I am afraid what you have said about this is incorrect. "Juan Carlos Amat's little book Guitarra Espanola y Vandola (?) was published already in 1596 but the earliest surviving edition is from 1627."
The earliest surviving copy is dated 1626 - this copy is in the Newberry Library Chicago. "Interestingly, the compendium is for spanish guitar of 5 courses, 2 pages about the 4 couse guitar and then the same again in catalan, but with improved diagrams. (The text says that the first version was made in 1586 already!)" The earliest edition of Amat's book was printed in 1596 not 1586. The correct title of the book is Guitarra espanola de cinco ordenes.....It comprises 8 chapters about the 5-course guitar. The last, ninth chapter is about the 4-course guitar. This version was reprinted several times in the 17th century. It was reprinted several more times in the 18th century with the title Guitarra espanola y vandola. 18th century copies include a supplement in Catalan in 4 chapters, three about the 5-course guitar and the last about the vandola. The earliest copy to include this supplement was printed in 1701. It is surprising that after all this time people still don't get it right about Amat. In the Castilian system of chord notation the basic chords were known by fancy names. These appear in Arte de la guitarra by Joseph Guerrero which survives in an obscure manuscript. 1 = G major [Dedillo] 9 = A flat major [Dedillo atrevesado?] 2 = C major [Puente] 7 = E major [Cruzadillo] 3 = F major [Vacas] P = A major [Patilla] 4 = B flat major [Patilla atrevesada] + = D major [Cruzado] 8 = E flat major [Dedillo?] There is a more comprehensive list in the Zuola ms. which I can't put my finger on at this time. Best wishes to all Monica To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
