A Transposable Temperament

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.

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.

 

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. 

Historic tuning on the Internet

Bicknell, Stephen. A beginner's guide to temperament.

www.users.dircon.co.uk/~oneskull/3.6.04.htm

Bremmer, William. The true meaning of well-tempered tuning.

www.billbremmer.com/WellTemp.html

Foote, Edward. Six degrees of tonality; The well-tempered
piano.

www.uk-piano.org/edfoote/well_te mpered_piano.html

Gann, Kyle. An introduction to historical tunings.

http://home.earthlink.net/~kgann/his tune.html

Greenberg, Bernard S. What does "well-tempered"
mean?

www.bachfaq.org/welltemp.html

Kellner, Herbert Anton. Instructions for tuning a
harpsichord "wohltemperirt." 

ha.kellner.bei.t-online.de/

Palmer, Frederic. Meantone tuning.

home.pacbell.net/jeanannc/mpro/art icles/MeanTone.htm

Rubenstein, Michael. Well vs. equal temperament.

www.ma.utexas.edu/users/miker/tun ing/tuning.html

Taylor, Nigel. Tuning, temperaments and bells; The
ill-tempered piano.

www.kirnberger.fsnet.co.uk/   

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.    

by Herbert Anton Kellner

I read with very great interest and pleasure the recent contribution by Jan Overduin to The Diapason1, "Bach and Die Kunst der Fuge." Therein, the author presented about two dozen typical examples, illustrating how the composer has interwoven the musical texture of the oeuvre with the notes of his name b, a, c, h, within the various counterpoints. (In English nomenclature, the German b is designated b-flat.) By this procedure BACH has inscribed--so to speak--in many places his signature to his compositions. Beyond this most simple form, a variety of permutations of these four basic letters can also be found, or else, transpositions to other pitches, as shown by R. Kreft,2 a comprehensive special study printed in multicolor.

For the present article, three examples from Prof. Overduin's article will be extracted and discussed. Beyond the occurrence of the name BACH in these particular musical passages, possible simultaneous allusions by the composer to his mathematical system of unequal well-tempered tuning3 will be identified. This musical temperament--due to its intrinsic mathematical nature--is necessarily based on a certain set of numbers. The rationale for the present approach to study Die Kunst der Fuge is the fact that Bach has frequently structured the form of his compositions via numbers of a set belonging to the  wohltemperirt system. From this observation originated my "Vienna manifesto" of the Bach-year 1985: to analyze Bach's works with particular attention to the aspect of numbers pertaining to well-tempering.4 Utilizing this artifice, Bach attains an elaborate unity between features of the musical form and structuring in the widest sense and the harmony of tuning--initially and nominally the harpsichord. The most specific composition for this system was, of course, Das Wohltemperirte Clavier. A harpsichord can be well-tempered in not more than 19 elementary tuning-steps.5 This is the number for the closure of the circle, and the 19 intervals are 12 fifths followed by 7 octaves in the opposite direction.

In view of the essential occurrence of the name b, a, c, h for carrying out this study, the number alphabet and its gematrial correspondences needs first of all to be introduced. Thus, the letters are numbered along the Latin alphabet from A=1, B=2, C=3,  . . . I=9, J=9 [sic],  . . . K=10,  . . . U=20, V=20 [sic],  . . . X=22, Y=23, Z=24. Expressed via that numbering, B, A, C, H will appear as 2, 1, 3, 8. The adding-procedure as prescribed by the gematria, 2+1+3+8, yields the correspondence BACH=14. Likewise, J.S. BACH will be 41, the crab or inversion of the number 14.

Now the well-tempered system will be concisely laid out, putting special emphasis on the way it will be ultimately reflected here in Die Kunst der Fuge. This temperament comprises 7 perfect fifths and 5 well-tempered ones. It derives from the central key of tonality, C-major.6 In its triad C-E-G, the enlarged third beats at the same rate as the reduced fifth--an ideal mutual adaptation. To complete the description, four well-tempered fifths ascend from c and reach the second octave of the initial third e closing this chain of fifths c-g-d-a-e. From c downwards extends a chain of six perfect fifths, reaching g-flat (f-sharp). Of course, octave-transpositions must be applied in practical harpsichord tuning wherever necessary. The last tempered fifth of the system results as B-f-sharp, closing the circle. From the third e upwards ascends the seventh and last perfect fifth e-b.

