Using ‘difference tones’ to perfect your intonation when tackling double stopping passagework
When I was studying Dvořák’s Cello Concerto for the first time, I found it difficult to identify which notes were out of tune in some of the double-stop passages, so I felt confused and insecure about my playing. To help me, my teacher Hans Jørgen Jensen taught me about Tartini tones.
A Tartini tone – a concept established by Guiseppe Tartini in 1714 – is the third tone produced when you play a double-stop perfectly in tune. It creates a soft, bell-like vibration that resonates quietly at an interval below the notes being played. Sometimes it is called the ‘difference tone’ because its pitch reflects the difference in frequency – measured in hertz (Hz) – between the two pitches of a double-stop.
For example, if you play a perfect 5th of an A at 220Hz (the cello open A string) and the E above it, at 330Hz, a third tone is produced: an A at 110Hz (330Hz minus 220Hz), which is an octave below.
Most of my examples are in the treble clef, because Tartini tones are easier to hear when you play in a higher register. Be patient and try to sustain the notes at forte or fortissimo, with a fast, legato bow. To begin, listen for the Tartini tone when you play double-stopped 5ths, as shown in exercise 1. Make sure that your strings are perfectly in tune before you start! Now play the double-stops in exercise 2, using a harmonic A each time – this should be your reference note. If you need to adjust your tuning, adjust only the bottom note of each double-stop.
You can hear these being played in the videos below – use headphones to hear the Tartini tones clearly. Then try the same again, one octave above what is written.