You can find out a little more about the manipulation of musical ratios in my article on music and Euclid’s algorithm:
‘Music and Euclid’s Algorithm’, Plus online mathematics magazine, Sep. 2006:
For a good general introduction to music and mathematics, see:
John Fauvel, Raymond Flood, and Robin Wilson (eds), Music and Mathematics: From Pythagoras to Fractals (Oxford, 2006)
Mark Lindley, Lutes, Viols and Temperaments (Cambridge, 1984).
For more information on Nicolaus Mercator, see
Christoph J. Scriba, ‘Mercator, Nicolaus (1620?–1687)’, Oxford Dictionary of National Biography, Oxford University Press, 2004.