# [chuck-users] Diatonic tuning system

Hans Aberg haberg at math.su.se
Sun May 3 13:55:24 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?

Sure.

> 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.

Basically, it is shortage of terminology. The word "octave" means the
eighth scale degree, the same as the pure eighth P8, often fixed to
the ratio 2.

But when generalizing, first the octave needs not be the interval
ratio 2. And it seems common to use it to denote the span of a whole
scale, even if the number of scale degrees in it is not seven - just
my impression.

So, when generalizing, I simply decided to use the word "octave" for
the whole scale span, and use P8 for the eighth scale degree.

Try the Georgian scale Ge and the Bohlen-Pierce scales BP and BPM to
see hat happen when you try to play a traditional octave.

I just made this up terminology for now. So if there is a better
suggestion, just let me know. :-)

Hans