The Merits of Nearly Equal Temperament

Herbert L. Huestis

If one may indulge in melodrama, one might refer to "The Curse of Equal Temperament" when commenting on the method of tuning that steadfastly refuses to take into account the relationship between an instrument, its music and player. "Equal" is tuning for the sake of tuning, done by successive generations of tuners who practice their craft exactly the way they were taught to do it, no questions asked. And the whole business has been cast in cement by electronic tuning devices--ETDs--in widespread use today!

Looking back over the past two centuries, we can take note of several events that contributed to this situation. They include the invention of tuning forks, the industrial revolution (with its myriad of factories that produced musical instruments) and the emergence of ETDs such as the Conn Strobotuner.

Tuning forks as we know them appeared in the early 1800s. Their fixed pitch enabled a reference to specific frequencies for tuning of musical instruments; tuning practices previously had varied widely by region and nationality. Tuning forks were a valuable resource for the stabilization of tuning everywhere. By the end of the 19th century, they were used for temperament tuning in the great piano houses such as Broadwood and Moore.

The turn of the 19th to the 20th century was surely the golden age of the piano, and in North America the houses of Steinway and Heintzman represented a pinnacle of musicality and at the same time promoted the artisanship of factory craftsmen unparalled in our own times. The revival of the organ as an "authentic" instrument would wait some fifty years, and with it the same emphasis on tuning as an integral part of a musical instrument.

Thinking back on the piano and its artists of the early twentieth century, one can reflect on the incredible tuning of these instruments, made for Rubinstein, Horowitz, Richter, Gilels and so many others. Pianism was almost a cult, and the tuners who worked on these instruments behind the scenes contributed a rare form of art to the piano. They defined its sound, its carrying power and its musicality as surely as the artists who played it so superbly.

With the revival of the tracker organ, tuning once again became an integral aspect of the musicality of these instruments. Temperament is most carefully thought out by artisan organ builders today with or without the help of tuning machines.

Machines? Yes, the same tuning devices that began with tuning strobes evolved into electronic displays of one sort or another, as varied as one might imagine. To some extent, they displaced "aural" tuning, so highly valued within the community of piano tuners and technicians. Unfortunately, some tuning practitioners passed "go" on the Monopoly board and skipped ear training by jumping into machine tuning as a quick means to an end. However, fine tuners the world over incorporated tuning devices into their tool kit as important aids to the musical ear that was already hard at work. It is this kind of practitioner that exemplifies the best in the tuning business.

The "curse" of machine tuning is that it implies that equal tuning is mathematically precise, and that the ear is irrelevant to the outcome of setting a temperament. Semantics are everything, and it is something of an understatement to say that "equal" tuning is not at all equal! An artistic tuning, whether in a baroque temperament for Bach cantatas or a modern tuning for a Rachmaninoff piano concerto, is anything but equal. It is what the music demands. A marvelous example is the use of the Vallotti temperament for performances of Beethoven's "Emperor" Piano Concerto. Yes, it works very well. One can only marvel at the work of the world's best piano tuners on the concert stage. The tuner's ear is alive and well in our finest recordings and live concerts--as it should be in the presentation of our finest pipe organs.

The "blessing" of machine tuning is that it provides the opportunity to record "best" tunings for various instruments and occasions--for tuning devices are not only tone generators of various pitches with an array of mathematical relationships, they are recorders, too. They make possible the quantification of any kind of tuning, from pianos to organs to gamelans. They are, in a sense, the power that destroyed some important aspects of tuning by ear, but they are also the force that brings back aural tuning. This is a happy conundrum that should be exploited for all it is worth.

The tuning device as recorder provides the opportunity to use temperament in an artistic manner to give expression to the best qualities of an instrument (and sometimes, to suppress the worst ones). For example, a concert grand piano in a large hall derives carrying power from vibrations generated within the temperament, as well as the soundboard and case of the instrument. For this reason, mild temperaments with more- and less-pure thirds benefit these pianos if they are speaking in a vibrant hall. On the other hand, a pure temperament can go a long way to smooth out a small piano with short strings that are full of false beats. Try that on your spinet in the choir room. You will be amazed at the improvement in sound!

Some practical considerations for the tuner

For the benefit of the reader who is truly interested in investigating the benefits of 19th-century (or earlier) temperaments with the help of machine tuning, this last of three articles will be devoted to the practical application of tuning techniques. Since it is widely available at low cost, the ETD (Electronic Tuning Device) of choice will be Robert Scott's TuneLab97 software, available at <www.tunelab-world.com&gt;. A basic computer and sound card are also required. With this tuning program, there will be a set of historical temperaments that offer a wide range of options for the tuner. Temperament files are extremely simple. They are notated in cents deviation from an equal distribution in this manner:

Representative Victorian Temperament (Moore)

C   2.5

Cs  0.0

D   1.5

Ds  1.0

E  -1.5

F   2.0

Fs -0.5

G   3.0

Gs  0.5

A   0.0

As  1.5

B  -1.0

Armed with this modification to equal proportional tuning, the tuner can proceed to lay bearings for a temperament. Fear not! I am not going to give the reader blow-by-blow instructions on how to tune. But it is important to note that most tuning failures result from tempering the wrong intervals first! Therefore, with this temperament one can follow the practice of using F, A and Cs tuning forks to divide the circle of fifths into manageable portions, so that one will not choke on a cumulative error. In this case, A and Cs may be set from tuning forks A=440 and Cs=277.18. "A" is used to embark on the white notes in the circle of fifths, and Cs is used for the black notes. As a rule of thumb, the intervals involving black notes are tuned first, pure or nearly so, and the intervals involving white notes are tempered and tuned last. Follow that rule, and you will avoid the trap of "reverse well" tuning.

The tuning fork F=349.23 completes the triad of foundation notes. In well-tempered tuning, "F" will be raised to provide the desired effect of the third F-A. Generally, the F-A and C-E triads will determine the nature of the well-temperament desired, whether mild, moderate or intense, as in the baroque temperaments. This is where the sound and character of the instrument and its music come in.

If one is tuning "equal" temperament, the thirds F-A-Cs¢-F¢-A¢ provide a very useful octave and a third in which to lay the bearings. These thirds will increase their vibrations as they ascend. This is one of the tests used in setting equal temperament. Conversely, in laying well-tempered bearings, the thirds will alternate in vibrancy between white and black keys. F-A will be slower than equal, A-Cs will be the same as equal (13.7 cents wide), Cs-F will be faster than equal, and once again, F¢-A¢ will be slower than equal. So far, the only adjustment has been to sharpen "F" to make a relatively slow third F-A.

Once this has been accomplished, one should tune Cs-Fs-B relatively pure and Cs-Gs-Ds-As-F relatively pure, monitoring the computer screen while one tunes these notes. Then, tune A-E-B and A-D-G-C-F relatively tempered, while monitoring each note on the computer screen. This will provide well tempered bearings, while applying tuning tests to the process. There will be little chance of a cumulative error of any significance.

Since the tuner is applying aural tests as well as reading a computer screen or a dial tuner to monitor progress, this work can be carried out at the organ console or the inside of the organ case, or preferably both. A tuner's assistant can do much more than hold keys. It is very helpful if they monitor an ETD while the tuning is in progress. This prevents errors and speeds up the tuning.

Which temperament to use?

There are literally hundreds of temperaments from which to choose, so it is very useful for each tuner to develop criteria which work for them. Several points are worth consideration.

It is most helpful to adopt a temperament that allows equidistant bearings for the tuning of a circle of fifths. The F-A-Cs method provides this option in both well and equal tempered tunings.

Another consideration is the provision of various degrees of purity within a related group of well tunings. An example of three temperaments that progress from mild to moderate are Moore, Peter Prelleur, and Young (1799). All are based on zero deviation in cents for the notes A and Cs, and increased purity for the triads C-E-G, F-A-C and G-B-D.

One may take into consideration the balance of triads in a symmetrical or non-symmetrical array. A symmetrical array of triads will increase vibrancy in direct proportion to the number of accidentals in each key. Asymmetrical triads will favor certain keys and are more consistent with harpsichord tunings where temperaments are chosen for specific literature.

