Tuning
Meister - Observations on cello Sarabande
Below are some few thoughts on the intonational information
revealed
from TuningMeister's analysis of Bach's c minor Sarabande from the
cello suites. Perhaps the score will be useful for our discussion:
I have set the pitch for this cut from
the bottom note C, which is an open string. However, if you observe the
bottom Cs you will notice that the pitch varies a bit - bow pressure
seems to change the pitch. So even an open string is never quite in
tune all the time!
First let me discuss a few anomalies in the trace, they are
unavoidable but if you understand the reason for the imperfections in
the tuning trace you can skip over some seemingly false information.
They all result from
having more than one note sounding simultaneously. The orange
boxes
locate where the trace would lie if the results were perfect.
At the end of measure 3
you will notice
the upper g does not register right away, in fact hardly at all; mostly
it
appears to be the lower G [outlined in blue]. This happens because the
lower G is an open
string so it continues to ring even while the bow has moved to the g.
The pitch in the lower graph is probably a good approximation of the
upper g, as it is quite close to the lower G. If they were different,
the difference would be greater than shown, as the calculation produces
a weighted average
In
measure 6 the f doesn't
appear right
away as the preceding d continues to sound - I
believe that is an open-string d, or perhaps
it
is just the
resonance of the room. Since the difference tone of d to f is a
Bb, that appears for a short time before the f is graphed
[outlined in brown, lower graph. The actual Bb lies below the bottom of
the upper graph]. In fact,
many
notes may show a slight delay
before being drawn on the graph, mostly because of the resonant room
acoustic.
The first note in measure 11 in the
repeat comes out
F# [blue box] instead of db' - again because the previous open-string G
is still
sounding. And the final note in that measure, c', shows an octave lower
[deep red box] because the open-string C continues to sound. In fact,
when the c' is
released, the graph briefly shows C still sounding [green box].
In the penultimate bar the low G on the last beat begins while
the previous c is still sounding (either the string itself, or room
resonance) and the resultant difference tone is a low CC [octave below
the graph]; so the beginning of the G shows instead a blue trace from
that CC [outlined in grey]. Then the following upper b makes
a major tenth with the still-sounding open-string G; TuningMeister
hears the difference tone which is two octaves below G, so the trace
remains brown for a G [outlined in blue, lower
graph]. The strong b influences the pitch
measurement. If the b were a pure
major tenth it would not change the pitch of the fundamental at all.
But since tenths are quite high in Equal Temperament (henceforth ET)
and even higher if raised as a leading tone, the pitch of the G seems
to go up. In general it doesn't give much information about the
b at all.
Thus most of the strange results come
about because of interference from notes still sounding, even if it is
just from room resonance, with bass notes having the greatest staying
power. So close microphone placement during practice sessions would
remove many of these
problems, but of course that is not what is done for the best sound in
a recorded performance, which we are analyzing here.
****************
Now let us look at some of the details
of the playing itself.
The most basic particular criticism that
I can offer is that the octave descent at the end of measure 12 is
woefully out of tune, even more so in the repeat, where the lower F is
about 20 cents, a fifth of a semitone, sharp [blue box, lower graph -
compare to previous red trace]. If played simultaneously
they would sound horribly out of tune. Did you notice this when
listening? [Typically a piano's octaves need to be less than 1/2 cent
off from true. In fact that 20 cent difference is the difference
between say an Eb and a D# in 18th century tuning.]
It is
fairly easy to hear in this
recording the slender semitones of the raised leading tones
of modern intonation. And these are fairly modest compared to some.
They are quite consistent, and clearly the second note of the pair is
tuned by relationship to the leading tone. That is, even if the overall
placement of the notes wanders, the relative pitch of the leading tone
and its resolution is pretty much the same throughout the piece. This
relationship is also reflected in the descending semitone,
appoggiatura-like movements of the melody. Almost all of these
successive semitonal movements, both rising and falling. are about 10
to 15 cents narrower than ET. Even when the same interval isn't placed
precisely in the overall pitch scheme, the interval itself is quite
accurate. It is easy to understand that the intonation is guided more
by a note-by-note process than by any precise long-term feel for a
constant tonic.
It looks like the open G
string is tuned way too sharp (end of measure 3). If the string were
tuned to a perfect fifth above the C, it would be 2 cents sharper than
ET. Here it seems about 6 or 7 cents above ET, and although as
mentioned, it is hard to get a precise measure of the open C string
(end of measure 4), that C is very close to center.
Here's something I don't really
understand. Typically, modern intonation lowers the minor third and
raises a bit the major third. The way the final (arpeggiated) chord is
tuned is
consistent with this idea,
with the eb slightly lower than ET. But the modulation to Eb
major (the relative major) in the first section ends up with the Eb
quite a bit higher
than ET. The repeat is remarkably consistent. Actually, quite a few of
the flat notes in this section are higher than I would expect (note
especially some Abs). The best explanation for the arrival at a higher
Eb
that I can give is that its leading tone D (end of measure 7) has
become quite sharp; even with the drop of about 10 cents via the
slender leading tone relationship to the Eb, the Eb ends up sharp. But
all the Ebs in the first section are higher than ET. It is quite
curious.
Overall there is not a great tendency to
raise the pitch in the upper octaves that we find with many string
players, although there is some. The final high c' is very well in tune.
This performance is by János
Starker, his RCA
recording from the 1990s.
