# A technique for simulating an octave below the 5th of the power chord

In this video:

John Petrucci says: "He's playing a 7 string song on a 6 string guitar.. that song utilizes the lower 7th string, but there's a trick on the guitar where if you play a power chord and you finger the 5th below the root, if you play that a certain way the octave lower root will sound. It's like a weird aural illusion."

What is he talking about? How can I recreate this?

• The phenomenon is called fundamental tracking. It cannot be due to the wave interference alone as that is a linear process and will never create a sub-harmonic. However, the ear is non-linear and the brain is programmed to identify the harmonic sequence. So, if you feed the ear a sequence of tones that do NOT obey the harmonic sequence the brain tries to ID an f0 such that the rest of the tone fit the sequence relative to that f0. The brain then thinks that this is the fundamental of the sequence. – ggcg Oct 11 '19 at 11:46
• However, there is more to the story than that and each of the notes has their own set of harmonics. It is not entirely clear at first glance that those harmonics will NOT interfere with the tracking process as the brain will hear those and use them to ID each note as an f0 in their own right. If you really hear the sub-harmonic then it works. – ggcg Oct 11 '19 at 11:48

Technique

This video by guitarist Peter Hodgson seems to be describing the same thing, and the technique he uses in reasonable detail.

It seems to be as straightforward as Petrucci describes. Assuming standard tuning, playing a power chord rooted on the A string, but also fretting the lower 5th interval on the E string.

(low to high)

• E: 5
• A: 5
• D: 7
• G: 7
• B:
• e:

The Science (possibly)

The brain perceives the pitch of a tone not only by its fundamental frequency, but also by the periodicity implied by the relationship between the higher harmonics; we may perceive the same pitch (perhaps with a different timbre) even if the fundamental frequency is missing from a tone.

A low pitch (also known as the pitch of the missing fundamental or virtual pitch) can sometimes be heard when there is no apparent source or component of that frequency. This perception is due to the brain interpreting repetition patterns that are present

That is to say, even if your root note is missing, the brain can still "hear" it. Possibly (my uneducated guess) because we are trained by the musical culture to expect it.

It's about the period of the resulting wave. If you play a root note and its fifth dropped by one octave (i.e., a perfect fourth below, e.g., a C with a G below) then the frequencies are

`3/4*f, f`

if `f` denotes the frequency of the C note. The question is now what the frequency of the resulting wave will be. We know that periodic waves can be represented by a weighted sum of (phase-shifted) sinusoids with integer multiples of the fundamental frequency (Fourier series). So we just have to figure out if there's some fundamental frequency `f0` that results in the two frequencies `3/4*f` and `f` as integer multiples of `f0`.

We get

`3*f0,4*f0`

with `f0=f/4`. So the fundamental frequency `f0` of the resulting wave corresponds to a C that is actually two octaves below the C that was played. Even if that low C is not actually played, it is, and can be perceived as, the fundamental frequency of the resulting wave.