Blessing or curse: from anathema to good fortune

If one looks upon machine tuning as a curse for its illogical suppression of musical values (modulation being the first victim), the descendants of strobo-tuners must bear a heavy burden of resentment. However, the computer and its dedicated mechanical brethren have rescued those who still tune by ear by providing the means to record their "best" tunings, and experiment with the most musical tunings for each instrument. Credit must be given to a significant group within the Piano Technicians Guild for their unflagging efforts to promote both aural tuning and the use of unequal, "well" and nearly-equal temperaments. A review of the comments of these technicians reveals a dedication to musical performance that stands as an inspiration to organ technicians and tuners as well. Commendation and approbation is also well deserved by artisan organ builders who have often stood alone in a sea of indifference by insisting that temperament and tuning are significantly related to each musical instrument they produce. There are many organ builders who will not resign their instruments to "ordinary tuning and care," but who steadfastly maintain their own instruments so that among other things, the tuning will be preserved. Bravo (!) to these dedicated builders.    

Herbert L. Huestis

Herbert L. Huestis is a contributing editor of THE DIAPASON.

Most of the time, pipe organs and pianos share equal
temperament--at least in theory. Compared to an average piano tuning,
organ tuning is a massive job. Organs are relatively easy to touch up, but a
major operation to tune thoroughly. A number of factors are critical for
accurate organ tuning, including temperature, location and condition of the
pipes, the accumulation of dirt, and wear and tear. In addition to these
factors, it is just plain hard to get around in them. One must manage walkways,
ladders and work in scary places. Hardly any piano tuners have fallen off a
piano or dropped their tools in the strings, but we often hear of organ tuners
taking fateful trips down ladders or worse, winding up in the pipes!

Some years ago, I learned that it was not a very good idea
to change organ tunings on a whim. An organist might ask a tuner to lay on a
Werckmeister III tuning, so they can hear what Bach should really sound like.
After the enthusiasm for Bach has worn off, the next organist to take that job
will insist that the organ be returned to equal temperament. (Don't ask
me how I know that these things can happen.)

It is unfortunate that what passes for equal temperament on
many instruments is really no temperament at all. The sound is all a jumble.
Other situations occur, where tracker organs that should be well-tempered bleat
unmercifully with equal thirds, and lovely turn-of-the-century heirlooms howl
in baroque temperament. So often, the punishment really does not fit the crime,
and perfectly good tunings are wasted in the wrong places.

More organists have come to realize that tuning is an art,
and pleasing musical results come to those who invest time and attention to the
details of a well constructed and pleasing tuning. A good tuning is more than
theory and strategy and hard work. It is understanding of what is possible and
taking some effort to achieve those possibilities.

This is where the piano tuner comes in. If an organist is
going to understand temperament as it applies to his instrument, a good place
to start is with pianos. Historic temperaments are manifold with many different
names and variations. They are represented by lists of numbers that may defy
rationality and sometimes beg the question of authenticity. Who is to say the
numbers are right, when many versions of each temperament make their claim to
be authentic? Scholarship is sadly lacking.

Machine tuning is often used to set temperament with varied
results, depending on how good an aural tuner the technician is. The best
tuners never abandon aural tuning--in fact tuning by ear is still the best
source of a superior tuning. Both equal and historic temperaments can be set
with an electronic tuning device, but the real test of any tuning is the way
the intervals work. Theoretical tunings may be derived by study and transmitted
by tuning charts, beat rates, or deviations from a theoretical point. But in
the final analysis, it is the ear of the technician that makes the decision to
go flat or sharp. In my own experience, I look for logical relationships
between intervals, no matter what the name of any tuning.

This is the direction in which organists can go as well.
When they hear a fine instrument, the tuning should also make an impression.
It's not a matter of sour notes, but how the stops of the organ sound
both in the quality of the pipes and the tonality of the ensemble. Temperament
contributes purity, harmonicity, and overall aesthetic satisfaction. The sound
of the finest organs will contribute immensely to an individual's musical
understanding and appreciation.

In addition to listening to fine organs, some experiments
can be made with pianos in a church setting. When these instruments are tuned,
purely equal temperament can be set aside in favor of historically derived
tunings. This does not mean that they must be severe. In fact, some of the most
delicate temperaments are very close to an equal distribution of intervals.
However, the deviations they display are intentional and often the result of
the best tunings of bygone technicians. If nothing else, they displace random
errors in favor of intervals that lean the right way for a musical result. A
good example of this type of tuning are "Viennese" or
"Victorian" temperaments. They are found on reed organs and other
19th-century instruments.

In addition, there are well-tempered tunings of a more
moderate nature that are appropriate for romantic or classic (but not baroque)
organs. They are often derived from English sources, such as
"Broadwood's Best" and "Handel's
Well-Temperament." These tunings give good key color and favor the white
note triads. They also have the excellent feature of providing consistent ear
tests and do not require the uncritical setting of pitch according to the dial
on a machine. Yes, you can use your ears when tuning these temperaments. And
your ear will reward you when you play the music.

Organists can open up aural vistas with pianos at hand by
arranging for their tuner to assist with well-tempered tunings. This is not to
be confused with changing pitch. Piano tuners are taught to maintain pianos at
A=440 and should be encouraged to do so. It is not hard to find a tuner who has
an active interest in historic temperaments, since this subject is an area of
lively scholarship and discussion in conferences of the Piano Technician's
Guild, the parent organization for most piano tuners. A search for the right
technician will be well worth the effort. Organists will be rewarded with
instruments that "teach" them how to listen to music.

After some time with pianos, the question of the ultimate
tuning of the organ can be considered with much more clarity and logic than
"tuning on a whim." It is far more likely that good insight and
perceptive decisions will prevail.

Gavin Black

Gavin Black is the director of the Princeton Early Keyboard Center www.pekc.org. He can be reached by e-mail at [email protected].

Intervals, tuning, and temperament, part 3
In the first two columns on tuning I did not refer at all to names of temperaments—neither the rather familiar terms such as “Werckmeister,” “Kirnberger,” or “Vallotti,” nor less familiar ones such as “Fogliano-Aron,” “Ramos,” or “Bendeler.” It can be interesting or useful for a student to learn something about these historical temperaments; however, there is a reason that I have avoided framing my discussion of temperament with these established tunings. It is much more useful for students to grasp the principles that underlie any keyboard tuning. It is then possible for the student to both understand any specific tuning system—historical or hypothetical—and to invent his or her own, and also to understand some of the practical and artistic implications of different tuning approaches.

Underlying tuning principles
1) It is impossible for all twelve perfect fifths on a normal keyboard instrument to be tuned absolutely pure. This arises out of the mathematics of the fundamental definition of intervals, and it is an objective fact. If you start at any note and tune twelve perfect fifths pure, then the note that you come back to—which is supposed to be the same as the starting note—will be significantly sharp compared to the starting note.
2) Therefore, at least one perfect fifth must be tuned narrow. Anywhere from one to all twelve perfect fifths can be tuned narrow, as long as the overall amount of narrowness is correct.
3) The need to narrow one or more fifths is an objective need, and doing so is the practical side of keyboard temperament. The choice of which fifths to narrow and (bearing in mind that the overall narrowness must add up to the right amount) how much to narrow them is subjective and is the esthetic side of keyboard temperament.
From these principles it is possible to understand, or indeed to re-invent, any of the historical temperaments, each of which is of necessity simply a way of approaching and solving the issues described above.

Major historical tunings
1) Pythagorean tuning. This is the simplest practical approach, in which eleven fifths in a row are tuned absolutely pure, and the remaining fifth is allowed to be extremely narrow: so narrow that human ears will not accept it as a fifth and it has to be avoided in playing.
2) Well-tempered tuning. In this approach, the narrowness of fifths is spread out over enough fifths that the narrowed fifths sound acceptable to our ears. Practical experience suggests that this means over at least three fifths. The fifths that are not narrowed are left pure. All intervals and thus all chords and all keys are usable.
3) Meantone tuning. Here the tuning of fifths is configured in such a way as to generate pure or relatively pure major thirds. When this kind of tuning was in very widespread use (primarily the 16th and 17th centuries), this was a widely and strongly held esthetic preference. In order to generate a large number of pure major thirds, it is necessary to tune a large number of unusable intervals, both thirds and fifths—actually more than in Pythagorean tuning.
4) Equal temperament. In this temperament, each of the twelve perfect fifths is narrowed by exactly the same amount. In this tuning, alone among all possible keyboard tunings, each specific instance of each type of interval—perfect fifth, major third, and so on—is identical to all other instances of that interval.

