Tuning forks: design, alloys and tuning

The frequency of a tuning fork depends on two dimensions: the thickness of the prong and its length. A thicker prong gives a higher tone, in direct proportion. A longer prong gives a lower tone, and by the square: twice as long means four times lower.

The width of the prong does not enter the formula at all — it has no effect on the frequency. Neither does the handle: its length and thickness change how comfortable the grip is and barely change the tone. But doubling all the dimensions at once lowers the sound by exactly one octave — which is why a set of forks in different octaves looks like the same fork at different scales.

The same object comes in a set in several octaves: low, middle and high. It is literally one note taken lower or higher — but they are used differently, and the difference lies not in symbolism but in physics.

This is the most unexpected thing about how the instrument works, and guides to sound practice almost never mention it. While a tuning fork sounds in the air, you hear its own tone. But press the handle against a hard surface — a table, a bone, a soundboard — and what passes into that surface is the doubled frequency, often louder than the fundamental tone.

The reason is simple and elegant: the prongs swing together and apart, and the center of mass of the fork dips TWICE in a single period of vibration — once when the prongs are furthest apart and once when they are closest together. The handle feels exactly this motion, and so it passes on a push twice as frequent.

A practical conclusion that changes the usual wording. An “Om” at 136.10 Hz placed handle-down on bone also sends 272.20 Hz into the bone — the upper octave of the same tone, often more strongly than the fundamental. So the phrase “the frequency of the Earth sounds in the body” is only half true: the tone is the same, but in the bone the octave is often a different one.

This is also the published reason for weights: mass at the ends of the prongs reduces this octave at the handle, so what goes into the bone is mostly the tone itself. In other words, weights do not only “amplify the vibration”, as people usually write — they also clean it up.

Look at steel and aluminum: their constants differ by a few percent — less than the reference values of the elastic modulus vary for each metal on its own. The reason is elegant: steel is three times stiffer than aluminum but also three times denser, and the formula uses the ratio of the two — so the difference almost cancels out.

And this is not just arithmetic. In a published measurement, forks of identical dimensions made of 6061-T6 aluminum and of stainless steel gave the same frequency, 260 Hz; a different grade of steel in the same measurement came out at 267 Hz — a quarter-tone off, and that is the honest limit of the rule.

Everything else, though, the metal changes a lot. In the same measurement, the ringing time of the different alloys ranged from “dies away in seconds” to “rings long and loud”, and the overtones from “none” to distinct harmonics. So choosing a metal means choosing not a note but a character: the weight in the hand, how long it rings, its brightness, how the vibration passes into bone. Brass changes the geometry as well: at the same frequency the prong comes out about one-sixth shorter.

The school describes its tuning forks as made of a “proprietary aerospace non-magnetic aluminum alloy” and warns separately that cheap alloys supposedly give an inaccurate tone and “leach into the body”. Let us go through this calmly, word by word.

• Aluminum and paint — checkable and true.
• “Non-magnetic” — true, but it says nothing: all aluminum is non-magnetic, and so are the stainless steels that competing tuning forks are made of.
• “Aerospace” — not a technical term but a word. Ordinary 6061, which costs next to nothing, fits it too.
• The alloy grade is not disclosed, so the claim cannot be checked in principle — not by us and not by anyone else.
• “A cheap alloy gives an inaccurate tone” — not true: pitch is set by dimensions and tuning, not by the grade of metal. That is exactly what the formula above shows.
• “Leaches into the body” — no measurements exist. A tuning fork touches the skin for a few seconds and does not dissolve into it.

This does not mean their tuning forks are bad: a painted, balanced, precisely tuned instrument is worth its price. It means you pay for the making and the quality control, not for a secret metal — and that difference is worth knowing before buying a set that costs several hundred dollars.

Calculated for 6061-T6 aluminum with a prong thickness of 8 mm. ⚠ The formula describes an ideally clamped straight prong, while a real fork has an elastic curve at the bottom — and because of it, it sounds slightly LOWER than calculated. That is why the blank is made to these dimensions and then tuned upward by filing down the tips.