10 works, 1999 takes, in pursuit of perfect ‘just intonation’
Composer and critic Kyle Gann — one of Johnston’s former students — literally called the Seventh Quartet “the Mount Everest of string quartets.” The Kepler Quartet, the ensemble that devoted fourteen years and over 1,999 recording takes to capturing all ten works on disc, described the project as one they had “no idea what they had gotten themselves into” when they first agreed to it.
So what makes these pieces so extraordinarily difficult? And why did Ben Johnston (1926–2019) write them that way? The answer requires a short journey into the physics of sound itself — but I promise it will change how you listen to music forever.
First: Who Was Ben Johnston?
Benjamin Burwell Johnston Jr. was born in Macon, Georgia, on March 15, 1926, and taught composition and theory at the University of Illinois at Urbana–Champaign from 1951 to 1986. He was not the kind of radical who showed up to concerts in a cape. He was a quiet, methodical academic who loved Glenn Miller, Broadway show tunes, and eventually Stan Kenton’s jazz. It was the first time he heard real jazz improvisation, and it changed his whole approach to harmony. WikipediaNPR
His interest in non-standard tuning emerged early, sparked at age 12 by a lecture on Debussy that introduced him to Hermann von Helmholtz’s On the Sensations of Tone, which affirmed his sense that equal temperament limited musical possibilities. Grokipedia
The pivotal moment came when Johnston read Harry Partch’s Genesis of a Music as a graduate student. This prompted him to contact Partch directly, leading to a six-month apprenticeship in Gualala, California, where he lived and worked on Partch’s ranch, daily tuning instruments using the Chromelodeon as a reference and honing his ability to hear and reproduce precise just intonation pitch relationships. Grokipedia
Unlike Harry Partch, Johnston did not build specialized instruments for his music. He preferred either to retune conventional instruments or to have players find his pitches between those they were used to playing. This is the crux of everything. Johnston wanted the purity of Partch’s tuning ideas, but he wanted them played on a regular violin, viola, and cello. That ambition is why the quartets are so hard. Pulse Nigeria
The Problem with the Piano — and with All of Western Music
To understand what Johnston was doing, you need to understand a bit about how Western music is tuned, and why he found it deeply unsatisfying.
Every string player knows that you can tune your instrument more “in tune” than a piano. When a string quartet plays a perfectly resonant chord — really locks in — the room seems to bloom with extra sound. That’s not an illusion. It’s physics.
When two strings vibrate, they each produce not just their main pitch (called the fundamental) but a whole cascade of quieter pitches above it called overtones or harmonics. These overtones vibrate in mathematically simple ratios to the fundamental: the first overtone is exactly twice the frequency (an octave), the next is three times (a perfect fifth plus an octave), the next four times, and so on. When two notes share many of these overtones — when their frequencies relate by simple whole-number ratios — the sound is smooth, pure, resonant. We perceive it as “in tune.”
This system is called just intonation: tuning intervals so that their frequencies relate in simple whole-number ratios. Just intonation is the tuning of a musical interval without beats — the result is an acoustically pure sound that resonates within the harmonic series. Wikipedia
In just tuning, any interval is tuned so as to eliminate “beating” — the result of vibrations interfering with each other. Just intonation is the easiest to achieve by ear. In this kind of tuning, all intervals have vibration rates related by small whole-number ratios. Wikipedia
Here is the catch: the beautiful, resonant intervals of just intonation don’t add up neatly. If you stack perfectly tuned fifths on top of each other — the way Pythagoras did — you eventually don’t quite arrive back where you started. The math refuses to close the circle. This is called the Pythagorean comma, and it has caused headaches for instrument makers for over two thousand years.
The solution Western music settled on, around the 17th and 18th centuries, was equal temperament: divide the octave into 12 perfectly equal steps, each slightly wrong. No interval except the octave is acoustically pure in equal temperament — every fifth, every major third, every minor third beats slightly. The beating is subtle enough that we’ve all learned to ignore it. The advantage is enormous: you can play in any key on a piano without retuning. The disadvantage, Johnston felt, was that we had traded away something acoustically precious.
Johnston believes that an equal tempered tuning system based on irrational intervals contributes to the hectic hyper-activity of modern life. The wildly beating sonorities of equal temperament are thought to resemble — and perhaps foment — the fast-paced, unmeditative current of present-day Western existence. Whether or not you share that philosophical view, the acoustic argument is simply true: equal temperament chords beat. Just intonation chords don’t. UMMP
Johnston’s goal, as he put it himself, was “to reestablish just intonation as a viable part of our musical tradition.”