Tuning intervals
When two close pitches are sounding at the same time we hear, alongside those notes, a beating or undulating sound that is the difference between the two pitches that are sounding. If a note at 440hz and a note at 442hz are played at the same time, we hear a beating at the speed of twice per second. If the two notes were 263hz and 267hz the beating would be at four times per second. This kind of beating sounds more or less like a (quiet) siren or alarm. It is so much a part of the background of what we hear when we listen to music that most people initially have trouble distinguishing it or hearing it explicitly. Normally once someone first hears beats of this kind, it is then easy to be able to hear them and distinguish them.
These beats are a real acoustic phenomenon. They are not psychological, or part of the physiology of hearing: they are present in the air. If you set up a recording in which one stereo channel is playing one pitch and the other is playing a close but different pitch, then if you play those two channels through speakers into the air, they will produce beats that can be heard. However, if you play them through headphones, so that the two notes never interact with one another in the air but each go directly to a separate ear of the listener, then no beats will be created and the listener will hear the two different pitches without beats.
Notes that are being produced by pipes or strings have overtones. When two such notes are played together, the pitches that mingle in the air include the fundamental and the overtones. Any of those component sounds that are very close to one another will produce beats if they are not in fact identical. It is by listening to these beats and comparing them to a template or plan (either no beats or beats of some particular speed) that we carry out the act of tuning.
For example, if we are tuning a note that is a fifth away from an already-tuned note, then the first upper partial of the higher note is meant to be the same pitch as the second upper partial of the lower note. (For a discussion of overtones see this column from July 2009.) If these overtones are in fact identical, then they will not produce any beats; if they are not quite identical they will produce beats. If the goal is to produce a pure perfect fifth, then beats should be absent. If the goal is to produce a narrow perfect fifth, then beats should be present—faster the narrower a fifth we want. In tuning a major third, the same principle applies, except that it is the third upper partial of the higher note and the fourth upper partial of the lower note that coincide.
Listening for beats produced by coinciding overtones is the essential technique for tuning any keyboard instrument by ear. Any tuning can be fully described by a list of beat speeds for each interval to be tuned. For example, in Pythagorean tuning the beat speed for each of the eleven fifths that are tuned explicitly is zero. (The twelfth fifth arises automatically.) Any well-tempered tuning can be described as a combination of fifths that have beat speeds of zero and fifths that have various moderate beat speeds. In equal temperament, all the fifths have beat speeds greater than zero, and they all reflect the same ratio, with higher notes having proportionately higher beat speeds. In most meantone systems, major thirds have no beats or very slow beat speeds, while those fifths that are tuned directly have beat speeds that are similar to those of well-tempered fifths.
These beats have a crucial effect on the esthetic impact of different tuning systems. For example, in Pythagorean tuning, while all of the perfect fifths are pure (beatless), all of the major thirds are very wide and beat quite fast. This gives those thirds, and any triads, a noisy and restless feeling. A triad with pure fifths and pure thirds—a beatless triad—is a very different phenomenon for a listener, even though it looks exactly the same in music notation. Other sorts of triads are different still: those with a pure major third and a narrow fifth, for example, or with all of the component intervals departing slightly from pure.

Temperaments throughout history
General tendencies in the beat structure of different temperaments may explain some things about the history of those temperaments, why they were used at different times, or at least how they correlate with other things that were going on musically at the time when they were current.

Pythagorean tuning
For example, Pythagorean tuning was in common use in the late Middle Ages. This was a time when the perfect fifth was still considered a much more consonant or stable interval than the major or minor third. Thus it made sense to use a tuning in which fifths were pure and thirds were wide enough—buzzy enough—to be almost inherently dissonant.
(But it is interesting to speculate about the direction of causality: did Pythagorean organ tuning suggest the avoidance of thirds as consonant intervals, or did a theory-based avoidance of those intervals suggest that a tuning with very wide thirds was acceptable?)

Meantone tuning
The rise of meantone tuning in the late fifteenth century corresponded with the rise of music in which the major third played an increasingly large role as a consonant interval and as a defining interval of both modal and tonal harmony. A major triad with a Pythagorean third does not quite sound like a resting place or point of arrival, but a major triad with a pure third does. During this same period, the harpsichord and virginal also arose, supplementing the clavichord and the organ. These new instruments had a brighter sound with a more explosive attack than earlier instruments. This kind of sound tends to make wide thirds sound very prominent. This may have been a further impetus to the development of new tuning systems in those years.
Meantone tuning, since it includes many unusable intervals, places serious restrictions on composers and players. Modulation within a piece is limited. In general, a given piece can only use one of the two notes represented by a raised (black) key, and must rigorously avoid the other. Many transpositions create impossible tuning problems. Many keys must, as a practical matter, be avoided altogether in order to avoid tremendous amounts of re-tuning.
Some keyboard instruments built during the meantone era had split sharps for certain notes, that is, two separate keys in, for example, the space between d and e, sharing that space front and back, one of them playing the d#, the other playing the e♭. Composers do not seem to have relied on it more than once in a while to write pieces in which they went beyond the harmonic bounds natural to meantone tuning. These split keys were probably intended to reduce or eliminate the need to re-tune between pieces, rather than to expand the harmonic language of the repertoire.
Meantone was no easier to tune than what came before it, or than other tuning systems that were known theoretically at the time but little used, since by limiting transposition it placed significant harmonic limitations on composers and improvisers, and thus made accompaniment more difficult. Yet it remained in use for a very long time. It seems certain that whatever it was accomplishing esthetically must have seemed very important, even crucial. Many listeners even now feel that the sonority of a harpsichord is most beautiful in meantone.

Well temperaments
In the late seventeenth century, composers and theorists began to suggest new temperaments that overcame the harmonic restrictions of meantone. These were the well-tempered tunings, in which every fifth and every third is usable as an harmonic interval. In order to achieve this flexibility, these tunings do away with most or, in some cases, all of the pure major thirds. This change can be seen as a shift from an instrument-centered esthetic—in which the beauty of the sound of the pure thirds was considered more important than perhaps anything else—to a composer-centered esthetic and philosophy, in which limitations on theoretical compositional possibilities were considered less and less acceptable. There were strong defenders of the older tunings well into the eighteenth century. It is interesting that in one well-known dispute about the merits of meantone as opposed to well-tempered tuning, the advocate of the former was an instrument builder (Gottfried Silbermann) and the advocate of the latter was a composer (J. S. Bach).
The crucial esthetic characteristic of well-tempered tunings is that different keys have different harmonic structures. That is, the placement of relatively pure and relatively impure intervals and triads with respect to the functional harmonies of the key (tonic, dominant, etc.) is different from one key to another. (An interesting experiment about this is possible in modern times. If a piece is recorded on a well-tempered instrument in two rather different keys, say C major and then E major, and the recordings are adjusted by computer so as to be at the same pitch level as one another, then they will still sound different and be easily distinguishable from each other.) Their differences are almost certainly the source of ideas about the different inherent characters of different keys. Lists of the supposed emotional or affective characteristics of different keys arose in the very late seventeenth century, at about the same time that well-tempered tuning took hold.

Equal temperament
In equal temperament, which became common in the mid- to late-nineteenth century, every interval with a given name and every triad or other chord of a particular type is the same as every other interval, triad, or chord of that type. Part of the appeal of this tuning in the nineteenth century was, probably, its theoretical consistency and symmetry. Many people have found the concept of equal temperament intellectually satisfying: it does not have what might be thought of as arbitrary differences between things that, theoretically at least, ought to be the same. Equal temperament took hold in the same era of organ history that included logarithmic pipe scalings—another theoretically satisfying, mathematically inspired idea. During this same time, designers of wind instruments were working to make those instruments sound the same—or as close as humanly possible—up and down the compass. This is another manifestation of a taste for avoiding seemingly arbitrary or random difference.
On an equal-tempered keyboard, the computer experiment described above would result in two indistinguishable performances: it is not possible to tell keys apart except by absolute pitch. The rise and dissemination of equal temperament also coincided with a general worldwide increase in travel. In a world in which equal temperament and a particular pitch standard (say a′=440hz) will be found anywhere and everywhere, a flutist, for example, can travel from Europe to America or Japan or anywhere and expect to be able to play with local musicians.
It is also likely that the general acceptance of equal temperament helped lead to twelve-tone and other atonal music by promoting the idea (and the actual listening experience) that all keys and all twelve semitones were the same.
In equal temperament, no interval is pure, and no interval is more than a little bit out of tune. This is a tuning that, just as a matter of taste or habit, appeals strongly to some people and does not appeal to others. I have known musicians with no training (or for that matter interest) in historical temperaments who could not stand to listen to equal temperament because they found equal-tempered thirds grating; I have known others who can accept the intervals of equal temperament as normal but who cannot tolerate the occasional more out of tune intervals of well-tempered tuning.
At the Princeton Early Keyboard Center website there are links to several resources describing and comparing historical temperaments and discussing further some of what I have written about here.

