Why are there 12 notes in Western music?

[wyclif]

This is a really nerdy post. TL;DR: The reason why is because 12 notes is a good tradeoff.

Why 12 notes? Here is my explanation

 

[Michael Poche]

There's also this from Leonard Bernstein...

 

[Greggorios]

'cause we have 12 fingers and 12 toes? (...never mind, that's my neighbor's cat.)

 

[Digital Larry]

Harry Partch did 43. Y'know, one more than 42. Like, one guy thinks 42 is the answer to life, the universe, and everything, and Harry went one louder. Or something like that.

 

[Mike Eskimo]

Derek Trucks (and a couple billion Asians) are sitting, having drinks, munching popcorn, and half-interestedly monitoring this thread…

 

[Skyhook]

This is a really nerdy post. TL;DR: The reason why is because 12 notes is a good tradeoff.

Why 12 notes? Here is my explanation

Because that's all I need to reach the next octave.

 

[Greggorios]

Derek Trucks (and a couple billion Asians) are sitting, having drinks, munching popcorn, and half-interestedly monitoring this thread…

...and Ry Cooder:

 

[Chester P Squier]

I didn't read the link in the OP and I didn't click on Leonard Bernstein. I can tell you that the cycle of 5ths will get you through the 12-note chromatic scale and back to where you started.

C-G-D-A-E-B-F#-C#-G# (same as Ab)-Eb-Bb-F-and back to C. See there? Twelve notes. The chromatic scale.

 

[dougstrum]

Hey, it's an even dozen, works for me

 

[MarkieMark]

If anyone is really interested in the complex history behind the question- read this book
I really enjoyed the little book and found it fascinating. Some may find it too nerdy.

Temperament

 

[ce24]

Math....music is math.

 

[tintag27]

David Bennett can tell you:

 

[Michael Poche]

Math....music is math.

Among many other things.

 

[Michael Poche]

If anyone is really interested in the complex history behind the question- read this book
I really enjoyed the little book and found it fascinating. Some may find it too nerdy.

Temperament

Read it and loved it. He actually manages to inject a sort of dramatic narrative into a very dry subject. He has a new book out called Musical Revolutions: How the Sounds of the Western World Changed.

 

[bebopbrain]

the cycle of 5ths will get you through the 12-note chromatic scale and back to where you started.

Yeah, but that is circular logic.

 

[Oxidao]

This is very interesting, I've read a bit but don't get too far yet.

AFAIK Pitagoras realized that hitting metals of different weight, vibrate in a different frequence and produced different timbres.
Experimented in some way, getting those different frequencies from a cord with variable tension.
He made a "monocord", and started dividing it in equal halves to end up with 12 notes that sounded good to him (harmonics) before reaching the Octave. Then got the Natural scale (7)
I am a bit confused yet on that process.

Being a Mathematic, he saw the logic of the V degree to form scales and explained *theoreticaly/Maths what was actually sounding century's ago.

*edited.

 

[SRHmusic]

Rather than starting with the math, it's interesting to me to look at how these notes emerged just from what people had at hand.

If we start with any resonant object (string, pipe, log, kettle, etc.), and are able to either make another of different sizes, or with a string or pipe effectively change the length, then the root, M2, M3, P5 and b7 are easy to create - as they are from low ratios, and their octaves. Try it with harmonics up the E string on your guitar. Then if we start with another, say at the 5th of that first root, we end up with some notes very close to the ones from the root harmonics (e.g. the M3 of the 5th is the M7 of the root), but we also get the M7 and P4. Do it again from the 3rd and we get similar notes plus the M6. And so on.

So rather than starting from math, the notes we ended up with are pretty inherent in the physics of things. The math came later, esp. for equal temperament. The Wikipedia articles and references are pretty good on this.

 

[timbgtr]

I didn't read the link in the OP and I didn't click on Leonard Bernstein. I can tell you that the cycle of 5ths will get you through the 12-note chromatic scale and back to where you started.

C-G-D-A-E-B-F#-C#-G# (same as Ab)-Eb-Bb-F-and back to C. See there? Twelve notes. The chromatic scale.

To really nerd out, it’s that the note a fifth above where you started has 3/2 times the frequency of that initial note. Repeat 12 times and you get (almost) the note you started with, 7 octaves up. The “almost” is the tempering that allows separate keys for all of the notes in those 12 steps, as Chester P. listed.

 

[Addnine]

Temperament aside, those notes are about the physics of sound, about the mathematical relations among the tones, about the harmonic series. I taught philosophy for many years, and when I would hit the Pythagoras unit, we talked a lot about the mathematics of music. As a way of provoking discussion, I used to describe (Western) music as "base 12 math, graphed in sound." The actual musicians in the class would say. "Yeah, I guess that is really what it is." The Romantics in the room, blithering on about "self expression" and so on, disagreed. The actual musicians realized what a crock the self expression model really is. Music is about ....music, and about he beauty it offers....period.

 

[loopfinding]

Rather than starting with the math, it's interesting to me to look at how these notes emerged just from what people had at hand.

If we start with any resonant object (string, pipe, log, kettle, etc.), and are able to either make another of different sizes, or with a string or pipe effectively change the length, then the root, M2, M3, P5 and b7 are easy to create - as they are from low ratios, and their octaves. Try it with harmonics up the E string on your guitar. Then if we start with another, say at the 5th of that first root, we end up with some notes very close to the ones from the root harmonics (e.g. the M3 of the 5th is the M7 of the root), but we also get the M7 and P4. Do it again from the 3rd and we get similar notes plus the M6. And so on.

i think the harmonic series is generally a suitable explanation for how we derived the diatonic scale in western/indo-european traditions. we had the 7 note diatonic scale way before sharps and flats.

I can tell you that the cycle of 5ths will get you through the 12-note chromatic scale and back to where you started.

C-G-D-A-E-B-F#-C#-G# (same as Ab)-Eb-Bb-F-and back to C. See there? Twelve notes. The chromatic scale.

but this is the meat of it i think. important to note that after monophony, chant was harmonized in 5ths (the 5th being a privileged interval in many cultures, including western). they had to add more notes accordingly to avoid tritones in harmony (not because of any "devil's note" woo, it was just the odd one out and they didn't like how it sounded). it follows that a 5th of a 5th of a 5th of a 5th, etc. will lead back to the tonic.

the equal temperament ratio of 2^(x/12) is the compromise to keep all 5ths from tonic to some octave of it with minimal deviation from the ideal 3/2 ratio of the natural harmonic.