The 14 Cents That Separate a Good Ensemble from a Great One

A brass quartet walks on, breathes, and the first chord locks: the overtones bloom, the room seems to widen, and nobody on stage flinches. Down the hall, a community choir takes thirty seconds to settle the same chord. Across town, a jazz horn section plays a dominant seventh that doesn't just sound in tune. It sounds fat: round, dense, almost three-dimensional.

The same thing is happening in all three rooms. The players aren't playing equal temperament. They're moving specific chord tones by a few cents, sometimes as little as two and sometimes as many as thirty-one, so that the chord lines up with the overtone series. This post is a short field guide to the adjustments that matter, which one is yours on any given chord, and how to drill them with your section this week.

Equal temperament and just intonation in 60 seconds

Equal temperament (ET) is the tuning built into every piano, fretboard and chromatic tuner. It splits the octave into twelve equal half steps of 100 cents each. You can play in any key without retuning, but every interval except the octave is slightly off the pure ratios of the overtone series.

Just intonation (JI) uses those pure ratios: 3:2 for a perfect fifth, 5:4 for a major third, 6:5 for a minor third. Tune a chord to them and the beating between its notes slows and stops, and the chord rings. The catch is that just intonation only works relative to one root. When the harmony moves, the targets move with it.

So ET is a fixed grid and JI is a moving target that follows the harmony. Good ensemble players learn to move between the two without thinking about it. If you want the math, our introduction to just intonation walks through it. The classic book-length treatments are David Doty's The Just Intonation Primer and Hermann von Helmholtz's On the Sensations of Tone.

The adjustments that matter

These eight numbers do most of the work in a tonal ensemble. Each is the just interval above the chord's root, compared with equal temperament.

A few things to notice:

• The major third is the one that matters most. An equal-tempered major third is 14 cents wider than a pure 5:4. If you play the third "in tune" by your tuner, you're 14 cents sharp of where the chord wants you. That's a large part of why a chord can sound bright and edgy in one group and warm and settled in another.
• The harmonic seventh is the dramatic one. At 31 cents below equal temperament it sounds wrong against a piano and exactly right inside a dominant chord. It's the sound of a barbershop tag and of a horn section leaning into a V7.
• The perfect fifth is the smallest adjustment. A pure fifth is 2 cents wider than an equal-tempered one, and string players already tune their open strings that way.
• The minor seventh has more than one just version. 9:5 (+18¢) is a pure minor third above the chord's fifth, which is the version Virtuosic's chord drone uses. You'll also see 16:9 (−4¢) in some tables, and on a dominant chord the ♭7 can drop all the way to the harmonic seventh.

Which adjustment is yours depends on your place in the chord

Knowing the numbers is half the job. The other half is knowing which number is yours on the chord in front of you.

If you have the root, hold steady. You're the reference, and the chord tunes to you.

If you have the third, you carry the most important adjustment. Lower a major third by about 14 cents. Raise a minor third by about 16 cents. This is the move that separates great ensembles from good ones, and it almost never happens by accident.

If you have the fifth, raise it by about 2 cents. The change is tiny, but it can take a chord from "fine" to ringing.

If you have the seventh, it depends on the chord:

• On a major seventh chord, tune the seventh about 12 cents low.
• On a minor seventh chord, tune the seventh about 18 cents high, a pure minor third above the fifth.
• On a dominant seventh chord, if the style allows it, take the ♭7 down to the harmonic seventh, about 31 cents low.

Your place in the chord is also why bass parts and inner parts approach tuning differently. The bass holds; the inner voices adjust. If you play 2nd horn, viola or alto, more of these numbers live on your stand than on anyone else's.

A brass section drill

Ten minutes to build the instinct for the major third and the harmonic seventh:

1. Drone the root. The bass voice (tuba or bass trombone) sustains a concert F. Everyone else listens for at least eight seconds.
2. Add the fifth. The next voice adds a concert C, slightly high (+2¢). Listen for the beating to stop. If it doesn't, adjust until it does.
3. Add the third. The top voice adds a concert A, about 14 cents low. This is the moment: the chord should suddenly open up.
4. Move to the dominant. The bass moves to concert C. Stack E (the third, −14¢), G (the fifth, +2¢) and B♭ (the harmonic seventh, −31¢). Alone, the B♭ will feel uncomfortably flat. In the chord, it locks.
5. Repeat in three keys: concert F, B♭ and E♭. Five minutes per key is plenty.

Lead trumpet can sit out until step 4. This drill is for the inner voices.

A string quartet drill

Strings start from a different place. Your open strings are already tuned in pure fifths, so you already know how to tune by listening for beatless intervals. You're transferring a skill, not learning a new one.

1. Tune the open strings to each other by pure fifths from the A. For this drill, keep the fifths pure rather than narrowing them toward a piano.
2. Sustain a unison A, all four players, no vibrato, until the sound is still.
3. Build an A major triad. Cello on A (the root, no adjustment), viola on C♯ about 14 cents low (the third), second violin on the open E (pure fifths have already put it 2 cents high), first violin on the A an octave up. Hold it. If you've been tuning to a piano all week, the C♯ will sound startlingly low. That's the point.
4. Move through three keys: A major, D major and G major, same procedure each time. The players on the third learn the most.
5. Before rehearsing with a piano, narrow the fifths slightly so your open strings sit closer to the piano's. It matters most on the low strings: tuned in pure fifths down from A, the C string ends up about 6 cents flat of the piano's C.

Pure fifths also have a cost in the thirds. Stack four of them (C, G, D, A, E) and the major third between the C string and the E string comes out about 8 cents wider than the piano's and about 22 cents wider than a pure 5:4. That's why fingered thirds still need adjusting even when the open strings are perfect.

When not to use just intonation

Just intonation isn't a universal upgrade. In three situations it works against you.

With a piano or any fixed-pitch instrument. The piano is in equal temperament and can't adjust. Play a major third 14 cents low against a piano playing the same note and you'll sound 14 cents flat, because you are. With piano, organ, harp, mallets or fretted instruments, match the fixed instrument on shared notes.

In passages that modulate. Just intonation is built around one root at a time. If the harmony changes every two bars, you can't retune fast enough, and trying makes the group sound seasick. For chromatic or quickly modulating music, stay close to equal temperament and adjust only where the music settles.

In fast passages. You don't have time to move the third of every sixteenth note. Just intonation is for sustained chord tones: pads, fermatas, cadences, slow movements, the moments that ring.

The skill is knowing which mode you're in. A great section player moves between the two without announcing it, sometimes within a single phrase.

See the targets while you play

Virtuosic's tuner has a just-intonation mode, and it's free. Pick your concert key and the needle centres on the just target for the note you're playing instead of the equal-tempered one, with the interval named on screen (for example, "Major 3rd · in C concert"). The Both view (Premium) shows equal temperament and the just target together on one meter, so you can see exactly how far the two are apart.

With the Premium chord drone sounding in just intonation, the tuner's target follows the chord: play the B♭ over a C7 drone and it aims you at the harmonic seventh. If you've never practised against a drone, start with how to practice with a drone. The instrument guides also list the just-versus-equal-tempered numbers for the intervals each instrument meets most.

Memorise the eight numbers. Drill the third and the harmonic seventh until your ear goes looking for them. Notice which note of the chord you have, and hold or adjust accordingly. Those 14 cents are where the chord comes alive.