 

Gavin Black

Gavin Black is director of the Princeton Early Keyboard Center in Princeton, New Jersey. He can be reached by e-mail at [email protected].

Intervals, tuning, and temperament, part 2
Last month I wrote about some of the fundamentals underlying the art of keyboard temperament: aspects of the nature of musical sound and of intervals, the overtone series, and the so-called circle of fifths. This month I want to discuss keyboard temperament itself, using last month’s column as a foundation. I will talk about why temperament is necessary, what the major approaches to temperament have been over the centuries, some of what the different systems of temperament set out to accomplish, and about how different temperaments relate to different historical eras. Next month I will also discuss the practicalities of tuning and a few miscellaneous matters related to tuning and temperament.
As I said last month, my main point is to help students become comfortable with tuning and temperament and to develop a real if basic understanding of them, regardless of whether they are planning to do any tuning themselves. Before describing some of the essential details of several tuning systems, I want to review how we discuss tuning and how our thinking about tuning is organized, so that the descriptions of different temperaments will be easy to grasp.
1) For purposes of talking about tuning, octaves are considered exactly equivalent. (This of course is no surprise, but it is worth mentioning.) The practical point of this is that if I say, for example, that “by tuning up by a fifth, six times in a row, I get from C to F#” I do not need to say that I also have to drop the resulting F# down by three octaves to get the simple tritone (rather than the augmented twenty-fifth); that is assumed. To put it another way, simple intervals, say the perfect fifth, and the corresponding compound intervals, say the twelfth or the nineteenth, are treated as being identical to one another.
2) Intervals fall into pairs that are inversions of one another: fifth/fourth; major third/minor sixth; minor third/major sixth; whole tone/minor seventh; semitone/major seventh. For purposes of tuning, the members of these pairs are interchangeable, if we keep direction in mind. For example, tuning up by a fifth is equivalent to tuning down by a fourth. If you are starting at C and want to tune G, it is possible either to tune the G above as a fifth or the G below as a fourth. It is always important to keep track of which of these you are doing or have just done, but they are essentially the same.
3) When, in tuning a keyboard instrument, we tune around the circle of fifths, we do not normally do this:

but rather something like this:

going up by fifths and down by fourths—sometimes up by fourths and down by fifths—in such a way as to tune the middle of the keyboard first, thus creating chords and scales that can be tested.
4) In tuning keyboard instruments we purposely make some intervals impure: that is, not perfectly (theoretically) in tune. When an interval is not pure it is either narrow or wide. An interval is wide when the ratio between the higher note and the lower note is greater than that ratio would be for the pure interval; it is narrow when the ratio is smaller. For example, the ratio between the notes of a pure perfect fifth is 3:2, that is, the frequency of the higher note is 1½ times the frequency of the lower note. In a narrow fifth, that ratio is smaller (perhaps 2.97:2), in a wide fifth it is larger (perhaps 3.05:2). Here’s the important point—one that students do not always realize until they have had it pointed out: making an interval wide does not necessarily mean making some note sharp, and making an interval narrow does not necessarily mean making some note flat. If you are changing the higher note in an interval, then raising that note will indeed make the interval wider and lowering it will make the interval narrower. However, if you are changing the lower note, then raising the note will make the interval narrower and lowering it will make the interval wider.
5) Tuning by fifths (or the equivalent fourths) is the theoretically complete way to conceive of a tuning or temperament system. This is because only fifths and fourths can actually generate all of the notes. That is, if you start from any note and tune around the circle of fifths in either direction, you will only return to your starting note after having passed through all of the other notes. If you start on any given note and go up or down by any other interval, you will get back to your starting note without having passed through all of the other notes.1 For example, if you start on c and tune up by major thirds you will return to c having only tuned e and g#/a♭. There is no way, starting on c and tuning by thirds, to tune the notes c#, d, d#, f, f#, g, a, b♭, or b. Tuning is sometimes done by thirds, but only as an adjunct to tuning by fifths and fourths. Any tuning system can be fully described by how it tunes all of the fifths.
6) As I mentioned last month, tuning two or more in a row of any interval spins off at least one other interval. For example, tuning two fifths in a row spins off a whole tone. (Starting at c and tuning c–g and then g–d spins off the interval c–d). Tuning four fifths in a row spins off a major third. (Starting at c and tuning c–g, g–d, d–a, a–e spins off the interval c–e). The tuning of the primary intervals—pure, wide, or narrow—utterly determines the tuning of the resulting (spun-off) interval. For example, tuning four pure perfect fifths in a row spins off a major third that is wider than the theoretically correct 5:4 ratio: very wide, as a matter of human listening experience. Tuning three pure fourths in a row (c–f, f–b♭, b♭–e♭, for example) spins off a minor third that is narrower than the theoretically correct 6:5.
So, what is temperament and why does it exist? Temperament is the making of choices about which intervals on the keyboard to tune pure and which to tune wide or narrow, and about how wide or narrow to make those latter intervals. Temperament exists, in the first instance, because of the essential problem of keyboard tuning that I mentioned last month: if you start at any given note and tune around the circle of fifths until you arrive back at the starting note, that starting note will be out of tune—sharp, as it happens—if you have tuned all of the fifths pure. The corollary of this is that in order to tune a keyboard instrument in such a way that the unisons and octave are in tune, it is absolutely necessary to tune one or more fifths narrow. This is a practical necessity, not an esthetic choice. However, decisions about how to address this necessity always involve esthetic choices.
There are practical solutions to this practical problem, and the simplest of them constitutes the most basic temperament. If you start at a note and tune eleven fifths, but do not attempt to tune the twelfth fifth (which would be the out-of-tune version of the starting note), then you have created a working keyboard tuning in which one fifth—the interval between the last note that you explicitly tuned and the starting note—is extremely out of tune. If you start with c and tune g, d, a, etc., until you have tuned f, then the interval between f and c (remember that you started with c and have not changed it) will be a very narrow fifth or very wide fourth. The problem with this very practical tuning is an esthetic, rather than a practical, problem: this fifth is so narrow that listeners will not accept it as a valid interval. Then, in turn, there is a practical solution to this esthetic problem: composers simply have to be willing to write music that avoids the use of that interval. This tuning, sometimes called Pythagorean, was certainly used in what we might call the very old days—late middle ages and early Renaissance. As an esthetic matter, it is marked by very wide thirds (called Pythagorean thirds) that are spun off by all of the pure fifths. These thirds, rather than the presence of one unusable fifth, probably are why this tuning fell out of favor early in the keyboard era.
The second-easiest way to address the central practical necessity of keyboard tuning is, probably, to divide the unavoidable out-of-tuneness of the fifths between two fifths, rather than piling it all onto one of them. For example, if in the example immediately above you tune the last interval, namely b♭–f, somewhat narrow rather than pure, then the resulting final interval of f–c will not be as narrow as it came out above. Perhaps it will be acceptable to listeners, perhaps not. Historical experience has suggested that it is right on the line.
In theory, what I just called the “unavoidable out-of-tuneness” (which is what theorists of tuning call the “Diatonic Comma” or “Pythagorean Comma”) can be divided between or among any number of fifths, from one to all twelve, with the remaining fifths being pure. The fewer fifths are made narrow—that is, “tempered”—the narrower each of them has to be; the more fifths are left pure (which is the same thing), the easier the tuning is, since tuning pure fifths is the single easiest component of the art of tuning by ear.2 The more fifths are tempered, the less far from pure each of them has to be; the fewer fifths are left pure, the more difficult the temperament is to carry out by ear.
Temperaments of this sort, that is, ones in which two or more fifths are made narrow and the remaining fifths are tuned pure, and all intervals and chords are usable, make up the category known as “well-tempered tuning.” There exist, in theory, an infinite number of different well-tempered tunings. There are 4083 different possible ways to configure the choice of which fifths to temper, but there are an infinite number of subtly different ways to distribute the amount of out-of-tuneness over any chosen fifths. From the late seventeenth century through the mid to late nineteenth century, the most common tunings were those in which somewhere between four and ten or eleven fifths were tempered, and the rest were left pure. In general, in the earlier part of those years temperaments tended to favor more pure fifths, and later they tended to favor more tempered fifths. The temperament in which all twelve fifths are tempered and the ratio to which they are all tempered is the same (2.9966:2) is known as equal temperament. It became increasingly common in the mid to late nineteenth century, and essentially universal for a while in the twentieth century. It was well known as a theoretical concept long before then, but little used, at least in part because it is extremely difficult to tune by ear.
In well-tempered tunings and in fact any tunings, the choices about which fifths to temper affect the nature of the intervals other than fifths. The most important such interval is the major third. The importance of the placement of tempered fifths has always come largely from the effect of that placement on the thirds. Historically, in the period during which well-tempered tuning was the norm, the fifths around C tended to be tempered so as to make the C–E major third close to pure, in any case almost always the purest major third within the particular tuning. This seems to reflect both a sense that pure major thirds are esthetically desirable or pleasing and a sense that the key of C should be the most pleasing key, or the most restful key, on the keyboard. In general, well-tempered tunings create a keyboard on which different intervals, chords, and harmonies belonging to the same overall class are not in fact exactly the same as one another. There might be, for example, major triads in which the third and the fifth are both pure, alongside major triads in which the fifth is pure but the third a little bit wide, or the fifth pure but the third very wide, or the fifth a little bit narrow and the third a little bit wide. It is quite likely that one of the points of well-tempered tuning was to cause any modulation or roaming from one harmonic place to another on the keyboard to effect an actual change in color—that is, in the real ratios of the harmonies—not just a change in the name of the chord or in its perceived distance from the original tonic.
In equal temperament, all intervals of a given class are in fact identical to one another, and each instance of a chord of a given type—major triad, minor triad, and so on—is identical to every other instance of that chord except for absolute pitch. Next month I will discuss ways in which the esthetic of each of these kinds of temperament fit in with other aspects of the musical culture of their times.
The other system of tuning that was prevalent for a significant part of the history of keyboard music—from at least the mid sixteenth century through the seventeenth century and, in some places well into the eighteenth—is known nowadays as meantone tuning. (This term was not used at the time, and is now applied to a large number of different tunings with similar characteristics.) In a meantone tuning, there are usually several major thirds that are unusably wide and one or more fifths that are also unusable. In fact, the presence of intervals that must be avoided by composers is greater than in Pythagorean tuning. However, this is in aid of being able to create a large number of pure or nearly pure major thirds. This was, perhaps, as a reaction to the earlier Pythagorean tuning with its extremely wide thirds, considered esthetically desirable during this period. The mathematics behind the tuning of thirds tells us that, if two adjacent thirds are both pure, say c–e and e–g#, then the remaining third that is nestled within that octave (see above), in this case a♭–c, will be so wide that no ears will accept it as a valid interval. Therefore only two out of every three major thirds can be pure—that is, eight out of the twelve—and, if they are tuned pure, the remaining major thirds will become unusable. This, of course, in turn means that composers must be willing to avoid those intervals in writing music. It is striking that composers were willing to do so with remarkable consistency for something like two hundred years.
The distribution of usable and unusable thirds in meantone is flexible. For example, while it is possible to tune c–e and e–g# both pure, as mentioned above, it is also possible to tune c–e and a♭–c pure, leaving e–g# to be unusable. In the late Renaissance and early Baroque keyboard repertoire, there are, therefore, pieces that use g# and piece that use a♭, but very few pieces that use both. There are pieces that use d# and pieces that use e♭, but very few pieces that use both. There are many pieces that use b♭ and a few that use a#, but almost none that use both. There are very few keyboard pieces from before the very late seventeenth century that do not observe these restrictions. This is powerful evidence that whatever was accomplished esthetically by observing them must have been considered very important indeed.