Extended Just Intonation: Going Further Than Anyone Had Gone
Simple just intonation — what Renaissance composers used — draws on the first few harmonics. Ratios like 2:1 (octave), 3:2 (perfect fifth), 5:4 (major third) give you a diatonic major scale of great purity. This is called 5-limit just intonation, because the largest prime number involved is 5.
Johnston was interested in going much further. The harmonic series keeps going: the 7th harmonic gives an interval that doesn’t correspond to anything in equal temperament but sounds like a very low, bluesy minor seventh. The 11th harmonic lands somewhere between a perfect fourth and a tritone. The 13th, 17th, 19th, and beyond each introduce new colours of sound that our ears have never been systematically trained to hear.
Extended just intonation, a term coined by Ben Johnston, refers to any tuning in the harmonic series regardless of prime limit. Xenharmonic Wiki
Johnston mapped out all of these harmonics and then gave players a way to notate them — a crucial contribution, because how do you write down a note that doesn’t exist on any standard instrument or scale? Ben Johnston’s notation is a staff notation system for just intonation that supports prime harmonics up to and including 31. The base notes (white keys on the piano) are selected so that F–A–C, C–E–G, and G–B–D are just major triads. On top of the usual sharps and flats, Johnston added a system of plus and minus signs, arrows, numbers, and other symbols — each one specifying a precise mathematical adjustment to a note’s frequency. Every accidental multiplies a pitch’s frequency by some defined constant. Running up to the 31st harmonic or down to the 31st subharmonic, these accidentals can be combined to create pitches with sometimes very elaborate names. Xenharmonic WikiLa Monte Young’s
Looking at a page of his later scores, you might mistake it for a mathematics exam. Each note may carry multiple small symbols telling the player to raise or lower the pitch by amounts like a syntonic comma (about 21.5 cents — roughly a fifth of a semitone) or a septimal comma. These adjustments are not stylistic suggestions. They are acoustically specific targets.
The Ten Quartets: A Journey into Deeper and Deeper Waters
The ten string quartets of Ben Johnston, written between 1951 and 1995, constitute no less than an attempt to revolutionize the medium. Only the first limits itself to conventional tuning. New World Records
After that, each quartet ventures further into the harmonic series, using higher and higher prime limits:
The Second Quartet (1964) begins the journey, working through a systematic 53-tone microtonal scale derived from 5-limit just intonation. It’s fiercely difficult already, but the logic is still followable.
The Fourth Quartet (1973) — Johnston’s most-performed work, based on “Amazing Grace” — introduces 7-limit harmonics. Johnston says the work has its roots in his childhood, in slavery, and in his desire to hear what the song might have sounded like if Beethoven had covered it late in his career. This is probably the ideal entry point for listeners new to his music: you know the tune, and the transformation it undergoes is breathtaking. NPR
The Fifth Quartet (1979) goes further still. By the beginning of the 1980s Johnston could say of his elaborately microtonal String Quartet №5: “I have no idea as to how many different pitches it used per octave.” Last.fm
The Seventh Quartet (1984) is the one everyone talks about in fearful whispers.
The Seventh Quartet: 1,200 Pitches, 176 Rows, and the Edge of the Possible
The piece has a reputation as the most difficult string quartet ever written. Before the Kepler Quartet recorded it in 2016, the immensely difficult String Quartet №7 had never been performed in public. ArtsJournalNew World Records
What makes it so extreme? The finale provides the clearest example. The structural tone row consists of 176 pitches — all different, 176 pitches within one octave, heard in the viola on each successive downbeat. Many other notes are heard in the other instruments whose harmonies link each note to the next, and altogether there are more than 1,200 discrete pitches in the movement. ArtsJournal
Think about what that means in practice. The violist must move from one downbeat to the next, each time landing on a pitch a tiny, specific fraction of a semitone away from the last. The violist is tasked to move upward from C and come back down on a pitch 9.7 cents higher — just under one tenth of a half-step — than she started on. At the downbeat of the next measure, the violist lands on another pitch, another ten cents higher. ArtsJournal
Meanwhile, the other three players are not waiting quietly. They are performing multi-voice counterpoint designed to acoustically guide the violist to the next pitch — each interval precisely calculated so that if the players lock in together, the ratios will naturally lead the ear to the correct destination. Between the first and second downbeats, the quartet is supposed to tune the F to the C and the B♭ to the F, the A♭ and E♭ in the cello to the B♭ in the first violin and the 7th harmonic above that, and find the 11th subharmonic below that — it’s just 4/3 × 4/3 × 2/3 × 2/3 × 7/4 × 8/11, and there’s your 896/891. ArtsJournal
That ratio — 896/891 — is an interval of about 9.7 cents. An interval that does not exist, in any form, in equal temperament. An interval that four human beings are supposed to find, accurately, in real time, in the middle of a performance.
