Keenan Justness

Dave (if you are out there), or
Paul (if you might know):

Why the second derivative of the "Harmonic Entropy" function?
What special significance is associated with differentiating?

Curiously, J Gill

> Dave (if you are out there), or
> Paul (if you might know):
>
> Why the second derivative of the "Harmonic Entropy" function?
> What special significance is associated with differentiating?
>
> Curiously, J Gill

Was there ever a reply to this? The post about
justness just seems to come out of nowhere in the
archives.

-Carl

Carl Lumma wrote:
>>Dave (if you are out there), or
>>Paul (if you might know):
>>
>>Why the second derivative of the "Harmonic Entropy" function?
>>What special significance is associated with differentiating? >>
>>Curiously, J Gill
> > > Was there ever a reply to this? The post about
> justness just seems to come out of nowhere in the
> archives.

Okay, well, a just intonation point is at the bottom of a basin of a dissonance graph. But so is the point where one basin meets another. So a zero first derivative tells you the either you've got a perfectly just tuning, or a perfectly ambiguous one.

The second derivative tells you if it's a maximum or a minimum. So a JI point is minimum dissonance, and so should have a positive second derivative, right?

The sharper the point is, the faster the gradient has to change. Hence the second derivative will tell you where the sharpest points are.

Graham