Let's start with what sound physically is. When something vibrates — a guitar string, your vocal cords, a speaker cone — it pushes and pulls on the surrounding air, creating tiny, fast changes in air pressure. Those pressure changes ripple outward as a wave and reach your eardrum, which vibrates in step. That's all sound is: a wobble in air pressure over time.

A synthesiser's job is to generate that wobble electrically — a voltage (or, in a chip, a stream of numbers) that swings up and down many thousands of times per second, which a speaker then turns back into moving air. How far the wave swings from its resting point is its amplitude — that's loudness. How many times it repeats per second is its frequency, measured in hertz (Hz): 440 Hz means 440 complete cycles every second. Higher frequency = higher pitch.

And shape is what makes one sound different from another. Play a flute and a trumpet at the same pitch and they still sound different because their pressure waves have different shapes. That shape is the waveform, and the character it gives — reedy, bright, hollow, harsh — is the timbre (say “TAM-ber”). A few shapes are so basic they have names, and every synthesiser starts from them:

• Sine — the purest possible tone, a single smooth frequency with no extra colour. A tuning fork or a gentle whistle. This one shape is the seed of all FM synthesis (Module 04).
• Square and saw(tooth) — jagged shapes that are secretly a sine plus a stack of higher tones piled on top. Bright and buzzy — the classic Genesis PSG “bleep.”
• Triangle — in between: a little richer than a sine, but still mellow.
• Noise — every frequency at once, no pitch at all. Your “shh” sound: wind, static, a hi-hat, an explosion.

Play with the scope below: switch the shape, sweep the frequency slider, and watch the trace change while you listen. The moving line is an oscilloscope — it draws amplitude (up/down) against time (left/right), so you're literally seeing the wave.

Module 01 measured pitch as a plain frequency in hertz. Music organises those frequencies into notes, and the organising trick is beautifully simple: double the frequency and you get the same note, one octave higher. 220 Hz, 440 Hz and 880 Hz are all the note “A” — our ears hear a doubling as “the same, but higher.” That's why frequency feels multiplicative, not additive: each octave up is a ×2.

Western music slices each octave into twelve equal steps called semitones. “Equal” here means equal ratios, not equal hertz: each semitone multiplies the frequency by the twelfth root of two (about 1.0595). Do that twelve times and you've multiplied by 2 — exactly one octave. This scheme is called equal temperament, and it's why a tune sounds right whether you start it high or low.

A sound chip doesn't think in hertz at all. It holds a frequency number that sets how fast an internal counter advances; a bigger number plays a higher note. On the Genesis' FM chip that value is an 11-bit F-number plus a 3-bit block (octave), so a driver picks a note by looking up its F-number and octave in a table — the same twelve ratios you just met, pre-computed. Play the keyboard below: each key is one semitone, and the whole thing is just those ratios turned into tones.

In Module 01 we said a square or saw is “secretly a sine plus higher tones.” That wasn't a metaphor. The mathematician Fourier proved a remarkable fact: any sound, however complex, is just a sum of pure sine waves at different frequencies and volumes. Pull any tone apart and you always find sines; add the right sines together and you can build any waveform. Building sound by stacking sines is called additive synthesis.

For a musical note the sines aren't random. They sit at whole-number multiples of the lowest one: if the fundamental (the pitch you hear) is 220 Hz, the stack sits at 440, 660, 880 Hz and so on. Those multiples are the harmonics, and their pattern is the timbre. A saw contains every harmonic fading gently; a square contains only the odd ones (1×, 3×, 5×…), which gives it that hollow, clarinet-ish honk.

The catch with pure additive synthesis is cost: a rich, evolving tone can need dozens of sines, each with its own volume changing over time. That's a lot of oscillators. This is exactly the problem FM synthesis (next module) solves so cleverly — it manufactures a whole forest of harmonics from just two oscillators. But first, feel additive synthesis directly. Drag the harmonic sliders below to mix your own tone; the scope shows the wave you're building and the spectrum shows your recipe.

Here is the idea that defines this course. Take two sine oscillators. Call one the carrier — it's the one you actually hear. Call the other the modulator. Now, instead of letting the carrier play a steady pitch, use the modulator's output to wobble the carrier's frequency up and down, very fast. That's it. That's frequency modulation — FM synthesis, discovered by John Chowning at Stanford and licensed to Yamaha, who put it in the chip inside your Genesis.

