DICTIONARY OF MUSIC - El Atril

378 HELMHOLTZ HELMHOLTZ
organ and piano. Itia extremelysimple, as it does
not add to the number of notes in the scale, and
requires no new system of fingering to be learnt
by the performer. This invention, originally
suggested by the extremely unpleasant ertect of
the equally tempered harmonium, may not im-
possibly revolutionise modern musical practice,
extending as it does to keyed instruments that
perfect intonation which has hitherto been attainable
only by stringed instruments and the
human voice. The following may be selected,
amongst many others, to illustrate the nature
of the discoveries of Helmlioltz :
1. Quality of 'musical sounds determined by
ha,rmonics.—By means of a series of reso]iators,
each of which on being applied to the ear reinforces
any harmonic of equal pitch which may
be present in a given note, Helmholtz has
effected the most complete analysis of musical
tone hitherto attained. The resonator is a hollow
sphere of glass or metal, with two openings
opposite to each other, one of which is funnelshaped,
for insertion into the ear. Let the note
of the resonator be c'", the air contained in
it will vibrate very powerfully when that note is
given by the voice or any nmsical instrument
and less powerfully when the note given is one of
those lower notes which ^ Ee,on.t„r.
are harmonic sub-ion^s of
c'", or is, in other words, a
note among the harmonies
of which the c'" occurs.
The chief results of Helmholtz's experiments
"with resonators have been given under the head
Harmonics.
More curious is his determination of the
nature of the vowel sounds of the human voice,
in which Helmholtz has developed the discoveries
of Wheatstone. The shape of the mouth-cavity
is altered for the pjroduction of each particular
vowel ; and in each of the shapes which it assumes
it may be considered as a musical instrument
yielding a different note, and in the case of
the compound vowels, yielding simultaneously
two separate notes of different pitch, just as the
neck and body of a glass bottle do. The natural
resonance of the mouth-cavity, independently of
the tension of the vocal chords, for different
vowels, is as follows (the jironunciation of the
vowels being not English but German) :
Compound vowels.
Thus, when the mouth- cavity is found to utter
the sound u (oo), it is in effect a musical instrument,
the natural pitch of which is/, and so on.
For the highly interesting experiments on
vowel-pitch by means of the resonators, and the
I
importance to singers and composers of the results
deducible from them, the reader must be
referred to Helmoltz's work (Ellis's translation,
pp. 153-172).
2. SuminationoJ tones.—The facts that when
two notes are sounded together they generate a
third and deeper tone, whose vibrational number
equals the difference of their several vibrational
numbers, has been known to violinists ever since
the time of Tartini. [See Taetisi.] These
tones Helmholtz calls differential tones, to distinguish
them from another set of generated
tones discovered by himself, the vibrational numbers
of which equal the sum of the vibrational
numbers of the generating tones, and which he
hence c&Wi summational tones,. These tones are
of course higher than thegeneratingtones. Thus,
if the chords in minims in the following figure
be played /or/« on the violin, the double series
of combinational tones above and below will be
produced :
!
,
I J
1
J?
I
bJ?i
Differential
or Tartinra
tones.
The summational tones are too weak to be
distinguished by the unaided ear ; while the
differential tones are on some instruments in-
trusively audible. (In fact the violin f>layer
obtains perfect fifths on his strings by tuning
until he hears the octave below the lower string.
The summational tones of the two last chords lie
between F and Fg and At> and A respectively.
3. Physiology of the minor chord.—Among
the most interesting of these discoveries is the
reason of the heavy and quasi-dissonant effect
produced by minor triads. Just intonation
deepens the well-known grave, obscure, and
mysterious character which belongs to minor
chords ; and the observations of Helmholtz on
accurately tuned instruments have enabled him
to trace this grave and obscure character to the
presence of certain deep combinational tones,
foreign to the chord, which are absent from
major chords, and which without being near
enough to beat, and thus actually to disturb the
harmony, make themselves sufficiently audible,
at least to a practised ear, as not belonging to the
harmony. No minor chord can be obtained per-
fectly free from such false combinational tones.
For the ordinary hearer the presence of these
tones gives to the chord its well-known obscure
and mysterious character, for which he is unable
to account, because the weak combinational
tones on which it depends are concealed by other
louder tones. The fact that this unsatisfactory
though not dissonant effect of the minor chord
is deepened when the chord is played perfectly
in tune, led musicians who wrote before the era
of equal temperament to avoid the minor chord