How I interpret Bach: Tomás Cotik on strings, intonation and vibrato

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Last week I discussed my choice to record my album of Bach’s Sonatas and Partitas with a Baroque bow and the implications on sound and articulation, as well as string crossings, written slurs, dynamics, chords and contrasting voices in these works. This week I’ll be focusing on the instrument itself, as well as intonation and vibrato.

The Violin

So…why didn’t I use a Baroque setup when it came to the violin? I do enjoy the sound, softness, and open reverberation of the unwound gut strings, and I have great respect for musicians that master them. I love how the E-string doesn’t shout and how the strings constantly remind us that pressing or digging in is not a good idea. Yet, in a practical sense, I acknowledge the convenience in maintaining the pitch with modern strings and my limitations with the time it would take me to adjust.

For my recording, I used synthetic strings that were slightly softer and more resonant than the ones that I use regularly, which project better but have more tension. Specifically on the G-string, I wanted and needed more resonance for this project.

In terms of the frequency of the tuning, we do need to remember that regular reproduction of a fixed average historical chamber pitch is an invented tradition. In Bach’s time, the same note-names were applied to different pitches on different instruments, and none of the implied standards was any more ‘real’ than another. Furthermore, the frequency of the A varied widely even in nearby cities. Although the tuning fork was invented in 1711, there were no measuring devices that could be used to measure the frequencies, nor a standard, uniform, or precise unit of measure.

The Chorton (ecclesiastical pitch) to which organs were tuned was usually between a whole tone and a minor third higher (460-489) than the chamber pitch (Kammerton) used for secular music. The ‘A’ played by the strings in Leipzig according to different studies was at 440 or 460.

In other places, it was between 392 and 415. In Köthen, however, where Bach wrote these works, the Chorton and Kammerton might have been the same.

Beyond all this information, my choice of recording at with the A at 440 was rather for personal reasons. Having perfect pitch in the range of violin frequencies, if I were to play these pieces at the actually not even settled A=415, they would sound to me as if in another key.

Intonation

Intonation is also complicated. There are many tuning systems to choose from and there is not a perfect one.

Which of the following should we try to go for?

• Pythagorean

• Quarter comma meantone

• Just intonation

• Equal temperament

• Bradley Lehman

• Well temperament

• Vallotti

• Werckmeister III

• Kellner

• Barnes

• Neidhardt

• Other regular and modified mean-tones

 

The issue to be considered here is the eternal paradox of the fifth and the third. It’s not possible to have it all in one system—nice fifths and nice thirds. Pure (non-beating) intervals (unisons, octaves, fifths, fourths, major thirds) cannot be combined freely if we have some fixed pitches. If we stacked five pure fifths (let’s say C-E) the resulting “major third” is higher than the pure third.

In Pythagorean Intonation, the fifths are pure. The thirds are complex and comparably much more dissonant.

Just intonation is a result of the overtone series. All the notes in the scale are related by rational numbers and use only pure intervals. The major third in a pure major chord is a comma low and the minor third a comma high. The pitch changes over the course of the performance depending on the key. The problem is that in using only pure intervals, the pitch migrates, and we end up on another pitch level. It’s also a problem because the violin has four fixed pitches in its open strings. We lose the sympathetic resonance and we don’t match the intonation horizontally when playing those notes. Also, when we prioritize the harmony, the melodic intervals are compromised and sound awkward.

In quarter comma meantone, each fifth is diminished by a quarter of a syntonic comma, and the thirds are pure. Equal temperament makes a compromise, dividing the difference equally in each interval. Bradley Lehman reconstructs yet another keyboard temperament in his interpretation of Bach’s Well Tempered Klavier, annotated in the picture below. And there are still many other possible temperaments…

 

I actually like starting from Pythagorean intonation: respecting the pure fifths and fourths that resonate and are congruent with our open strings, using strong melodic tendencies (tight leading tones that are exaggerated even more so in fast movements), maintaining the independence of different voices (giving every line its own weight), and adjusting (rounding up) thirds and sixths intuitively when needed in chords. In my recent recording, I enjoyed using open strings and low positions to achieve more resonance and brightness.

I think it’s not necessary to choose one system of intonation or another. We don’t need a fixed pitched system. And once our ears and understanding of harmonies develop, we can intuitively adapt to what we are looking for.

 

Vibrato

Different sources tend to indicate that vibrato was used as a kind of ornament to the sound but not as a standard continuous addition to the sound. L. Mozart was opposed to a continuous vibrato. Similarly, Tartini believed a good vibrato imitated and resonated like the human voice and was only to be used as an ornament on strong notes. Geminiani was more generous towards the use of vibrato, and went so far as to differentiate between the vibrato used on short notes and ornamental vibrato.

 

I avoid using a continuous vibrato. I also try to avoid pitch variation, or a monotonous vibrato. I think that vibrato should vary (in amplitude, ‘dynamic’ and speed). The vibrato can be used discreetly, to warm up long notes, as an ornament for expression, and also in a hardly noticeable way that doesn’t clash with the frequent open strings.

Next week Cotik discusses overdotting and rhythmic assimilation