Additive Synthesis: Building a Bell Out of Plain Tones

I thought a bell needed a recording

I'm a designer, and when I started on the Forest world I assumed the bells would have to be recordings. A bell seemed too particular a sound to make out of nothing. Then I read that a bell is a handful of plain tones ringing together, and that the metal in it comes from how those tones are spaced. So I tried it.

What "additive" means

A plain tone, the kind called a sine wave, is the simplest sound there is: one pitch and nothing else. I wrote about how dull one sounds on its own. Additive synthesis is the idea that you get richer sounds by playing several of them together. Wikipedia puts it in one line: it "creates timbre by adding sine waves together".

Each tone in the stack is called a partial. For each one you choose three things: how high it is, how loud it is, and how its loudness changes over time. That is the whole toolkit.

Neat spacing sounds smooth

A voice, a flute or a bowed violin has partials at tidy steps above the lowest one: twice as high, three times, four times. Your ear fuses a tidy stack into a single note with a colour. You don't hear three tones. You hear one note that sounds like a flute.

The idea is much older than electronics. The same Wikipedia article counts pipe organs as an early form of it: pull out more stops, more pipes sound together, and the colour of the note changes.

Slightly off spacing sounds like metal

Bells, chimes and cymbals don't follow the tidy steps. Their partials sit at untidy distances from the lowest tone. The word for this is inharmonic. Wikipedia defines inharmonicity as "the degree to which the frequencies of overtones depart from whole multiples of the fundamental frequency".

When the stack is untidy, the ear can't fully fuse it. You still hear one note, but with a shimmer and a faint sourness inside it. To me that is the sound of metal.

What surprised me was how little it takes. In my bells the upper tones sit only a hair off the neat positions, and a hair is enough. In the singing bowls they sit much further off, and the bowls come out rougher and more hollow.

The other half is how it starts and how it fades

Spacing alone doesn't make a bell. Two more things do the rest.

• The start. A real bell is hit, so it begins with a hard knock. I left the knock out on purpose. My bells swell in over a moment, so they never jab at you while you work. More on that in why a fast start turns into a click.
• The fade. A bell is loudest at the beginning and then dies away, with no steady middle. Mine ring for a few seconds and fade to nothing.

One shortcut I should own up to. The full version of the method gives every partial its own loudness curve. Mine all fade together under one curve. It was simpler to build, and in a quiet background bell I can't hear what I lost.

Where you can hear it

The bells, the singing bowls and the soft bowl strike that keeps time in Forest are all small stacks of plain tones, three or four each. Forest is one of the two paid worlds. Ocean, the free one, is built from the same kind of stacks, tuned to sound like deep water instead of metal.

Sources

• Additive synthesis, Wikipedia
• Inharmonicity, Wikipedia