 

Michael McNeil

The musical character of an historic tuning can be difficult to grasp— and the mathematics involved can be daunting. Modern descriptions of tunings use the mathematical concept of the “cent” because it is independent of a reference frequency.

Cents simply represent the convenient division of the octave into twelve equal intervals of 100 cents each. The use of cents, however, has absolutely no relationship to the natural harmonic series, i.e., cents have no relationship to the consonance or dissonance of the intervals we hear. To make this point clear, the equally tempered third is 400 cents (the pure third is 386 cents) and the equally tempered fifth is 700 cents (the pure fifth is 702 cents), and our ears tell us that the third is very impure. Cents tell us nothing about the purity of the interval. In the middle octave of the compass, the 700-cent fifth sounds like a warm celeste at about one beat per second, whereas the 400-cent third sounds a harsh ten beats per second. The purity and consonance of an interval improves with fewer beats, and the dissonance of an interval increases with more beats. The relationship of a tuning system to the natural harmonic series is represented by its beat rates. It tells you how the tuning will sound.

Pythagoras noted 2,500 years ago that if you tuned G pure to C, D pure to G, A pure to D, and continued this series of pure fifths to arrive again at C, the initial note C and the final note C would be different. These dissonant tones would be in the ratio of 81/80—this is known as the “Pythagorean comma.” In modern equal temperament we divide this error and dissonance equally across all twelve notes in the octave, and no intervals other than the octave are pure without beats.

 

Classes of tunings

The consonance of harmonic purity is alluring. Early compositions took advantage of tunings that featured both consonant purity and dissonant tension. These are the basic classes of tunings in a nutshell: Pythagorean tuning is the oldest and is based on the purity of fifths; meantone was developed in the Renaissance and is based on the purity of thirds; equal temperament became ubiquitous in the mid-nineteenth century, allows the use of all keys, and is based on an equal impurity in all keys without any pure fifths or thirds.

Meantone was a prevalent tuning for a very long period in the history of the pipe organ. J. S. Bach favored tunings that allowed free usage of all 24 major and minor keys; Bach was known to be at odds with the organbuilder Gottfried Silbermann, who used meantone tuning. Although equal temperament was gaining favor in the late eighteenth century, meantone was known to be in use in English churches well into the nineteenth century. What was its appeal?

There are eight pure major thirds in 1/4-comma meantone. The interval of the fifth in meantone is only slightly less pure than the fifths in equal temperament, which has no pure intervals. The appeal of meantone was a wonderful sense of harmonic purity and a deep, rich sonority. The natural harmonics, when played together, create sub-tones representing the fundamental of the harmonics. The interval of the pure fifth C–G produces a sub-tone one octave below the C. The interval of the pure third C–E produces a sub-tone two octaves below the C. This is a primary source of bass tone deriving from nothing more than the pure thirds of meantone tuning. The famous three-manual and pedal organ by the elder Clicquot at Houdan has a satisfying depth of tone, but it has no 16′ stops, not even a single 16′ stop in the Pedal. The 16′ tonal gravity is entirely the result of the tuning.

The later trend towards equal temperament produced sounds that lacked the gravity of meantone, and organbuilders responded in two ways. First, organ specifications often featured manual 16′ stops. Second, the new Romantic voicing style and higher wind pressures provided real fundamental power. The end of the eighteenth century saw a profusion of transitional “well temperaments,” which tried to bridge the gap between meantone and equal temperament. All of these attempted to preserve some harmonic purity while affording some degree of the freedom of equal temperament, but the results were largely unsatisfactory on both counts. It is worth taking a closer look at some of the early tunings, uncompromised by later efforts to dilute their character.

 

Comparing triads

We can visualize the sonority of major and minor triads as shown in illustration 1. The upper triangle of notes, B–F# and B–D, represents the B-minor triad. The B-major triad is shown in the lower triangle. Beat rates are shown between the notes, e.g., the minor third B–D dissonantly beats 26.7 times per second when playing B in the middle octave with the D above. A pure or nearly pure interval is represented by a green line connecting the notes. Intervals with more beats are represented by lines of different colors as seen in the table to the right, where very dissonant intervals are red, and violet intervals represent extreme dissonance, also known as the “wolf.” These colors allow us to “see” the relative consonance or dissonance of these intervals—numbers are more difficult to interpret at a glance. Black arrows point in the directions in which we will find intervals of fifths, major thirds, and minor thirds. Minor triads are shaded gray.

 

Comparing tunings

We can expand this model to include all 24 major and minor triads. And with this expanded model we can quickly compare different tunings based on pure fifths, pure thirds, and equal temperament, all of which are shown in illustration 2. (Beat rates are referenced to the 2′ middle octave, a = 440Hz.)

The first example in illustration 2, Kirnberger I (not to be confused with Kirnberger II or III) is a late Baroque tuning that features nine pure fifths, three pure major thirds, and two pure minor thirds. This is a variant of Pythagorean tuning and has the tonal color required for very early music. It also plays much of the later literature with radiant harmonic purity.

The second example shown in illustration 2 is the 1/4-comma meantone devised by Pietro Aaron in 1523. It is a wonderful representative of the class of tunings that emphasize the purity of major thirds. Also note the extreme dissonance in the “wolf” intervals in violet, the price paid for the purity in the thirds. A glance at this example will show why older organs tuned in strict meantone had no bass octave keys for C#, D#, F#, or G#. Many variants exist that rearrange the dissonant and consonant intervals, and it is important to match compositions created in meantone with their proper meantone variations. (The important reference for this is Claudio Di Veroli’s Unequal Temperaments, Theory, History and Practice, 3rd Edition.)

