Use Pythagorean Intonation for melodies and scales.

Click on 'Read More' for information on how to construct a Pythagorean scale.

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Use Just Intonation to play double stops on the violin as well as tune chords in string quartets.

Click on 'Read More' for the ratios of intervals within the diatonic scale system.


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In Equal Temperament, all half steps are an equal distance apart.

Click on 'Read More' for mathematical differences between the widths of the most important intervals.


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Use Pythagorean Intonation most of the time, particularly for all melodies, scales, and arpeggios.

Use Just Intonation for double stops and for chords in string quartets.

Pianos are tuned in equal temperament. Violinists should only adjust to piano pitches if both instruments are playing the same pitch for a long duration.


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Intonation is one of your most powerful musical tools.

For most expressive playing, exaggerate the Pythagorean tendencies:

• High leading tones
• Higher major thirds
• Lower minor thirds

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Select one short phrase and set your metronome to MM=40.

Alternate between single pitches and rests on each click.

Use each rest to anticipate the next note by singing the pitch, either in your head or aloud.

Progress first by removing the rests, then by playing the passage in the correct rhythm.

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Speed the metronome up in increments of 20 (MM=60, MM=80, etc.) until you reach the correct concert tempo.

Choose the next short phrase and repeat the process.

Spend 50% of your practice time on each piece for accurate and reliable intonation.


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Practice your piece note by note in Pythagorean Intonation.

Use large whole steps and narrow half steps.

Click on 'Read More' for each interval in a diatonic scale.


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When we play with piano, we basically remain in Pythagorean Intonation.

We adjust to the piano intonation when we play long notes in unison with the piano.


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Tune all fifths slightly narrow between the cello C-string and the violin E-string.

Play a few chords in the key of the piece.

All thirds have to be in Just Intonation, with high minor thirds and low major thirds.


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For each phrase, decide which notes are played in vertical (Just) or linear (Pythagorean) Intonation.

Thirds and sixths in chords are played in Just Intonation.

Melodies and passing notes are played in Pythagorean Intonation.


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