Actually, Josh is nearly right: In the equal temperament system, it's done
by frequency...
Each note has a particular frequency associated with it, for example the
note A below middle C has a frequency of 440Hz. To get the note that's one
octave above (A above middle C), you multiply the frequency by 2, so that
becomes 880Hz. Now, each octave has twelve semitone steps in it, so it would
seem sensible to mathematically divide each octave into twelve equal steps.
So the frequency of the B below middle C, should be 513.333Hz. This is not
how it works.
If you think about it, go up another octave (to 1760Hz) the number of Hertz
between the bottom note and the top note of the octave is now bigger than
before. Instead of *adding* on a constant number of Hertz to the frequency,
we *multiply* it by a constant factor, this being the 12th root of 2
(1.059463). So, in fact the frequency of B below middle C is 466.164Hz.
Of course, when tuning a piano or whatever, the guy usually uses a 440Hz
tuning fork to fix the A, and does the rest of the piano by ear. Watch
someone doing it, it's pretty interesting.
Hope this is useful.
G-love.
www.gram.org.uk
quoted 38 lines Equal Temperament is how instruments are tuned today in the
> Equal Temperament is how instruments are tuned today in the
> Western world.
> It means that every note is equidistant from the on before and
> the one after
> it. Basically, the octave is divided up into 12 equal half steps, thus
> making the perfect 5th a bit flat and the Major 3rd a bit sharp
> from their
> natural values. This differs from how instruments were tuned
> during, say ,
> the baroque era, when they were tuned in Just Intonation, in which the
> perfect 5th is made slightly flat but the "pure 3rd" between the
> 4th and 5th
> partial of the overtone series is preserved. This tuning was
> used because
> most music during that time was based on harmony of thirds. So,
> back in the
> day of JS Bach, some keys actually did sound "sadder" or "happier" to a
> certain extent, whereas there are no real differnces between one
> minor key
> and another minor key in Equal Temperament. Even older is the
> Pythagorean
> method of tuning, which is tuning based on "Perfect" 5ths, which
> facilitates
> music based on harmonies of 5ths but leaves 3rds badly out of
> tune. Equal
> Temperament equally allows 5ths and 3rds to be used harmonically,
> at least
> to our young western ears.
>
> Geez, I hope this clarifies things.
>
> take care, have fun with tuning!!
>
> Joshua
> \telefon tel aviv
> \benelli design labs
>
> sorry John last time
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