Two oscillators and a sideband
FM synthesis uses ordinary sine oscillators. One is the carrier and produces the pitch you hear. The other is the modulator, and its output is added to the carrier frequency input rather than its amplitude input. That single change is everything: modulating amplitude produces tremolo, modulating frequency produces new frequencies.
The result is called sideband formation. If a 440 Hz carrier is modulated by another 440 Hz sine, you get components at 0 Hz, 880 Hz and a component above and below. Raise the modulator to 880 Hz and the sidebands fall at 440 plus or minus multiples of 880, which puts them at 1320 and 1760 Hz, all sitting on the harmonic series of the fundamental. Integer ratios stay harmonic. Fractional ratios do not, and that is where the metallic, bell-like and mallet colours come from.
| Carrier:modulator | Character |
|---|---|
| 1 : 1 | Hollow, clarinet-like, octave-rich |
| 1 : 2 | Bright, brass-like, harsh at high index |
| 2 : 1 | Same spectrum, one octave lower |
| 3 : 2 | Inharmonic, bell and mallet territory |
| 1 : 1.41 | Metal, unstable, clanging |
| 1 : 7 | Buzz, atonal, effective as a layer |
Read that table as spectral description, not as recipe. A ratio of 3:2 produces a spectrum in which almost nothing is an exact multiple of the fundamental, which is exactly the description of a struck bar. It will not sound like a bell unless the index envelope also shapes it.
Ratios choose the character, the index chooses the cost
The modulation index is the second control, and it is the one that makes FM expensive. It is measured as the peak frequency deviation of the carrier divided by the modulator frequency. At an index near 1 the first sideband pair sits about 6 dB down. Above 4 you get a wide, bright cluster. Above 14 the signal is bright enough to be unpleasant and aliasing is severe.
The trick that defines most classic FM sounds is an index envelope rather than a static index. An electric piano voice uses a high index at the attack, where the bell transient lives, and drops to a low index within a fraction of a second. The result is bright on the front and mellow underneath, which is why an FM electric piano sits so easily in an arrangement.
- Index below 1 keeps the sideband cluster narrow and the tone clean and sine-like.
- Index 1 to 4 is the working range for pads, keys and basses.
- Index above 10 is for percussion layers and short transients, not sustained notes.
- Ratios above about 8 push partials past 5 kHz at ordinary keyboard pitches.
Four operators and the routing
Two-operator FM is a laboratory. Real instruments use more oscillators, each able to modulate or be modulated, and each able to modulate itself. Feedback, where an operator modulates its own frequency, raises the effective index over time and produces a slow bloom that no fixed index setting reaches. It also self-oscillates if pushed, which is useful and which will surprise you during a mix.
The practical lesson is to treat the algorithm as part of the timbre rather than as a routing puzzle. A stack of four in series gives a dense, bright, aggressive voice. Three parallel carriers modulated by one operator give a wide, organ-like chord source. Four operators in a chain with feedback at the end gives a bell. All four of those are different instruments, and they need completely different mixing decisions.
This is also where FM stops being a synthesis method and becomes an instrument design method. Once the operator count and the feedback path are fixed, you are not shaping a filter any more. You are deciding what the instrument physically is, and the mix decisions follow from that.
What FM costs you
Aliasing is the first cost. Because the modulator sweeps the carrier continuously, partials are generated at frequencies that a static filter would never produce, and those frequencies do not respect the Nyquist limit. They fold back. The fix is to oversample the oscillator itself, not the plugin output, because by the time the fold has happened in the output stage it is already a component of the signal and cannot be undone.
Unpredictability across the keyboard is the second. A subtractive patch keeps its spectrum shape as you move through the registers. An FM patch does not, because the sideband cluster moves in absolute frequency while the harmonic structure stays fixed, so the same patch can be polite at C3 and shrill at C6. Check the top of the range before writing the bass line.
The mitigations are unglamorous and they work. Oversample. Write bright patches an octave above where they belong and low-pass them back. Layer FM under something with a fixed spectrum rather than asking it to carry the melody alone. And measure: an FM patch that sounds enormous in isolation frequently measures far smaller than the sine it is built from, because the sidebands are spread rather than stacked.
The bottom line
FM is a way of describing a spectrum rather than filtering towards one, which makes it the fastest route to bells, mallet and Rhodes tones that no subtractive patch reproduces. The cost is aliasing and unpredictability, and both are worth budgeting for rather than discovering in the export.
Compare the same patch across a tuning
432Hz MASTER retunes the whole production by one ratio, so the sideband relationships inside an FM patch stay intact and only the absolute pitches move.
Frequently asked questions
What does the operator ratio actually control?
It controls where the sidebands land. A 1:1 ratio puts sidebands an octave apart and gives a hollow hollow tone; 1:2 gives a bright hollow tone an octave down; 3:2 gives an inharmonic bell-like spectrum with no partial that is an exact multiple of the fundamental.
What is the modulation index?
It is the peak frequency deviation of the carrier divided by the modulator frequency, and it is how wide the sideband cluster spreads. Around 1 gives roughly a 6 dB first sideband pair; above 4 the spectrum gets wide and bright; above 14 it stops sounding like a musical note.
Why does FM alias so badly?
Because the modulator sweeps the carrier continuously, so partials are born and die at high rates that a fixed filter could never produce. The result is wideband content that no longer sits inside the Nyquist limit, and it folds. Oversampling before the oscillator is the fix.
Is FM or subtractive better for mixing?
Subtractive is easier to place because the spectrum changes predictably as you filter it. FM changes its spectrum with the note you play, so bright patches can jump between registers. Write it an octave up and low-pass it, or use it as a layer under something with a fixed spectrum.