The unique and distinguishing feature of wohltemperirt is its musico-theological foundation; no other tuning has anything similar to offer. Due to the beat-rates in the triad at the perfection of the unitas,7 the system is founded upon a tri-unitarian basis. The nucleus of baroque thoroughbass is the triad, itself a symbol of the Holy Trinity. Just hearing a triad, its three components merge suavely and smoothly into an agreeable, pleasant unity.8 Furthermore, the beat ratio of 1:1 of the constituent intervals can be considered as a profound symbol of the monotheistic principle--it is here where Werckmeister's ideas on the perfection of the baroque unitas are rooted.

Returning now from theological spiritualities and mathematical ratios to the music itself, by what means could Bach reflect in a composition the numbered alphabet and the gematria? A few such examples will follow now. As concerns the numbered alphabet, for the onset of its table A=1, one may refer to the well known A-major fugue of The Well-Tempered Clavier I. Its theme starts with an isolated note a, followed by three 8th-rests. Such an incipit is highly unusual, if not bizarre, and correlating with the table's A=1 appears natural and not far fetched. For the correspondence BACH=14, the C-major fugue's theme--as well as that of B-major--starts with 14 keystrokes.9 Within Die Kunst der Fuge itself, following the first four pieces, already the theme of contrapunctus 5 (and others) count 14 keystrokes. For the gematrial correspondence J. S. BACH=41, not later than the initial two keystrokes d, a, of Die Kunst der Fuge--set in d-minor--show 41 if juxtaposed.

Now it will be indicated how musical structures can convey hints or allusions to the well-tempered system. It is based upon the ratio of the unitas between the beats of the tempered third and fifth, 3 and 5 in thoroughbass. Therefore, immediately the number 135--in juxtaposition--may be used, for instance, within the bar numbered by 135. Other possibilities may be derived from the two sorts of fifths, 5 well-tempered, 7 perfect, such as in juxtaposition 57, 75 (75 could be made up via the tri-unity as 31+13+3110), or even 577. Finally, in terms of musical notation, 5 relates  to e, 7 to g, and 3 to c. As to the number 19 and concomitant abstract structuring, looking now as an example at the B-major prelude of WTC I, it counts 19 bars, starts at bar 1913 and ends at bar 1931.11

The first extract from Prof. Overduin's article is contrapunctus 4 (BWV 1080, 4), measures 135 to 138, page 15 in Davitt Moroney's edition from G. Henle.12 Starting from bar 135 (unitas-third-fifth) the tenor sounds BACH, rhythmically comparable to a sigh. The fugue terminates at 138, which incidentally corresponds to ACH, the final letters of the composer's name; in German a sighing exclamation. Perhaps the terminating pedal on d (D=4) through the last four bars may be related to the four letters of BACH. (See Example 1.)

The second example, page 46 in the Moroney/Henle edition (BWV 1080, 11), concerns contrapunctus 11, bars 90 and 91. (See Example 2.) As Prof. Overduin points out, the alto introduces by theme three the notes B, A, C, H, but he mentions that Tovey rejected this as an allusion to BACH because in fact, it is B-A-C-C-C-H sounding here. However, Tovey could at his time not be aware of Bach's tri-unitarian temperament and thus, necessarily failed to understand the significance of A,C,C,C: 1,3,3,3 in numbers. As much as within B-AC-H, 2-13-8, the number 28, secundus numerus perfectus is centered upon 13, unitas-trinitas, the present extended theme 2-1333-8 includes three times the number 3. The frame still remains B and H. An essential factorization holds, 1333=31*43: the prime numbers 31, trinitas-unitas and 43 = CREDO (3+17+5+4+14)--a tri-unitarian Credo! Starting with the second half of this bar and counting from the bass fundament upwards, presents the notes e, a, c, thus 513, nothing else than a permutation of 135. This is interpreted as fifth 5, unitas and third 3 in thoroughbass. The crucial bar in this example is 91--the crab or inversion of 19--by which number of elementary steps the circle of fifths will close. Working backward in this bar to the second quaver shows a, a, c, thus 113: a numerical triptych of unitas and trinitas. This measure 91 not only sounds BACH in the alto, but its onset reads d, g, b, converted to numbers 4,7,2.

