Chances are, you’ve heard the terms overtone series and harmonic series when discussing modern music harmony and theory.
The Overtone series is a crucial factor in the history of modern “tonal” music.
Think of the Overtone Series as the “origin story” of the chromatic scale and modern harmony, and it’s the basis of the musical “logic” that we talk about in our courses.
Without going too deep into acoustics or math, let’s look at how the Overtone Series relates to some of the ideas we use.
Understanding The Overtone Series
The Overtone series (or Harmonic Series) is the basis for the natural acoustic relationship of modern “Tonal” harmony.
The overtone series is a natural phenomenon explained mathematically, and it is the basis for many aspects of modern harmony theory.
When you play any low pitch (except a synthetically produced sine wave), you get a complex mixture of tones, which follow a particular order and structure.
The lowest pitch of this series is called the fundamental, and every tone above it is called an overtone (or harmonic).
In this example, C2 is the fundamental, C3 is the first overtone, G3 is the second overtone, etc.
When played separately and sequentially, the Overtones series sounds like this:
While you mostly hear the fundamental, overtones are actually present in any single pitch. Each successive pitch is weaker in strength and importance than the one before it.
The relative strength of these different overtones gives an instrument its particular timbre, tone color, or character.
Much of what we know about modern music harmony is because of the natural relationship between a fundamental tone and its overtones (or harmonics)
The Overtone Series as the Basis For 12 Note Chromatic Scale
Our contemporary tonal language is firmly rooted in these basic notes of the harmonic series.
The division of the octave into twelve parts is our brains’ interpretation of this simple mathematical phenomenon.
When the frequency of a soundwave is doubled, our brains hear those two frequencies as sharing some fundamental commonality, so it interprets those two pitches as the “same” but separated by an octave.
Therefore, octaves always have a 2:1 ratio. (A110, A220, A440, and A880 are all A separated by octaves.)
The next two simplest ratios are a 3:2 ratio and a 4:3 ratio, which create a perfect 5th and a perfect 4th.
If you begin on any pitch class and begin moving by ascending perfect 5ths (or 4ths), you will find yourself back at the beginning after cycling through all twelve pitch classes.
Starting with the fundamental (Tonic) and the fifth (Dominant).
By simply following a simple sequence of notes, starting on a fundamental, then to the first overtone (or 5th) above that fundamental, with each subsequent fifth “pivoting” to act as its own tonic with its own fifth above and so on.
This produces an endless circle of 12 notes that make it all back to the original starting tone…
You get the 12 notes of the chromatic scale; all one half step apart.
It is important to note that we did make some small compromises to allow the ease of moving from octave to octave.
The overtone series from one note actually rises infinitely from the fundamental.
To create this clean “circular” 12 tone system, the concept of “equal-tempered tuning” was derived.
Equal-tempered tuning makes a minor “correction” to the slight drift of the tuning of the intervals of the overtone series, namely the 5th (lowering a “true” perfect 5th by two cents from 702 to 700 cents to give us our “perfect circle”)
The difference is barely perceptible to our ear. It creates a middle ground between scales being heard as “in-tune: with itself across multiple octaves and for the 12 tonalities based on all 12 chromatic notes to sound in-tune with each other.
A small price to pay for the cleanliness of our modern 12 tone system.
Overtone Series as the Basis for “Tonality”
But how do we make sense of these 12 tones as players, composers, singers, etc.?
As we saw before, if we start on a note and move through ascending perfect 5ths, each new perfect 5th moves us to a new note and note letter in an endless circle.
But what if we introduced a change or “restriction.”
Let’s look at what happens when we introduce a non-perfect 5th into the pattern and change the F# in the C overtones series to an F.
We break the pattern and take a shortcut back to our fundamental tone…
C – G – D – A – E – B – F – C
This slight change creates or “restriction” or is just enough for our ear to hear a sequence of notes as a “tonality” when played as a scale.
Creating or using restrictions is how our ear recognizes keys and hears notes functioning diatonically or chromatically. In this particular example, the restriction we created is the tonality of the Major scale.
The most basic and closest “restriction” is considered to be the Major scale.
So we can look at a Tonality as a specific restriction of notes which creates a specific tonal “impression” in relation to the overtone series.
And once that relationship has been established (the “Tonality”) to your ear, everything else is heard in relation to that context.