Intonation for String Players
Intonation is a
vexing problem for string players. In fact it is so much so, that often one of the
distinctions between the most sought-after string performers and ensembles
from their 
professional colleagues less in demand, is the quality and
consistency of their intonation. The notion of “in tune” as a goal,
however laudable is
simplistic. In order to achieve satisfying and consistent sounding
intonation, it is critical to have a concept for tuning, based on certain
acoustical realities, and based on the context in which you are working.
Any discussion of intonation in the modern era begins with an
understanding of the system of equal temperament. With equal temperament,
by adjusting every interval to the same degree in the scale, two problems
of tuning chords are dealt with via compromise: octave displacement, and
the effect of the qualities of different intervals of the triad in
different keys. In the equal-tempered system, music sounds relatively
in tune (or out of tune) to the same degree in every key. A keyboard tuned to
equal temperament frees a composer to write pieces containing any and
every possible modulation.
Because of this advantage, equal temperament has become the most
universally used tuning system for keyboard instruments. J. S. Bach was one of the first musicians
and composers to fully exploit the virtues of the system of equal
temperament. The great keyboard sonatas of the classical and romantic eras,
and most of the repertoire written in the years since would have been
impossible without the equal-tempered system. In the modern era,
the equal tempered system also provides a convenient base line for tuning
all non-keyboard instruments in a manner that requires no specific knowledge
of the harmonic context of a situation. Modern orchestras typically conceive of
tuning in equal temperament. Electronic tuning machines generally use
equal temperament as their default setting partly for this reason.
However practical it may be as a compromise, for non fixed-pitch
instruments equal temperament is not a means to the most beautiful or
satisfying intonation in either harmonic or melodic contexts. There are
situations where equal temperament makes sense for non fixed-pitch
instruments. In the modern orchestra for instance, any large deviance from
equal temperament can leave a player sounding less unified with the group. There are situations in chamber music settings as
well, where equal temperament is the most exigent solution to a conflict of
acoustical and technical realities.
In certain repertoire, even with fixed-pitch (keyboard and fretted)
instruments, there are tuning choices to consider besides equal
temperament, depending on the degree to which a piece modulates, and
depending on the actual keys to which the piece modulates. Early music
practitioners, especially keyboard players, must incorporate an
understanding of temperament as essential among the
tools they bring to the problems of performance. There are thousands of
possible temperaments for tuning, and at various points in history, prior
to the widespread adoption of equal
temperament as a universal tuning system, various temperaments have
informed composers and vice-versa.
The best non fixed-pitch instrumental performers invariably employ
intonation based on the harmonic, melodic, and instrumental contexts in
which they are playing, even if they don’t always know they are doing
so. When playing with
piano, string players are most often relegated to a modified version of
equal temperament. In some instances we can cheat and deviate from the
temperament of the piano, but many times such deviance will leave a string
player sounding out of tune with the piano. Other than the instrumental
context of playing with piano, there are two other common contexts that
present tuning problems: octave displacement and
harmonic-versus-melodic. String
players need to consider these problems, both intellectually and
intuitively in order to develop satisfying and consistent style of
intonation.
To understand octave displacement one need only experiment at
the keyboard. In the upper-most octave of the piano, sound one single
note. Then play the same pitch in the lowest octave. If the piano is well
in tune, the notes will sound too close together when played separately,
and too far apart when played together. In other words, when played
separately the upper note sounds sharp and the lower note flat. When
played together just the opposite is true. This is because of the inherent
conflict between the overtone series’ that the true notes produce. In
order to achieve consonance between the overtone series’ in the two
notes, they must be pulled together. But the point at which the overtone
series’ line up, leaves the notes sounding hopelessly out of tune in any
melodic context. The farther apart the octaves are, the more acute the
problem. This is the reason why chords built on a wide tessitura are
particularly problematic to tune. Equal temperament is a compromise system
that theoretically, leaves both pitches acceptably in (or out of) tune for
either context.
