Just Intonation has become an essential part of my practice as a violinist. I initially came to it from the perspective of contemporary music and from working with composers on particular projects, but I’ve found that Just Intonation has crept into almost everything that I do and has proven to be an immensely useful tool. Just Intonation (JI) is a broad term for tuning intervals according to the natural relationships of the harmonic series. In practical use as a string player, it provides a grid (really, many distinct grids) that can be mentally/aurally overlaid onto the framework of the open strings, providing precise measurements of whether something is “in tune” or “out of tune” using only the instrument and your ears, without the aid of piano, digital tuner, etc. (I place “in tune” and “out of tune” in quotes because these are highly subjective terms – what is “in tune” using the grid of JI would be “out of tune” using the grid of Equal Temperament. It depends on which grid you are measuring with and that depends on the goals of the music you are playing, the preferences of your fellow musicians, and myriad other factors that must be negotiated fluidly in any musical situation.) JI tunings can be verified with great precision by ear by listening for difference tones and aiming for a pure sound without beats (that is, the acoustic interference between sound waves). The great potential of JI as a teacher and tool in the practice room is not really part of Western classical conservatory training, and I think it should be.
I don’t intend to go deeply into the practicalities of JI on the violin here. I’ll just say that, given all of the complexities and emotional insecurities that come with tuning on a fretless instrument, the realization that I had under my own fingers the means to precisely measure tuning was a hugely empowering revelation. Beyond that, there is the multifaceted beauty of JI, which is what has brought me back to the well again and again. JI can function harmonically, melodically, timbrally, and as a means of heightening the character and emotional qualities of the music.
I’ve generally always been more interested in harmony than melody. I can’t easily recall the words of songs – I suppose my ear is elsewhere. I love a good melody, but the power of the motion from one harmonic field to another, that undercurrent that supports the tune, is what really makes me excited about a piece of music. As a violinist, I have devoted myself to an instrument made for melodic playing and celebrated for its vocal qualities. So I’ve found myself looking for any opportunity to engage with the instrument in a more harmonically (and timbrally) driven way. Performing contemporary music offers many ways to do this, as does playing string quartets and solo Bach.
J.S. Bach’s solo violin music strongly implies fully voiced harmonies, and though the modern violin can only sustain two pitches simultaneously, Bach’s music when played expertly gives the impression of polyphonic counterpoint, a sleight-of-hand illusion of polyphony. When I first started getting into performing music in JI, the realization that changed everything for me was that JI gives the violinist the ability to virtually access the bass register and to sustain three pitches simultaneously. This is made possible by the psychoacoustic phenomenon of difference tones. Sustain any two pitches and our brains fill in the fundamental of those pitches. Sustain two pitches that are tuned in a ratio that corresponds exactly to the harmonic series (say the 5:4 major third, which is the ratio between the fourth and fifth partials of the harmonic series), and the fundamental may be perceived clearly and strongly. If you know which fundamental you’re listening for and aim for a pure sound without beating, you can find almost any ratio on the violin involving up to the 17th partial or so. In the mid to high register of the violin, either standing up close or in a small room, the difference tone comes across as being extremely loud and resonant. It’s hard to believe that it’s just in our heads and not a real sound in the room.
As a treble instrumentalist, gaining access to the bass register was huge. It changed the way that I listen to the violin, expanding my focus downward to include a much broader range of frequencies. It also changed the way that I play, especially in solo and ensemble improvisation – empowered by the knowledge that inflections of pitch in double stops can have a real sway on the direction of the music. (Plus, playing JI intervals makes the instrument sound louder, an added benefit in an ensemble setting.)
JI intervals are used as a harmonizer to great effect in my Wet Ink Ensemble colleague Eric Wubbels’s “the children of fire come looking for fire” for violin and prepared piano, a duo that Eric wrote for us in 2012 that I count among my greatest influences as a musician. In a strikingly meditative moment in the middle of the piece, the violin plays a series of three dyads, each derived from a different prime of the harmonic series (three, five, and seven). The intervals expose a ghostly psychoacoustic bassline while tugging the listener from a complex, “minor” feeling to a simple “major” one. Wubbels then reinforces the function of the harmony by doubling the bassline on the piano. This motive is recontextualized in many colorful ways throughout this extraordinarily inventive piece, but it is in this particular moment of poignant austerity that the psychoacoustic underpinnings of the harmony are laid bare.
From a technical standpoint, it is a short journey from harmonic JI violin playing to melodic. Double-stops, with the aid of the fixed points of the open strings, provide a clear way to measure intervals precisely. Decouple the notes of the double-stop and you have a melodic interval. Memorize the sound and physical feel of the interval and you can begin to construct scales accurately.
