Season 2 Episode 3 [Why do we have 12 notes in Music]
Hello. Today we are going to visit quite an important question: Why do we have 12 notes in music?
Wait, wasn’t it 7?
Well, yes, a scale has 7, but an octave has 12 parts… Let me explain.
My name is Carlos Andres Botero, and this is Our Music, A podcast to unlock your imagination to the possibilities of Classical music. I hope you are having an inspiring week.
We can approach this matter by doing some math, two parts of biology, some careful listening, and a pinch of history.
Every sound you have ever heard is a vibration that travels as waves of pressure through particles in air, liquids, or solids. Such vibration has a frequency (how many times it vibrates every second). That’s the math.
Now, the biology: Our auditory system has 2 main parts:
1) The ear converts sound energy (vibration) into neural signals.
2) The brain receives and processes the information those signals contain.
We are wired to find patterns, to organize the information received daily into manageable packets. When two notes are played together, they sound pleasing only if their wave curves come together every few cycles. We call that harmonic sounding.
If the wave curves never come together, or don’t do so within a few cycles, they sound discordant.
All the way back to the Greek civilization (text: the Greeks again!), Pythagoras discovered that what sounds harmonic to us related to its mathematical relationship, for wave curves will only come together if the two frequencies are multiples of each other.
The reason for that is called the overtone or harmonic series, a fancy name for the harmonic proportion of frequencies that naturally accompany every sound. For every Fundamental Frequency (sound), there is a rich array of multiple frequencies (overtones) that accompany such sound, although we might not necessarily be aware of them.
Allow me to use a piano for reference. Here is how the sounds in that series relate to each other.
· Here is the Fundamental, the pitch we perceive immediately.
· If we multiply the frequency by 2, we obtain this sound. When they sound together we have the most stable of intervals, they are at peace with each other. In fact, musically we consider these two the same note, just in a different octave.
· Now let’s multiply the Fundamental 3 times. We obtain this note.
· For every multiplication we have a harmonic. They are all sounding simultaneously every time we play the fundamental, but our brain simplifies the sound wave for clarity.
· Now, let’s do a sound experiment. [my daughters call them conspiraments]
o Considering the first 8 harmonics…
o Changing only their octave let’s reorganize them together.
- From this
- To this
- To this
- To this
- And let’s repeat the octave for good measure. Do you perceive the sense of completion in it?
o This is the origin of the scale (seven notes), a human reshuffling of the naturally occurring consonant vibration in every sound.
Cool word to impress your friends: That’s a diatonic scale.
· One last thing. This is not symmetrical at all. The distance between these 2 and these 2 is not the same as between every other one.
· So, let’s create intermediate steps to match the naturally occurring, and voila, a symmetrical distribution of an octave! (12 notes) By dividing each octave into 12 intervals, you maximize the number of pleasant sounding intervals.
And even more, this pattern matches the set up we are familiar with: a piano.
· Another cool word: That’s a chromatic scale.
There you have it. It is truly remarkable what you can accomplish [by doing some math, two parts of biology, some careful listening, and a pinch of history]
With few exceptions the totality of western music is based on this system, thus proving that, even with few resources, often the creator’s imagination is the actual limit.
Thanks for listening….
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