A question of one aspect of Chord theory

[k-bird]

Sorry i'm late. Here's a comprehensive but easy text on music theory which explains scales and even why you make major chords based on the perfect fourths and fifths of the scale.

http://www.ravenspiral.com/ravenspiralguide.pdf

Once you've got the basics down there's enough in there to go forward a bit more, and it's free and you don't have to be able to read music to use it.

[JumpingJackFlash]

I should also note that it is not always the case that a C# is the same as a Db. String players for instance will play the notes differently. Obviously, they are the same with discrete semitone instruments (e.g., modern piano, guitars, etc.) Also, notes will be played slightly differently given the context of the note. As I recall, to make a chord sound really good, a third of a chord tends to be played a little sharp and the fifth a little flat.

Well, nowadays (in Western music), we use 'equal temperament', whereby C# sounds exactly the same as Db. Although some instruments (strings being the obvious example) can pitch them differently, if they are playing with other musicians, they will have to keep to the standard tuning, otherwise it will sound bad.

We didn't always use equal temperament; in the 17th century keyboards would often have 2 keys, one for C#, and one for Db (for example). The concept of 'equal temperament' was unacceptable to people back then, but it wasn't a very big deal, because music seldom had more than 3 or 4 sharps or flats at a maximum (unlike today).

The system of equal temperament divides the octave into 12 equal semitones. However, as you hinted at in your last sentence, in order for them to 'squash' the notes into the system, the tuning of some intervals such as the perfect 5th, was altered, so it's technically out-of-tune relative to physics (for example, the idea that stopping a sting exactly in half produces a perfect 5th). This was initially a problem for singers, because their natural tendency to sing as 5th actually contradicted equal temperament!

It's all quite complicated, but basically, if you want to play with other musicians today, you are more of less forced to use equal temperament, whereby tuning is standardised, all semitones are equal, and C# sounds the same as Db.

Oh, and don't even think about all this until you can distinguish a major chord from a minor one, otherwise your head might explode

[Barbed Wire Kiss]

What's the difference between a minor and a major chord? Or a diminished one come to that?

I thought I had answered that with the following 2 paragraphs...

Ah, yes it's seems you did. Sorry that one didn't seem to register when I read it.

Anyway I'm please I was acting a bit dim as robenestobenz's & racemize's further explanations were both interesting and very useful.

[bugs]

Keep reading.

[lynx]

Hi all, this thread has been a good education. I'm interested in the part about the laws of physics, its relation to a musician's hearing and equal temperament. Could you elaborate more on this fascinating subject, please?

(for example, the idea that stopping a sting exactly in half produces a perfect 5th).

If I may correct you here...

Stopping a string at half produces an octave above, not a perfect fifth.
The same happens with pipe organs and other wind instruments(a pipe with a length of 16" sounds an octave above a 32" one and an octave below a 8" one and so on). In frequency terms 440Hz (Hz = air vibrations/second) I think corresponds to A3; if we rise the frequency to 880Hz we have an A4...

So there's a rule regarding perfect octaves without the beats (don't know if it's the exact term in English) we use to add while detuning two synth oscillators to fatten up a sound for example, and mechanics, I think. Exactly half a string's length should be = exactly doubles the frequency = one perfect octave upper.

What I'm having trouble with is that it seems with perfect fifths (and fourths)things aren't so linear: If we apply the said rule, like dividing an octave into 12 perfectly spaced semitones, the resulting fifth won't appeal to every musician's ears as there'll be some minor detunings.
Modern synthesizers are tuned this way but pianos are not, and this is why it's so tough to tune a piano. And possibly why electronic music was always regarded as cold and 'unhuman'. If this is true we've been making music that's not mechanically correct thus not conforming to Nature.

I've read a story about an ethnologist who took a turntable to the saharian desert and played some Mozart for the Beduins. To his surprise they said the music was too simple. Not enough notes.
It seems the arab scales are made of 24 semitones and the indian scales are made of 48!

Cheers

[JumpingJackFlash]

Hi all, this thread has been a good education. I'm interested in the part about the laws of physics, its relation to a musician's hearing and equal temperament. Could you elaborate more on this fascinating subject, please?

(for example, the idea that stopping a sting exactly in half produces a perfect 5th).

If I may correct you here...

Stopping a string at half produces an octave above, not a perfect fifth.

Yes, you are of course correct. Must not have been thinking when I wrote that; silly me!
The ratio of 2:1 does indeed produce an octave, while a ratio of 2:3 corresponds to a perfect 5th.

I believe it was Pythagoras who first used different lengths of strings like that.
There is something called the 'Pythagorean comma', which says that if you go up the cycle of 5ths from a starting note using the 2:3 tuning from physics, - if you go up far enough so you reach the same note 7 octaves higher, then lower that pitch by 7 octaves, the resulting pitch will not be the same as the one you started with. - In fact, it will be slightly sharper by an amount known as the 'Pythagorean comma'.

In 'equal temperament', this problem was eventually solved by flattening each 5th by the Pythagorean comma/12, or about 2 cents.

Early music was based around hexachords; six-note scales with the pattern tone-tone-semitone-tone-tone. The problem was, G-flat and F-sharp for example, would not be the same in the cycle of hexachords. There would therefore be different tuning for each key (so, an F-sharp in D major wouldn't necessarily be the same as an F-sharp in E major.)

It's all very complicated really, and I'm no expert by any means. There are undoubtedly some good books on the subject worthy of a read if you're into that sort of thing.

[lynx]

There is something called the 'Pythagorean comma' [...] There are undoubtedly some good books on the subject worthy of a read if you're into that sort of thing.

Now I know what to look for. Thank you.