As concerns 472, Bach was certainly intimately familiar with the notion of permutations, thinking for example, of his choral fugues or certain three-part inventions. Thus, just from a cyclical permutation of 472 results the number 247 (=13*19). According to the baroque gematria, 247=MUSICALISCHE TEMPERATUR which is the title of Werckmeister's classical treatise, 1691. Furthermore, 247=112+135 holds additively, but the implications of such observations cannot be detailed here and these results were published elsewhere already some time ago.13

The third example still deals with contrapunctus 11, bars 144 to 145, page 48 in the Moroney/Henle edition. (See Example 3.) There the alto and treble sound BA-CH and the bass and tenor in the second quaver of 144 present G, E, converting to 7 and 5, the numbers of perfect and well-tempered fifths. The bass, in fact, now sounds G,G,G,E, in numbers 7775. It may also be mentioned that contrapunctus 11 starts in a Trinitarian fashion by three bars identically structured, with eighth-note rests on the downbeat and 3 subsequent eighth notes; one has 3+3+3=9, trias trinitatis per additionem.

Finally, a typical manifestation of the unitas, a determining and crucial element in Bach's structuring of his compositions can be pointed out at this occasion. The contrapunctus 11 extends over 184 bars, an even number. The midpoint therefore falls upon the bars 92 and 93, see the preceding example. The bar 93 (=3*31, tri-unitary factorization!) sounds, from the fundament of the bass upwards, a, c, e; in numbers 1,3,5: unitas, third and fifth in thoroughbass--on  the dominant of d-minor. In the central triad of C-major of wohltemperirt, third and fifth beat at the unison! Hence, this piece is obviously pivoted symmetrically upon the very nucleus of the well-tempered musico-mathematical system.

The considerations above represent a corollary to the examples of the underlying article in The Diapason. As to the aspects described and analyzed, there is no pretension whatsoever to be exhaustive. Rather, the purpose is, hopefully, to be thought provoking, to stimulate and encourage further, more systematic and complete investigations into the direction outlined here--as much as the article published by Prof. Overduin has led to the present study.

After having reconstituted the well-tempered system Werckmeister/Bach initially in 1975,14 it was gratifying for me to see how organ builders have taken up and followed the ideas, appreciating the technological and musical qualities of this baroque temperament. These builders include Rudolf von Beckerath, John Brombaugh & Associates Inc., T. S. Buhr, Paul Fritts & Co., Gerhard Grenzing, Otto Hoffmann Organs, Claude Jaccard, Yves Koenig, Michael Korchonnoff, Dominique Lalmand, Gebr. Oberlinger, Martin Pasi, Richards, Fowkes & Co., Charles M. Ruggles, Taylor & Boody, George Westenfelder, Karl Wilhelm, Hellmuth Wolff and Munetaka Yokota.

On these organs, tuned accordingly, many distinguished musicians have performed and recorded, including Martin Balz, Luc Beauséjour, Jonathan Biggers, Gavin Black, Robert Clark, David Dahl, George Edward Damp, François Espinasse, Bernard Foccroulle, Martin Gester, André Isoir, Calvert Johnson, Donald Joyce, George Ritchie, David Rothe, Wolfgang Rübsam, Yasuko Uyama-Bouvard and others.

