Adjusting String Gauges for Different Diapasons

I’ve been thinking about how to modify string gauges when you switch between different pitch standards—like A = 440 Hz vs A = 392 Hz in order to maintain the same string tension for a similar feel and playability.

It turns out Marin Mersenne’s (author of Harmonie Universelle 1636) laws on vibrating strings includes everything we need to derive this relationship. With a bit of massaging we come up with the simple relationship:

New diameter = old diameter × (old frequency / new frequency)

Let’s say you’re using a D string with a gauge of 112 at A = 415 Hz. If you want the same string tension at A = 392 Hz, you’d compute:

112 × (415 / 392) ≈ 118

That’s about a 6% increase in diameter per semitone (for small changes in pitch). This isn’t just a curiosity—it’s a practical way to figure out what gauge will keep the feel of your instrument the same when switching pitch standards.

This formula is quite practical and has a nice affordance: the actual frequency of the diapason or string does not matter, only the relative difference. Whether you are changing the gauge of the D or E string, if your diapason changes from A = 415 to A = 440, the semitone relative difference in frequency means your string gauge should increase by 6% to get the same tension.

You can also use this relationship to experiment with finding the right tension for your instrument. For example, if tuning up a semitone makes your instrument feel better under the bow, try increasing your string gauge by 6% to preserve that feeling under the original pitch.