> > So (as least within Western music) tones that are very
>> close together but not sharing sub-frequencies (such as
>> intervals of less than a half step) are not very harmonic
>> and are often dissonant.
>Here's where things already get hazy: Dissonance cannot be
>consciously created - one might say it doesn't even exist.
>The threshold between harmony and dissonance is like the
>threshold between fact and opinion: it lies entirely in
>what each of us as an individual can "handle". It's really
Exactly. That's why I used phrases like "very obviously harmonic."
I would argue that a major fifth interval is quite obviously
harmonic. Most vibrating objects vibrate at a primary frequency and
at other frequencies that are arithmetically related. A string
vibrates on its length, half its length, a third of its length, etc.
The half its length is a note an octave above. An A string vibrating
at 440 Hz also vibrates on half its length at at 880 Hz--the A above.
At a third of its length it is vibrating at an E above that higher A,
making an A and an E very obviously harmonic. That doesn't mean that
an A and an E flat are un-harmonic, dissonant, nasty, lousy, bad,
etc. It just means that the harmonies are less obvious.
Satisfaction based on harmony is another thing. Some may find the
major fifth of much of simpler Western music the most satisfying
interval in its "naturalness." Others might find the flat fifth of,
say, Billy Strayhorn's "Take the A Train" more exciting, refined,
sophisticated, etc. (I would argue that only a fool would undertake
honoring one over the other or claiming some sort of moral
>For example, I have a CD by Ali Akbar Khan, a renowned Indian
>musician, and some of it simply sounds horribly dissonant to
>me. But since it's man-made, I know deep down that it can't be
I specified Western music for a couple of reasons. The most important
is that it's the only music I really know anything about. Don't
assume that all music is based on the same notions. Harmony in the
sense of a chordal structure implied by music is very far from
universal, even in European and American musics.
>There is one question, though: does the human brain
>itself have some kind of limit as to the depth of
>harmony is can absorb, irrespective of "training"?
There may be but I don't know how one would go about finding it.
Raise babies while listening to brake squeals and cat yowls while
smiling and bobbing your head to see if they grow up nostalgic for
the sounds of their youth?
> > I won't belabor the analogy to type. If the application of this to
>> choosing multiple typefaces or multiple sizes or weights isn't
>> obvious to anyone, just ask.
>OK, but what about in the design of type?
I suppose that much of what I implied about visual relationships
between typefaces applies to visual relationships within typefaces.
Simple form tends to show up close differences more than more complex
form does. Large contrasts tend to mask differences in echoes more
than small contrasts do. Echoes and other repetitions of whatever is
going on within major forms tend to unite disparate major forms.
Damn, it sounds so much less romantic stated that way.
Hrant, I suspect that this will, pardon the expression, ring true for
you: Another parallel is that tuning systems are contingent. If you
start with an arbitrary A at, say, 440 and build an E based on that A
and a B based on that E and an F sharp based on that B, and keep
going around until you hit A again, you'll find it to be unlike the A
you started with. For an instrument to play well in a variety of keys
it needs to be fudged (although instrument makers prefer the term
tempered.) Ultimately ears and contexts win over frequency
measurements and arithmetic.
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