A discography as at that time I have published in The Tracker.15 Further references to analyses of Bach's compositions are contained--together with a heuristic derivation of the well-tempered system--in the Blankenburg-Michaelstein symposium proceedings.16 For those interested in more musicological details, a bibliography is also contained within my lecture publication on historical temperaments, held at the symposium in the Vienna Hochschule für Musik und Darstellende Kunst.17.

by Francesco Ruffatti

One of the most famous organbuilding "schools" in Italy was founded in Venice during the first part of the eighteenth century by Pietro Nacchini, a monk from Dalmatia.1 He established a factory and built over 300 organs mainly for the territories of the Republic of Venice,2 and for the Vatican State, which at the time comprised the largest portion of central Italy.  Although his designated successor was Francesco Dacci, with no doubt his most famous pupil was Gaetano Callido, born in Este, near Padova, who established his own organ factory in Venice and built well over 430 organs during his lifetime,3 some of which were for very distant countries.4

In manufacturing his instruments Callido basically followed the style of Nacchini, with only a few changes, both from the standpoint of tonal composition and type of construction. He conceived an organ as a one-manual instrument, with a limited pedal division. This is confirmed by the fact that in the original list of his works5 the relatively few two-manual instruments were designated as "double organs" and were given two consecutive opus numbers.

Callido's organs were by no means all alike, but their size was dependent upon the presence or absence of certain stops, all chosen among a limited pallet of stops from which the builder never departed.6 By giving the tonal composition of the Great division of the largest organ by Gaetano Callido, built for the Cathedral of Feltre,7 a good picture of his "selection" of organ stops is given.

The first part of the list includes all Principal-scaled ranks that form the "Ripieno". The stops can be used separately in various combinations or all together, collectively activated by a "Tiratutti" consisting of a rotating handle placed on top of the corresponding stop knobs.

Principale                (8')8 almost invariably divided, bass and treble

Ottava  (4')

Quinta Decima                        (XV - 2')

Decima Nona                           (XIX - 11/3')

Vigesima Seconda             (XXII - 1')

Vigesima Sesta                       (XXVI - 2/3')

Vigesima Nona                       (XXIX - 1/2')

Trigesima Terza                    (XXXIII - 1/3')

Trigesima Sesta                     (XXXVI - 1/4')

The last two ranks are often missing in the smaller instruments and are of full compass only in the larger organs, being normally limited to one or two octaves in the bass. The reason for limiting their compass is quite simple: since the highest pitched pipe in the ripieno of a Callido organ is C at 1/8', all ranks break back by one octave once they reach this limit. By doing so the "mixture" composition appears as in Table 1 (as an example I am considering a four-octave keyboard compass, C1 to C5).9

With this configuration, which is common to the majority of Italian historical organs (although the "breaking-back" points may vary at times), a number of pitch duplications are present from mid-keyboard up, to the point that, starting at F#4, only two different pitches are present while playing five pipes. In order not to extend the duplication of pitches towards the lower register and to avoid increasing the number of duplications at the treble, Callido normally ended the XXXIII and XXXVI ranks at the point where they would start breaking back (at F2 and C2 respectively) or further up the scale only by a few notes.

The "registri da concerto" or "consort" stops, as Callido called them, follow. First the flute scaled stops:

Flauto in Ottava (Flute in VIII - 4') often, but not always, divided, bass and treble. Normally built as a tapered flute, it is also found in the form of a metal stopped flute (with stoppers or caps made of leather-coated cork and inserted into the resonators of the pipes) or even as metal chimney flutes, with soldered-on caps.10

Flauto in Duodecima (Flute in XII - 22/3'), normally not divided in bass and treble (but it is divided for example in the Feltre organ). It was normally built as a tapered flute, although some examples of stopped pipes at the lower register and tapered at the treble do exist.

Cornetta (Flute in XVII - 13/5') - treble only, consisting of tapered flute pipes.

Voce Umana (principal-scaled, 8', treble only, tuned flat)

and finally the reeds:

Tromboncini      (trumpet-like regal at 8') bass and treble

Violoncelli (regal with wooden resonators - 8') bass and treble

Another "consort" stop, not present in the Feltre organ but rather common in Callido's instruments, is the Violetta, usually in the bass only, but also as a complete stop, especially in the later instruments. It is a 4' string stop of narrow cylindrical scale, tuned to the unison.

The Pedal division includes, in the Feltre organ, the following stops:

Contrabassi, Ottava di Contrabassi and Duodecima di Contrabassi.  These are three ranks of open wooden pipes at 16', 8' and 51/3' pitch respectively, which are activated simultaneously. In smaller organs only the first two (16' + 8') are present, or just the 16'. In the smaller instruments the 16' pipes are often found as stopped.