As the demand arose to have more freedom in the use of more remote keys in the eighteenth century, a virtual flood of attempts arose to trade off the purity of the meantone third for less dissonance in the more remote keys. These are known as the “well temperaments.” As noted earlier, these attempts mostly disappoint; harmonic purity was watered down to the point where the sense of consonance disappeared when any real sense of freedom emerged in the more remote keys. The logical consequence was, of course, the rise of equal temperament, which is ubiquitous today.

The third example shown is equal temperament. This tuning has a wealth of nearly pure fifths, but no interval has real purity, without beats. The major thirds are quite impure and very dissonant. Minor thirds are worse. We have simply grown to tolerate this dissonance through familiarity with it. The pure, or nearly pure, triad is rarely a part of modern keyboard experience. We pay a very dear price in the sonority of our music with the freedom we gain to access the tonality of any key.

We can make early compositions sound as exciting to us as they did to their composers if we play them in their appropriate tunings. The musical impact of a tuning is determined by its consonances and dissonances, and these sounds are described by beat rates, not “cents.” This model hopefully provides a more intuitive way to understand the variety of tuning styles for the pipe organ.

 

References

Di Veroli, Claudio. Unequal Temperaments, Theory, History and Practice, 3rd Edition. Bray, Ireland: Bray Baroque, 2013. Available as an eBook on Lulu.com.

Jorgensen, Owen. Tuning the Historical Temperaments by Ear. Marquette,  Michigan: Northern Michigan University Press, 1977.

McNeil, Michael. The Sound of Pipe Organs. Mead, Colorado: CC&A LLC, 2012.

Taylor & Boody Organbuilders, Staunton, Virginia

Goshen College, Goshen, Indiana

About the organ.

Designing an organ for Rieth Hall at Goshen College was a
pleasure. The opportunity to place the organ in the traditional location, high
in the rear gallery, was ideal both visually and aurally. The form and
proportions of the hall, with its austere yet warm and inviting interior,
called the organbuilder to respond with similar clarity and restraint. The
ample height of the room suggested a plain, vertical configuration of the
instrument, on which natural light from the clerestory windows would fall
gently. Everything about the hall spoke of its solid construction and honesty
of materials, qualities that we strive to reflect in our organs. Likewise the
acoustical properties of the hall, so warm and reverberant and at the same time
intimate and clear, allowed the organ’s tone to develop freely without
being forced. The result is an endearing musical instrument that is
aesthetically inseparable from the space in which it stands.

Initial inspiration for the Goshen case came from the organ
built by David Tannenberg in 1774 for Trinity Lutheran Church in Lancaster,
Pennsylvania. While only the case and façade pipes of that lovely
instrument have survived, they constitute the finest example we have in our
country of south German case architecture from the 18th century.
Tannenberg’s use of the double impost, with its Oberwerk division
gracefully placed as a reflection of the Hauptwerk below, was typical of organs
in his native Saxony and Thuringia. Other exterior influences from that time
and place include the two swags that bracket the center tower, and the broad
lower case that supports the full width of the impost and omits the spandrels
common to earlier styles. Apart from its simple springboard moldings, the
Goshen case is relatively flat and plain by comparison with its historical
counterparts. Its only bold three-dimensional element is the polygonal center
tower. The small pointed towers in Tannenberg’s design are here merely
implied by the V-shaped arrangement of foot lengths in the tenor fields. The
use of six auxiliary panels to raise the smaller pipe feet above the impost
moldings adds interest to the design. The considerable height of the lower case
was determined by the need for a passageway over the 2-foot concrete riser
behind the organ. This height gave space between the console and impost for the
eventual inclusion of a small Brustwerk with several stops for continuo
accompaniment. Cabinets for music storage are built into the back on both sides
of the lower case.

Another aspect of the design reminiscent of 18th-century
south German traditions is the position of the windchests in relation to the
action. The two windchests of the Hauptwerk are spaced apart from the center of
the case by the width of the keyboards. This leaves room for trackers of the
Oberwerk to reach their rollerboard without blocking access to the Hauptwerk
action and its pallets. It also provides optimum space for 8’ bass pipes
at the sides and leaves room for tuning the tenor pipes of the Hauptwerk with
only minimal obstruction by the Oberwerk rollerboard. The windchests for the
Pedal are located behind the case at the level of the impost, a placement that
Tannenberg could also have used.

Both the playing action and stop action are mechanical. The
manual keys are hinged at the tail and suspended from their trackers. There are
no thumper rails to hold the keys down, so they are free to overshoot slightly
when released, as is the case in traditional suspended actions. Trackers,
squares and rollers are all made of wood. There is no felt in the action. Keys
are guided by pins at the sides. Together these details combine to give a
feeling of buoyancy and liveliness reminiscent of antique instruments. The aim
is not so much to provide a light action as to arrive at one having the mass
and friction appropriate to the size and character of the organ. Such an action
may need occasional minor adjustment of key levels with changes in humidity,
but this is a small price to pay for the advantages gained over more sterile
modern alternatives. 

Wind is supplied by two single-fold wedge bellows (3’ x
6’) fed by a blower located in a small room below the organ. Natural
fluctuations of the wind pressure in response to the playing contribute to the
lively, singing quality of the organ’s sound. A wind stabilizer can be
engaged when unusually heavy demands on the wind system call for damping of
these fluctuations. The organ’s single tremulant is made in the old-fashioned
beater form. On seeing a tremulant puffing away in one of our organs, a
Japanese friend remarked that the organ was laughing! It is useful to think of
an organ’s wind as its breath and the bellows as lungs, for the
instrument’s appeal is closely tied to our perception of its lifelike
qualities. 

The tonal character of an organ is rarely revealed by its
stoplist. This is particularly true in an instrument of only twenty-four stops.
Once the builder accepts the constraints of a given style and the essential
registers have been chosen, there is usually little room or money left to
include stops that would make a modest design appear unique on paper.
Fortunately for the art, the musicality of the organ is not bound by its
stoplist; rather, it is determined by a host of other complex factors. These
can be partially defined in the technical data of pipe scaling and
construction, general design parameters, materials and the like, but in reality
much more rests on the elusive criteria of experience, skill and taste of the
builder. Taken together this means that each new organ, albeit small, presents
fresh opportunities for artistic expression. It is important that all the pipes
speak promptly, be they reeds or flues, except in the case of strings, which
gain charm from their halting speech. It is less important that the pipes
produce precisely the same vowel sounds from note to note, for here variety
adds refreshing character and interest to the organ.

At Goshen we chose to voice the 8’ Principal to be
somewhat brighter and richer in overtones than has been our wont. This was
achieved by giving the pipes lower cutups than was customary in German and
Dutch organs of the 17th century and before. The five distinctly different
8’ flue stops on the manuals deserve special mention. Although all
followed scaling patterns we have used frequently in the past, when voiced they
proved to be unusually satisfying, particularly in combination with each other.
Whenever the 16’ Bordun is used with them a magical new dimension is added
to the sound. If, for example, one draws the Bordun with the Viol da Gamba, the
effect is that of a quiet 16’ Principal. Used with the Spillpfeife the
Bordun reverts to its role as a flute. In an organ of this size it is crucial
that every stop work as well as possible with every other. Following south
German practice, both 8’ and 4’ flutes on the Hauptwerk are made in
the same form. This duplication of flutes within the same family was not the
custom in the north, where lower pitched flutes were usually stopped and those
above them progressively more open. The Oberwerk configuration at Goshen with
its two stopped 8’ registers and partially open 4’ Rohrflöte is
typical of the northern tradition. We look forward to the day that the 16’
Violonbass with its cello-like speech can be added to the Pedal.
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The distinctive musical effect of the Goshen organ is
strongly colored by the use of the recently released Bach-Lehman temperament
described in the accompanying article. Because the completion of the organ in
February coincided with the publication in Early Music of Bradley
Lehman’s treatise on J. S. Bach’s temperament, we chose to tune the
organ according to his plan. Here was the ideal opportunity to try the
temperament on an organ built in Germanic style and at the same time to honor
Dr. Lehman as a distinguished Goshen alumnus for his work in this field. The
experiment has been a fascinating one. It has provided a place to hear
Bach’s organ music as we have not heard it before. We are honored to have
played a part in translating the dry mathematical numbers of this temperament
into the vibrant sound of the organ. 

