Simon Stevin's equal division of the octave

Summary

Many pioneers of the Scientific Revolution such as Galileo, Kepler, Stevin, Descartes, Mersenne, and others, wrote extensively about musical theory. This was not a chance interest of a few individual scientists. Rather, it reflects a continuing concern of scientists from Pythagorean times onwards to solve certain quantifiable problems in musical theory. One of the issues involved was technically known as ‘the division of the octave’, the problem, that is, of which notes to make music with. Simon Stevin's contribution to this issue, in his treatise Vande Spiegheling der Singconst (‘On the Theory of Music’), is usually conceived of as a remarkably early plea for equal temperament, which is the tuning system we nowadays all take for granted. In this paper I show that, even though it is true that Stevin calculated the figures for what is now known as equal temperament, in fact the subject of temperament has almost nothing to do with his accompanying considerations, and that, therefore, his calculations served another purpose. A careful analysis of the problem situation in the science of music around 1600, reveals that Stevin's treatise highlights a particular stage in the history of what has always been the core issue of the science of music, namely, the problem of consonance. This is the search for an explanation, on scientific principles, of Pythagoras' law: ‘Why is it that those few musical intervals which affect our ear in a sweet and pleasing manner, correspond to the ratios of the first few integers?’ Through an analysis of the source material available (including contemporary comments on Stevin's ideas) we find that Stevin's theory, which makes no sense if interpreted as an early stage in the ‘evolution’ of equal temperament, was meant as a solution—as freshly original as it was wrongheaded—to this perennial problem of consonance, which has continued to baffle some of the best scientific minds from the very beginning of science to the present day.

Part of the material that makes up the present paper has been used before in my book Quantifying Music. The Science of Music at the First Stage of the Scientific Revolution, 1580–1650 (Dordrecht, 1984). In this paper the focus is on whether or not Stevin's musical theories belong to the history of equal temperament, which issue is treated in a far more implicit way in the Stevin sections of Quantifying Music, which centre on the problem of consonance.

Part of the material that makes up the present paper has been used before in my book Quantifying Music. The Science of Music at the First Stage of the Scientific Revolution, 1580–1650 (Dordrecht, 1984). In this paper the focus is on whether or not Stevin's musical theories belong to the history of equal temperament, which issue is treated in a far more implicit way in the Stevin sections of Quantifying Music, which centre on the problem of consonance.

Notes

Part of the material that makes up the present paper has been used before in my book Quantifying Music. The Science of Music at the First Stage of the Scientific Revolution, 1580–1650 (Dordrecht, 1984). In this paper the focus is on whether or not Stevin's musical theories belong to the history of equal temperament, which issue is treated in a far more implicit way in the Stevin sections of Quantifying Music, which centre on the problem of consonance.