Grove's dictionary of music and musicians

.
RESULTANT TONES EESZKE 77
to treat at some length of the nature of beats,
and the reader is therefore referred to the article
Beats, for this side of the question. The later
mathematical theory given by Helmholtz is too
abstruse to admit of popular exposition.
It was also part of Young's theory that the
differential tone was produced in the ear alone,
and not in the external ail-. But Helmholtz
found that stretched membranes and resonators
responded very clearly to differentials, produced
by the siren or the harmonium. This he considers
to prove the existence of vibrations in the
external air corresponding to the differential
tones. But when the two generating tones were
produced by separate iustniments, the differential,
though powerfully audible, hardly set
the resonator in vibration at all. Hence
Helmholtz concludes that the differential tone
is for the most part generated in the ear itself.
He further points out that certain features in
the construction of the ear easily permit the
action of the law which he has stated. The
unsymmetrical form of the drum-skin of the ear,
and the loose attachment of the ossicles are, he
thinks, peculiarly favourable to the production
of resultant tones. [A practical use of resultant
tones is shown in the article Okgan,
vol. iii. p. 552a.]
As a consequence of his theory, Helmholtz
deduced a different series of resultant tones,
which he calls summaiional tones, because their
number of vibrations is the sum of those of the
generators. The existence of the summational
tones which Helmholtz believed he verified
experimentally, has recently been called in
question by Dr. JVeyer. He points out that
in some intervals, as, for instance, 1:2, 1:3,
1 : 5, there will be a partial tone present of
the same pitch as the presumed summational
tone, and these cases therefore prove nothing.
Again, if we take 2 : 3, the note 5 is not
necessarily a summational tone, but may be the
differential of 4 and 9, which are the 2nd partial
of 2 and the 3rd of 3 respectively. Dr. Preyer.
was unable to find any trace of the summational
tones when care had been taken to exclude the
upper partials. But to do this he could only
use sounds of tuning-forks gently bowed, which
were far too weak to produce any resultant tones
in the air. The question, however, is one of
theoretic interest merely.
Not only the origin, but also the discovery
of differential tones has been disputed. The
earliest publication of the discovery was made
by a German organist named Sorge in 1745.
Then came Romieu, a French savant, in 1751.
Lastly, the great Italian violinist, Tartini, made
the phenomenon the basis of his treatise on
Harmony in 1754. But Tartini :— explicitly claims
priority in these words 'In the year 1714,
when about twenty-two years of age, he discovered
this phenomenon by chance on, the,
violin at Ancona, -sphere many witnesses wha
remember the fact are still living. He communicated
it at once, without reserve, to professors
of the violin. He made it the fundamental
rule of perfect tuning for the pupils in
his school at Padua, which was commenced in
1728 and which still exists ; and thus the phenomenon
became known throughout Europe.'"
Tartini in some cases mistook the pitch of the
differential tone ; but there does not appear to
be any reason for taking from him the credit of
the discovery which has so long been associated
with his name. j. L.
RESZKE, DE, Edotjakd, born at Warsaw,
Dec. 23, 1855, was taught singing by his
brother Jean, Ciaffei, Steller, and Coletti, and
made his d^but April 22, 1876, as the King in
'
Aida,' on its production at the Italiens, Paris.
He sang there with success for two seasons, and
afterwards went to Italy, where, in ISSQ, at
Turin, he made a success in two new parts—^^the
King in Catalani's Elda,' Jan. ' 31, and Charles
V. in Marchetti's 'Don Giovanni d'Austria,'
March 11, and appeared at Milan on the production
of Ponchielli's 'Figliuol Prodigo,' Dec. 26;
From 1880 to 1884, he was engaged with the
He made
Royal Italian Opera, until its collapse.
his d^but on April 13, 1880, as Indra (' Roi de
Lahore '), but his success as a foremost lyric
artist was established by his admirable perfonnances
of St. Bris, the Count in Sonnambula,'
'
Basilio, and later as Walter (' Tell'), Peter the
Great, Prince Gudal ( ' Demonio '), June 21,
1881 ; Senon (Lenepveu's 'Velleda'), July 4,
1882 ; Almaviva ; Mephistopheles ;
Alvise, on
production of La ' Gioconda,' May 31, 1883 ;
Hageu, on production of Reyer's ' Sigurd,' July
15, 1884, etc. In 1883-84 he reappeared in
Paris at the Italian Opera (Theatre des Nations),
with great success, in Simone Boccanegi'a' ' ; in
Massenet's Herodiade,' ' on its production in
Paris ; in Dubois' ' Aben Hamet,' Dec. 16, 1884,
and in other operas. He was engaged at the
French Opera, where he first appeared April 13,
1885, as Mephistopheles, a part he sang subsequently
in the 500th performance of ' Faust.'
He appeared as Leporello in the centenary performance
of Don ' Juan,' Nov. 4, 1887, and has
sung in Le Gid and ' ' ' Patrie.' He played at
the Italian Opera at Drary Lane in 1887 the
part of Ramfis in Aida, ' ' and sang during the
season as Basilio, St. Bris, Mephistopheles, and
Henry the Fowler (' Lohengrin '). From 1888
to 1900 he sang every season (except 1899), and
added to his repertory the parts of Almaviva,
Marcel, the Mefistofele of Boito, and the Wagnerian
parts of Hans Sachs, King Mark, Hunding,
and Hagen. From 1890, for many seasons,
he sang in America with his brother, with the
greatest success. He sang at the Mozart (concert)
Festival at. the Nouveau TheS,tre in Paris
in the spring of 1906, under the direction pf
M. Reynaldo Hahn. In.Feb. 1907 he advertised
1 De Princi^i delV Armania^ Pa(Joyaj 1767. P- 36.