Neutral Thirds

I'm glad to hear discussions about the neutral third, probably best characterized
as 11:9 or thereabouts. I think that "ambiguous" is indeed good way to
describe it,
and that Jeff's comment:

> It is an interesting interval since it sounds like some
> kind of third but not any kind in particular. It doesn't
> seem to want to move anywhere but doesn't give any trouble
> if it does.

Is very definitely correct and insightful.

In particular, I've found that we are so conditioned to think of thirds as either
major or minor that when we hear something right between the two, our ears
have a
tendency from habit, to characterize it as one or the other. The option to portray
that kind of ambiguity can be a useful to tool for composers; it makes listeners
reconsider the basis behind our impressions of majors and minors.

I have found, at least in an 88CET environment, that melodic considerations
suddenly have a stronger effect upon our impressions of whether a neutral
third leaves
a major-like impression, or a minor-like impression. I suppose that's not surprising,
since the harmony suggests neither.

One interesting-sounding progression in 88CET based upon the ability to
split the
fifth in half to get a neutral third, then that in half to get a small whole
step, is
the following ... "horn-shaped" perhaps? ... voice leading pattern. I'll
characterize
it below in 88-cent steps above whatever root note you'd like to use, that
root being
represented here as 0 of course:

16
14
12 12
10 10
8 8 8
6 6
4 4
2
0

I used this progression to begin the fourth movement of my "Alternative
Fuels"
suite. I find stacks of four, five, and more neutral thirds more interesting
than
just neutral triads. That's true of 9:7s as well: I find stacks of four or
more
9:7s interesting-sounding than supramajor triads.

As for using 8 per 3:2 rather than 88CET, that strikes me as an interesting
thought. Clearly the two are very similar of course. I originally conceptualized
88CET as 11 per 7:4 (88.075CET), but 88 was more convenient. I suppose
87.745CET
is at a slight disadvantage when it comes to approximating 5:2 and 7:4. But
there
are probably counterexamples, and the difference is pretty small either way.

I have toyed with the idea of expanding an 88-cent interval size to
somewhere
around 88 1/4 cents to make it less like 41 per triple-octave. 88.25CET would
miss
the triple-octave by 18.25 cents rather than 8.

Jeff mentioned not liking 9:7 as much as 11:9 and 7:6. As I've mentioned before
on the list, I think the key to understanding 9:7 is to avoid thinking of it
as a
major-like third, but instead as a shocking or perhaps "freaky"-sounding third
instead.