With few exceptions the many parts of the organ were
constructed from raw materials in our Virginia workshop. Through the skills of
each craftsman the design moved from an idea to paper and then through raw wood
and metal into a large and impressive object. Note by note the tonal picture
has been filled in by voicing and tuning until in the end we experience a new
instrument with an identity all its own. We hope that it will give pleasure to
those who play and hear it far into the future.

--George Taylor

The organ project at Goshen College

“Dienlich, Ordentlich, Schicklich, Dauerlich”

In 1999 we were asked by the organ consultant for Goshen
College, Roseann Penner Kaufman, to make a proposal for the new Goshen College
Music Center. As with any new project, I went to Goshen full of excitement at
the promise of participating in what was to be a spectacular project. My
enthusiasm was short-lived when I saw the design for the recital hall. It was a
standard fan-shaped, sloped-floor, small college recital hall, with theatre
seats and carpet in the aisles. The space for the organ was planned in a niche
at the back of the stage. The design would have been fine for small chamber
recitals, but it was not a proper home for an organ. The prospects for the
organ looked bleak. We would not have felt productive or inspired. We always
say that the room is more than half the organ. I took a deep breath and told
the Goshen committee what I thought of the plan. The committee listened and
asked us to offer suggestions on how the recital hall might be designed to work
best with the musical programs envisioned for this space.

I returned to Staunton eager to develop a plan. One of the
first things I did was to research the Mennonite Quarterly Review for articles
describing historical Anabaptist worship spaces. I hoped that the essence of
these rooms would lead me to an aesthetic that would tie the new hall to the
old tradition, which would, in turn, also be good for music, especially the
organ. My research acquainted me with four German words used to express the
qualities of the historical spaces: dienlich, ordentlich, schicklich and
dauerlich--serviceable, orderly, fitting and lasting. I also found prints
of the interiors of some of these churches. Rectangular in shape with open
truss timber roof framing, clear glass windows, galleries on several sides,
rough stone floors, moveable chairs, unadorned, honest and powerful, these
spaces had all the qualities that I was looking for. They also had enduring
musical-acoustical qualities and so many are used today for concerts.

The simple sketch that I made went first to the Goshen organ
committee who, led by Doyle Preheim and Chris Thogersen, embraced the plan.
Then the concept went to Rick Talaske and his team of acousticians. They
transformed the plan into practical geometry and surface treatments to make the
space an acoustical success. Mathes Brierre Architects took the acoustical plan
and translated it into a visual design that evokes the warehouse or
brewery-turned-church concept of the early Dutch Mennonite spaces. Schmidt
Associates worked through the technical details with Casteel Construction to
conceive the simple pre-cast concrete panels and graceful curved steel arches
that make the hall appealing in its architecture, superior in acoustical
performance and straightforward and durable in construction. There was creative
and sensitive work done by a Goshen group concerned with decor and furnishings.
The result is successful beyond our expectations. The collaboration of all the
partners made the project exceed the ability of any one of us.

Once the hall was underway, we scheduled a meeting at St.
Thomas Fifth Avenue in New York with a group from Goshen and Calvin and Janet
High from Lancaster, Pennsylvania. We had a great day in New York showing
everyone our organ in the gallery of St. Thomas. The Highs’ enthusiasm
for the St. Thomas organ and the Goshen Music Center paved the way for their
generous gift that underwrote the cost of the organ.

We realized that the floor area of Rieth Hall was small in
relation to the height. We saw that if there could be the addition of one more
bay to the length there would be significant improvement in the proportions of
the space and at least 50 more seats could be added. Again, the Goshen design
group supported our suggestion. At a time in the project when the building
committee was attempting to control costs and squeeze performance out of every
dime, they found the funds for this most important late addition.
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I predicted at the time we were creating the designs for
Rieth Hall, that the unique qualities of this space would have something to say
to the Goshen students about music and worship. This prediction has been
realized. First, there is genuine enthusiasm for a cappella singing in Rieth
Hall, encouraging this wonderful Mennonite tradition. Second, there has been a
spontaneous seizing of the space by the students for their own student-directed
Sunday worship. In this age of searching for the right path in worship and
liturgy, of debating the influence and appropriateness of mass media and
popular music for worship, we have built something at Goshen College that
reaches across the span of time to those Mennonite roots. Led by the seemingly
old-fashioned qualities of dienlich, ordentlich, schicklich and dauerlich, we
have made a  music space and organ
that inspire and excite us to make music and to celebrate and serve our God and
Creator.

Wood and the Goshen organ

The traditional pipe organ is a wooden machine. Early on in
our careers as organ builders we realized that getting control over our
materials in both an aesthetic and technical sense was essential to our success
as organ makers. Our first path was to make friends with our neighborhood
sawmillers. One of these was an octogenarian whose experience reached back to
horse logging and steam power. He taught us the value of long, slow, air-drying
of lumber. He also knew the old traditions of sawing, how to take the tension
out of a log, how to saw through the middle of the log and keep the boards in
order so that the cabinetmaker could match the grain. He remembered the methods
of quarter sawing that impart the most dimensional stability to the boards and
in oak bring out the beautiful fleck of the medullary rays. We have built our
own sawmill based on a portable band saw. For quarter sawing, we have built a
double-ended chain saw that can split logs up to 60 inches in diameter. The
half logs (or quarters in extremely large timber) are then aligned on our band
saw and sawn in a radial fashion into boards. This lumber is then air-dried for
a number of years. At the end, we put the wood in our dry kiln and gently warm
it up to stabilize the moisture content at 8% to 10%.

Oak is the traditional wood of Northern European organ
building so it was natural for us to choose white oak for the Goshen organ. We
have long admired the Dutch and German organs dating back to the 16th century.
The earliest organs show only the natural patina of age and no finish; the
concept of finishing wood as in varnishing or oiling came well into the 18th
century. We followed this earlier practice for the Goshen organ. The oak has
been hand-planed to a smooth polish, much smoother than can ordinarily be
produced with sanding. The hand-planed wood will resist dirt. We feel there are
also musical benefits from using wood in its natural state. The case and
carvings together with all the interior parts transmit sound energy and reflect
and focus the sound of the pipes. Also, the open pores and surface
imperfections of the natural wood have an effect on the sound reflection.

Another aspect of wood use in historic organs is how
efficiently the old builders utilized their wood. Before the age of machinery,
cutting, transporting and converting timber to sawn, dried lumber ready for use
was costly. The best wood was always used for the keyboards, playing action,
wind chests and pipes. The next selection went to the most visible parts of the
case, especially the front of the organ. The rest was used for carvings, heavy
structural members, walkways, bellows framework and back panels. Some of this
wood shows knots, cracks and other defects that might offend our modern sense
of perfection. However, in addition to demonstrating good wood utilization, the
varying density and differences in surface texture of these so-called defects
may indeed benefit the music. How we perceive the sound of an organ is a very
complex and subtle equation. This is one of the wonderful aspects of the real
pipe organ that differentiates it from the sterile sound of the electronic
substitute. We feel it is good stewardship to apply the hierarchy of selection
as practiced by the old masters. We try to use all the wood, through careful
selection, with thoughtful conservation of a vanishing resource.

--John Boody

Acoustic design of Rieth Recital Hall at Goshen College

In 1998, the design team of design architect Mathes Group
(now Mathes Brierre Architects), architect of record Schmidt Associates and
acoustician The Talaske Group (now Talaske) began preliminary work on a new
music education and performance building for Goshen College’s campus.
This project was the College’s greatest building investment to date and
they were determined to do things right . . . with a very modest budget. The
Recital Hall (now Rieth Recital Hall) was slated to house a new tracker organ
of exceptional quality. As acousticians, we offered some general planning
recommendations--not the least of which was a 50-foot ceiling
height--and recommended that the organ builder be hired as soon as
possible.

Enter John Boody of Taylor & Boody, organ builders from
Virginia. John energized the subsequent meetings with some profound advice that
proved to set the final direction for the space. He moved our thinking from a
“fixed” seating configuration to a flexible arrangement based on a
flat floor where seats can face either end of the room. This unique concept
facilitated the accommodation of a conventional “recital hall” or
assembly arrangement with musicians or presenters on a small stage. The cleverness
of the concept is the seats can be turned to face the opposite direction in the
room, offering a classic organ recital arrangement. Furthermore, John
recommended that the proportions of the room would be better served if
lengthened by adding another bay of structure. These fundamental planning ideas
changed the direction of the design in perpetuity.

