BJG145 wrote:I haven't read up on this, but I'd have thought it was more likely that the scale started with the maths, and it only "sounds good" because we're used to it. Would someone who'd never heard music before find something inherently attractive about those frequencies...? Dunno.
Yes, they would. We use these scales because they produce mathematical relationships which please our ears. Give a hymn tune to large congregation and some folks will sing it a fifth higher or lower. Why? Because of the mathematical relationship.
Mind you. it does have to be learned to some extent. The major third was considered a dissonance and was pretty much off-limits until the Brits popularised it. It still is a dissonance but now seems a nice one. Nowadays we have got used to sevenths, ninths, eleventh,s thirteenths and just about anything. But look at these numbers, it's all maths and physics connected to the harmonic series.
I would suggest studying the way a string with fixed ends vibrates. All of diatonic music is in those vibrations and their relationships.
CS70 wrote:Say you look at the frequencies which sound good starting from 440Hz and name them A, B, C, D, E, F, G. Then you look at the numbers and you discover that these sound have an interesting arithmetic property - the ratios between the corresponding frequencies are made by small integer numbers: 1/1, 2/1, 3/2, 4/3, 5/4, 6/5.
As long as we stick to the scale frequencies...
As a general point I'd agree that music theory is often taught very badly. But teaching young players about the background physics and the psycho-acoustics is not usually practical, and later it may be forgotten.
A classic case was a pupil of mine who arrived having carefully learned all the notes on the stave, but nobody had mentioned to her (aged about nine) that they proceed alphabetically and she hadn't noticed. She was amazed when I pointed it out. Another beef is that often pupils are not taught what the treble clef actually is, to wit a G written on the first line. If the basics are missed then the rest of the the system may make little sense.
My view is that the best and possible only completely effective method for understanding notation and why things are done as they are is to write music. Then you start to see the logic because you're in problem solving mode. Then you see why the solutions are as they are.
To confuse matter in Germany there is a half-step between B and H, and between H and C. But a half-step is a certain number of 'cents' and nothing to do with what we call the notes.
A guitarist has the wonderful advantage of understanding how strings vibrate and if we understand this we understand a lot of music theory and quite a lot of mathematics. For instance, number theory (the study of the primes) is almost all about vibrating strings and the number line can be modeled as one.
Maybe check out Pythagoras. Also try googling 'grand staff'. Maybe also have a look at early plainchant notation. Then you'll be glad of the 'alphabet-on-the-stave' system.
I'd second the idea of finding a cheap keyboard to doodle on. Much easier to learn the theory on a keyboard, which may be why keyboard players are usually better at it than guitarists, who are often accused of a lack of general skills compared to other instrumentalists.