Why is that powerful? Because when you wobble a sine's pitch fast enough, the ear stops hearing “wobble” and starts hearing new harmonics — a rich, buzzy, metallic spectrum that a plain sine never had. Two oscillators do the work that additive synthesis (Module 03) needed dozens for. Two numbers steer the whole sound:

Play with the two-operator FM lab below — this is the single most important lab in the course. Drag ratio and index while it plays and watch the spectrum on the right sprout new harmonics in real time. Try ratio 1 and 2 (warm, musical), then a non-integer like 1.41 (clangy bell), and slide the index from 0 (pure sine) to full (harsh buzz). Everything the YM2612 does is this, four oscillators deep.

So far our tones just switch on at a steady volume. Real notes don't. Pluck a string and it snaps loud then rings away; bow it slowly and it swells in and holds. That shape of loudness over time is the note's envelope, and it's a huge part of why two instruments playing the same pitch sound completely different.

The classic way to describe an envelope has four stages, abbreviated ADSR:

This matters enormously on the Genesis because its FM chip gives every one of the four operators its own envelope — so the brightness of an FM sound can change over the life of a note (Module 09). A piano's bright attack that mellows as it rings? That's a modulator's envelope decaying faster than the carrier's. For now, get the basic shape in your ear. Move the four sliders and watch the envelope redraw live, then play a note shaped by it. Try a percussive pluck, then a slow pad.

Not every sound has a pitch. A hi-hat, a snare, an explosion, a rush of wind — these are noise: every frequency at once, in random proportion, with no repeating wave to latch a pitch onto. Where an oscillator makes an orderly wave, a noise source makes a chaotic one. On a spectrum it's not a few tidy bars but a solid wall.

Raw noise on its own is just static. Percussion comes from two things we already have: a filter and an envelope. A filter carves the noise into a colour — keep only the very high frequencies and it hisses like a cymbal; keep a mid band and it cracks like a snare. Then a fast envelope (near-instant attack, quick decay, no sustain) turns the steady hiss into a sharp hit.

This is doubly relevant to the Genesis, because it has two ways to make noise. The PSG (Module 11) has a dedicated noise channel — a stream of pseudo-random bits — perfect for cheap hats and zaps. And the FM chip's channel 6 can be switched into an 8-bit DAC mode (Module 10) to play back short recorded drum samples. Below, build percussion the classic way: pick a drum, sweep the filter, and hear a hat become a snare become a tom.

The heart of Genesis sound is the YM2612, Yamaha's FM chip (its family name is OPN2). It runs the exact FM trick from Module 04, but scaled up: it has 6 independent channels (so six notes at once), and each channel is built from 4 operators instead of two. An operator is just one sine oscillator with its own frequency ratio, output level and envelope — the carrier/modulator of Module 04, generalised.

With four operators per voice you can build far richer sounds than a single modulator/carrier pair: you can stack modulators three deep for screaming metallic leads, or run several carriers in parallel for fat, organ-like pads. Exactly how the four operators are wired — who modulates whom — is chosen from eight fixed patterns called algorithms, which is the whole of Module 08.

A few more facts worth carrying forward. Output is stereo, but only as a switch: each channel can be sent to the left, the right, or both — there's no fine panning. The chip is clocked from the main system and produces samples at roughly 53 kHz. And it has a global LFO shared by all channels for vibrato and tremolo. Press the buttons below to hear three four-operator patches the real chip is famous for — a punchy bass, a bright brass stab, and a glassy bell — all synthesised live here by the same FM maths.

Four operators are only useful if you can connect them. An algorithm is a fixed wiring diagram that says which operators are modulators (they bend another operator's pitch) and which are carriers (their output is actually heard). The YM2612 offers eight of them, numbered 0–7, and they run from “one long chain” to “four separate voices added together.”

The two ends of the range tell the whole story. Algorithm 0 is a single stack: OP1 modulates OP2 modulates OP3 modulates OP4, and only OP4 is heard — deep, complex, evolving timbres, perfect for basses and leads. Algorithm 7 is the opposite: all four operators are carriers, simply summed — no FM at all, just four sine waves added, which is additive synthesis (Module 03) and makes soft, organ-like or bell tones. The six algorithms in between mix stacks and parallel branches in every useful combination.

One more ingredient: OP1 (and only OP1) can feed itself — its own output loops back to modulate its own input. This is feedback, and turning it up gradually pushes a clean tone toward buzz and eventually noise — a cheap way to add grit or even to fake a noise source. Pick an algorithm below: the graph redraws to show the routing (carriers glow gold), and pressing play runs a real four-operator FM voice wired exactly that way, so you can hear the difference the plumbing makes.

