Manually Placing Harmonics and Harmonizing Tones

This is a technique that I’ve iterated on for many years now. It’s a technique that I’m forever drawn to, and for me it has two applications:

1. When I want to give a tonal quality to something that doesn’t yet have one, and
2. When a sound already has a tonal quality, and I want to enrich it

The demonstration for this is in the context of sound design to picture, however, I have used this technique in a professional context to enhance drum cymbals, guitar resonances/feedback and create a piano ‘feedback’ effect.

The technique is a bit mathsy and nerdy, but we all love that, right? And I want to point out that the results are very different to distortion/saturation plugins.

The differences are:

• As you’ll see in the demonstration, tonal qualities can be created where there were none previously
• Musical intervals below an octave do not appear in any harmonic series and as such, this technique gives different qualities to saturation/distortion

The concept is this that musical intervals can be formulated using the following:

(number of semitones above) = (frequency) x (2 ^ (semitones / 12))

                note that ^ means ‘to the power of’

For example. If you want to find the frequency of B flat above A 440:

Bflat = 440 x (2 ^ (1 / 12))

Bflat = 466 Hz

For sound design enhancement, I generally gravitate towards the ‘Perfect’ intervals, which are:

Perfect 4th (5 semitones up)

Perfect 5th (7 semitones up)

Octaves (12 semitones up)

Using the base frequency of A 440 Hz as an example for these:

Perfect 4th up (D) = 440 x (2 ^ (5/12)) = 587 Hz

Perfect 5th up (E) = 440 x (2 ^ (7/12)) = 659 Hz

Octave up (A) = 440 x (2 ^ (12/12)) = 440 x 2 = 880 Hz

I’m so fascinated by this technique that I even built an app that calculates these for me:

In the following video, I use this technique to give a tonal quality to an otherwise noisy whoosh sound. The video uses the following frequency and harmonies (and just a final word of pedantism: a Perfect 5th up is not a harmonic, it’s a harmony, hence why this technique gives very difficult result to distortion, which produces harmonics, not harmonies):

Base Frequency: 600 Hz

Perfect 5th above = (600 * (2^(7/12))) = 899 Hz

Octave above 600 = (600 * 2) = 1200 Hz