The lucky dozen

Have you wondered why the are twelve notes in the scale? Why not thirteen? This is actually just a lucky mathematical coincidence. The individual frequency of the tones are really not important(in Mozart's days an A was not the same as today), what is important is the relative frequency of the notes. All frequencies does not sound good together, there need to be harmony or chords striving towards harmony. Harmony is achieved when the frequencies relate to each other in sequences of natural numbers like 3, 4, 5 or 4, 5, 6, 7. When the frequencies double up we think they sound so similar so we say they are the same tone just in another octave. When you try to fit these relations together within an octave you will arrive at 12(or 19,31,72 or more) different tones for the tempered scale. Twelve is normally chosen because it accomplishes what is needed and is the least amount that does it. The tempered 12 tone scale is a good compromise because 2^(4/12) is very close to 5/4, 2^(5/12) is very close to 4/3 and 2^(7/12) is very close to 3/2 for example. You can also chose to tone your instruments for the exact chords(Just Interval) but then some of the tones outside the chord or in another octave will sound strange. The interesting thing is that it is not really agreed upon which tuning is the best, there are several rivals 'equal tempered'(most common), 'Just interval', 'Well tempered', 'Mean-tone' or 'Pythagorean'.

This is something to tell those who claim to have the ability to recognize 'absolute pitch'. They simply have a very good memory for frequencies and there isn't really an absolute pitch to remember. Mozart who is said to have had the ability would not recognize the 'A' of today's tunings.