Module 05's ADSR was the friendly version. The YM2612 uses a close cousin with Yamaha's own names, and — crucially — every operator has its own. Because a modulator's envelope controls how much it modulates over time, an operator's envelope doesn't just change volume; on a modulator it changes the whole brightness of the sound as the note evolves. A hard, bright attack that settles into a mellow tone is simply a modulator whose envelope decays faster than the carrier's.

The chip splits ADSR's “decay” into two rates and adds a level control, giving five envelope parameters plus one master level per operator:

The lab gives you a four-operator voice (algorithm 2 — two modulators into a carrier). The TL board sets each operator's level; drop a modulator's TL and the tone gets purer, raise it and it gets buzzier. The shared envelope sliders (AR/D1R/D2R/RR + SL) shape how the whole patch moves. Try a fast attack with a quick D1R on the modulators for a piano-like “bright then mellow,” then a slow attack for a pad that blooms.

Three features turn the raw FM engine into a full instrument. The first is the LFO — a Low-Frequency Oscillator, a single slow sine (a few Hz) shared by all six channels. It's too slow to hear as a pitch; instead it gently wobbles other things. Routed to pitch it's vibrato (PM, phase modulation); routed to volume it's tremolo (AM, amplitude modulation). Each channel chooses how much of each it wants.

The second is feedback from Module 08 — OP1 modulating itself — which we'll revisit in the lab as a grit control. The third is the most surprising: the DAC channel. At the flip of a register bit, channel 6 abandons FM entirely and becomes a plain 8-bit DAC: the driver writes raw sample bytes to it as fast as it can, and it plays them back directly. That's how the Genesis produced drums, sampled hits and the famous grainy speech (“SEGA!”) — at the cost of losing an FM channel and pinning the Z80 or 68000 busy feeding it.

The lab has two halves. The LFO half takes a sustained FM brass tone and lets you dial vibrato (PM) and tremolo (AM) depth and speed — hear the tone come alive. The DAC half synthesises a short 8-bit drum sample in your browser (decaying noise + a sine thump, quantised to 8 bits like the real thing) and plays it through a simulated DAC channel.

Alongside the mighty FM chip sits a tiny veteran: the SN76489, a Texas Instruments PSG (Programmable Sound Generator) carried straight over from the Sega Master System. It's almost comically simple next to the YM2612 — but Genesis composers used it constantly for chiptune melodies, arpeggios, sparkle and hi-hats sitting on top of the FM.

It has exactly four channels: three square-wave tone channels and one noise channel. Each tone channel has a 10-bit frequency and a 4-bit attenuation — a volume control with just 16 steps, where each step drops the level by 2 dB and step 15 is silence. That's the whole per-channel state: a pitch and one of 16 volumes. The noise channel is a LFSR (linear-feedback shift register) that can run in a “white” hiss or a “periodic” buzzy mode, and can borrow tone channel 3's pitch to tune its noise.

Build a little PSG arrangement below: three square channels (set each one's note and 4-bit volume) plus the noise channel for a hat. Press play and it arpeggiates the three tones with the noise ticking underneath — a whole chiptune backing from four of the simplest voices imaginable.

The sound chips are just registers; something has to write notes into them, in time, sixty times a second. On the Genesis that something is a whole second CPU: a Zilog Z80 running at about 3.58 MHz with its own 8 KB of RAM. It's the same chip that was the Master System's main processor — which is also how the Genesis stays backwards-compatible with Master System games.

In a Genesis game the Z80's usual job is to run the sound driver: a small program (SMPS/GEMS were the popular ones) that reads the music data, converts notes into YM2612 and PSG register writes, ticks envelopes and, when needed, spoon-feeds bytes to the DAC channel. The main 68000 just sends it high-level cues — “play track 3,” “stop” — and gets on with the game. It's the same division-of-labour idea consoles use everywhere: a dedicated processor for sound so the main CPU isn't stuck counting envelope timers.

There's a catch that shapes Genesis audio programming. The Z80 and the 68000 partly share the bus to the sound hardware, so they can't both touch it at once. When the 68000 needs to reach across — to load new music, say — it asserts a Z80 bus request, waits for the Z80 to let go, does its business, then releases it. Get the timing wrong and you get stuck notes or crashes — a classic Genesis homebrew bug. Watch the handshake play out below.

