So, I learnt a thing about music last night. I learnt what a major chord is.
This may seem paltry to those of you with any musical training, but it’s something that I genuinely never understood before. I had that moment of insight where it suddenly became clear, and it’s now a piece of knowledge in my head that I never had before.
I’ve known for a long time how to play a C major chord on a piano. Someone showed me that way back when I was a kid. You find C – that’s a white key immediately to the left of a pair of black keys. Then you find E, which is two white keys to the right. Then you find G, which is another two white keys to the right. Play C-E-G simultaneously, and that’s a C major chord.
I’d got it into my head that these “major chord” things therefore involved the same finger pattern on the keyboard. So, for example, if you just shift one white key to the right, you end up on D-F-A. And that should be “D major”. Right?
It turns out that’s wrong!!!
What you really need to do is count all the keys between the notes, the white and the black ones. Going back to C major, the keys are: C, C#, D, D#, E. You need to count 4 keys from C to get to E. (C# is 1, D is 2, D# is 3, E is 4.) And then to go from E to G, you need to go: F is 1 (because there is no E# black key), F# is 2, G is 3. 3 keys.
So a major chord is a note, plus the note 4 keys above it, plus the note 3 keys above that.
So if you start at D, you go: D# is 1, E is 2, F is 3, F# is 4. Then G is 1, G# is 2, A is 3.
Which means that D major is in fact D-F#-A, and not D-F-A as I’d always assumed!
I was genuinely delighted when I realised this. And now, I can actually figure out the correct major chords starting at any note I want! I honestly feel like going to a piano and figuring them all out and playing them. It’s one tiny piece of knowledge and understanding that has opened up a way for me to expand my horizons beyond a rote-learnt single chord, into a larger field of chords that I can just calculate correctly, on-the-spot, any time I need them.
And you know, in hindsight, it actually makes sense. I know that a piano is conventionally tuned so that the tone interval between each successive key – regardless of whether they’re black or white – is equal. So the interval from E to F is the same as the interval from F to F#, called a semitone. So in a major chord the intervals are always 4 semitones, and 3 semitones. I had never made that realisation before.
As I said, this may seem trivial to anyone who knows any music theory, but to me this is a revelation, like a blindfold being lifted from my eyes. I was, and still am, genuinely excited. Music theory has always seemed completely opaque to me. No longer! (I know there’s a lot more to be learnt, but I gotta start somewhere.)
Congratulations! I can’t remember if I’ve read in any of your blogs why you want to know this, apart from the sheer pseudo-mathematical aspect of music theory. Incidentally, I was in a choir rehearsal this evening where the conductor was trying to get us to sing in a tuning more like just intonation http://en.wikipedia.org/wiki/Just_intonation rather than equal temperament http://en.wikipedia.org/wiki/Equal_temperament , which was interesting. A friend suggested that one might be able to devise an electronic keyboard that would play in the correct just intonation for the current key, but I’m pretty sure a piece of machinery that smart would have its own opinions on the music it was being asked to play!
“the tone interval between each successive key … is equal”
Depends what you mean by equal :-) Musically, yes… physically, no.
If they were physically the same, you’d have what is called “equal temperament”, where the ratio of frequencies between notes a semitone apart is 1+2^(1/12):1 Do that 12 times, and you end up with a ratio of 2:1 for twelve semitones, which is equal to one octave (i.e. the gap between two notes of the same name). However, music played on a piano tuned that way will have a “bland” feel. The problem is that if you take an interval of one fifth (7 semitones), it sounds best with a ratio of 3:2 rather than 1+2^(7/12):1 (although the difference is small). Now, you can try and tune a piano so that all notes seven semitones apart are tuned with a ratio of 3:2… but then you’ll find that the octaves don’t work. (Take a low C on the piano, go up a fifth twelve times, and you’ll end up on a C again, seven octaves higher). If you do the maths, you’ll find that (3/2)^12 = 129.74 is very close to 2^7=128.
So, what piano tuners have to do is pick a set of ratios for each note in the scale that preserve octaves (always), and try and keep as many fifths “correct” (or nearly so) as possible – with a bias towards those fifths that occur more often in written music (e.g. C-G rather than G#-D#). A given set of ratios is called a “temperament”… which one you end up with will depend mostly on your piano tuner’s preferences. (Also, different temperaments go in and out of fashion.)
(If you were to only ever play music in one key, you can use “just temperament”, where all the ratios are integers and powers of 2, 3 or 5. That’s also the temperament into which unaccompanied singers will gravitate)
Hope this interests you!
I’ve always thought that music is best learned by ear and intuitively through this sort of discovery, rather than by rote sight reading. After all, we learn to understand and speak our native language before we learn to read and write it.
You gain so much more appreciation for music when you actually *hear* this kind of stuff going on.
And: Minor chords are just like the major chords, with the middle note down one key.