Taylor Brook is a composer who has a great affinity for melodic JI string writing. I first got to know Taylor’s music through his wonderful solo violin piece Vocalise, which has been a favorite of my repertoire for nearly a decade, and Taylor and I have since worked together on many different projects (another of my favorites is El Jardín de Senderos que se Bifurcan for string quartet, which we recorded with the Mivos Quartet in 2016). Vocalise, for violin and drone, presents a familiar vision of the violin, but one in which its traditional “beauty” is delicately teased and pulled into strange and surprising realms. In what Taylor describes as an “honorific recontextualization” of structural and theoretical elements of Hindustani music, the characteristically lush sound of the violin is heard over a drone, weaving through an intricate JI pitch space. As the pacing of the music evolves from reflective meditation to ecstatic action, the pitch relationships become increasingly adventurous and the tone of the violin shifts from sweetness to a big, bright, extremely colorful palette.
Timbre is an important component of Vocalise, especially as it relates to the overall form, but the melodic pitch relationships are the prime movers of the piece, vivifying individual gestures, while timbre functions as a distinct layer on top. A different and equally rich use of JI is to employ the timbres inherent to the intervals themselves as an orchestrational device.
When sounded simultaneously (e.g., as double-stops), intervals derived from different primes of the harmonic series have remarkably distinctive characters. For example, ratios of three might sound “earthy,” ratios of five “sweet,” ratios of seven “restless,” and ratios of eleven “screamy.” Regardless of which subjective terms one might choose to describe them, the ear can readily identify these fields of harmony, and the fields are defined by prime number families. The idea of using JI dyads as color is employed beautifully in the recent works of Alex Mincek, another of my Wet Ink Ensemble colleagues whose artistry has inspired and shaped my musical practice. Alex is a superb saxophonist, and his relationship to musical material as a composer is rooted in the tactile immediacy of his experience as a performer. Alex often talks of instrumental “malfunction” as a gateway to finding novel forms of expression. For example, playing a simple scale on the saxophone while depressing one extra key such that, instead of notes, a string of shimmering multiphonics is manifested.
Performing JI dyads on the violin is not exactly a “malfunction,” but it is a filtering of something rather simple (that is, diatonic intervals) that yields a widely varied and extremely colorful result. In the first movement of Mincek’s Harmonielehre for violin and piano, the harmonic progression that drives the form of the piece is filtered by JI inflections of violin dyads up to the 11th partial. This relationship is further enlivened by the equal tempered tuning of the piano – ET intervals that are inherently complex and beating interact with the violin’s JI intervals in fascinating and unpredictable ways. The range of timbral possibilities opened up by these myriad combinations allow Mincek to richly orchestrate using spare musical means.
Parsing JI into these components – harmonic, melodic, timbral – is helpful for me as a performer and enriches my appreciation for the music, though I acknowledge that attempting to parameterize something as unified as JI is somewhat arbitrary, and in another sense each of the pieces I’ve used as examples employ JI in an immersive, all-inclusive way. But what I really appreciate is how these composers have used JI with such intention. Far from a catalog of arcane tunings or a compendium of “crazy sounds,” each of these pieces by Wubbels, Brook, and Mincek uses JI as a means of human expression and as a tool for musicality rather than as an academic exercise.
The expressive potential of JI is perhaps what draws me to it most. The timbre-characters of the primes are so strong, so affecting. I imagine that this is part of our nature, some fundament of the universe that is embedded in us on an evolutionary scale. But there is also almost certainly a cultural component – as modern listeners and musicians we are steeped in Equal Temperament from an early age, and the differentness of JI intervals combined with their unimpeachable internal logic may be what makes them so moving.
This expressivity is a big part of what makes the pieces by Wubbels, Brook, Mincek, and many other of my favorites by composers such as Kate Soper and Sam Pluta so compelling. I think practices like JI that add such life and interest to pioneering contemporary works can be a part of a holistic musical approach, an overarching performance practice that has just as much to offer when projected back on established repertoire—as trumpeter/composer Nate Wooley writes, a “model of how the new cannot only move forward, but to be active in 360 degrees and three dimensions.” For the past six years, I’ve been working on applying my study and practice of JI to a reinterpretation of Bach’s famous Sonatas and Partitas for solo violin. My Just Intonation Bach project began as an analytical challenge, a search for tuning ratios that would reinforce harmonic motion already implied by the notation. This intellectual exploration quickly developed into an intuitive, creative process that considers how juxtapositions of tunings and timbres might heighten the emotional qualities of the music, and how a contemporary approach to sound production on the violin might illuminate hidden details. The fissures that form between prime interval families open up endless expressive possibilities. When applied to Bach on a micro level, dissonances are heightened, resolutions sweetened. On a phrase level, zones of light and dark are revealed. Globally, the shift between key areas takes on a wrenching immediacy.
Just Intonation holds great potential for string players, both as a creative and pedagogical tool. It has certainly changed the way I think about my instrument and music in general. The techniques described in this writing, and the artists who are so creatively employing them, have wonderfully enriched my own musical practice and are contributing beautifully to the kind of broad and inclusive approach to musicmaking that I’d like to see define the role of the 21st-century classical musician.