Jason wrote:
<< The virtue
of seeing major third AND fifth together means that you can assess what keys
will sound best and worst (you have a good view of all the major triads). >>
Greetings,
The more ways to look at something, the better. My unbending rule is
to be flexible!
I've been amazed at how differently some things appear from a different
perspective. Things like Salvadore Dali's image-within-an-image paintings,
or an off-camber decreasing radius corner on a motorcyle track, OR maybe a
series of thirds that are all different and organized in line with the
circle of fifths. There can be completely different things there, depending
on where you are coming from. I suppose the greatest shift of perspective in
my musical life came when I heard "Switched-On Bach. It was something
entirely different than the tired, old, tuned-by-choir-director's wife (who
had "issues"), wind-blown, two manual organ in my boyhood church, but I
digress.
I can't figure out how to graph it, but I have a vertically oriented,
3-D chart with the fifths represented by bars on a right-angle axis to the
thirds, ie, If the bars representing thirds were stretched from East and
West, and those representing fifths were aligned North and South, and both
perpendicularly centered on the same axis, when rotated there would be two
views that showed only the thirds and two that showed the fifths. These four
views would be 90 degrees apart and whatever row of bars that was viewed
"edge-on" would effectively disappear. However, at 45 degress of rotation,
one would see the profile of both at the same time. This allows the visual
comparison of compound factors (two sizes of intervals) in one key to those
in another.
By way of visualization, to do this for 12ET with 1"= 1 cent, you simply
take two pieces of cardboard, one13" X 2" and the other 13"X 13.7" and cut a
lengthwise slot half way up both. Mark off 12 1" spaces on both sides of both
pieces. Then by sliding the slots together, you would have a 3-D display
showing equality along both lengths. (it looks sorta like a big Christmas
tree ornament a 2nd grader would make in school. )
Since the thirds' effect on triadic harmony is more pronounced, and the
fifths are tempered by slighter amounts, the fifths may be logically
represented by bars that used a larger "length per cent" . It increases the
visual contrast without skewing any comparison since the idea here is to
demonstrate how the size of interval is associated with a given key, not how
much farther from Just the fifths are from the thirds, or vice versa.
However, that isn't what I wanted to make a point about.
What I wanted to talk about was value judgments, as in labeling things as
better or worse. When the keys in an unequal tuning are described as best
and worst, a certain bias seems evident, one of which consonance is good and
dissonance is bad. I think this is a limiting perpsective, for several
reasons.
In the Western tradition, music has encompassed far greater complexity
than simply "consonance is good", otherwise, we would still be singing
Gregorian chant. I think there is an implied value we feel for consonance,
perhaps because it does not occur as readily as dissonance. (There are many
ways an interval can be dissonant, but there is only one "Just"). When
objects vibrate in sympathy with one another, they do so along modes that are
consonant between them, requiring no more energy than the original signal,
so we can perhaps view consonance as harmony that requires work for us to
attain, but occurs effortlessly in nature. Of course we like it, 2,500 years
of pursuing it can't have been the result of a casual interest.
Consonance is also a source of relief. For us little piggies who have
learned to recognize a pearl, it often makes us slow down and think beautiful
thoughts, (ear candy, sonic sucrose, the noisey nard of the nervous). We
know that those listeners raised in the Western tradition of harmony exhibit
sedative responses to purely tuned intervals, so consonance has its effect.
However, with consonance, like opium, optimism, or rising stock futures, we
can get too much of a good thing and take it all for granted. Then what?
Well, then we look to consonance's spikey cousin, dissonance. Edgy sort
that. We know that those same Western listeners find dissonance to be
stimulative. Too much and one is "incited to fury", but how 'bout just
enough to wake up a world that listened to pure fifths for 1000 years? A
natural by-product of the Pythagorean tuning was a harsh third, but even it
was used! Surviving manuscripts of the 13th and 14th centuries lead us to
believe that it was in use at the time, as Gothic music seemingly consisted
of tremendously dissonant intervals mixed among very harmonious ones.
How much is too much? How much salt does the stew need? Spices aren't
something one can live on, but what do you do without them? We can see where
the Crusaders' enthusiasm really came from, they were looking for trade and
spice was a big part of it, (if I had been eating unflavored gruel for 10
centuries, I would probably kill somebody for a handful of pepper, too.) My
father remembers fighting in the South Pacific during WWII, he said the
weather was so perfect all the time that even the hint of a thunderstorm
crossing the small islands they were on was much anticipated. Anything to
break the sameness!! In the same vein, I think the dissonance that is the
lightning and salt in our music is essential to the maintenance of interest,
though how much is a subjective quality. Hence the decision depends on the
knowledge (thus expectation) of the listener, and that is where the tuner
finds his opportuninty.
We know a consonant chord feels good, but does it feel better when it
follows something something that contrasts with it? A "tight-shoe" theory of
harmonic release? I think so, and it certainly appears that Beethvoen had
the same notion. His music too often demonstrates the use of unequal
temperament to heighten expressive passages for us to overlook its possible
effects. Deciding on a palette for such use is now the chore of the tuner,
since the established piano demogogues seem to know virtually nothing of this
subject and often seek the safety of the familiar equal temperament.
If we are to accept the 13.7 cent third as the only one, we have
accepted a level of dissonance that was historically regarded as fairly high.
So how can we then say that consonance is good and dissonance is bad when we
are using a tuning in which every third is so dissonant? This seems possible
only when we no longer hear the beating, when we no longer listen on close
enough terms to hear the contrasts. If we are that inured to the actual
sounds, we have no ability to hear consonance and we have given up the
greatest qualities in keyboard music for the convenience of a "standard"
tuning.
The cost of this safety is the loss of true consonance and dissonance,
all of which is averaged into a tuning with one size third. So, my point, (I
remember having one somewhere earlier...), if an unequal temperament has
"good" and "bad" keys, then the ET has everything "sorta" bad with all that
beating. I, however, don't think of ET as "bad", just restless,
unresolving, and bland. It is also generally true that unless one plays the
same amount in all 12 keys on the piano , a well-temperament creates less
total dissonance!
Regards,
Ed Foote
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