Vallotti temperament

Círculo de quintas correspondiente al temperamento de Vallotti de 1/6 de coma, según Tartini.

The circulating temperament today referred to as Vallotti temperament (or simply Vallotti, Vallotti-Barca, Vallotti-Tartini, or Vallotti-Young) is a shifted version of Young's second 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. It is however audibly indistinguishable from a slightly different temperament that was in fact devised by Vallotti.

Vallotti's description of his temperament appears in book 2 of his treatise, Della scienza teorica e pratica della moderna musica (On the theoretical and practical science of modern music). Although he stated that he had developed his theoretical system—presumably including the details of his temperament—by 1728, the first book of his treatise was not published until 1779, the year before he died. At the time of his death, the other three books had not been published, and remained only in manuscript form until an edition of all four books was published in 1950, under the title Trattato della moderna musica (Treatise on modern music).[1]

Vallotti's temperament received very little attention during his lifetime and for some time thereafter.[2] In a treatise published in 1754,[3] Vallotti's friend and colleague Giuseppe Tartini praised the former's approach to temperament, and outlined some of its features, but without giving sufficient detail for the temperament itself to be identified.[4] In 1781, the mathematician William Jones noted Tartini's preference for Vallotti's temperament, and gave a similarly vague and unspecific description.[5]

The temperament originally devised by Vallotti has six fifths tempered by 1⁄6 of a syntonic comma, five perfectly just, and one tempered by a schisma. In a manuscript which remained unpublished until 1987,[6] the Italian chemist and musical theorist, Alessandro Barca, proposed that this latter fifth be sharpened by 5⁄6 of a schisma, and all the pure fifths be flattened by 1⁄6 of a schisma. Barca's version thus has six fifths tempered by 1⁄6 of a syntonic comma, and six tempered by 1⁄6 of a schisma. In the temperament now commonly misattributed to Vallotti, the odd fifth out in his original is sharpened by a full schisma, and each of the six tempered fifths is flattened by a further 1⁄6 of a schisma. This modern version thus has six fifths tempered by 1⁄6 of a Pythagorean comma, and six perfectly just. 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. In practice, none of these four versions is audibly distinguishable from any of the others,[7] because no interval in any of them differs from the corresponding interval in any of the other three by as much as 2 cents.

  1. ^ Damschroder and Williams (1990, p.365); Hansell (2001, 2007).
  2. ^ Barbieri (1982, pp.63, 65). Barbieri quotes the chemist and musical theorist, Alessandro Barca, writing sometime after Vallotti's death, as saying that his temperament had been little more than merely referred to in his unpublished writings.
  3. ^ Trattato di musica secondo la vera scienza dell' armonia (Tartini, 1754)
  4. ^ Tartini (1754, p.100). Benjamin Stillingfleet translates the relevant passage from Tartini's treatise as follows (Stillingfleet, 1771, p.35):
    "and I infinitely applaud the opinion of P. Vallotti, our organ-master, as the most reasonable of all. He says, that you ought to give to the white keys of the organ all their natural perfection –, both because they are the natural notes of the diatonic genus, and because in church-music the greatest use is made of them; throwing thus the greatest imperfection upon those black keys, which are most remote from the diatonic scale, and which are hardly ever used."
    The original Italian reads (Tartini, 1754, p.100):
    "ed io lodo infinitamente il sentimento del Padre Valloti nostro Maestro come il più ragionevole di tutti, perchè il più prudente. Egli, dice, che si deve lasciare a' tasti bianchi dell' organo tutta la loro naturale perfezione; sì perchè sono li naturali del Genere diatonico; sì perchè di quelli nel servigio Ecclesiastico sé ne fa il maggior uso: riducendo la massima imperfezione a que' tasti neri, che fono i più lontani dal Genere diatonico, e di quasi niun' uso."
  5. ^ Jones (1781, pp.325–326).
  6. ^ When it was published in Patrizio Barbieri's Acustica accordatura e temperamento nell’Illuminismo veneto. Con scritti inediti di Alessandro Barca, Giordano Riccati e altri autori (Barbieri, 1987).
  7. ^ Except by carefully timing the beats generated by some non-just intervals.