

=

870 vibrations)

adopted nearly everywhere, I have founded upon calculations of

or proportional

relative

Diagram; and

is

now

the numerical

it

as unit of calculation for the

longitudinal measurements, I have taken a cylinder open at both ends, 670 of the

m.m. in length, and giving the note C^ - 517.30 vibrations

French normal

pitch.

Thus we obtain the following proportionate numbers Absolute number of Vibrations,

C|^

Djf

...

Db 5ia06

632.39

D

580.65

596.90

E'^ 615.18

563.40

....

...

...

A Ag

...

B

The

670.00

517.30

G G$

Eelative Longitudinal Measurements. Millimetres.

C^

E F Fjf

:

651.76

531.77

690.51

501.93

Gl> 731.57

473.76

775.08

447,17

A!> 821.11

423.07

870.00

398.38

Bl, 921.73

376.02

976.54

354.91

1034 60

335.00

relative longitudinal proportions of

my

flute,

here expressed

in millimetres, are, of course, merely adopted for the purpose illustration.

Although the vibration numbers

of the

normal

of

pitch,

asal 80 the longitudinal proportions for all instruments are constant,

yet each wind instrument has

its special

length,

which depends upon

66 M^. the means by which tone

an

of

oboe,

more

and

The tube

generated.

is

particularly

that

of

a

must be made very much shorter than

clarinet,

the tube of a flute of like pitch, because of the influence

flattening

For

only

the reed or mouth-piece.

of

small

a

portion

corre8}X)nding to that note

or

when blown

reed

really, there.

of

air-column,

F

m 5^

which the mouth-piece

separately

would

give,

is

Wherefore a wind instrument, when

shortened by one-half octave

the

of

/

/

its

fundamental,

its

«

length, will not give the

but

a

1

considerably

flatter note.

The

length

for

must

the octave

therefore

ascertained

by

the tube.

Then, by doubling the length of the is

int-o intervals,

i'

obtained, answer-

ing to the string of a monochord, and which

be divided

^

by shortening

calculation, or simply

shortened tube, an air-column

^

be

may

1

so as to coincide with the

numerical and longitudinal proportions given in the «c;

diagram.

Now

the flattening influence of the cork and the

embouchure amounts on

my

flute to

51.5 m.m., and

in calculating the relative longitudinal

of

intervals this

existing length of the

;

measurement

has to be taken as an actually

therefore, in the practical application

formula this quantity (51.5 m.m.) has to be

deducted from each relative longitudinal measure-

For instance, 01

ment.

= 670.0 — 51.5=618.5.