To understand harmonic and melodic context as it relates to tuning, one
can experiment with any string instrument. ‘Cello reveals the issues
most acutely because the relationship of intervals in the lower range is
broader and the pitch issues are more clearly audible. If you play an F
natural on the D string of the ‘cello against the open A string, your ear
will naturally perceive the basis of an F major triad. This will cause you
to place the F on the high side, in order to leave the third of the chord, in this
case the open A string, sounding sweet and low, where the overtone
series’ line up and “ring” in a major chord. That same F rendered
against the open G string and perceived as a seventh in a G 7 chord will
sound hopelessly sharp. A lower placement of the F will be necessary to
arrive at a lined up set of overtones in this context, and achieve the
ringing sound of the lowered seventh in
the G 7 Chord. The same F, as the third degree in a melodic passage in D
flat major, will once again sound sweeter on the high side, as long as it
doesn’t have to resonate against the D- flat major triad in the same
register. The reality that the third degree of the scale sounds more
satisfying higher in a melodic context, and sweeter lower in a harmonic
context is a problem with which all non fixed-pitch instrumentalists must
contend.
Arguably, intonation in a string quartet raises some of the most problematic
tuning issues in music. Modern instrumental training
generally doesn’t stress an understanding of temperament, octave
displacement, and harmonic and melodic contexts for tuning. This
deficiency in training leaves many string players ill equipped
for sorting out the issues of tuning in a string quartet. The nature of the repertoire, and the possibility of a totally blended
sonority, along with the high standards continually being set by active rehearsing groups, all conspire to highlight intonation deficiencies for
groups that fail to meet the highest standards. The attainment of a high
standard for intonation in a string quartet is a labor intensive project.
It requires that the members spend enough rehearsal time to become
familiar with the harmonic role each line serves in a chord, and it
demands that the members agree on a shared concept for intonation and pitch temperament in
the group.
One example of a tuning problem from the
string quartet repertoire is in the beginning of the second movement of
Mozart’s Quartet, K. 465, marked Andante Cantabile. The movement is in F
major. The opening melodic note in the first violin part is a C natural,
one octave above middle C. The second violin plays an A that corresponds
with the open A string. If either violinist tunes their note to their open
A string, the first violin will be tempted to push the C natural high, in
an attempt to achieve a ringing chord with a sweet and low third, in this
case A natural. This will ultimately push the whole group sharp to their
open strings and the group will lose the sympathetic ring of the open
strings. The resulting blended quartet sound will have a deadened quality
similar to what one experiences in keys with many flats such as D flat
major. In practice there are several possible compromises that will yield
a more satisfying result: In one system, both of the violinists must
adjust slightly low to their sympathetic open A and E strings in the
opening chord, depending upon what the group can agree sounds best. With
the first violin adjusting downward slightly, the C natural will sound
just a bit low to both the open E and open A strings. The second violin
will also compromise, with a note that is neither as low as a
“beatless” third, nor as high as the open A string. This type of
adjusted temperament is just one example of the complexity involved in
bringing a satisfying of intonation to a string quartet. Frequently the
quickest path to resolving intonation conflicts in string quartet work is
to adopt equal temperament as the goal when such problems arise.
With regard to octave displacement in a string quartet, it is necessary for the group to be mindful of the problem
when tuning their individual instruments, as well as when tuning chords. Generally, the
outer extremes of range need to be brought together, as in the earlier
example of the piano. This will avoid one or the other end of the group having to make an extreme and odd
sounding adjustment in a particularly widely spaced chord. I recommend
that a group tune as follows:
First the ‘cello should find an A that the group can all agree on. The cello should then tune the tightest possible fifths that still ring. By the time the C is tuned it should be relatively high, possibly even as measured against equal temperament.
The remaining instruments should line up their A string with the cello one at a time, (use open strings, not harmonics) and then proceed to tune the tightest possible fifths.
Then the players should each check their G strings (the viola should check the C as well) against the cellos C string and against the cello’s D string. Some adjustment of the upper players’ G strings’ is likely to be necessary in order to have all of the fifths line up.
By starting from the same tight temperament in the open fifths
the group has the best possible chance to sound ringing and in tune in a
wide range of contexts. ###
Stefan Hersh is a violinist who
teaches at De Paul University and Chicago School of the performing arts.