# [sdiy] frequency shifter

rburnett at richieburnett.co.uk rburnett at richieburnett.co.uk
Fri Mar 13 12:51:59 CET 2020

```To add to Gordon's frequency shifter explanation...

The reason why a frequency shifter often sounds odd is because it breaks
the harmonic series of typical sounds.  For example if an instrument
plays an "A" at 220Hz, the sound typically consists of a series of
harmonics at 220, 440, 660, 880, 1100Hz, etc.  But if you frequency
shift this up by say 50 Hz, those spectral components get shifted to
270, 490, 710, 930, 1150Hz, etc.  These are clearly now not in a simple
harmonic relationship!  This sounds dissonant or "metallic" to our
hearing because we expect sounds that typically have an approximately
harmonic spectrum.

This is in contrast to a pitch shifter that multiplies the frequencies
of all of the harmonics by the same scaling amount.  This preserves the
harmonic series, just shifted to a different fundamental frequency,  and
therefore sounds much more musical and natural.

I think a lot of terminology surrounding frequency shifting is confusing
because the same thing is referred to in different fields by different
names.  e.g. Pitch shifting is achieved by multiplying signals together,
but it doesn't result in a multiplication of the frequency, it results
in a linear frequency shift.  Also, this operation can be referred to as
multiplying, heterodyning, mixing, modulation, etc. depending on what
engineering background the person is coming from!

Unfortunately, it is hard to understand exactly what is going on in a
pitch shifter without stepping into a bit of maths and talking about
trig identities, complex vectors, positive and negative frequency, etc.

-Richie,

On 2020-03-12 22:09, Gordonjcp wrote:
> On Tue, Mar 10, 2020 at 10:51:12PM -0400, ColinMuirDorward wrote:
>> Also, can you explain like I'm stupid the difference between pitch and
>> frequency shifting? It sounds like a linear vs exponential thing, but
>> must
>> be more to it than that...
>
> It is indeed a linear versus expo thing.  Pitch shifting is what you
> get when you speed tape up - double the speed, double the pitch.  An
> octave jump is still an octave, it's just both are an octave higher
> than before.  You multiply the frequency.
>
> a low A on a guitar string at 110Hz shifted up 110Hz would be 220Hz,
> an octave up.  But, if you fed in 220Hz you'd get 330Hz out, an E
> instead of an A, and 330Hz in would give you 440Hz, an A, and 440Hz in
> would give 550Hz or a slightly flat C#, and 550Hz would give you an E
> again, and so on.
>
> You can imagine how mangled that would make things sound.
>
> Or actually, you don't need to:
>
> https://minecraft.gjcp.net/9970kHz.ogg
>
> This is an AM shortwave radio station being tuned in and out on an SSB
> receiver, which is really just a big Bode frequency shifter.

```