well - there are severyl kinds of approaches for why nowadays music sounds the way it sounds.

There are a few kinds of tunings:

Clean Tuning (Natural tuning/diatonic tuning)

is the mathematically correct way to tune an instrument.
It is based on a partial tone series which is divided by 12 tones per octave. A fifth for example whould have factor 1.5 and a third factor 1.25 from the root tone.

The problem with this tuning:
Since frequencies of the partialtones depend on the root tone the tone "f" for example would sound slightly different on an instrument that is tuned in G than on an instrument that for example is tuned in C. In other words: on an instrument that is tuned in C with this kind of tuning you would only be able to play C Major. Playing in another scale would sound like crap for the intervalls would not be correct anymore.

In order to avoid this problem the "well tempered tuning" has been set up at the beginning of the 18th century (which was replaced by equal tempered tuning in the 19th century)

Well Tempered Tuning:

From aprox 1700 the well tempered tunings where winning through (yes - there where more than just one well tempered tuning). Those where specific tunings with the same goal - a tuning that allows you to play all scales on one instrument. The most common one of those was probably the "Werckmeister-Tuning" introduced by Andreas Werckmeister in 1691 in Europe.

In the first half of the 18th century Johann Sebastian Bach was inspired by Werckmeisters work and wrote his pieces of "the well tempered Clavier" which finally helped the well tempered tuning to make its breaktrough. From this point on it began to replace the still conventional diatonic tuning more and more.

All those well tempered tunings have one thing in common: a very distinct tone-characteristic. since the frequency-ratios are not identical to those of the equal tempered tuning, every key has its own characteristic sound.

Equal tempered tuning (chromatic tuning):

In 1559 price Chu Tsai Yü (china) was doing calculations on frequency ratios that allow to play an instrument cromatically (actually he worked out the 12th root of 2:1 precisely to 9 places). The resulting equal tempered tuning is therefore also called "Cromatic tuning".

Basically this tuning is a controlled detuning of the partialtones. The definition of a halftone is a frequency that is multiplied by (aprox) 1,0594631 (1,0594631 = 12th root of 2). A wholetonestep therefore would be a multiplication of a frequency with factor 1,0594631².
An equal tempered fifth would be 1,0594631^7 respectively the root multiplied by 1,4983. IN diatonic tuning the fifth would be 1.5 (see the difference?)

Because of the equal tempered tuning there comes a special intarvall into play: the tritonus. It is an intervall of exaclty 3 fulltones and divides the octave in exactly two halves. The tritonus cannot realy be compared with an interval of the diatonic tuning and therfore it sounds extremely out of tune to peeps who are used to diatonic tuning. Thats why it was called tonus diabolicus or diabolos in musica (devil in music).

[Edited by Azrael on 10-28-2002 at 10:32 AM]