The violinist, pedagogue, and pioneering acoustical researcher Giuseppe Tartini (1692–1770) is credited with the discovery of these elusive tones and is the first well-known advocate for them. He called them terzi tuoni (third sounds) and taught his students that their double-stops were not in tune if they didn’t hear them.

The violin teacher Leopold Mozart dedicated an entire section in his landmark text A Treatise on the Fundamental Principles of Violin Playing to the subject. He stated that Tartini tones are a device that “a violinist can use in playing double-stopping, and which will help him to play with good tone, strongly, and in tune.”

But by the 20th century, Tartini tones had fallen into obscurity.

The violin virtuoso and pedagogue Carl Flesch was dismissive of the importance of this phenomenon in his The Art of Playing the Violin: “The so-called combination tones … have in my opinion not much significance when it comes to practical application.” Ivan Galamian, one of the most influential violin pedagogues of the 20th century, neglected to even mention Tartini tones in his Principles of Violin Playing and Teaching.

It was with the rise of the great romantic style of string playing that Tartini tones fell out of favor. One reason is that so-called expressive intonation and constant vibrato—required to push sound out above an orchestra and into a large concert hall—can obliterate such subtleties.

But we live in more eclectic times. A career as a concerto soloist is no longer the only conceivable path for the aspiring string player, and alternate career opportunities are expanding every year. Teaching, playing in string quartets, and performing earlier styles of music have brought about a resurgent interest in just intonation and Tartini tones.

FIND THE DIFFERENCE TONE

In order to hear a Tartini tone, play a consonant double-stop with firm bow control, no vibrato and precisely in tune—a lower third tone should emerge. This is a Tartini tone—a powerful aid to solid intonation and rich tone. This third tone has a frequency equal to the difference between the two original tones (see chart). It can be produced with any instrument—or pair of instruments—that can sustain two tones simultaneously.

Tartini tones are a type of difference tone, which results whenever any two tones are played simultaneously with sufficient vigor. Most string players are familiar with the beating that occurs when you play two tones that are close in pitch. But to achieve a Tartini tone, the interval must be a pure, consonant interval.

Why should pure consonants produce difference tones that are so much more audible than those that other intervals produce? Difference tones produced by any pair of pure tones are audible, even if they fall between the cracks of the keyboard, but Tartini tones are unique because they create a beautiful, tuned chord.

The reason, discovered by Tartini, is elegant. Consider the harmonic series, the basis for all tonal music (see Figure 1).

The harmonic series is a theoretically infinite series of whole-number multiples of its first member, the fundamental. You can hear the harmonic series by playing harmonics on any string, the open string being the fundamental.

As shown in Figure 1, members of the harmonic series provide all of the consonant intervals. If you subtract the frequencies of any adjacent members of the overtone series, the result is the fundamental or a multiple for sixths.

This means that all consonant intervals will have a Tartini tone that is a member of the same harmonic series, and thus consonant with both tones, creating a consonant chord. For example, violinists, play an F♯ on the D string with an open A. The resulting Tartini tone will be an octave below the open D: a nice, warm, major chord, with the root well below the range of your instrument.

Another reason for the richness of Tartini tones compared to other difference tones is the phenomenon of the “missing bass.” When we hear several harmonics, our hearing system automatically supplies the missing fundamental. This is why you can listen to a symphony out of tiny loudspeakers and hear the whole orchestra, including the basses. The loudspeakers are far too small to physically reproduce the bass, but we hear it nonetheless.

APPLY THE DIFFERENCE

To take things a step further, let’s consider the practical applications of these Tartini tones for your string playing. They can provide an objective test of intonation for double-stops—and by extension, all intervals—which makes them useful in a wealth of repertoire. Without such an objective test, intonation becomes a matter of taste, what “sounds right.” The problem is, what sounds right to one person doesn’t necessarily sound right to another. This may be just fine for a soloist, but in an ensemble, quibbles over just how wide to make the major thirds based on personal taste are sure to start interminable debate.

To the casual ear, the most important factor in intonation is consistency, which is why a tuned piano—even though it is theoretically out of tune—sounds in tune. The objective test afforded by Tartini tones makes it much easier to be consistent.

Also, since a focused tone is required to produce them, Tartini tones promote good tone. They encourage the player to coax tone out of the violin with a solid bow stroke and pure intonation, and reinforce using vibrato as an enhancement instead of a means for covering up tone and intonation problems.

HEAR THE DIFFERENCE

Once you are able to generate Tartini tones, another interesting harmonic element emerges: a new bass line. Every double-stop with Tartini tones is a three-note chord, creating a bass line with notes that may be below the range of the instrument. This is a huge benefit to the performance of unaccompanied works like solo Bach Sonatas and Partitas. They also work well in such later works as the Stravinsky Elegy (see Figure 2). This example demonstrates the rich bass line that results when playing this miniature masterpiece with Tartini tones.

Soloists aren’t the only players who can use Tartini tones. Ensembles, particularly string quartets, can benefit from tuning with Tartini tones, carefully tuning notes in pairs, then adding notes to build chords from these purely tuned intervals. All things considered, there is no shortage of applications for this phenomenon, and finding ways to use Tartini tones can be fun and exciting for all string players.

Listen closely next time you play a double-stop—you might hear a world of possibilities.

Hearing is Believing