The Interesting Relationship Between Music And Numbers
Over the years as a musician and piano player I have noticed some remarkable connections between music and mathematics, but since I am not a mathematician at all, I will leave it to someone who is to explain all the many details of the relationship between math and music. Today let’s just take a brief look at the relationship between music and numbers.
You know, of course, that sound is simply something vibrating at a certain speed, whether the sound comes from a Woodpecker or a drum or a human voice or whatever. Sounds that are pleasant and sustained we sometimes call “musical tones”, and we then organize those sounds into patterns that translate into music in the form of songs, pieces, etc.
But for now, just let me show you a few relationships dealing with the numbers 3, 7, and 12:
Major chords have 3 notes in them – the root, 3rd, and the 5th notes of a major scale.
Minor chords have 3 notes in them – the root, lowered 3rd, and the 5th notes of a major scale.
Augmented chords have 3 notes in them – the root, 3rd, and raised 5th notes of a major scale.
Diminished chords have 3 notes in them – the root, lowered 3rd, and lowered 5th.
Now some people will argue that a chord can have only two notes, and if they want to believe that, that’s fine. But I will agree with most musicians and say that when you have just two notes, you have harmony all right, but you don’t have a complete chord. See the Wikipedia article on chords here:
And chords can have MORE than 3 notes – I use 4 and 5 and even 7 note chords all the time, but the basic structure of a chord comes down to those three notes – a root, a 3rd, and a 5th.
And it each key you can play in, there are 3 primary chords, so:
There are 3 primary chords in the key of C…
3 primary chords in the key of Db
3 primary chords in the key of D…and so on.
So we have the number 3 showing up all the time in music.
The number 7 occurs a lot in music also:
There are 7 notes in a diatonic scale, with the 8th note being a repeat of the root note an octave higher. So in each of the 12 diatonic major scales there are 7 notes.
If you look at your piano keyboard you will see that there are exactly 7 different white keys: A, B, C, D, E, F and G. After that it repeats all over again.
You will also notice that there are 7 octaves on your piano keyboard (if you have a piano with 88 keys, that is).
The number 12 occurs a lot also:
There are 12 notes in a chromatic scale.
There are 12 different keys on your piano keyboard – 7 white keys and 5 black keys.
There are 12 major keys you can play in – the key of C, the key of G, the key of F, and so on.
There are 12 minor keys you can play in – the key of C minor, the key of G minor, the key of F minor and so on.
There are 12 different major chords.
There are 12 different minor chords.
12 different augmented chords, 12 diminished chords, 12 major 6th chords, 12 minor 6th chords, 12 dominant 7th chords, 12 major 7th chords, 12 minor 7th chords, 12 diminished 7th chords, 12 9th chords, 12 11th chords, 12 13th chords, and on and on.
Well, you get the idea. I have only scratched the surface. We could dig a lot deeper and find much more complex relationships. I hope that as you continue to study and learn more about music and the piano you will notice some of these relationships and benefit from them.
(By the way, for some reason some folks like to argue about this stuff. I have absolutely no interest in arguing – they can believe what they believe – it makes no difference as far as producing or playing music is concerned.)
Here is an interesting article in Wikipedia about music and math: http://en.wikipedia.org/wiki/Music_and_mathematics
If you are as interested in music theory as I am, check out this excellent course: