On the Production of True Consonance

Sound installation after Giovanni Battista Benedetti (1530-90). Elm wood monochord, yellow brass harpsichord wire, Arduino, servo motors, 8-channel audio, MaxMSP. 

In 1563, Giovanni Battista Benedetti, an Italian mathematician, wrote a letter to a progressive composer of his day, Cipriano de Rore. Benedetti set out to show that if the singers in a choir tune their voices according to a system known as ‘just intonation’ in certain musical compositions the choral sound slowly ‘drifts’ out of tune.

Just or ‘pure’ intonation is system of tuning that derives from the harmonic series. The frequencies of musical notes are related by small-number ratios, such as 2:1, 3:2, and so mirror the relationship between ‘adjacent’ harmonics (1st, 2nd, 3rd etc). Using the example reproduced below, Benedetti showed that in order for the lowest voice to tune a pure major 6th (5:3) with the top voice in bar 2, it will need to raise the C by a small amount known as a ‘comma’. Accordingly, all subsequent notes will have to be raised by a comma in order to be tuned as pure intervals. The sound of the choir will drift ‘upwards’ by one comma each time the phrase is repeated.


The fact that the ratios of just intonation are given in nature in the form of the harmonic series was of great significance for Renaissance music theorists. But it was also highly problematic. For instance there was no possibility of musical modulation, without the consequence of strange sonorities.

A considerable amount of ink was therefore expended in the sixteenth-century and beyond on the merits of just intonation in relation to the demands of progressive musical composition. The debate eventually led to the introduction of ‘temperament’ – and later, to Equal Temperament, in which the ‘purity’ of just intervals is compromised, essentially because it allows a single instrument to render a variety of different pitch relationships of acceptable quality without retuning.

Computer-based music technology today makes such questions of practicability largely irrelevant. Given that electronic technology permits composers easy access to a far greater frequency range for musical design than has previously been the case, it also makes the question of retuning a trivial matter. On the Production of True Consonance is a demonstration of Benedetti’s argument rendered in a creative context. But it is also a meditation on the role of electronic technology in releasing musical composition from its historical inheritance, namely, temperament – the solution to a problem of impracticality in instrument design.

Nicholas Brown
April, 2016

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This programme note for On the Production of True Consonance by Nicholas Brown is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.