[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.


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