Vallotti temperament

Its attribution to the 18th-century organist, composer, and music theorist, Francesco Vallotti is a mistake, since there is no evidence that he ever suggested it.

[4] In 1781, the mathematician William Jones noted Tartini's preference for Vallotti's temperament, and gave a similarly vague and unspecific description.

More recently, the tuning and keyboard construction expert, Owen Jorgensen, has proposed a version of Vallotti's temperament in which the beating frequencies of the tempered fifths, rather than their sizes, are chosen to be equal.

[14] Jorgensen gave two sets of instructions for tuning Valotti's temperament in a way which he considered representative of what he believed would have been the results achieved by 18th- and 19th-century tuners.

As a consequence, the diminished sixth G♯–E♭, which is required to be a perfectly just fifth in Vallotti proper, turns out to be tempered narrow by 0.6 cents in this version of Jorgensen's.

The sizes of its major thirds in cents are:[17] The following table gives the pitch differences in cents between the notes of a chromatic scale tuned with Jorgensen's equal-beating version of Vallotti temperament and those of one tuned with equal temperament, when the note C4 of each scale is given the same pitch, 220 4√2 Hz.