We embraced these new directions yes">  and identified the many other room acoustics design features
that would support the client’s needs. The 50-foot ceiling height remained,
and we worked with the architects and construction manager to render the room
as a sound-reflective concrete enclosure, embellished with wood. The goal was
to maintain the warmth of sound created by the organ. Within the “theatre
planning” process, we guided and exploited naturally occurring
opportunities for introducing sound diffusing shaping to reflect low- and
mid-pitched sound in all directions--by introducing one side balcony and a
rear balcony, recesses from circulation paths and recesses created by
deeply-set windows. We recommended deliberate articulation of the walls to
diffuse mid- and high-pitched sound. Wood surfaces were detailed to minimize
absorption of low-pitched sound. Retractable velour curtains and banners were
recommended in abundance and specified by Bob Davis, theatre consultant.
Architecturally, curtain and banner pockets were created so the sound-absorbing
materials could be retracted completely on demand. These features make possible
a broad “swing” of the sound of the room from very reverberant for
choral and organ performance to articulate for assembly events or amplified
music performance. Fundamental to the acoustic design was the need for silence.
This was accomplished by structural discontinuities in the building (acoustic
isolation joints) and the proper placement and design of heating and air
conditioning systems.

Within their mission statement, Goshen College states:
“Musical expression is a human manifestation of the divine impulse and,
as such, serves as a window into the individual soul, a bridge between human
beings and a means of corporate religious experience.” In light of the
students adopting the Rieth Recital Hall for their weekly convocations and the
many other uses, we are pleased to say the happy story continues!

--Rick Talaske

Bach temperament

This organ is the first since the 18th century to use Johann
Sebastian Bach’s tuning, as notated by him in 1722 on the title page of
the Well-Tempered Clavier. This tuning method is a 2004 discovery by Bradley
Lehman. The article about this discovery is published in the February and May
2005 issues of Early Music (Oxford University Press), and further details are
at <www.larips.com&gt;.

The layout, dividing the Pythagorean comma, is:

F-C-G-D-A-E = 1/6 comma narrow 5ths;

E-B-F#-C# = pure 5ths;

C#-G#-D#-A# = 1/12 comma narrow 5ths;

A#-F = a residual wide 1/12 comma 5th.

In this tuning, every major scale and minor scale sounds
different from every other, due to the subtle differences of size among the
tones and semitones. This allows music to project a different mood or character
in each melodic and harmonic context, with a pleasing range of expressive
variety as it goes along. It builds drama into musical modulations.
style="mso-spacerun: yes"> 

The result sounds almost like equal temperament, and it similarly
allows all keys to be used without problem, but it has much more personality
and color. In scales and triads it sounds plain and gentle around C major (most
like regular 1/6 comma temperament), mellower and warmer in the flat keys such
as A-flat major (most like equal temperament), and especially bright and
exciting in the sharp keys around E major (like Pythagorean tuning, with pure
fifths). Everything is smoothly blended from these three competing systems,
emerging with an emphasis on melodic suavity.

The following chart shows the relative size of each major
third, resulting from each series of the intervening four fifths. This system
of analysis is from the 1770s, published in the theoretical work of G. A. Sorge
who was a former colleague of Bach’s. The intervals having higher numbers
sound spicier, more restless. In this measurement, a value of 11 would indicate
a major third that is one syntonic comma too sharp (a “Pythagorean major
third,” having been generated by four pure fifths).
style="mso-spacerun: yes">  A pure major third would be represented
here as 0.

Bb-D    6
style='mso-tab-count:1'>             D-F#
    7
style='mso-tab-count:1'>             F#-A#
8

Eb-G    7
style='mso-tab-count:1'>             G-B
      5
style='mso-tab-count:1'>             B-D#
   9

Ab-C    8
style='mso-tab-count:1'>             C-E
       3
style='mso-tab-count:1'>             E-G#
   10

Db-F     9
             F-A
       3
style='mso-tab-count:1'>             A-C#
   9

Equal temperament, as opposed to the variety shown here, has
a constant size of 7 in all twelve of the major thirds.

In functional harmony, the Bach tuning sets up especially
interesting contrasts within minor-key music. The key of A minor has the
plainest tonic juxtaposed with the most restless dominant. F minor, a major
third away, has the opposite relationship: troubled tonic, calm dominant. And
C# minor has the average character between these behaviors, where the tonic and
dominant are both moderately energetic. 

In major-key music, the tonics and dominants have characters
similar to one another. The sizes of major thirds change by only 1, 2, or 3
units from each key to its neighbors, moving by the circle of fifths (through
typical subdominant/tonic/dominant progressions). Any change of Affekt is
therefore gradual and subtle, as if we never really leave the home key
altogether but it feels a little more or less tense as we go along.

In any music that modulates more quickly by bypassing such a
normal circle-of-fifths cycle, the contrasts are momentarily startling. That
is, the music’s dramatic harmonic gestures become immediately noticeable,
where the major thirds have changed size suddenly from one harmony to the next.
This comes up for example in the Fantasia in G Minor (BWV 542), Gelobet seist
du, Jesu Christ (BWV 722), and the fourth Duetto (BWV 805), and especially in
music by the Bach sons.

This system turns out to be an excellent tuning solution to
play all music, both before and after Bach’s. It is moderate enough for
complete enharmonic freedom, but also unequal enough to sound directional and
exciting in the tensions and resolutions of tonal music.

A recording will be ready for release this summer, including
music by Bach, Fischer, Brahms, et al.

--Bradley Lehman

A brief history of the organ in the Mennonite Church

Some people might find it unusual to find such a remarkable
organ in a Mennonite college. Aren’t the Mennonites those folks with the
buggies and suspenders? It is true that some Mennonite congregations still take
literally founder Menno Simons’ caution against the organ as a
“worldly” invention, but most, especially in the last fifty years,
have embraced it as a vital contributor to the musical and worship life of the
community. 

The Mennonite Church has its beginnings in the 16th-century
Protestant Reformation. Because of persecution, most of the early worship
services were held secretly, in homes or out-of-the-way places. Mennonites also
believed that the true church existed in small, simple gatherings; therefore,
it was uncommon for early Mennonites to even set aside a separate building for
worship. 

Two hundred years after the beginning of the movement,
churches in Germany and the Netherlands had grown to the point of meeting in
dedicated buildings, and by the 1760s several in urban areas had installed pipe
organs. It was another two hundred years, however, before organs became common
in the Mennonite conference that supported Goshen College. Even now, the organ
is not necessarily assumed to support congregational singing, but contributes
other service music. Organ study is now offered at all of the Mennonite Church
USA-affiliated colleges, and the new Taylor & Boody organ at Goshen will
certainly have a profound impact on the future of worship and organ study
throughout the denomination.

--Roseann Penner Kaufman

Roseann Penner Kaufman, DMA, is adjunct instructor in organ
at Bethel College, N. Newton, Kansas, a four-year liberal arts college
affiliated with the Mennonite Church USA. She also serves as director of music
for Rainbow Mennonite Church in Kansas City, Kansas. Dr. Kaufman served as the
consultant to Goshen College for their organ project.

Specifications for Opus 41

Hauptwerk

16' Bordun (C-D# wood, rest metal*)

8' Principal (77% tin)

8' Spillpfeife

8' Viol da Gamba (77% tin)

4' Octave

4' Spitzflöte

3' Quinte

3' Nasat

2' Superoctave

IV-V Mixtur

8' Trompet

Oberwerk

8' Gedackt (99% lead)

8' Quintadena

4' Principal (77% tin)

4' Rohrflöte

2' Waldflöte

II Sesquialtera

IV Scharff

8' Dulcian

Pedal

16' Subbass (wood)

(16' Violonbass) space prepared

8' Octave

4' Octave

16' Posaune (C-B wood, rest 99% lead)

8' Trompet (99% lead)

Couplers

Oberwerk / Hauptwerk

Hauptwerk / Pedal

Oberwerk / Pedal

Tremulant to entire organ

Mechanical key and stop action

Compass: manual 56 notes C-g''', pedal 30 notes C-f'

Lehman-Bach temperament

Interior metal pipes of hammered alloys

*All unmarked metal alloys of 28% tin, 72% lead

Case of solid white oak

Windchests of solid oak, pine & poplar

Number of pipes: 1604

Wind pressure: 75mm

Wind stabilizer

The builders

George K. Taylor

John H. Boody

Bruce Shull

Emerson Willard

Christopher A. Bono

Kelley Blanton

Chris A. Peterson

Sarah Grove-Humphries

Robbie Lawson

Jeffrey M. Peterson

Larry J. Damico

Holly Regi

Thomas M. Karaffa

Bob Harris

Katie Masincup

Ryan M. Albashian

Kristin E. Boo