JI vs. ET

Much thanks to all of you who have responded to my request for a
justification of ET studies! Wow, I think I started an avalanche. By the
way, I noticed to my dismay that I had used "ET-x" rather than the standard
"x-tET" in the Subject box; thanks for not criticizing my amateurishness.
I'm gonna get a little bolder this time out, hoping for the same level of
graciousness from you all.

The best reason given so far, in my judgement, is compatibility with the vast
majority of other musicians and their instruments:

>I still use ancient 12-ET when writing for piano, winds, etc., in order to
get music >performed by the majority of musicians. (Brian Belet)

But, of course, that would only apply to 12-tET. This being a list on
alternate tunings to 12-tET, naturally all the x-tET discussions posted are
of the other, non-standard types. It's those that are causing me to stroke
my beard.

The reasons given for those seem to me to boil down to "just to be
different," e.g.:

> 1. The approximations of basic JI intervals also sound interesting in
their own right.
> 2. These tunings provide a new, nontraditional compositional paradigm.
(Gary Morrison)

>...their structures, and widely differing ones at that, make a fascinating
musical-->and yes, expressive--difference. (Paul Rapoport)

Superficially, that seems rather like climbing a mountain "because it was
there," an admirable goal. I could be wrong, but isn't it more arbitrary
than that, more like climbing to any old peak in a range when you could just
as well have been the first to reach the top of the tallest one? Exploration
is fine, and it's always exciting, but it tends to do the most good for the
most people when it's guided by goals that are formed with an understanding
of the fundamental natural principles related to whatever is being explored.
For example, it would be possible to explore the possibilities of building a
house from East to West, but it just makes a lot more sense to build from
bottom to top - it works better for a reason: it takes into account the
natural forces relevant to the situation.

There is a natural order to the way pitches are generated by the oscillating
vibrations of objects. For thousands of years musicians world-wide have
sought to match their tunings to this order. As I understand it, ET first
came about because technology was insufficiently developed to make keyboard
and fretted instruments that would provide enough justly tuned pitches to
allow further progress in the direction of polyphony, without being
prohibitively cumbersome to play and expensive to build. Wouldn't the
musicians and theorists of the Rennaissance have stuck with JI if they could
have? ET is a compromise, however many steps you use to divide the octave,
or any other interval.

But then, any tuning system involves compromises. Paul R. made the following
point:

>... you have true enharmonic equivalent pitches and intervals in equal
>temperaments, which you may get in just systems only by fudging things
>theoretically.
>
>Then there is the practical problem in just systems of treating all notes
potentially >the same way.

While true, I would contend that these are ET-specific issues. We're all
used to taking advantage of enharmonics, and of having uniform distances
between repeating intervals, because we grew up with ET. (Close encounters
of the m3 kind? Sorry :-) Bet I'm not the first to come up with that, huh?)
But they are not necessary, I think, to good music. Why try to force
compositional techniques from one tuning system into another? More to the
point, in what way does enharmonicity correspond to the way that sound
behaves in nature or to human perception of it? Correct me if I'm wrong, no
one has discovered any correspondence; it merely provides the convenient
organizing principle of sustaining or reusing a pitch within a changing
harmonic context; still rather arbitrary to me.

Besides, "been there, done that." By the late 19th century the potential of
those relationships had been thoroughly exhausted; some would even argue that
J. S. Bach exhausted it by himself. Sure, we can hear how those same kinds
of things happen when other roots of various intervals are taken. It's
different. But different is not necessarily better.

>... there are plenty of disadvantages to equal temperaments as well. None of
which >means they are superior or inferior to anything overall. (Paul R.)

> ... a partly valid and partly faulty premise ... that the only goal in
tuning pitches is >to get as close as possible to just intonation. (Gary
Morrison)

Actually, as you now can see, my premise for suspecting that JI may be
superior to ET is not that one tuning system is the basis of judging the
value of others, but that nature is the best basis of judging any tuning
system. Not saying you must accept that premise - whether or not you do
probably depends on the amount of relativism in your world-view. (Aye,
there's the rub.) But if correspondence with natural forces/principles can
be agreed upon as the basis from which the value of a musical theory is
measured, is the pursuit of more resonant polyphony not a loftier goal? I
see JI as a way of picking up where we left off (read "went astray") in the
15th century, and re-continuing development of Western music in the direction
it had been heading up to that point, with the tools to do the job right this
time.

Speaking of tools, I must also accept Marion 's correction:

>>Finally, technology is giving us keyboards with virtually
>>continuous pitch possibilities, ...

>That is what the manufacturer's of these keyboards would like you to think,
but >actually, the pitch possibilities are far from continuous. The
granularity is quite >coarse, both from the perspective of the relative pitch
perception capabilities of the >ear, and from the perspective of what is
possible to modern technology.

You're right. And I should have known better than to state it so
imprecisely. Most commercial "synths" (really little more than sample
playback devices, but all I have to work with) released over the past 2 or 3
years have user tuning tables with 1-cent resolution. I have noticed that
there is always still some beating in JI chords played with pure waves, and
when I figured out how to do the calculations to find what the exact number
of cents difference from ET should be (I'd been tuning by ear for several
months), I saw why.

However, most of the time I'm triggering samples that have some amount of
loop artifact, and/or applying "chorus" effect, and/or using PM vibrato and
inflectional pitch bends for expressive purposes. Under these circumstances
would finer resolution make a significant difference, do you think? I'm
talking here about music for the masses, not theory for us mathematicians.
:-) I've learned to discern 1-cent increments in a harmonic context, but my
wife, a trained pianist, has difficulty discerning between some JI triads and
the same chord in 12-tET even when differences of several cents are involved.
This makes me wonder how fine the resolution really needs to be for most
musical purposes. Then again, when you get beyond triads, small tuning
differences really start to show.

Finally, I do hope that Marion is off the beam about laziness being a
frequent factor in choices over whether to study ET or JI. Although, if I'd
heard that suggestion after spending a few days last month organizing
hundreds of ratios by various means, I'd probably have accepted that
explanation out-of-hand! What's really maddening is having to use ET-based
synth tuning tables to produce JI scales. If only more manufacturers would
make tables that allowed direct entry of ratios! My scientific calculator is
still smoldering.

But his suggestion that "there is the perception that transcendental math is
'higher' than grubby old arithmetic" is very interesting. It's the sort of
thing sounds so intellectually superior; although, like Gary Morrison, I've
never heard anyone actually say that they believed it.

Hope I haven't really ticked anyone off with all this old-school thinking!
:-)

David J. Finnamore
Nashville-based musician, recording engineer, music-technology consultant

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