Maximizing Your Mix: Leveraging Odd and Even Harmonics for Pitch, Waveform, and Transient Clarity in Music Production

Odd harmonics and even harmonics are very important concepts in music and acoustics. They are components of the complex timbres produced by instruments and play a key role in shaping the character and texture of sounds. This post will discuss what odd and even harmonics are, and how they create different acoustic effects. For more information on harmonics, refer to the post below.

Link to Harmonics document

Odd Harmonics? Even Harmonics?

Harmonics

Odd harmonics are harmonics that appear as odd multiples of the fundamental frequency. For example, in a note with the fundamental frequency of A4 (440Hz), the odd harmonics could be 1320Hz (3 times), 2200Hz (5 times), 3080Hz (7 times), and so on. These harmonics can give the sound a ‘rough’ or ‘sharp’ texture, often making the timbre of an instrument ‘sharper’.

On the other hand, even harmonics are harmonics that appear as even multiples of the fundamental frequency. In the same note of A4, even harmonics could be 880Hz (2 times), 1760Hz (4 times), 2640Hz (6 times), etc. Even harmonics typically provide a ‘smoother’ and ‘more harmonious’ feel.

So, why do these differences occur, and what effects do they produce? Let’s explore this in more detail.


Are Odd Harmonics Sharp and Even Harmonics Smooth?

Harmonics

It’s often said that odd harmonics are sharp and even harmonics are smooth. In reality, odd harmonics tend to sound much rougher. To understand this, it’s useful to look at harmonics from the perspective of musical notes. Below is a brief summary of the pitches of odd and even harmonics based on C4.

Odd Harmonics:

  • 1st Harmonic (Fundamental): C4 – 261.63 Hz
  • 3rd Harmonic: G5 – 784.89 Hz (3 times C4)
  • 5th Harmonic: E6 – 1308.15 Hz (5 times C4)
  • 7th Harmonic: B♭6 – 1831.41 Hz (7 times C4, can be slightly lower in tuning)
  • 9th Harmonic: D7 – 2354.67 Hz (9 times C4)
  • 11th Harmonic: F♯7/G♭7 – 2877.93 Hz (11 times C4, can be slightly higher in tuning)
  • 13th Harmonic: A7 – 3401.19 Hz (13 times C4)

Even Harmonics:

  • 1st Harmonic (Fundamental): C4 – 261.63 Hz
  • 2nd Harmonic: C5 – 523.26 Hz (2 times C4)
  • 4th Harmonic: C6 – 1046.52 Hz (4 times C4)
  • 6th Harmonic: G6 – 1567.98 Hz (6 times C4)
  • 8th Harmonic: C7 – 2093.04 Hz (8 times C4)
  • 10th Harmonic: E7 – 2618.30 Hz (10 times C4)
  • 12th Harmonic: G7 – 3141.96 Hz (12 times C4)

c7
C7 chord

While the actual pitches might slightly differ, the pitch of odd harmonics can be seen to form a C7 dominant chord with tension notes.

C
C major chord

In contrast, even harmonics are mainly composed of perfect intervals and major thirds, akin to the notes of a C Major chord.

Thus, from a harmonic perspective, odd harmonics are unstable, while even harmonics are stable.
This harmonic consonance and dissonance are what create the differences in sharpness and smoothness.

The Transient Differences Between Odd and Even Harmonics

These harmonics are often added during the saturation process in music. They are commonly used to add a high edge to the music.

However, the addition of these harmonics implies distortion, meaning the sound becomes somewhat distorted. Even in this process, there is a marked difference between odd and even harmonics.

The photo shows the peak level difference when I applied Vpre 73 from Black Rooster, one of my favorite clippers, and adjusted the unity gain. Turning on the analyzer, it’s noticeable that it primarily induces odd harmonics.

In essence, the closer the sound source gets to a square wave, the more odd harmonics are generated.

Peak Level after Tube Saturation
Peak Level after Tube Saturation

On the other hand, applying Tube Saturation, which is closer to even harmonics, barely reduces the peak level. It’s also said that even harmonics tend to create a sound with an emphasized attack and edginess.

This process allows us to understand the transient changes in harmonics. In practice, it’s common to use a clipper on drum sources with overly prominent peaks to control them. Analog processing that induces THD (Total Harmonic Distortion) also tends to control peaks. However, it’s important to note that even harmonics have a completely different characteristic.