After loosing any hope to understand anything in this thread, I am asked to add my two cents... well, I will try
I am able to play the computer indeed, but I fear that I am not able to write the sounds as in the English way.
Our "notes" are do re mi fa sol la si do. Don't remember where the intervals are simple or double, anyway from a note and the same note in the following octave( is that correct?) there are twelve such semitones.
Well, La is, for example, 440 hertz ( in basic, sound 440, 10 gives a sound "la"for 10 units of time)
The following La is 880 hertz.
In between, in the well tempered way of tuning, all the notes can be obtained in this way:
la = 440
la + one semitone = 440 times (twelveth root of two)
la + two semitones = the previous number times (twelveth root of two)
and so on.
Approximately,
(twelveth root of two) = 1.059463094359295264561825.
It is an approximation, of course, since the number is not rational = it is proven that it cannot be written exactly with a finite number of decimal digits.
