Chapter 1
Each note on an instrument is individually tensioned (tuned) to its fundamental frequency.
We now know that a tensioned string that is fixed at both ends simultaneously produces multiple vibrations that in turn produce multiple note sounds.
We will now examine why this phenomenon is so important to music creation and the understanding of melody and harmony.
The harmonic series identifies the frequencies of the multiple vibrations that naturally occur when a string is set in vibration.
The largest vibration which produces the loudest sounding note is the:
fundamental frequency.
Each note on an instrument is individually tensioned (tuned) to its fundamental frequency.
We discussed that the standing waves produced by the harmonics are occurring much more frequently, as they have higher values. These multiple harmonics at higher frequencies correspond with many other note frequencies on a musical instrument. This is the secret.
The multiple harmonics at higher frequencies correspond with many other note frequencies on a musical instrument.
You can see from the image that a single vibrating string will produce many specific note combinations.
For example, when you play the middle “C” note on a piano, a hammer hits a string that is tuned to the fundamental frequency of middle “C” at 262 Hz.
The piano string vibrates at the fundamental frequency, 1X, and simultaneous at multiple higher harmonics of 1X. The Fundamental is a C note sound. The harmonic at 2X corresponds with the note C5, an octave higher, and the harmonic at 4X corresponds with the note C6, an octave higher again.
The harmonics at 3X correspond with the note G5 which is an octave and a half above the fundamental C4. The harmonic at 6X corresponds with the G6 note, which is an octave higher than G5.
The harmonic at 5X corresponds to the E6 note.
Why are the first six harmonics so important?
So we have pressed the key on the piano, the hammer has hit the string, but what exactly are we hearing?
Let’s recap.
For this example we are going to use the low C2 note.
The lower C2 note string has been tensioned to the fundamental frequency of 65hz.
However the string vibrating will produce many other sounds. The most important being the first six harmonics.
From this graphic, we notice that harmonics are identified by adding the fundamental frequency to each preceding note frequency or by multiplying the fundamental frequency.
KEY TAKEAWAY
Understanding harmonics helps us understand the natural relationships between notes and why they may work well together.
If C2 naturally produces a E4 sound, then there is a good chance they will sound good together when played together.
Using the C note as an example (it works equally for any notes), we can clearly show that the first six harmonics of any fundamental note frequency produce two other crucially important note frequency sounds.
When combined with the fundamental frequency sound, these two harmonic frequency sounds are the foundation stone of harmony in music.
Harmony in music is based on combinations of three or more notes that sound good when played together.
The three-note combination formed from the first six fundamental harmonics has the strongest and most harmonious relationship in music and nature.
As an example, we will use the fundamental C note vibration to show that the most crucial harmony combination in music is formed from the first six harmonics of the fundamental frequency.
The fundamental frequency is the first harmonic, producing the highest amplitude (loudest) note sound.
Using the C note vibrations, the table above shows that that same C note sound is represented in the harmonic series at specific multiples of the fundamental frequency at 1X, 2X, 4X etc.
These specific multiples of the fundamental correspond with its higher octave frequencies. The other two crucial harmonic frequencies are at 3X and 5X.
In the example of the C note, these two notes are the G and E notes.