why are Do Re Mi Fa Sol La Si the standard notes?

Question

If you take an instrument without predefined notes, such as a trombone or a violin, you can produce an infinite amount of notes between Do and Re for example (applies with out of tunes instruments as well). With that logic, you could have an infinite set of 7 notes that are as evenly « spaced » as our current standard. Im sure im missing something obvious.

In: Physics

Answer 1

It has to do with mathematical ratios of the frequencies of the notes, notably determined by Pythagoras, I believe (but it could pre-date him), so they’re at least 2,600 years old.

Imagine a basic wave on a graph, that goes above the X-axis and then down below, over and over. You could add another wave to it that fit perfectly into it twice, crossing the x-axis at the same points and also halfway between. That would make the frequency of the wave twice the original one – we call that an “octave” and say they’re the same note, just an octave higher or lower, a 2:1 ratio of wavelengths.

Now we add a wave that has a 3:2 ratio – that means that for every 2 waves of the base note we end up with 3 waves of the new note. This new tone is very consonant (i.e. pleasant to hear). Unlike the octave, it’s definitely not the same note, but they still sound nice together.

So now we take *that* note, and find the note that has a 3:2 ratio to it. Then we take that third note, etc. etc. After some time (12 iterations), you end up getting to a note that is the same as the first note, but 6 octaves higher. Those 12 notes are all of the notes used in traditional western music (basically everything you’ve ever listened to, unless you listen to a lot of indian/chinese traditional music). This is known as the “circle of fifths”, and you can find a number of different images of it.

“But,” I hear you say “do re mi is only 7 notes!”. That’s true – from those 12 notes, we pick 7 *not* equally spaced notes to build a scale out of called a “diatonic” scale. Those notes are chosen for again, more complicated mathematical ratio reasons (mostly dealing with thirds instead of fifths). But it’s basically all math, all the way down.