Tromboni ai Pedali (a trumpet-like reed, with 1/2 length resonators at 8' pitch)

Of particular interest are the reed stops, for their unusual shape and sound. The resonators of the Tromboncini are made of tin and consist of a lower four-sided portion and a "bell" on top. Their four-sided lead sockets are inserted into walnut boots. The tuning wires are made of brass, with cow horn sledges to facilitate the sliding over the tongues for tuning. The stop at low C (8' pitch) is of 1/8 length, the resonator approximately one foot long.

The Violoncello is even more unusual and complicated. Its resonators are made of cypress wood in the form of a stopped wooden pipe, the stoppers or caps being made of boxwood. The shallots are also made of hand carved boxwood, while the tuning wires, which go through the resonators and their caps on top, are equipped with cow-horn sledges. Unlike the sound of the Tromboncini, rather "biting" and penetrating, the harpsicord-like sound of the Violoncello is very sweet and gentle.

For many of his instruments Callido left a series of "operational instructions" for the organist, intended to give suggestions on how to best use the organ stops in combinations. Several of them, if strictly followed, show us how different the musical taste of the time was from the present. For example, under the title "Elevazione," or stops to be used during Consecration, for opus # 10 Callido specifies: Principale, Voce Umana, Contrabassi . . . and Tromboni! Not the type of pedal combination that we would consider appropriate for quiet meditation. And under the title "Corni da caccia," or sound to simulate the hunting horns, he suggests: Principale, Contrabassi, full ripieno (tiratutti), Tromboncini and . . . Voce Umana! An off-unison stop used along with the ripieno! (Opus # 5, 7, 9, 12, with the addition of the pedal Tromboni in opus # 10). Other combinations of stops are closer to what a contemporary organist would choose to do.

From the standpoint of construction, the instruments built by Callido are of unsurpassed quality. Each pipe is a true masterpiece, with thin, regular, absolutely perfect solder joints. The windchests and all other parts are manufactured with the highest attention for details. Callido was quite obviously trained in a very strict way and demanded the same perfection from his workers.

The contracts with his customers contain a very meticulous description of materials: pure tin for the façade pipes "without any alloy"11; "the rest of the internal pipes made of lead with a 20% alloy of tin."12 And he goes into detail to the point of stating that "the Contrabassi will be manufactured with spruce and painted inside and outside, and will be made of walnut at the mouth . . . " and also "the windchests will be made with walnut from Feltre13 . . . with metal parts made of brass."

It is certainly worth examining in closer detail some of the manufacturing characteristics of Callido's instruments. I will try to do so by describing the most significant components of the instrument in as much detail as it is possible within the reasonable length of a magazine article.

The keyboards

The most common compass of Callido's keyboards was C1-C5, for a total of 45 keys (with first "short" octave)14 or C1-D5, for a total of 47 keys. For the organs featuring the "counter" octave the compass consisted of four complete octaves, plus an extension at the bass consisting of a short octave, real from F1 as in the case of the Feltre Cathedral organ, whose Great manual has a total of 57 keys. When two keyboards were present, the Great Organ division keyboard was always placed on top and the coupling of manuals (Positiv to Great) was made possible by sliding the Great keyboard towards the back by a very short distance (drawer-type coupling, as it is often called in Italy).

The natural keys were normally covered with boxwood and the sharps were made of walnut painted black, capped with a strip of ebony, simple or with boxwood or bone inlays.

The "breaking point" between bass and treble was normally located between the notes C#3 and D3, except for the instruments featuring the "counter-octave," where it was placed between notes A2 and Bb2 .

The total width of a full octave was practically constant at 167 mm and the length of the keys was considerably smaller than in today's keyboards: 71 mm for the sharps and only 39 mm for the front portion of the naturals.

The pedalboard

It was always made with short, parallel and tilted pedals, common to the vast majority of historical pedalboards in Italy. It featured a first short octave and was always permanently connected to the corresponding keys of the manuals (of the Great, when two manuals were present). Its compass was of 17 notes, C1 to G#2, plus a pedal for the "Rollante," or drum, a device simultaneously activating a number of harmonically unrelated wooden pipes, thus reproducing the sound effect of the rolling of a drum. The compass of the pedal division in essence consisted of a full octave, since the notes of the second octave activated the corresponding pipes of the first.

