Dept. for Speech, Music and Hearing

Quarterly Progress andStatus Report

Measurements on flutes fromdifferent periods

Fransson, F.

journal: STL-QPSRvolume: 4number: 4year: 1963pages: 012-016

http://www.speech.kth.se/qpsr

111. MUSICAL ACOUSTICS

A. MEASUREMENTS OB FLUTES FROM DIFlTERENT PERIODS, Par t I

The f l u t e of today i s an inven t ion of t h e German

f l u t i s t and instrument maker Theobald Boehm i n 1847. The

na in p a r t of t h i s instrument c o n s i s t s of a c y l i n d r i c a l tube

and t h e upper p a r t o r head-joint i s con ica l , t ape r ing aga ins t

t h e top.

The f l u t e used before Boehm was con ica l , t ape r ing ~ g c Z ~ ; s t

t h e lower end but with a c y l i n d r i c a l head-joint . This type

of f l u t e was f o r many years a f t e r Boehm considered t o be super io r

regarding t h e tone q u a l i t y and i n t h e e a r l i e r pa r t of t h i s

century many f l u t i s t s p r e f e r r ed t h e con ica l f l u t e but modified

with t he Boehm mechanism f a c i l i t a t i n g e a s i e r f inger ing ,

The old type of wood-wind ins t ruments a r e again

becoming popular, e s ~ e c i a l l y f o r performance of baroque music

and an i nves t i ga t i on of t h e acous t ic p rope r t i e s of ins t ruments

from d i f f e r e n t per iods i s of general i n t e r e s t .

Some measurements have been made n t t he Speech

Transmission Laboratory of t h r e e r ep re sen t a t i ve f l u t e s :

A, a modern c y l i n d r i c a l Boehm-flute of cocus wood with a

metal head-joint , B, an old conical f l u t e of boxwood with 5

kcys manufacturized about 1850, and C, a con ica l f l u t e o f

cocus wood with metal head-joint and Boehm-mechanism.

Measurement g

The resonance f requencies and t h e bandwidths rrere

measured with STL-ionophone ( r e f . : STL-&PSR-~/I 962) . The

ionophone-electrodes were appl ied on an attachment cons i s t i ng

of a plaster-moulding of t h e l i p s of a f l u t i s t . This attachmen:

w a s placed a t t h e flute-embouchure i n a p o s i t i o n resembling

t h e normal pos i t i on of t h e l i p s of t h e p layer . I n order t o

f i n d t h e r e l a t i o n between t h e blown tones and t h e corresponding

resonance f requencies , recordings were made of long tones

played a t mezzo-forte i n t e n s i t y by d i f f e r e n t i n s t rumen ta l i s t s .

Di f fe ren t schemes were t r i e d , a s p laying of d i f f e r e n t s c a l e s

and a f t e r a w r i t t e n score with t h e succession of notes chosen

at random. These experiments d id not g ive a s u f f i c i e n t l y

r ep re sen t a t i ve s ca l e f o r t h e instrument on account of t h e f l u t i s t

compensating t o attempt co r r ec t i n t e r v a l s . A b e t t e r r e s u l t was

obtained without a score,each tone played according t o ve rba l

d i r eo t i ons from t h e experimenter. This method was however

s l i g h t l y confusing f o r t h e performer and a method with s i g n a l l i n g

lamps i n d i c a t i n g a s e l e c t i o n of notes w i l l be t r i e d out ,

Results

The s c a l e L o - - - The, f o r any tone represen ta t ive , instrument resonances

measured by t h e ionophone technique a r e shown i n Fig. 111-1,

By comparing these ionophone-frequencies wi th a mean va lue from

t h e blowing t e s t s a somewhat i r r e g u l a r d i f f e r ence func t ion

cpponrcd. However, t h e tendency of a sys temat ic r e l a t i o n i s

evident and a more exact d i f f e r ence func t ion w i l l be found by a

g r e a t e r number of independent blowing t e s t s without o r wi th

t h e l e a s t pos s ib l e i n t e r v a l guiding as ou t l i ned above.

The do t t ed curves i n Fig. 111-2 show a rspresenta-

t i v e d i f f e r ence funct ion. The reason why t h i s c o r r e l a t i o n i s

frequency dependent has t o some extent been i nves t i ga t ed and

i s maily due t o a change i n t h e e f f e c t i v e embouchure-opening

due t o d i f f e r ence i n t h e p o s i t i o n of t h e l i p s when playing

d i f f e r e n t tones . When playing a low note t h e a i r pressure i s

low but t h e flow i s high and t h e upper l i p i s not pressed

against t h e lower l i p , t h e e f f e c t i v e embouchure-opening i s

m a x i m u m . When playing a high note, t h e a i r p ressure i s higher

and t h e upper l i p i s pressed more aga ins t t h e lower l i p r e s u l t i n g

i n a dimirishod e f f e c t i v e ambouchure-opening,

Fig. 11-2. F versus F p lo t of Swedish susta ined vowels and 2 1

F ' ve rsus F of two-formant syn the t i c approximations, 2 1

L2 - L1 ranging from 12 dB i n [a], t o 22 dB i n [y]

and [i]. The very high F2 of [i] may probably be

ascr ibed t o t he p a r t i c u l a r syn thes i s technique.

X Human vowel.

Two formant synthesis. Two resonant circuits in

parallel with phase

.

L_

-

- I I

I I I I

- [il \ \

inversion.

r - 14 - Cvl

I

-

.I

R [a1

T"' y Col

Rca

I

R col

.

FLUTE A. FLUTE C

$3 c/s

FLUTE B 6, c i s

Fig. 111-1. S.T.L. Ionophone excitation

Frequency deviation b, f m m

equally tempered scale.

