The Merits of Nearly Equal Temperament

August 6, 2003

Herbert L. Huestis

Hearing a pipe organ tuned in a sympathetic temperament is
like discovering fine wine after a lifetime of roadhouse coffee. There is
simply no comparison between the delights of pure tuning and the frustration of
cadences that beat unmercifully, no matter what the key or modulation.

When the listener does not hear this woeful tuning,
psychologists call it habituation. In other words, the average person does not
hear the inharmonicity of equal tuning because they know nothing better, and
have come to accept the ragged chords that have echoed in their ears for so
long as normal everyday music. One may take a holiday from equal temperament by
listening to a barbershop quartet for a dose of close harmony. Or take in a
concert on an organ made by an artisan builder who regards tuning as an
integral part of the instrument, reflective of its true baroque heritage. This
journey is worth the expense of rethinking all that we have taken for granted
in years past.

Ironies abound in the world of musical bias and each new
discovery can be delicious. In the late 19th century, we find a reliable bearer
of tempered tuning in that most unassuming of instruments, the reed organ. Free
reeds can hang on to their original tuning at least as well as cone tuned
pipes--in fact, they suffer less from wear and tear. Pump them up, and they
continue to play with the same sweet harmonies that their original tuning gave
them.

There are some aspects of 19th-century tuning that are tantalizing
indeed. Victorian temperaments are nearly equal, which means that in the
tradition of well-tuning, they render harmonious chords in all keys, though not
without individual key color. They are subtle, providing tension and relaxation
behind the scenes, rather than by the blunt contrast of sheep and wolves, as in
baroque temperaments. Their intervals gently progress from calm to agitated,
depending on the complexity and remoteness of each key. Somehow, they walk a
fine line between purity and utility. It seems that their particular strength
is modulation, where the prime keys assert themselves like the sun appearing
through cloud or the calm after a storm.

Of late, Victorian models of tuning have become popular with
both piano technicians and organ builders. The late 19th century was no less
rich in its diversity of temperaments than the 17th and 18th centuries.
Although theorized very early on, equal temperament was a child of the
industrial revolution. Perhaps it was the factory production of musical
instruments that propelled it into nearly universal practice among tuners and
musicians. Studies of ethnomusicology have informed us that the practice of
equal tuning was unique to western civilization and that other cultures
simultaneously developed far more rich and complex modes of intonation.

As we reflect on the revitalization of early music and an
increased regard for performance practice, we take equal tuning less for
granted. The realization that tuning methods have varied tremendously according
to time and place has awakened our ears in such a way that we can now explore
the world of sound and imagination, unfettered by musical prejudice. Take the
challenge: play through the modulations of your favorite 19th-century composer
and see what a "less than equal" temperament does for the music! style="mso-spacerun: yes">

Three practical considerations

If one is going to change an organ from equal to
well-temperament, it should be an operation that is undertaken with
considerable planning. One should consider the nature of an appropriate
temperament and what music will be the primary repertoire. It is important to
look at the objectives of a major change and to evaluate the musical results,
insofar as possible, ahead of time.

The sound of an organ goes a long way to dictate temperament.
Compatibility of organ building style and repertoire are major issues. If equal
temperament is one frustration among many, the organist must decide if a change
to well temperament is going to help change musical values for the better. It
is comforting to know that even a spinet piano can be satisfying when tuned in
a historic temperament. By the same token, there are many organs that will
benefit immensely from the natural harmonicity and increased resonance of a
carefully chosen temperament.

Once the decision is made, one should not use the
"candy store" approach to the selection of a temperament! It is a
good idea to seek out a consultant who has the sounds of various tunings in his
ears. Experience can be most helpful! There are several practical matters that
should be considered when evaluating the pros and cons of various tunings:
balance of thirds, regular or irregular intervals, and shared tuning with equal
temperament.

Balance and width of thirds (in cents)

The reason for tuning in well-temperaments is to achieve key
color. As a composer calls for various keys with a lesser or greater number of
accidentals, the key color is expected to change from pure and restful chords
to vibrating and agitated harmonies. These shifting key colors are relatively
subtle, perhaps even obscure to the layperson, though quite obvious to most
musicians. As one evaluates diverse temperaments, the issues revolve around the
amount of key color desired and the achievement of an even balance that
increases the frequency of beating thirds in accordance with a greater number
of accidentals, both in sharp and flat keys.