The pipes

The façade pipes were made of pure or almost pure tin and all internal metal pipes were made of a tin/lead alloy with high lead content (about 80 to 85%). The metal was not poured on the table over cloth or marble, but over sand, and then planed by hand. Both the inside and the outside surfaces of the pipe resonators were made perfectly smooth. For the smaller internal pipes a laminating machine was used to roll cast metal into thinner sheets.

Since a few Callido organs, especially in the former territory of the Vatican State, have been found almost intact,15 it has been possible to identify not only the voicing parameters used by the builder but also, in some instances, the original tuning temperaments and wind pressures.

The flue metal stops were invariably voiced with some kind of wind control at the toe. Toe openings were generous, but the voicing could not be defined of the "open toe" type. Consequently, the flue was rather wide and this determined the need for nicking of the languids in order to avoid an excessive transient at the attack, which was obviously considered not desirable in 1700s Venice. Languids were nicked all the way to the smallest pipe in the ripieno ranks, but the nicks, although numerous, were very lightly marked and in some cases almost invisible. This created a precise, clean attack and still a clear and beautiful sound. This voicing practice has one exception: the languids of the Viola pipes were left totally unnicked. And no tonal bridges or beards, which were unknown to the Venetian tradition of the eighteenth and early nineteenth centuries, were used. Consequently, their sound features a very prominent transient at the start, intended to simulate the "noise" produced by the bow of the orchestral Viola when hitting the strings.

The low wind pressure was also a determining factor for obtaining a rich, unforced sound. It was usually set between 48 and 55 mm at the water column, with only a few verified examples of slightly higher pressure.16

Tuning was strictly done by cutting the pipes to length and adjusting with the cone, except for the façade pipes, which were cut close to length and subsequently fine tuned by further carving the back of the resonator at the top in a curved shape. These cuts are called "lunette", or moon-shaped cuts by Italian organbuilders.

Wooden pipes were always made of spruce, painted with a composition of light hot glue and red clay powder, with lower lip and upper lip made of walnut. The lower lip "cover" was fastened with hand-made iron screws. At 16' pitch these pipes could be stopped or open, depending on the size of the instrument. All open pipes were tuned with the cut-to-length method, with an occasional end correction made by applying small pieces of lead sheet or wood on top of the resonator to "shade" the note.

The windchests

The builder exclusively used the conventional slider chests, with table, top boards and sliders made of walnut. The sliders were all built parallel and of constant thickness.17 They always worked "wood-on-wood," without any form of leather seal or any other device intended to avoid the sticking of sliders. This of course required the use of high quality materials, but also a very clever choice of manufacturing techniques. It must be said, from this standpoint, that the "table" or the portion of the chest located under the sliders, which includes the note channels, was made of a solid board of walnut, 40 to 45 mm thick, on which the note channels were carved. This procedure is quite common in historical Italian slider chest construction, and differs substantially from techniques used at the time in northern Europe. Carving out channels from a single piece requires much more work than building a frame and creating the channels by means of inserting dividers, but this technique has a number of advantages. First, and most important, the whole unit is made from the same piece of wood, and this avoids warping and cracking due to contrasting tensions from different pieces of material. Also, the risk of air bleeding between note channels caused by an imperfect gluing of the different elements (table and dividers) is totally avoided, since gluing is not necessary, the elements being built from the same piece of wood. But since no tree would be wide enough to form a windchest table all in one piece, several portions were joined together for the purpose, with alternating direction of the grain in order to compensate for the tendency of warping all in one direction.18

The channels were always of generous size in order to provide adequate supply of air.19 Wooden dividers were placed inside the channels to avoid interference and wind supply instability between the larger pipes of the façade and the reed stops, which were invariably placed in front of the façade, exposed to facilitate tuning by the organist. The pallets were always made of light, straight-grain spruce from the Alps. Their seal consisted of a double layer of sheepskin leather, and the surface on which they rested was also covered by leather. This provided a very effective seal for the wind and apparently did not affect in any way the precision and sensitivity of the tracker action.

