About Intonation

In this post, I (Gabriel Taubman) have summarized Professor Misha Amory‘s recent studio class discussion on playing in tune, and how it can relate to interpretation.  Any errors are my own.  At the end of the post you can find an outline of the discussion from Professor Amory himself.


Professor Amory began by discussing an inherent problem with intonation: the notes of the overtone series aren’t the same as the notes we’ve picked for our scale in western music.  For example, if you stack major thirds on top of one another, you’ll arrive close to a perfect octave, but not quite.  One of of the first people who began thinking about this problem was the Greek philosopher and mathematician Pythagoras.  Pythagoras was especially interested in perfect fifths and octaves.  He developed a system of tuning derived from stacking  fifths on top of one another.  As an example, if you centered yourself on D you would produce:

Eb – Bb – F – C – G – D – A – E – B – F# – C# – G#

This method of tuning reproduces fifths very well, but has the downside of giving extremely wide major thirds and sixths, and extremely narrow minor thirds and minor sixths.  Fortunately, music up through the medieval era was concerned mostly with perfect intervals, so wide or narrow thirds and sixths were not an inconvenience, and the Pythagorean system of tuning is believed to have been widely used.

By the 18th century, music had expanded to the point where thirds and sixths being out of tune was becoming a problem.  Well tempered tunings were introduced, which expanded the number of chords which would sound in tune.  For example, C major and the chords around it could sound great, but F# major still had many notes which sounded out of tune.  This fact was often used by composers such as Bach, who in his Well-Tempered Klavier would set each movement in a different key to explicitly make use of the notes which would sound in or out of tune, providing added color to the composition.

Ultimately equal temperament won out, which allows playing in all keys with all chords sounding in tune.  At the time of its introduction though, many music lovers lamented the loss of the very major major thirds and very minor minor thirds that were generated by a well tempered instrument.  To the people of that time, equal temperament sounded boring.


With all of that background on temperament, Professor Amory asked how as string players (who get to choose the tuning of our notes) do we play “in tune”?  As a string player, should we always play in equal temperament?  His advice was that if you’re playing with a pianist, you likely need to play in equal temperament.  However, learn what the pure intervals are, how to play them, and then accept that most of the time you can’t play them.  We listened to a recording of Casals performing the D minor Sarabande, noting that Casals would use very narrow half steps and very wide whole steps, producing a tuning not so unlike well-temperament to great success.

On the topic of practicing intonation, Professor Amory remarked that your fingers can only go in places corresponding to notes you can hear in your head.  You should listen for the next pitch coming, and hear your fingers into the right place.  Pretending that you are hearing someone else perform can alleviate the nerves of missing the note.  He also mentioned that healthy practicing requires balance, so after practicing listening closely you can try just letting your fingers fall and see how the notes feel as opposed to sound.  James Buswell was quoted as having said the following regarding practicing intonation: “Any pitch you want to play in tune, play it with the confidence of Heifetz.  Then as soon as you’ve played it, immediately start criticizing and fixing.”

Another intonation related topic Professor Amory discussed was the concept of horizontal pitch memory.  This is the idea that if you play a note (C for example), followed by other notes, and ultimately return to your original note (the C), those C’s need to be the same.  For example, in Bach’s 6th Cello Suite, E natural shows up over and over, and often arrived at from a different place.  The same with the prelude from the E-flat Suite.  He importantly pointed out that if your intonation needs adjusting, these notes which are repeated can not be the ones getting adjusted.  For example, if you play a C natural, followed by some other notes, followed by a major third from C to E, only the E can be adjusted since you just recently played the C and they need to sound the same.

Finally, Professor Amory discussed the idea of finding the harmonic center of a passage.  As an example, he cited the final movement of Hindemith’s solo Sonata, Opus 25 No. 1 which suggestive of being in E major.  That approximate E major can be used as an intonation guide while practicing.

Questions from the studio:

One student asked about tips for performing with clarinets.  Professor Amory pointed out that in low registers clarinets to be on the flatter side, and in high registers on the sharper side.  Additionally the blending can be harder because they’re not string timbre.  He concluded that tuning note by note with the clarinet is often the best course of action.

Another asked about intonation and tuning in quartet playing.  Professor Amory discussed how the color of a piece can have a huge effect on intonation.  For example while working on the Cavatina of Opus 130, his quartet would try to keep B-flats as low as they could to darken the color.  With regard to convincing others that your tuning is preferable, remember that tuning is always specific to a context and try to find a rational case for your feelings.

Professor Amory’s outline can be found here:  About Intonation

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