Originally Posted by: CSchlegelEqual temperament means dividing the octave in 12 equal half steps. Every half step is separated by exactly the same amount - the ratio of the twelfth root of two.

http://en.wikipedia.org/wiki/Equal_temperament

As opposed to just intonation (and other systems) that divide the notes in between the octave in unequal amounts.

http://en.wikipedia.org/wiki/Just_intonation

Equal temperament makes it possible to modulate, transpose and harmonize across the range low to high of possible musical tones.

Equal temperament does have "black notes" in between some notes. Consider the chromatic scale:

A
A# (or) Bb
B
C
C# (or) Db
D
D# (or) Eb
E
F
F# (or) Gb
G
G# (or) Ab

The sharps and flats are "black notes" on the piano. But here is where the crucial distinction comes into play.

In equal temperament the musical distance between one note and the next is a half step.

In just intonation the musical distance between one note and the next is also a half step.

However ...

In equal temperament the physical-acoustic distance (measured in hertz - cycles per second of the sound wave of each note) between each of these is exactly the same: one times the twelfth root of two.

In just intonation the physical-acoustic distance (measured in hertz - cycles per second of the sound wave of each note) between each of these is different from note to note for some of the half steps. This makes for a very inconsistent system.

Make sense?

well i understand a little and would like to say that an octave up from 220hz would be 440hz

what i do not understand is ok so it is equal tempered 12 tone scale but why is it not the case that we have A A sharp B B sharp C C sharp D D sharp E E sharp F F sharp G G sharp

that is what I do not understand