An add i t i ona l change i n t h e e f f e c t i v e opening i s I I

i n t e n t i o n a l , i .e., t h e i n s t rumen ta l i s t knows t h a t t h e low tones

on t h e instrument a r e s l i g h t l y below and t h e high no tes a r e

above t h e tempered s ca l e and a t r a i n e d f l u t i s t w i l l make some

spontaneous cor rec t ions . These co r r ec t i ons a r e , however, not

of t h e same order a s when he i s guided from known i n t e r v a l s

o r by o t h e r instruments i n an ensemble. A second f a c t o r of

perhaps some importance i s a s l i g h t l y h igher a i r temperature

at t h e embouchure at low tones than a t high tones due t o t h e

v a r i a t i o n of t h e a i r v e l o c i t y . A d i f f e r ence of about 2 ' ~ has been

measured wi th a small the rmis to r i n t h e f l u t e near t h e embouchure.

Then, f i n a l l y an impedance change at t h e embouchure i s pos s ib l e

on account of v a r i a t i o n s i n t h e a i r v e l o c i t y .

From t h e instrument resonances, Fig. 111-1 , and

",he d i f f e r ence funct ion i n Fig. 111-2, t h e probable s c a l e i s

found and t h e dev ia t ions i n cen t s from t h e tempered s c a l e a r e

shown i n F'ig. 111-3 . Besides t h e curve f o r t h e f l u t e A t h e

Cotted curve shows measurements by D r . J. Meyer on a s i m i l a r

f l u t e ( r e f . ( 5 ) ). The t e s t s by D r . Maysr were made by blowing

a chromatic s c a l e aver t h e whole range o f t h e instrument. Ths

c o r r e l a t i o n from C t o C sharp i s f a i r l y good but then t h e r e 4 5

mists a discrepancy up t o A As t h e no tes from E t o C6 sharp 5' 5 a r e produced by t h e same f i nge r ing as E t o C sharp by ovsr-

4 5 blowing,a s i m i l a r i t y should e x i s t between corresponding no tes .

This discrepancy depends poss ib ly on spontaneous co r r ec t i ons by

t h e i n s t rumen ta l i s t , This agrees wi th our e a r l i e r experiences

mentioned above and shows what a f l u t i s t can produce but not

tho t r u e s c a l e of h i s instrument. Normalizing t h e curvcs f o r

t h e f l u t e s A, B, and C shows a max. dev ia t ion , f o r A = +I9 -21 cents ,

f o r B = +31 -36 cen ts , and f o r C = +36 -35 cen ts , i . e . a nax.

d i f f e r ence f o r A < + 1/8 tons , f o r B and C > + 1/8 tone.

The app l i ca t i on of t h e attachment with t h e ionophone

e lec t rodes was found t o cause some ambiguity regarding an

oquivalent p o s i t i o n on d i f f e r e n t f l u t e s . A new e lec t rode holder

i s t he r e fo re designed without t h e mould and prel iminary t e s t s

with t h i s device have been promising.

A dependable and simple method f o r explor ing t h e

s ca l e of t h e f l u t e by means of t h e ionophone i s now poss ib le .

~-values-(~ig-,1~1=41 B*,, , , , The f l u t e s B and C have nea r ly t h e same Q and t h e

f l u t e A has a h igher Q over t h e whole range of t h e instrument.

It i s remarkable t h a t B and C a r e about equa l , t h e f l u t e B

i s a l t oge the r made of r a t h e r s o f t boxwood and t h e f l u t e C is

of hard cocus wood and metal head-joint as i s t he f l u t e A.

The inductance and r e s i s t ance per u n i t l eng th

of an i d e a l c y l i n d r i c a l p ipe is:

9 1 1 1

L = - [ I + 2nr(p/2w9)']; Ro = ( 2 ~ ~ 9 ) ~ , see r e f . 0 A

(3 )

1 - and Qo i s approx. propor t ional t o r e f 2. The Q-values

from Fig. 111-4 a r e normalized accordingly i n Fig. 111-5. The

normalized Q of t h e f l u t e A i s more r egu l a r over t h e whole

compass than B and C . They have f o r ins tance between E and 4 F a conspicuous drop due t o pronounced coupling t o t h e lower 4

par t of t h e f l u t e on account of smaller f inger-holes (keys) '

than A. F lu t e B , with t h e smal les t finger-holes, has high

normalized Q a t D and % due t o low r a d i a t i o n , a s here a l l ho les 5 5

a r e c losed except one a t t h e upper resp. lower end. The f l u t e

A has lower va lues than t h e o the r from D6 upwards depending upon

comparatively g r e a t e r r ad i a t i on . The f l u t e C with t h e medium

s i zed finger-holes has a Q-curve i n between A and B and with t h e

same t rend.

F, Fransson

References:

( 1 ) Benade , A. He : "On woodwind instrument bores " , J . Acous t . Soc .A.m. , 2 ( I 959), pp. 137-1 46.

(2) Benade, A.H,: "On the mathematical theory of woodwind finger holes", J.Acoust .Soc.Am., 32 (1960)~ pp. 1591-1608.

(3 ) Fant , G. : Acoustic Theory of Spsech Production, Mouton & Co- , s-Gravenhage 1 960, pp 32-33.

(4) Fransson, Fog "An ionophcne for acoustic measurementst', STL-&PSR 4/1962, pp. 22-26.

(5) Meyer , J. : "fiber die Messung der Frequenz-skalen von Holzblasinstrumenten" , Das Musikinstrument , Heft 10, 1961, Frankfurt a.M.

Fig . 111-4. Q-values f o r f l u t e s

from S.T. L. Ionophone excitation.

Fig. 111-5. Normalized Q-values for flutes.