dissonant scales

Hi,

I notice that you talk about many different scales that are more or
less consonant. What about dissonant scales? I don't know why one
would want to create a scale that sounded lousy, but it should be
possible.

My thought was to use the golden ratio, since they say that it doesn't
approximate well with a fraction. If you take the first twelve powers
(and then divide to get them back into the same octave) you get:
1
1.618
1.309
1.059
1.713
1.386
1.121
1.814
1.468
1.188
1.922
1.555
1.258

The thirteenth power of phi divided by 256 is about 2.035 We could
just use the thirteen notes given, and raise or lower by octaves. I
suppose in the keeping of the spirit of dissonance, we might raise or
lower these notes by 2.035...

Any thoughts?

John Berglund

Good questions. There's a lot of unanswered questions about
dissonance. It's easy to describe a particular dissonance as merely a
deviation from a certain justly tuned interval, but I think there's a
lot more involved than just that.

One issue that I think is worth exploring is the combination tones
that develop from dissonant intervals. Some of these tones are low
frequency and may have physiological effects that we don't understand
very well.

A good steady low frequency beat is common in ritual music and can
have a strong effect on the listener. It seems that low frequency
difference tones may also produce unconscious effects.

Different parts of the body resonate at different frequencies and
there are brain wave frequencies that may also be affected by
external vibrations. It may be that reactions to dissonance are very
personalised. I find that some dissonances have a calming effect on
me whereas others will actually make me feel ill.

I discuss this issue to some extant at
http://danielthompson.blogspot.com/2006/10/is-dissonance-as-bad-as-
people-think.html

I also find dissonance interesting because of ambiguities that arise.
Ambiguity might not always be desirable, but it can be used to good
effect. A simple major chord in just intonation is pretty direct, but
if you take a similar chord in a more dissonant tuning, you may find
that it can be open to multiple interpretations. You might view it as
a basic chord built on thirds, or as a more exotic chord built on
fifths. You could view certain chord progressions as either
increasing or decreasing in tension depending on your interpretation
of its underlying structure. The possibilities are endless and it's
all very exciting to me.

I have experimented, somewhat, with scales like yours that are based
on the golden ratio. I found them to be hard to work with, but I know
that I haven't given them the attention that they deserve. I'm hoping
to return to them at some point. In the meantime, I would be
delighted to hear about your explorations. I do enjoy dissonant
tunings like 13 or 15 tone equal temperament. I'm working on some
pieces now that I hope to make available soon.

I don't like dissonance for the sake of dissonance and am actually
pretty conservative in my musical tastes, but I do think that
dissonance is worth studying and can be part of meaningful,
structured and emotionally compelling music.

Daniel Thompson

--- In tuning-math@yahoogroups.com, "anisohedral" <anisohedral@...>
wrote:
>
> Hi,
>
> I notice that you talk about many different scales that are more or
> less consonant. What about dissonant scales? I don't know why one
> would want to create a scale that sounded lousy, but it should be
> possible.
>
> My thought was to use the golden ratio, since they say that it
doesn't
> approximate well with a fraction. If you take the first twelve
powers
> (and then divide to get them back into the same octave) you get:
> 1
> 1.618
> 1.309
> 1.059
> 1.713
> 1.386
> 1.121
> 1.814
> 1.468
> 1.188
> 1.922
> 1.555
> 1.258
>
> The thirteenth power of phi divided by 256 is about 2.035 We could
> just use the thirteen notes given, and raise or lower by octaves. I
> suppose in the keeping of the spirit of dissonance, we might raise
or
> lower these notes by 2.035...
>
> Any thoughts?
>
> John Berglund
>

Erv Wilson has done much in this way of scales based on what he calls recurrent sequences of which the fibonacci series is just one.
you can find many of these here under the title
Scales from the slopes of Mt. Meru
http://anaphoria.com/wilson.html
where i have also added an introduction

Temes might be the first person to investigate this. http://anaphoria.com/temes.PDF
a copy of his letter sent to Walter o Connell who wrote an article on it that was refused by Die Reihe
since it fell outside of 12 et

some examinations by myself exist here
http://anaphoria.com/MERUcream.PDF

anisohedral wrote:
>
> Hi,
>
> I notice that you talk about many different scales that are more or
> less consonant. What about dissonant scales? I don't know why one
> would want to create a scale that sounded lousy, but it should be
> possible.
>
> My thought was to use the golden ratio, since they say that it doesn't
> approximate well with a fraction. If you take the first twelve powers
> (and then divide to get them back into the same octave) you get:
> 1
> 1.618
> 1.309
> 1.059
> 1.713
> 1.386
> 1.121
> 1.814
> 1.468
> 1.188
> 1.922
> 1.555
> 1.258
>
> The thirteenth power of phi divided by 256 is about 2.035 We could
> just use the thirteen notes given, and raise or lower by octaves. I
> suppose in the keeping of the spirit of dissonance, we might raise or
> lower these notes by 2.035...
>
> Any thoughts?
>
> John Berglund
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning-math@yahoogroups.com, "anisohedral" <anisohedral@...>
wrote:

> Any thoughts?

I've suggested tunings based on zeros of the Hardy Z function
such that the derivative is also relatively small. I don't think anyone
has pursued this goofy idea.

>Any thoughts?

I think a better approach would be to use harmonic entropy. We
could just take the local maxima of entropy between 1/1 and 2/1
and call it a scale, but this would only ensure high entropy for
intervals in one mode of this scale. To take all intervals into
account, we might turn to the method Paul Erlich used for his
"diadic entropy minimizer". Here's his description of this method:

""... start at the stack of 5-tET intervals, and roll down (Matlab
uses the Nelder-Mead simplex [direct search] method) the total
entropy hypersurface to the bottom of the basin. Sometimes, the
starting point is equally close to two basins, one of which is the
mirror-inversion of the other ...""

By seeding this with a variety of random scales (instead of an ET),
Paul was able to find the "minimum diadic entropy" scales for 5, 6,
and 7 notes/octave. I don't know about Matlab's implementation or
the restrictions of this technique, but presumably it could be
'reversed'.

Phi has also been used in attempts to get the worse "beat ratios".
For example, the ratio between the beat rate of the 5:4 and 6:5
in an approximate 4:5:6 triad. The results don't sound any worse
(to me or Dave Keenan), when controlled for total mistuning, than
'simple' beat ratios like 2:1 or 3:2.

-Carl