Johnston recalled that his original proportional scheme would have made the piece last 48 years. He scaled it back. Good. Luck, as Gann wrote. ArtsJournal
The Ninth Quartet: Everything at Once
If the Seventh Quartet is the mountain of raw difficulty, the Ninth Quartet (1987–88) is perhaps the most systematically complete statement of Johnston’s project. His String Quartet №9 uses intervals of the harmonic series as high as the 31st partial. It draws on every prime limit Johnston had developed across his career and applies all of them within a single, large-scale form. Wikipedia
Just-intonation tunings eliminate beats between pitches to create just intervals, whereas equal temperaments often approximate just intervals while still beating to some degree. The Ninth makes this difference audible across extended stretches of music: chords that are simply purer than anything a piano can produce, because the mathematics is tighter and the physics is real. Music Theory Online
Why Did He Do It?
The difficulty of Johnston’s quartets is not accidental. It is not avant-garde posturing. Johnston was not trying to be difficult — he genuinely believed that equal temperament had cost Western music something irreplaceable, and that string players were uniquely placed to get it back.
In a way, this is a return to an older conception of string quartet practice, since players used to — and often still do — intuitively adjust their tuning for maximum sonority while listening to each other’s intonation. Every string player has experienced this: the moment when the group locks in and the chord seems to fill the room with extra sound. Johnston was asking players to pursue that moment systematically, all the way to the 31st harmonic. New World Records
He used “potentially hundreds of pitches per octave” in a way that was “radical without being avant-garde”; in contrast with much twentieth-century music, he used microtones not for the creation of dissonance but in order to “return to a kind of musical beauty,” which he perceived as diminished in Western music since the adoption of equal temperament. Wikipedia
And what happened when musicians actually committed to learning his system? A student who studied Johnston’s Ninth String Quartet said: “Before studying Ben Johnston’s 9th String Quartet, I saw intonation as right or wrong, in tune or out of tune. I have learned that playing ‘in tune’ is relative.” The group was astonished by the impact their work on the Johnston had on classical repertoire: chords shimmered; intonation fell into place with ease. Sharanleventhal
The Kepler Quartet’s second violinist Eric Segnitz says of Johnston: “People think of him as this avant-garde composer but actually he’s using these techniques to go back to basics with the overtone series.” Strings Magazine
The Kepler Quartet’s Achievement
The Kepler Quartet — violinists Sharan Leventhal and Eric Segnitz, violist Brek Renzelman, and cellist Karl Lavine — spent years working with Johnston to plunge into his unconventional harmonic world. After 14 years and more than 1,999 takes in the recording studio, they completed the cycle just after Johnston’s 90th birthday. Strings Magazine
Segnitz says the rehearsal process required both learning and unlearning: “There was a fair amount of invention and learning curve and getting rid of any preconception of what a chord actually sounds like.” NPR
Johnston was reportedly delighted. He told the quartet that with their fastidious accuracy, they had “actually created an entirely new language.” Sharanleventhal
The three-album set on New World Records stands as the definitive document of these works. All ten quartets are available to stream and represent — in Kyle Gann’s phrase — “possibly the most ambitious string quartet project in history.” New World Records
Where to Start Listening
If you’ve never heard Johnston’s quartets, start with the Fourth Quartet (“Amazing Grace”). You’ll recognise the tune immediately, but you’ll hear it dissolving into harmonies that shimmer with a strangeness and purity unlike anything in standard repertoire. From there, move to the Tenth Quartet, which ends with a revelation of “Danny Boy” that most listeners find genuinely moving. Once your ears have adjusted, the Seventh and Ninth Quartets will reward deep listening with sounds that feel, at their best, like accessing a layer of acoustic reality that equal temperament had been blocking all along.
Ben Johnston didn’t write difficult music for its own sake. He wrote music that takes the harmonic series — the physics of sound itself — completely seriously. That just turns out to be very hard.
Further reading: Kyle Gann’s analysis of Johnston’s notation system at kylegann.com. The Kepler Quartet recordings are available on the New World Records label. For microtonal theory terms used in this article, the Xenharmonic Wiki is the best reference: see entries on just intonation, the harmonic series, equal temperament, prime limit, the syntonic comma, and Ben Johnston’s notation system.
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