Why every pop is a note: the pentatonic idea behind Carillon

A carillon is a set of tuned bells, usually hung in a tower and played from a keyboard below. I named the game after it because every dot you pop rings a note, and a chain of pops rings out like a run of bells. The trick is making that sound like music every time, whatever order the dots pop in.

Colour is the note, size is the octave

Every dot’s note is fixed by how it looks, so you can learn to hear a field before you tap it.

• Colour picks one of five notes: coral is C, amber is D, mint is E, sky is G and lavender is A.
• Size picks the octave: big dots are low, normal dots sit around middle C, and small dots are high.

Five colours times three sizes makes fifteen notes, from a low C at about 131 Hz to a high A at 880 Hz.

Why do big dots sound low? A big dot’s ring is the long, far-carrying one, and a low note is what a large bar or a large bell plays. The small dots, with their short reach, get the bright high notes, like the small treble bells of a real carillon.

Five notes that never clash

C, D, E, G and A are the C major pentatonic scale. It is the scale of the black keys of a piano, moved onto the white ones, and it turns up in folk music all over the world.

What makes it right for Carillon is what it leaves out: no semitones, two notes a half step apart, and no tritone, the tense interval between, say, F and B. Those are the two intervals that grate, and without them any handful of these notes sounds fine together.

That matters because you don’t choose the order of a chain. A big dot can pop six neighbours at almost the same moment, and two separate rings can meet in the middle of the field. With a pentatonic scale, all of that still sounds like music and never like a wrong note.

Chains that climb

Sounding fine together is not the same as sounding like a tune, so the level generator gives the melody a nudge. Each chain starts on a colour picked for it, and as the field grows outward from that start, each new ring of dots tends to take the next note up the scale. About one dot in four skips a step or repeats one, so the lines don’t all sound like the same exercise.

A ring front travels at one steady speed, so dots further from the start pop later. Put those two facts together and a chain tends to play a rising line, spreading across the field in time and in pitch at once.

The first five levels go further. Their colours are chosen to give each chain the best tune its sizes allow, and the dots are spaced so the rings arrive on a steady beat. Level 1 is an arch of nine dots, and a chain from one end plays C, D, E, G, A and back down to C, one note every 0.27 seconds.

A few rules need a colour of their own, since tuning forks and glass work by colour and the gold home note is always C, the note the scale comes home to. On those dots the puzzle picks the note, and the melody fills in around it.

How a note is made

None of the sounds are recordings. Every note is built in code as a marimba tone from a few simple parts.

• The fundamental, the note itself.
• A twin of it tuned a hair sharp, which makes a slow, gentle beat.
• A woody partial at nearly four times the frequency that fades fast, like the knock of a wooden bar.
• A faint glassy partial much higher up.
• A soft thump, like a felt mallet.

High notes cut through more than low ones, so the small dots are mixed quieter to sound even. A short reverb is baked into each note file rather than added live, so the game sounds the same in a web browser as on a phone. Measured by frequency analysis, every marimba note lands within a quarter of a hertz of its target pitch.

The marimba is the game’s own voice, and there are four more. The instrument pack plays the same fifteen notes on a music box, a glass harp, a kalimba and a steel pan. The music box and the glass harp sit an octave up, where real ones play, and every instrument is matched to the marimba’s loudness, so switching never makes the game louder or softer.

Small touches in play

In the game, each note is detuned at random by a tiny amount, up to about 7 cents. When two dots of the same colour pop together, they shimmer instead of doubling into one flat tone.

Each pop also plays where the dot is. Notes are spread over two dozen voices placed at their dots on screen, so a pop on the left leans gently to the left.

The rules have voices too, each one quiet beside the note itself. A heavy bell’s first strike is a dull note an octave down. An echo stone replays the note from its twin, softer. A grace note flicks up an octave like an ornament, glass adds an octave above, and a slow dot adds an octave below. The home note and a chord bell add a fifth, horns and duet partners a third, a round bell a knock that rises with its number, and a beat dot a tick.

When you clear a field, the win climbs C, E, G, C, E and lands on a high C, over a low C and a soft held chord. However a level went, it ends at home. Run out of taps and the line drifts down instead, A, G, E, D, and stops one step short of home, gently, since retrying is one tap away.

Why there is no music switch

Most games have separate sound and music settings. Carillon has Sound, with a volume slider, and Vibration, because the notes are the music. The slider is shaped to how ears hear loudness, so its middle sounds about half as loud as the top. Turn sound off and the game goes silent, and the rings still spread and read exactly the same.

The title screen plays a small version of the whole idea. A little field reads its first dot, taps it and sings across, a low big dot leading a line that rises as it spreads, then grows back and does it again, a touch quieter than play.

If you want the game at its best, play a few levels with sound on and listen to a clear. One tap, a whole chain covers the rules, and calm by design is about the rest of how the game feels.