How to generate odd and even harmonics in Reason?

Almost all devices in Reason that are capable of overdriving a signal will generate ODD and/or EVEN overtones/harmonics. Here’s how.

Almost all devices in Reason that are capable of overdriving a signal will generate ODD and/or EVEN overtones/harmonics. Most do both, some do either ODD or EVEN harmonics. The good old Jack Endino article is highly recommended when you are not familiair with these concepts. But well, I will explain this as easy as I can in the blogpost below as well. Jack states that tape-devices generate ODD overtones and that tube can do both ODD and EVEN overtones.

EVEN harmonics are frequencies which are 2, 4, 6, 8 times and so on multiplications of the main/root frequency.
ODD (also called UNEVEN) harmonics are 3, 5, 7 times and so on multiplications of the main/root frequency.

So the difference between the two is either an even number as multiplier or an uneven number as multiplier. Simple stuff right?

The ODD and EVEN list

I often use a pure sine wave using the fantastic Wavetable OSC in Thor to generate a A3/440 Hz tone. The EVEN and ODD harmonics of A3/440 Hz then are:
#1 A3 (main/root)
#2 EVEN – A4 – octave
#3 ODD – E5 – perfect fifth
#4 EVEN – A5 – 2 octaves above
#5 ODD – C#6 – a major third 3 octaves above
#6 EVEN – E6 – perfect fifth 3 octaves above
#7 ODD – G6 – dominant seven 3 octaves above
#8 EVEN – A6 – 3 octaves above

Here’s a picture made with Ableton Spectrum:


The numbers as you can see correspond with the list above. The first 3 harmonics (2, 3 and 4 as multipliers) are super nice, only octaves and a perfect fifth! But as you can see all tones are musical frequencies which correspond to the note-names of our modal system.

There’s a lot of discussion about what sounds better EVEN or UNEVEN/ODD? Check out this video for example:

In my opinion it’s about the mix between ODD and EVEN harmonics which creates the best saturation. And the level at which they are generated. Although I only mentioned the first 7 harmonics, most saturation devices will generate overtones which will go much higher than that. Some even go beyond 20 kHz (beyond the 10th octave!) and might even cause aliasing issues!

Very high harmonics might result in a thin sound. So adding a low pass filter before distortion can be super useful, using the lovely Reason Pulveriser for example. And don’t forget that using a high pass filter before overdrive is a great way to minimise nasty intermodulation.

Only EVEN harmonics?

How to generate only EVEN harmonics in Reason? The Shaper in Thor can deliver. It needs a special trick to open the Filter 1 gate in Thor so you can run an audio signal through it. And since it’s MONO you need 2 Thors to process STEREO input.

The Rectify Shaper will deliver only EVEN harmonics. And if you turn the Drive all the way up it will kill the 1st frequency, the root frequency! It’s as if you pitch shift the whole audio signal an octave! ๐Ÿ™‚ Kinda cool, right?

The Unipulse Shaper will also deliver only EVEN harmonics. But it will always kill the 1st, the root frequency no matter the Drive amount. Its saturation process generates more high frequencies than the Rectify Shaper. In short: Rectify is warmer than Unipulse.

Only ODD harmonics?

The Bipulse Shaper in Thor will deliver only ODD harmonics. Same as The Echo using its OVDR setting. And the Synchronous device at Dist 1 and Dist 2 settings. And also the Soft ShaperHard Clip ShaperSaturate Shaper and Sine Shaper in Thor will only deliver ODD harmonics.

Great for getting some lovely tape like saturation!

The Pulveriser has some nifty saturation features: it generates only ODD harmonics at lower drive settings (or when you’re pushing its input not too hard) but will start adding EVEN harmonics to the signal as well when you raise the drive/input. So it can do ODD or ODD+EVEN harmonics depending on the amount of drive/input.

Please don’t be blinded with science! I am not either. Sending a 440 Hz tone through devices is not a real life kind of thing you want to do for a long time. You better apply some saturation to cool sounding stuff. Just experiment, using your ears. Apply some overdrive to guitars, bass, drums, vocals, anything really. Overtones are lovely additions for a signal.


Hi Marco, thanks for you articles. I found a litttle error in this one.

“The Rectify Shaper will deliver only EVEN harmonics. And if you turn the Drive all the way up it will kill the 1st frequency, the root frequency! Itโ€™s as if you pitch shift the whole audio signal an octave! ๐Ÿ™‚ Kinda cool, right?”

This is false. A signal having its fundamental harmonic removed is not pitch shifted. Its timbre changes of course, but its perceived pitch remains the same: the frequency of the fundamental harmonic, even if it has no energy.

Think about a high-pass filter: it removes the first harmonics of a signal, altering its timbre, but do not change the frequency or shift the pitch, even if its perception becomes more difficult as the cutoff frequency increases.

yes that’s what I mean. not pitch shifted but since the root falls away it gives you the feeling as if the pitch was shifted up an octave.

OK, but “pitch shift the whole audio signal” may not be the best way to describe this phenomenon. IMO, the problem with this expression is that it’s confusing for readers and may lead them to the common misconception that suppression of the fundamental frequency is the same thing as pitch shifting.
I would describe what happens here as a timbre alteration caused by suppression of the fundamental and addition of harmonics a few octaves above the fundamental, making the note pitch more difficult to identify, using an analogy with a blurred picture. And I admit it’s probably a clumsy description, as English is not my primary language. ๐Ÿ™‚

Yes, but we’re not talking about the same thing. I realize that I haven’t been precise enough in my first message, sorry. I have nothing against your description of the Rectify Shaper. It’s just the analogy between removal of the fundamental and pitch shifting that I found a little bit problematic.

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