Equal temperament and the goodness of creation

When skeptics point out apparent imperfections in creation as evidence either against God, or against his goodness, a standard response is that such “evils” are necessary for God’s greater purposes. One modern example of this is the free will defence best expressed by Alvin Plantinga (but probably much older). John Polkinghorne, for example, talks about tsunamis as the price we must pay for a universe governed by regular laws in which alone human freedom can operate.

There are also other, much older, ways of expressing it. I like this from St Augustine’s Confessions:

To you nothing at all is evil, not only to you but to your creation at large, because there is nothing outside to break in and upset the order you have imposed on it. But in parts of it some things do not harmonise with other parts, and are considered evil for that reason. But with other parts they do harmonise and are good, good in themselves… Let it be far from me to say: “These things should not be”, for if these were the only things I could see, I should still long for the better, and should be bound to praise you for these alone. [But when I understood from Scripture the praise arising from all things both in earth and heaven] I did not now long for better things because I considered everything.

The allusion to harmony puts me in mind of a small musical illustration that might be helpful. Most non-musicians, and many musicians, are unaware that the musical scale used in our western music is a severe compromise, called the tempered scale. This is opposed to what is called just intonation, on which all ancient music was, for good reason, based.

In just intonation, each scale is based on the natural harmonics of the fundamental note, that is on simple (and therefore beautiful) mathematical ratios. Listen to this example.

The same thing played in the modern scale found on, say, a piano (or an electronic tuner) sounds rather different. Compare this next clip with the first.

If your ear is good, the first sounds much sweeter – indeed, you can hear beating on the second, which as any physics student will tell you, is the result of something being out of tune. You may be able to hear slightly better by alternating the two clips, or from the next clip of two chords, the first of each in tempered intonation and the second in just – it may take a couple of hearings to appreciate the difference fully.

A last clip shows the difference on a square wave – which is ugly anyway, but more like the waveform of, say, a violin. As you can hear, the difference is even more obvious, and the beating can be heard to slow and disappear in the last section where the tempered intonation is slowly morphed into the just.

Given the obvious imperfection of the tempered scale, why on earth would anyone use it, let alone make it the universal western standard? The answer is that it enables pretty well all the complexities that we have come to enjoy in our music: multiple chords, multiple voices, and multiple keys. If you listen to recordings of mediaeval or other ancient music, it appears “primitive” because it usually has only an unaccompanied melody line, perhaps with simple harmonies of a third or fifth. But it’s not primitive – it’s just aiming at perfect harmony and beauty, which only the just scale gives you. But if, for example, you were to play a minor chord when tuned for a major, it would sound awful. If mediaeval minstrels had tried jazz chords, the cats would never have taken to the dance floor. Just intonation limits you to relatively simple music, especially on tuned instruments.

So gradually, the scale was tweaked and adjusted until a compromise was reached where nothing sounded perfect, but pretty well any combination of notes sounded acceptable. And it revolutionised music. The most notable early example celebrating the change is J S Bach’s Well Tempered Clavier, a series of preludes and fugues which, for almost the first time, enabled the same instrument to play in all the keys without retuning. The possibilities became boundless.

It’s interesting that the music of Bach brings to mind, more than perhaps any other composer, such words as “perfection” and “sublimity”, when it is entirely based on a scale tuned deliberately away from harmony towards dissonance. I think that’s apretty reasonable analogy to God’s good creation, which necessarily misses what one could reason to be “perfection” in every detail, because of the possibilities the whole assemblage allows. Compare a couple of notes, and you may hear the beating of harmonics and tut-tut at how God has left creation to sub-optimal mechanisms or chance. But one really ought to hear to the whole symphony before passing judgement.

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About Jon Garvey

Training in medicine (which was my career), social psychology and theology. Interests in most things, but especially the science-faith interface. The rest of my time, though, is spent writing, playing and recording music.
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2 Responses to Equal temperament and the goodness of creation

  1. Avatar photo penman says:

    Hi Jon

    Oddly I was just speaking (briefly) about this a few days ago, & cited the Augustinian “solution” as the right approach.

    The free will defence works as theodicy for moral evil, but I don’t see its relevance to natural evil, unless all natural evils are classified as punishments for moral evil, which is problematic. The idea that a risky physical universe is necessary for a risky human free-will seems incoherent to me. Angels have free will & are non-physical beings, requiring no evolution, quantum physics, or anything of that sort in order to exist as pure spirits.

    The Augustinian way is the “via antiqua”: some things about the observable universe seem unworthy of a wise or good Creator only from our finite, fragmentary, imperfect perspective. See the whole – see as God sees – and the “imperfections” are swallowed up in the vast, complex, awesome totality. The attitude “I could have created a better universe” is a sort of cosmic impiety. The book of Job has application.

    I’m glad you provided the musical analogy since I’m certain I couldn’t have…

  2. Avatar photo Jon Garvey says:


    “The free will defence works as theodicy for moral evil, but I don’t see its relevance to natural evil”

    I don’t know if you’ve been following the BioLogos thread on John Polkinghorne ( http://biologos.org/blog/motivated-belief-john-polkinghorne-on-the-resurrection-part-2/P0 ), but I quoted (from Wikipedia) what he said about his extension of the FWD to nature:

    “I have added to it the free-process defence, that a world allowed to make itself is better than a puppet theatre with a Cosmic Tyrant.”

    That seems to me the equivalent of “argument weak here, shout louder.” That thread has alluded to theistic personalism a lot, and your “cosmic impiety” angle seems to arise directly from that. “If God is a person like me, then his judgements ought to match my own – and if not, it must be because my ways are higher than his.”

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