Francisco de Salinas (1513-1590)

Francisco de Salinas was an organist, theorist, and professor of music at the University of Salamanca. He was born on 1 March 1513 in Burgos and had been blind since around the age of ten. He spent a long period in Italy, where he became abbot of the monastery of St. Pancras de Rocca Salegno in the Kingdom of Naples.
Salinas and Gioseffo Zarlino are considered the first to describe meantone tuning in mathematically precise terms. In his major work De musica libri septem (1577), written in Latin, he describes three types of meantone tuning that he deemed suitable for keyboard instruments, namely the 1/3-, 1/4-, and 2/7-comma meantone tunings. The first of these, in which each fifth is 1/3 comma, or 7 cents, smaller than the pure fifth, possesses unique properties compared with the other meantone tunings.
It represents an attempt to create a system in which not only the genero cromatico (F♯, C♯, G♯, B♭, and E♭) but also the genero enarmonico (G♭, D♭, D♯, A♭, A♯, C♭, and E♯) could be realised. This was already possible on the archicembalo with 31 keys, as described by Zarlino in his Istitutioni harmoniche, but Salinas found a 19-note keyboard more practical to execute.
In this system, the difference between a sharp and its enharmonic flat is extreme: each note is divided into three equal steps, with the first step forming the chromatic and the second forming the diatonic minor second. For example, starting from C: the first step is C♯, the second is D♭. As a result of the 1/3-comma reduction, the fifths sound even less pure than in ordinary meantone tuning. Salinas noted this himself, considering them less sonorous and ‘fading’, but still not ‘offensive to the ear’. The pure minor thirds in this temperament, however, make it relatively easy to tune. The notes are almost identical to those in the division of the octave into 19 equal parts (1/3 tones). By using 19 keys, one avoids the wolf fifth of ordinary meantone tuning. Salinas’ tuning was studied and appreciated by, among others, the Dutchman Quirinus van Blankenburg (18th century), Helmholtz (19th century), and many microtonal composers of the 20th century.

Statue of Salinas in Salamanca

He explains in his book the comma distribution of the three tunings he considered most useful. The syntonic comma of 21.506 cents, or the difference between the minor major second (10/9) and the major major second (9/8), is divided into three parts in the first tuning, with one part added to the minor and two subtracted from the major. In the second tuning, the comma is split into seven parts, of which three are added to the minor and four subtracted from the major. Finally, the 1/4-comma, or “ordinary” meantone tuning, divides the comma into two equal parts, making the two major seconds equal in size, hence the name meantone.

A.J. Ellis suspected that Salinas made a mistake in his description of the 1/3-comma temperament. Despite his explicit claim of enlarging the minor major second by 1/3 comma and reducing the major by 2/3 comma, he may actually have meant the opposite, as being blind he could not see a figure’s error. His intention would have been to make the tritone equal to three whole tones. This corresponds to the 1/6-comma meantone tuning, in which the tritone is 590.224 cents (45/32) and the whole tone 196.741 cents. In the 1/3-comma meantone, the tritone consists of two large whole tones plus a minor, essentially forming an augmented fourth of 568.717 cents (25/18). Salinas indeed cites this ratio, equating the tritone to half an octave reduced by a major diesis (648/625), which Ellis considered incorrect. The 1/6-comma meantone comes very close to equal temperament.

Salinas was also a great connoisseur and admirer of the Greek genera, which he discusses extensively in his book, with the enharmonic being his favourite. His enharmonic tetrachord reads 1/1 25/24 16/15 4/3; intervals: 25/24 128/125 5/4. His 24-note per octave tuning, called instrumentum perfectum, encompasses the enharmonic, chromatic, and diatonic genera:
1/1 25/24 16/15 10/9 9/8 75/64 6/5 5/4 125/96 4/3 25/18 45/32 64/45 36/25 3/2 25/16 8/5 5/3 125/72 225/128 16/9 9/5 15/8 125/64 2/1.

The pitch layout, ignoring commas and transposing E to C (fifths horizontal, major thirds vertical), appears as:

      F#  C#  G#

      D   A   E   B   F#

      Bb  F   C   G   D

      Gb  Db  Ab  Eb  Bb

      Ebb Bbb Fb  Cb  Gb

                      Ebb
  

He brought his enharmonic scale to life on his special instrument in Salamanca with 19 keys per octave (five fewer keys: the instrumentum imperfectum). His interest in ancient music was shared with Vicentino, whom he also discusses in his book. In Vicentino’s system with 31 notes per octave, he saw little practical application. Salinas died on 13 January 1590 in Salamanca.

Literature

• Salinas, Francisco de. De musica libri septem. Mathias Gastius, Salamanca, 1577, 1592. Reprint M.S. Kastner (ed.), Documenta Musicologica I no. 13, Bärenreiter, Kassel, 1958.
  Books I–IV cover intervals, scales, and modes; books V–VII cover metre and rhythm.
  Text available in the Thesaurus Musicarum Latinarum:
  • Book I
  • Book II
  • Book III (with meantone tunings)
  • Book IV
  • Book V
  • Book VI
  • Book VII
• Helmholtz, Hermann L.F. von. On the Sensations of Tone as a Psychological basis for the Theory of Music. 2nd English edition translated by Alexander John Ellis, based on the 4th German edition of 1877 with extensive notes, foreword and afterword: 1885. Reprint by Dover Publications, 1954.
• "Salinas", in New Grove Dictionary of Music and Musicians, MacMillan, London, 1980.
• Fray Luis de León's famous poem Oda a Salinas, written after Salinas had testified for him before the Inquisition in 1573.