Have you ever thought about the connection between sound and music? It seems intrinsic enough, but there is something inexplicable about it. A sound is just a vibration in the air, so what magical property does the brain possess to turn a few vibrations into a symphony? That a combination of sounds can make us feel joy, suspense, sorrow, triumph… it is remarkable.

Every sound has a frequency (measured in Hertz), which we know in music as ‘pitch’. Imagine you are going to see how low and how high your voice can go, and to do this, you start to hum as low as possible and then continuously raise the pitch of your voice until you are humming as high pitched as possible. You’ll notice that there are no set intervals or pitches that your voice marks out, it’s just a continuous spectrum of pitches. You can stop ascending in pitch at any point and you will be making a sound with a certain frequency. This is quite problematic when we’re dealing with music, because it means that writing music is impossible unless you want to write in Hertz, which would be a nightmare. It makes sense to define a set of pitches that are universally used, so that music can be repeated and performed and read by other musicians.

That’s where 12 tone equal temperament comes in. 12 distinct tones were chosen, that are each an equal distance apart, that repeat every cycle of 12. When I say repeat, I’m talking about octaves. An octave is two tones that have the same letter name, but with either double or half the frequency, i.e. a different pitch. You can hear the similarity if you play a low E and a high E together. Something about those two pitches, despite being different, seem to harmonise perfectly. That’s the mathematical beauty of the doubling and halving of frequency manifesting in our brains.

Turns out, mathematics is the real reason why we perceive some tone combinations as more consonant than others. The more neat the mathematical relationship, the more consonant we find the harmony. Starting at A = 440Hz, and the A above that being 880Hz, splitting the frequencies in between into 12 equal sections gives us the most mathematically harmonious selection of equally spaced tones that we could come up with. The minor second (A#) is approximately 16/15 of 440Hz, the major second (B) is 9/8; each semitone increase gives you a different fractional relationship to the starting A. 16/15 and 9/8 aren’t exactly the most satisfying fractions, which is why the minor second and major second, when played with the root note, aren’t particularly consonant. However, when you start looking at the harmonies that we know are highly consonant, like the perfect fifth, it is 3/2 times the frequency of our root note, so played together they create everyone’s favourite chord, the power chord! The simpler the fraction, the nicer the sound. That’s why the tritone sounds so devilish, because it is 64/45 of the root note – ergh!

Nothing is ever perfect, and in fact when you look at 12 tone equal temperament closely, we are actually rounding to the nearest fraction. When you split the scale perfectly into 12, what you get is a close approximation to these fractions, so in reality, the only two tones in 12 tone equal temperament that coexist in perfect harmony are octaves, everything else is slightly out of tune! But people don’t notice and it means we are free to write, share and learn music amongst ourselves with our almost perfect system of music, ignorant of the fact that most of what we listen to is out of tune. But, if it sounds good, who cares?