Today we’re going to talk about harmonics.

A question that comes up very often is why an A note on a piano sounds different than an A note on a guitar, even though they are both technically playing the same pitch. The answer to that question has everything to do with harmonic content.

Harmonics are what give sound its character, its color, and its identity. Without them, every instrument would sound the same.

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The Two Core Components of Sound

The harmonic content of a sound can be categorized into two groups:

• The fundamental frequency
• The harmonics

These two elements together define everything we hear when a note is played.

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The Fundamental Frequency

The fundamental frequency is a sine wave.
It is the frequency that determines the pitch of the sound.

For example:

• The fundamental frequency of an A2 note is 110 hertz.

This means that when you hear an A2, what your ear identifies as “A” is coming from that 110 Hz sine wave.

If a sound consisted only of this fundamental frequency, it would be a pure sine wave—very clean, very sterile, and very unnatural.

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Harmonics: Whole Multiples of the Fundamental

In addition to the fundamental frequency, we have harmonics.

Harmonics are also sine waves, but they occur at whole-number multiples of the fundamental frequency.

Using the A2 example at 110 Hz, the harmonics would be

1. 220 Hz—the second harmonic
   • Exactly one octave up
2. 330 Hz—the third harmonic
   • This happens to be an E note
3. 440 Hz—the fourth harmonic
   • Another octave higher

From this, we can already see an important rule:

Doubling the frequency represents an octave.

This doubling relationship is the reason octaves feel so closely related to the original pitch.

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When Harmonics Stop Sounding Musical

Not all harmonics line up nicely with musical notes.

Some examples:

• The 7th harmonic
• The 11th harmonic

These produce unrelated pitches.

That doesn’t mean they’re “wrong,” but it does mean that:

• Our ears can’t easily relate a pitch to them
• They don’t strongly reinforce the sense of pitch

This is why some harmonics feel musical and stable, while others feel strange or disconnected.

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Listening to the Harmonic Series

If we take an A2 note and listen to its harmonic series, we don’t just hear one frequency.

We hear:

• The fundamental
• A stack of harmonics above it
• Each harmonic contributing something subtle to the overall sound

This harmonic balance is what makes instruments sound rich instead of flat.

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Visualizing Harmonics with a Frequency Analyzer

In a project environment, we can take a closer look at harmonics by comparing:

• The fundamental frequency
• The instrument sound
• A frequency analyzer

When you run an audio signal through a frequency analyzer, you can literally see the harmonics as peaks above the fundamental.

This visual feedback makes it very clear that sound is never just one frequency—it’s a complex structure of frequencies working together.

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Octaves and Frequency Doubling

We’ve already seen that the distance between an A2 and an A3 is a doubling in frequency.

This relationship is called an octave.

And what’s interesting is that:

Our ears perceive octaves as being the same pitch.

Here’s how that looks numerically:

• A2 – 110 Hz
• A3 – 220 Hz
• A4 – 440 Hz
• A5 – 880 Hz

Each octave doubles the frequency, but the pitch identity remains recognizable.

This is one of the most fundamental principles in music and audio.

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Frequency Charts and Reference Tools

Charts that map notes to frequencies can be extremely helpful when learning harmonics and pitch relationships.

These charts make it easy to see:

• Where notes sit on the frequency spectrum
• How octaves relate to each other
• How harmonics align—or don’t align—with musical notes

They’re especially useful when working with analyzers, synthesizers, or equalizers.

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What Happens When Sound Passes Through Electronics

When an audio signal travels through an electronic device, ideally:

• The input should be identical to the output

But in reality, this never happens.

Every processor—no matter how clean—adds something to the signal.

And what it adds is usually harmonics that were not present in the original input.

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Harmonic Distortion Explained

Because these added harmonics were not part of the original signal, they are technically a distortion.

This is referred to as

Harmonic Distortion

In technical specifications, this is expressed as

• THD – Total Harmonic Distortion
• Measured as a percentage

The lower the percentage, the closer the output is to the input.

But lower doesn’t always mean better sounding—it just means more accurate.

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Testing Harmonic Distortion in Practice

One way to understand harmonic distortion is to run a pure sine wave through an audio processor.

For example:

• A sine wave is sent through a compressor
• The compressor is completely neutralized
• No compression is applied
• The signal is simply passing through the device

Even in this neutral state, the output is no longer a perfect sine wave.

That’s because:

The device itself adds harmonics.

This is simply the nature of electronic components.

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Why Analog Gear Is Often Described as “Warm”

When people talk about the warmth of analog sound, they are really talking about added harmonics.

Analog devices don’t just pass signal—they shape it.

And the type of harmonics they add matters a lot.

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Tubes vs Transistors: A Harmonic Difference

There is a clear difference between tube-based and transistor-based equipment.

Tube Equipment

• Adds more even harmonics
• Even harmonics reinforce the fundamental
• The result sounds like this:
  • Warm
  • Smooth
  • Pleasant

Transistor Equipment

• Tends to add more odd harmonics
• Especially higher-order odd harmonics
• These tend to sound like
  • Harsh
  • Cold
  • Aggressive

This difference in harmonic structure is why two devices doing the same job can sound completely different.

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Harmonics as the Identity of Sound

Harmonics explain:

• Why instruments sound different
• Why analog gear feels musical
• Why distortion can be pleasing or unpleasant
• Why “clean” and “sterile” are not the same thing

They are not an extra detail—they are the foundation of sound itself.

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Harmonics and What Comes Next

Understanding harmonics makes it much easier to understand:

• Frequencies
• Equalizers
• Tone shaping
• Audio processing as a whole

Harmonics are where pitch, timbre, and technology all intersect.