[chuck-users] Diatonic tuning system
Hans Aberg
haberg at math.su.se
Mon May 4 04:32:03 EDT 2009
On 3 May 2009, at 19:26, Kassen wrote:
>> In order to illustrate that the octave needs not the interval ratio
>> 2,
>
> This is a very confusing sentence to me, roughly on par with "to
> demonstrate a Km needs not consist of a hundred meters...". Could you
> kindly link to a explanation of the why and how of this?
The word "diapason" can mean "all notes in the scale". So I will
change that.
> I'm quite interested in tunings but I know little about the
> established theory and I thought the octave as a doubling in frequency
> was the one thing I *could* depend on. Clearly this was naïve so it
> would be nice to get a definition of "octave" from the perspective
> that you're using.
The octave is the eighth scale degree, just the interval numbered
eight, which needs not be the interval ratio 2. (In Swedish, one
prefers the Latin names, for example, the 7th is called "septima", so
a distinction between octave an 8th is not possible.) Also, the
interval ratio 2 needs not be a doubling of the frequency, because one
may use a tuning that stretches or compresses the scale.
So the octave needs not be the interval ratio 2, the diapason needs
not be the octave, and the interval ratio 2 needs not be a doubling of
the frequency.
Hans
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