Meantone Tuning

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A defining feature of Renaissance music was the move away from the active 3rds of Pythagorean Tuning to consonant 3rds at their natural pitch ratio of 5/4 relative to the tonic or 386 cents. To achieve this Meantone tuning was introduced in the early 1400s and remained the primary method of tuning for the next 250 years. The basic idea was to reduce the syntonic comma, the difference between the natural 3rd and the Pythagorean 3rd, by detuning the 5ths, aiming to make the 3rds as consonant as possible without the 5ths becoming dissonant.

The most obvious choice, known as 1/4 comma Meantone reduced each of the 5ths by one-quarter of the syntonic comma (5.4 cents) which creates a set of perfect 3rds. Meantone, because every 5th is reduced by the same amount and therefore the 3rd is always made up of two equal tones, as can be seen if the pitches are shown relative to the tonic.

1/4 comma Meantone, sometimes called Aaron's Meantone or just plain Meantone has perfect 3rds in the near keys and seen relative to itself allows free modulation to near keys which all have identical properties. One drawback, however is that the wolf, which was -24 cents in Pythagorean Tuning has worsened to 35 cents in 1/4 comma Meantone.

A further drawback is that the human ear is more sensitive to poorly tuned 5ths than it is to 3rds and making the 3rds perfect, at the expense of a 5.5 cent reduction in the interval of the 5th is not the best compromise. The alternative is to use different fractions of the syntonic comma and the following table, along with the diagram, shows their properties:

Tuning5th Interval3rd IntervalWolf Interval
1/3 comma Meantone - Salinas's Meantone-7.2-7.255
2/7 comma Meantone - Zarlino's Meantone-6.2-3.144
1/4 comma Meantone - Aarons's Meantone-5.4036
1/5 comma Meantone-4.44.324
1/6 comma Meantone - Silberman's Meantone-3.67.216
1/8 comma Meantone -2.710.86
1/11 comma Meantone - Equal Temperament-2.013.7-2

A number of interesting facets become apparent. Although 1/4 comma has the best 3rds, 1/6 comma is arguably the best compromise. The wolf note can only be reduced at the expense of poorer 3rds. However, 1/8 comma Meantone is considered 'well-tempered' since the wolf is less than 10 cents, though the 3rds are too active for Renaissance and Baroque music. Something special happens with 1/11 comma Meantone. The wolf disappears completely and this tuning turns out to be the same as our modern day Equal Temperament, for reasons which should be obvious when seen relative to itself.

Return to 'Commas Explained'Go to 'Well Temperament'