To emulate the YM2612 you face a fork in the road. You can reimplement FM from the datasheet — build operators, envelopes and algorithms in clean C and run them at the output rate. This is fast and sounds broadly right; it's how many older emulators (and the long-serving MAME “ym2612” core) worked. Or you can go the other way and model the actual chip, gate by gate.

That second path is Nuked-OPN2, by Alexey Khokholov (nukeykt). It was built by decapping a real YM3438 (the CMOS sibling of the YM2612), tracing the silicon, and reproducing the chip's internal 24-stage operator pipeline cycle by cycle. The result is sample-accurate: it doesn't just approximate the sound, it reproduces the chip's exact internal timing, its rounding, and — critically — its bugs. Genesis Plus GX and BlastEm both offer Nuked-OPN2 as their high-accuracy YM2612 core.

Why go to such lengths? Because the YM2612 is full of behaviour that isn't in any datasheet — quirks that games unknowingly relied on, so that a “correct” textbook implementation actually sounds wrong. The most infamous is the DAC “ladder effect,” a distortion baked into the analogue output stage that a clean digital model simply doesn't have. Reproducing quirks like that is the entire subject of the next module — and the reason die-level emulation exists.

A textbook FM chip would be easy to emulate. The real YM2612 is a minefield of quirks, and getting them right is the difference between “sounds like a Genesis” and “sounds like a cheap FM app.” Here are the big ones.

The DAC “ladder effect”

The most famous quirk. The YM2612's output DAC is slightly non-linear right around zero: because of how its digital-to-analogue conversion is built, there's a small gap straddling the zero crossing — positive and negative values are nudged apart. On quiet or bass-heavy sounds this ladder effect adds a characteristic gritty buzz — and famously, it's louder on quieter notes. Composers wrote basslines that leaned into it. A clean digital model omits it and sounds sterile; the later surface-mount YM3438 actually fixed it, which is why some Genesis models sound subtly different.

You can hear it in the lab below: the same soft FM bass, rendered clean versus with the ladder crossover distortion modelled. Listen for the extra edge and buzz on the ladder version — that grit is the sound of a hardware bug, faithfully reproduced.

The other traps

The SN76489 is far easier to emulate than the FM chip, but it has its own little authenticity details. Its square waves come from simple counters, so those are trivial — the interesting parts are the volume table and the noise generator. The 4-bit attenuation isn't linear: each of the 16 steps is 2 dB, so an accurate emulator uses a lookup table of the real output voltages rather than a naive “volume ÷ 15.” Get that table wrong and PSG balance sounds off.

The noise channel is an LFSR with a specific bit width and feedback tap, and different SN76489 variants used slightly different taps — so Genesis Plus GX carries the Sega-flavoured LFSR to make the noise's exact timbre match real hardware. There's also a subtle detail where writing the volume produces a tiny DC step; some cores model it because a few tunes rely on it for click-drum effects.

That balancing act is the mixer's job, and it's where emulators finish the audio path. The YM2612 produces samples at about 53 kHz and the PSG at a different clock; both get summed and resampled to whatever your sound card wants (usually 44.1 or 48 kHz). Emulators differ in how carefully: BlastEm is known for a low-pass reconstruction filter and band-limited output that mimics the console's own analogue tone, while the relative FM-to-PSG mixing level is a small but real balance choice each core makes. Get the resampling lazy and you re-introduce the aliasing from Part I; do it well and it sounds like the machine.

You now have the full picture, so let's make it hands-on. Grab Genesis Plus GX (standalone or as a RetroArch core) or BlastEm, load a game, and dig into the audio options — every one maps to something you can now explain:

• YM2612 core: Nuked-OPN2 vs. MAME/fast — the Module 13 choice. Nuked is bit-exact (and gives you the ladder effect); the fast core saves CPU. On weak hardware, pick fast.
• “Ladder effect” / DAC distortion — Module 14. Some cores let you toggle it; on for authentic YM2612 grit, off for the cleaner YM3438 sound.
• Low-pass / audio filter — Module 15. BlastEm's reconstruction filter softens the highs the way the real console's analogue output did.
• PSG volume / FM-PSG balance — Module 11 & 15. If the squares sound too loud or too buried, this is the knob.

Final exam — six broken soundtracks

Six situations, straight out of how the chips really behave. You're the one at the keyboard: pick the answer that fits. Every one points back at the module that taught it.