Circle of fifths: regular or irregular intervals

This consideration is often overlooked until one makes music
with orchestral and chamber players. Regular intervals ensure the best tuning
of obbligato instruments because the transition from various intervals within
the temperament is predictable and intuitively correct. Some well tunings have
a fine balance of key color, but present such irregular intervals that out of
tune playing by ancillary instruments is unavoidable. It is not a reflection
upon the players--actually, the more experienced and intuitive the players are,
the more likely they are to have difficulty with irregular temperaments. It is
precisely the "anticipatory" nature of "tuning on the fly"
that causes the problem.

Certainly, the best chamber players always tune with the
continuo for each open string or major interval, usually in a circle of fifths.
If that circle of fifths is predictable, things go well. If each successive
fifth is a bit wide or narrow, almost at random, how is an instrumentalist
going to remember the exact tuning? "Regular" temperaments solve this
problem by the use of predictable intervals for the circle of fifths.

Convertible or shared tunings

This is a special consideration where a well temperament
will actually share part of the circle of fifths with equal tuning, usually the
notes A-E-B-F#-C#. These five notes may be tuned exactly the same in both
temperaments! In an equal temperament, the remaining seven notes are tuned in
the same ratio as the first five. However, in a convertible or shared
temperament, the remaining seven notes are altered to the new temperament. The
benefits of a shared tuning are considerable, particularly if the instrument is
to be tuned back and forth between well and equal tuning. This is often the
case with a continuo organ which is featured in various temperaments and often
at various pitches from one concert to another.

Graphs

It is very helpful to see these relationships in a graph, as
well as text and numbers. It has become very common to express numeric
relationships among various temperaments in terms of deviation in cents from
equal temperament. This is not because equal temperament is best or right, but
because each interval is a mathematical division. Thus, a rendering of equal
temperament is not given as a "norm," but as a mathematical point of
reference.

Using an electronic tuning device vs. tuning by ear

It is ironic that tuning in equal temperament became
standard practice about the same time as electronic tuning devices became
commonplace professional tools. At this time, it may be said that most tuning
of musical instruments is done with an electronic reference. That is not to say
that "tuning by ear" is no longer practiced, but aural tuning has a
new perspective, to "test" temperament rather than set it. Before the
reader jumps to any conclusion, it should be emphasized that the "art of
tuning" is still very much intact, and fine piano and organ tuning has not
suffered at all. The very finest tuners still use their ears, and the machines
are just another tool in the box.

Paradoxically, the resurgence of well temperament coincides
with the widespread use of electronic tuning devices and computerized tuning
programs. Virtually every device available offers a synthesis of historic
temperaments that are available at the touch of a button. One might argue that
this enables those without sufficient ear training to "tune" various
instruments--it also enables quick and precise tuning by professional
technicians who have more than enough ear training to do the entire job without
an electronic tuner. It is very advantageous to move from theoretical considerations
to practical application so easily
and effortlessly. It is a conundrum, but a happy one. Without electronic
assistance, historic tunings would be sufficiently tedious that they might well
be left undone.

Tuning by ear remains indispensable. The name of the game in
tuning is to reduce error--especially cumulative error. "Tests" are
the most important aspect of any tuning. They keep the tuner on the straight
and narrow, and prevent compound or cumulative errors that seriously degrade an
artistic tuning.

Recommended computer programs

Two fine computerized tuning programs are Robert Scott's
TuneLab program, available from Real Time Specialties, 6384 Crane Road,
Ypsilanti, MI 48197 ([email protected]) and Dean Reyburn's CyberTuner,
available from Reyburn Piano Service, 2695 Indian Lakes Road, NE, Cedar
Springs, MI 49319.

These are devices for tuning both historic and equal
temperament. Cost varies from less than $100 to about $900, depending on the
range of software desired. The best feature of these programs is that each
historic temperament file may be edited with a word processor. Other electronic
tuning devices are available, usually with pre-programmed historic
temperaments. The author suggests that they be compared on the basis of
accuracy (up to 1/10 cent) and the ease of programming various temperaments.
After that, there are issues of cost, portability and so forth.

As an aside, one may also consider style of tuning. The
author prefers the use of not one, but two electronic tuning devices--a
portable one to use inside the organ and a fixed unit at the console to monitor
tuning as the job progresses. This keeps the tuner's helper quite busy at both
organ and computer keyboards and reduces cumulative error by a considerable
amount.