FM Synthesis – Ratios

Ratios. Great, More Math…

In the last video, we went over the basics of Frequency Modulation (FM) Synthesis and how it worked. This time we’re going to dive into just the ratio section in a bit more detail. This section is a crucial part to using FM synthesis, so you have to really understand what’s going on. Unfortunately, FM Synthesis can get very math heavy, and this section is probably the worst in that regard, so buckle in… (unless you like math, then this should be fun!)

Depending on which plugin or hardware synth you’re using, the ratio section may look different from mine, but the general idea is all the same. Try to take my explanation here and apply it to your synth. If you still can’t figure it out, then the manual will be a super helpful resource. You can also leave a comment on the video or send me a message and I’ll do what I can to help you out.


How Do Numbers Make Better Sounds?

If we look at the main ratio section in FM8, you’ll see basically just a bunch of numbers. There’s the Ratio and Offset headers, then under them is a list of numbers. At first glance this may seem useless, but this is one of the two most important parts of FM Synthesis. (The actual routing is the other, in my opinion.)

The ratio section is how each operator will play it’s note, either to the output or to modulate a carrier. At 1, it plays the exact note you press on your keyboard or through Midi. If you move that up to 2, the note will play an octave higher. Note that this does not make the output note an octave higher, but changes the sound by modulating the carrier’s signal. A higher octave note will make it modulate faster, and the affected output will have higher harmonics added. If you then move the modulator’s ratio up to 3, it will not actually be another octave higher. This is something a lot of people get wrong at first. These numbers are not linear, but more exponential. (Math is not my strong suit so that may be the wrong term, but you get the picture.) So if you start at 1, the next octave is at 2, then 4, then 8, then 16, etc… doubling each time. The reverse is also true, starting at 1, the next lower octave is 0.5, then 0.25, then 0.125, etc… dividing by 2 each time.



This can get confusing quickly, but if you just stick to those octaves you’ll get sounds that work no matter what note you play. If you start tweaking things or just making an interesting sound on it’s own, it’s very easy to change the fundamental pitch so much that everything you play is way off key and sounds terrible! I’ve made this mistake before, and it took me a while to figure out what I did wrong, so make sure you always have a second track to compare your FM sound with to make sure it stays in key.

If you adjust the ratio by just a tiny amount, say 2.0055 or so, you can start to get some nice phasing or dissonance. This can help make your sounds a bit less clean, and give them some character. If you’re using a lot of modulators, I wouldn’t do this on too many of them though, or your sound could start to sound out of tune easily. One or two is enough to give it some grit though.


Comparing Another Synth: Ableton Live’s Operator

Now that you’ve seen how the ratio section in FM8 works, let’s take a look at another synth and compare them a bit.

This is the ratio section of Operator, Ableton Live’s built in FM synth. Instead of the rows of numbers in FM, we get 2 knobs here. The Coarse and Fine knobs are how we adjust the ratio for each operator. Coarse changes the same thing as the whole numbers in FM8, so that’s how you change octaves easily. Starting at 1, it can go up to 2, 4, 8, 16, and all the whole numbers in between. Remember that not all whole numbers are an octave apart! The Fine knob ranges a whole octave, which can be confusing, but if you have the Coarse knob set to 4, then the Fine knob would cover from 4 to 8. I would always try to keep the Coarse knob on an actual octave number until you really get a handle on this stuff works, otherwise you could easily end up with something that sounds way out of key.


Get Out Your Calculators

Now that we’ve covered how ratios work in FM synthesis it’s time for you to start using it to make your own sounds, and start branching out from presets or the default ratios!





Beginner – Use whatever FM Synth you have available and set one operator to go to the output and one other to modulate that carrier. Stick to both sine waves for now. Now play a note a few times to see how it sounds. Start to raise the modulator up an octave, and try to go up 3 or 4 octaves. Notice how the sound changes as you go up octaves. Do the same thing, but go down a couple octaves now. Next, pick an octave you liked and play different notes up and down the keyboard. Pay attention to where the notes sound really good and where they sound bad. Sometimes playing higher notes don’t sound good at all, but the lower ones sound great or vice versa.

Advanced – Using your favorite FM synth, follow the same setup as in the beginner action step (with just two operators) but this time try to make some sounds using a 3rd or a 5th with the modulator. You may need to go back to the video for the examples I put on the screen, or use some math to figure out the exact number to use. Next set up a second track and have both tracks play the same notes and pattern at the same time. Create 3-4 patches that sound good even with the other track playing the same notes. (This helps you make sure your patch stays in key.) This requires a lot of attention and a very good ear, so don’t worry if you find it difficult at first, keep working at it!

Question: Did you know how to use ratios at all before this video? How about the fact that in the synths we used today that octaves are not linear? How do you feel about using math to create your sounds?