Music has some mathematical aspects, to be sure. Musical intervals are ratios of frequencies of air pressure variation. Musical tone quality is partly a result of the cumulative effect of various frequencies on/in the overall pattern of air pressure change (what physicists would call the “waveform”). Scale degrees are numbered in some systems, and mathematical relationships of scale degrees are observed. Rhythmic relationships are described in numerical terms.
Nevertheless, the experiences of musicians and listeners are not fundamentally mathematical, any more than the perception of color is experienced mathematically, though the frequencies of reflected light are essential aspects of the physical reality behind our experience of “color.” It is a canard that music and mathematics go together in some a priori way, either in content or in perception, except in the same senses that most aspects of human living can be counted or measured.
The rate of breathing can be counted, the volume of breath can be measured, the percentage of oxygen uptake can be measured… but breathing isn’t fundamentally about mathematics, either.
Some musicians are also gifted mathematically; but many are not. As a professor of music theory and music technology, I’ve observed many talented music majors struggling with their math classes. I’ve also seen them scratch their heads trying to do the low level math involved in converting sample rates and resolutions into RAM usage for a length of time to be sampled. Binary arithmetic is at the bottom of many concepts in music technology, and I’ve seen no particular affinity on the part of music majors for absorbing it.
So what does all of this imply? Theories comparing the “internal elegance” of mathematics to music don’t tell us much more than comparing mathematics and breathing. There is no causal relationship (in either direction) between musical ability and mathematical ability, though they may coexist in many people. Music and mathematics both involve perception of patterns, but so do about a million other things.
The relevance of all this to faith integration and music is straightforward: if their is no privileged relationship between music and mathematics, then faith integration strategies that are appropriate for mathematics aren’t particularly likely to apply to music.
Coming next: music and language.