Harmonics

harmony

Hey! We all want to live in harmony don’t we? It’s so good when we can get along together. You can tell when it’s good because you hear the laughter and happy voices.

But sometimes people fall out. They argue, they clash. They might shout and call each other names. That’s the opposite of harmony right? One word for it is discord!

arguing

Well it’s exactly the same with music. We have harmony and discord. Have you ever wondered why a song by your favourite singer, or music by your favourite band can sound so good?

harlem gospel choir

Sure, the melody (the tune) is important, and the rhythm, and so are the words of the song (the lyrics), but what really brings it to life is the harmony.

Listen to a group or choir singing, and they aren’t all singing the same thing. Listen to a band and you’ll hear some instruments playing high, some low and some in the middle. But they still sound great because of harmony!

encuentro street band

To understand how we can play music that sounds good, and not just make a lot of noise (discord), we need to look at how our musical instruments work and produce a nice sound.

Read our pages on What is sound? and How is sound produced in a brass musical instrument?

sound wave reaching ear

A musical note is produced in a brass instrument when the air vibrates within the length of the tubing. This produces a sound wave that travels out from the bell of the instrument to reach your ear.

The musical notes that can be produced on a brass instrument depend on the length of the tubing and the way the player vibrates their lips.

The speed at which the air vibrates is called the “frequency”.

post-horn

In the simplest brass instruments such as this post-horn, the length of tubing is fixed and the musical notes that can be produced are limited to a series of “harmonics”.

A harmonic is a sound wave that vibrates a whole number times faster than another, lower, note.

If we vibrate our lips twice as fast we get a note that sounds very like the first note, but higher in pitch. They sound very similar because the vibrations are so closely related. For example, look at the diagram below:

The higher note is vibrating twice as fast as the lower one and this means the vibrations fit together very well. For every single vibration of the lower note there are two vibrations of the higher note.

This very close fit makes the notes sound the same in some way, except that one is higher than the other. Play both notes at the same time and they are in perfect harmony. We call this relationship an “octave” and we give them the same name e.g. A and A, or B and B etc (more below).

For example here is the note A with the A an octave higher and the A 2 octaves higher, played separately in turn, then together adding one octave at a time:

But we can make the vibrations even faster. So if the lowest note you can play is vibrating at one speed, then we can play notes that vibrate at 2 times, 3 times, 4 times etc. that speed. These are called harmonics or partials.

E.g. the lowest note that can be played on a cornet with no valves pressed (“open”) is a low C. This is known as the “fundamental” note. By blowing faster you can also play the C an octave higher, when the air in the instrument is vibrating twice as fast as for the low C.

If the air vibrates 3 times as fast as the low C then you get a G, and at 4 times as fast you get another C but 2 octaves above the low C (because 4 is 2×2). If the air vibrates 5 times as fast you get an E; 6 times as fast and you get another G an octave above the one at 3 times (because 6 = 3×2); etc.

This diagram shows the first 6 harmonics of low C:

Harmonics

Note that the 7th harmonic B♭ on a brass instrument will be a bit flat, as are all the 7th harmonic notes, so players usually find alternate ways to play them e.g. with 1st valve instead of open on a valved instrument or in 3rd position instead of 1st on a trombone.

The reason why some musical notes sound so good together is because of this mathematical relationship between them! Listen to the harmonic intervals on C above and see what you think.

A very common harmony in music is the 3 note “major” chord consisting of a root note with the 3rd and the 5th notes above. E.g. if the root note is C, then the major chord would be C, E and G. These notes have a mathematical ratio of 4:5:6.

The notes of a scale are repeated using just 7 letters: A, B, C, D, E, F, G followed by another A an octave above the first one. It is called an “octave” for this reason, that the higher A is the 8th note in this scale, counting the first A as 1: A=1; B=2 (a “second”); C=3 (a “third”); D=4 (a “fourth); E=5 (a “fifth”); F=6 (a “sixth”); G=7 (a “seventh”); A=8 (an “eighth” or “octave”).

Who would of thought that maths was so useful when learning about music?

Also see our page on Musical Intervals

To find out more about harmony see BBC Bite Size on Music Harmony or Harmony on Simple Wikipedia

Now read our page on Music scales

Return to Introduction to Music

Return to An Introduction to Brass Music