Why are notes created the way they are today?

Question

The main question I have is admittedly broad. I'd like to know why the notes we use today are the way they are. By that I mean how is it that we have converged upon the specific discrete set of notes commonly found on Western instruments such as the piano.

Though some have asked, why are there 12 notes in an octave, I am not only curious about this but about the specific choice of both the number of intervals as well as the relation between intervals. Some questions that come to mind related to this are:

1. We have more notes in an octave than we use in any key so why do we need them?

Here we have all the notes: Cb, C, C#, Db, D, D#, Eb, E, E#...(so goes on) Bb, B, B#.

2. How did we decide on the spacing between half steps?

3. I can hear notes in between a half step so why aren't they part of music? At least why not part of the list of notes I mentioned above?

4. I hear of terms like concert Bb, or A, and thought that A was defined as 440Hz. Yet I also see other numbers like 432Hz.

4a. Which is it?

4b. And why is it a set value?

4c. Could it be any random value and be called an A?

5. Related to Q1. How was it that a specific set of 8 notes became a "key"? Why not choose a set of 10 notes, or 5 notes and call it a key?

I am assuming that the "keys" were chosen from the list I provided but perhaps that is false. I really want to know which came first.

I realize that there seem to be a lot of sub-questions and that stack exchange prefers one at a time but I'm merely trying to provide context. Without a deep understanding it's hard to frame the question. So I guess what I'm really interested is a bit of music history, why is it that Western music has evolved into the specific set of notes we have today? Was it always that way? Could it have been different?

Answer 1

First off, the twelve note pattern is not the only one in existence. There are several others, and those are well documented in other questions. I wont go into them in any detail.

Going further, we have to point out that while "sounds good" is an incredibly subjective thing, there is some precedence for approaching it psycho-acoustically. Our ears, and the wiring attached to them, is designed to support our lives before music came to be. There are patterns that come up in nature, such as the open-ended pipe which proved fruitful for our brain to process quickly and efficiently. They made the difference between life and death long before H. sapiens walked the planet.

We see this relationship in things like the perfect fifth, which captures harmonics that could correspond to things we heard on the savanna. I do believe it is generally accepted that every respectable tonal system will include the ability to reproduce such common harmonics. Where they will differ is in the dissonant sounds that can be produced.

Both five and seven note scales are common. The 12 tone system we have today is chosen because it does a very good job of approximating a seven note scale which starts at each of those seven notes. There's a matter of convenience there. You won't always find it used. Famously, barbershop quartets don't use the same 12 tones of a piano. They form their chords from a true equal temperament (as the human voice can slide to whatever pitches are needed), and they get much of their distinctive sound from this. They're very close to the ones used on a piano, but they're a little different-- they're what you would use if you could retune the piano multiple times during a song to get the sound as harmonic as possible.

Beyond that, there is the question of how we assigned frequencies to these notes. There was actually quite a lot of disagreement regarding this, if you look in history. It's Hollywood that really forced us to 440Hz. Some instruments are harder to re-tune than others. It was expensive to maintain multiple pianos with different tunings. So there was a strong effort to pick a standard and make it the standard.