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!
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? 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!
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.
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.
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 that another, lower, note. The speed at which the air vibrates is called the “frequency”. So if the lowest note you can play is vibrating at one speed, then the harmonics will be the notes that vibrate at 2 times, 3 times, 4 times etc. that speed.
E.g. the lowest note that can be played on a cornet with no valves pressed (“open”) is a low C. 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 then you get a G, and at 4 times as fast you get another C, but 2 octaves above the low C, etc. This diagram shows the first 6 harmonics of low C:
And the reason why some musical notes sound so good together is because of this mathematical relationship between them!
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.
Who would of thought that maths was so useful when learning about music!