The worst scale

It might be interesting as a psychoacoustic experiment to create the
WORST musical scale, in which, presumably, virtually all attempts to create music would
sound bad.

On Mon, Oct 24, 2011 at 1:43 PM, WarrenS <warren.wds@gmail.com> wrote:
>
> It might be interesting as a psychoacoustic experiment to create the
> WORST musical scale, in which, presumably, virtually all attempts to create music would
> sound bad.

A composer with stage named "Igliashon Jones" did this a while ago; we
gave him our "worst scales" and he made something nice out of every
one. The pieces were often very dark, dissonant, etc, but I wouldn't
say it was "bad." He then made an album called "Transcendissonance"
that aimed to use only the "worst" scales possible.

Maybe we just failed at our goal, but I don't think it's possible. The
introduction of bad features into a scale doesn't remove any good ones
that might have been sneaking in there.

-Mike

A brief computer investigation reveals that apparently there aren't any
really bad equally-tempered scales.

That is, let X be the frequency ratio between two adjacent notes in the scale and
let 1.02 < X < 1.10. Then the scale
1, X, X^2, X^3, ...
always contains at least one frequency ratio R=X^k
with k>0 integer and 1<R<=3
such that R is pretty consonant (my figure of merit <= 0.06127
where FoM<0.08 if good and FoM<0.16 if ok sound).

I'd been hoping there would be an X that would dodge all consonances,
but apparently no such X exists.

The worst scale my computer found is
X = 1.09258181
(in the sense it meets that upper bound).

Searching the wider range 1.02 < X < 1.20
found this bad frequency ratio as the basis of an equally tempered scale:

X = 1.13238997

with no consonances better than Fig.Of Merit = 0.123421.

It only has about 5 and a half notes per octave, though.

On Mon, Oct 24, 2011 at 2:41 PM, WarrenS <warren.wds@gmail.com> wrote:
>
> A brief computer investigation reveals that apparently there aren't any
> really bad equally-tempered scales.
>
> That is, let X be the frequency ratio between two adjacent notes in the scale and
> let 1.02 < X < 1.10. Then the scale
> 1, X, X^2, X^3, ...
> always contains at least one frequency ratio R=X^k
> with k>0 integer and 1<R<=3
> such that R is pretty consonant (my figure of merit <= 0.06127
> where FoM<0.08 if good and FoM<0.16 if ok sound).
>
> I'd been hoping there would be an X that would dodge all consonances,
> but apparently no such X exists.
>
> The worst scale my computer found is
> X = 1.09258181
> (in the sense it meets that upper bound).

That's about 7.8-equal.

I think you'd be very interested in Gene Smith's work in using the
zeta function to do exactly what you just did. By looking at the
Riemann-Siegal Z function, we can see which EDOs best approximate
which primes, or which integers depending on how you look at it. See
here:

http://xenharmonic.wikispaces.com/The+Riemann+Zeta+Function+and+Tuning

-Mike

Igliashon Jones' compositions in "bad scales":

http://split-notes.com/007/

Apparently his real name is "Jason Yerger."
Interview: http://untwelve.org/interviews/jones.html

My reaction: I think he's doing his best, and it is surprisingly good...
but the bottom line to me is it IS a bad scale,
and it is fairly apparent Jones is doing his best within the confines of
what clearly is a bad scale. Too much dissonance.