Mathematics and Tuning

Anyone who compares the musical theory of the past to that of the
present, and especially musical theory as it relates to tuning
questions, will be immediately impressed by one great difference. The
theorists of the past used mathematics only very charily, but language
copiously. In some cases this may have been due to mathematical
ignorance; no doubt it was. But in other cases it seems to have been
highly deliberate. It was felt that mathematics, if applied before one's
_assumptions_ had been presented with the utmost clarity, could lead
only to mistaken conclusions.

Modern theorists on the other hand, painfully trained in mathematical
habits of thought, but little accustomed to think profoundly in
language, and often under the vague impression that to state anything
mathematically is to gain public respect, very often pass over their
musical assumptions with an apologetic air, then turn to the most
involved calculations with an audible sigh of relief.

>From such persons using such a method, musical truth is most unlikely to
emerge. For it is in the assumptions which should be made, and not in
the mathematical methods, which are, in comparison, trivial, that the
true difficulties arise.

None of this is to disparage mathematics or abate its just claims;
mathematical truths compare in beauty to the highest conceptions of art,
and without mathematics there can be no sure foundation for musical
speculation at all. Used with circumspection, this science can stimulate
and condense thought in a very wonderful manner.


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