Why does an octave have 12 notes?
Category: Miscellaneous
- Image via Wikipedia
Why does an octave have 12 notes? Well, it turns out that this is one of those questions that is not easily answered. There are theories; there are mathematical models; there are stories of UFOs and divine intervention. We may never know the right theory, but some seem more plausible than others.
While I generally lean towards the theory that “aliens did it”, I’m going to offer up an alternative scenario, then you can decide for yourself what to believe.
I’m sure you have noticed that when you play two different notes on the keyboard at the same time they can either sound good together, or they can sound bad. In music, the good sounds are called consonant sounds. Bad sounds are called dissonant sounds. My theory is that the 12 notes of the octave were chosen based on their consonant tonal qualities.
Imagine you have 2 strings, one is twice as long as the other. The longer string will produce a tone that is exactly one octave lower than the shorter string. That is, both strings will produce the same note in a different octave. (For example, low A vs high A). This must have been a pretty exciting discovery way back in the day. I don’t expect you to be too excited about it given all of the new fandangled technology that we are exposed to, but I’m going to pretend you are. Carrying on..
Well, you can imagine that the dude who just discovered octaves was curious… What would happen if he took another string, and cut it so that it was longer than the shorter string by a half? (That is, 1.5 times the length of the shorter string) And voila, another interval was discovered. The interval from the shortest string to the middle string is a perfect fifth.
What made this discovery exciting was that the perfect fifth interval sounds consonant to us. That is, it sounds good and harmonious to us. So, now that octaves and perfect fifths were discovered, what was discovered next? The truth is, nothing else NEEDED to be discovered.. from the discovery of octaves and perfect fifths, the 12 note octave may have been born… If you know about the circle of fifths, you will know why.
The circle of fifths shows the relationship between every note in the scale. You can pick any note in the scale, and end up back at the same note by using the circle of fifths. Let’s start with C:
C -> G -> D -> A -> E -> B -> F# -> C# -> Ab -> Eb -> Bb -> F -> C
Here is the same thing described in a graphical format:
You can see that no matter where you start, eventually you will end up right back where you started, but only after traversing through all of the notes in the octave.
The moral of this story is: Just because you CAN explain something with mathematical models, doesn’t mean that is how it was discovered. Sometimes a guy banging on wires is all you need.
**Disclaimer: There may or may not have been a dude banging on wires, and he may or may not have discovered the 12-note octave. I made him up. However, the circle of fifths is a real and valuable tool that I will discuss in more depth at a later time.
Related Posts
Posted on September 26th, 2010 by sharlene
1 Comment
October 20th, 2010 at 8:37 pm
[...] help you identify the 12 tones in the chromatic scale (which we have already discussed here) [...]