The Pedal division consists of only one windchest, located at the back of the organ case. The stop knobs for the Contrabassi pipes open or close a large valve located inside the windline, which controls the air flow to the chest. The reed, when present, is activated by a slider. In practical terms this means that the Tromboni cannot be played separately from the Contrabassi, because the Contrabassi stop knobs, and consequently the air valve, must be open to feed the whole windchest.

The mechanical action

Callido always used the suspended action, which is the simplest and most direct mechanical transmission mechanism. When a Positiv divison was present, always located at the left side of the keyboards, the corresponding keyboard worked in the same fashion, except that the keys is this case pushed down the trackers istead of pulling them.20

The rollerboards for the manual divisions, for the stop action and for the pedal, were made with forged iron rollers fastened to spruce boards by means of brass wire. The "swords" pulling the windchest sliders were also made of forged iron.

The winding system

The most common winding configuration in Callido organs includes two multiple-fold bellows (consisting of five folds) made entirely of spruce wood. They were normally placed one on top of the other and were activated by ropes through a system of pulleys. Their size was rather standardized: larger size bellows were used for the larger instruments, and smaller size for instruments requiring less wind.

Restorations are conducted in such a way that the original winding system is always preserved and carefully restored and, where not present, in many instances built new as a replica of the old.21 A modern blower is usually connected to the system, in such a way however as to keep the hand pumping system operational. This makes it possible to make a very interesting comparison between the original wind supply, slightly irregular due to the small but detectable differences in pressure caused by the manual pulling of the reservoirs, and the more stable supply furnished by the blower. "Flexible winding" as it is referred to today is a different matter: it has to do with the response of the wind and, in practical terms, the drop in wind pressure at the use of certain combinations of stops or notes. From this standpoint, although the phenomena of the so-called "flexible" wind is present in Callido organs, the design of the wind supply system, starting from the size of the bellows all the way to the generous dimensions of the windchest channels, indicates that Callido was trying to avoid instability in the wind supply.

The tuning system

As far as we know Callido never used equal temperament, already present in other parts of Europe at the time. Already well known for a few centuries, it was considered uninteresting and not desirable, especially due to the unpleasant "wide" tierce intervals which are present even in the most commonly used keys. An interesting statement on this subject is given by Giordano Riccati.22 In his book, "Le leggi del Contrappunto" written in 1754, he states: "Practically speaking, I have never been able to find an organ or an harpsichord tuned with the equal 12 semitones." In 1780 and 1790 he stated the same concepts again. But equal temperament continued to be rejected in Italy well into the 19th century. Giovan Battista de Lorenzi, a very ingenious builder from Vicenza, in 1870 created a "moderate temperament" which, although very close to equal, was intended to reduce the "out of tune" effect of the most used tierce intervals.

We know that Callido's master, Pietro Nacchini, for some of his works used a tuning method which consisted in tuning the 11 quint intervals from Eb to G# flat by 1/6 comma each, a method which was very close to the practice of Gottfried Silbermann.24 Callido may also have used this method, but he departed from it at some point and he adopted a variety of similar systems,25 among which the temperament invented by Francescantonio Vallotti, Music Director at the Basilica of St. Anthony in Padova, and Alessandro Barca in 1779, which avoided the wide G#-Eb interval, making it almost pure.26

A unique example of a non-codified temperament comes from the organ built by Callido's sons Antonio and Agostino in 1813 (the year of Gaetano's death at age 86) for the Parish Church of Tai di Cadore (Belluno). This instrument was restored by Fratelli Ruffatti in 1980-81. Prior to restoration, the pipes were found in almost perfect condition, due to the fact that the organ had been left untouched early in its history when the access stairway to the balcony was removed. After cleaning, the pipes were  almost in tune and it was relatively easy to identify and restore a type of unequal temperament which did not follow codified methods and which represented one of the many "variations" introduced by the tuners at the time for a "sensitive" tuning of the instruments.27

The tonal ideals and manufacturing techniques of the Callido factory were carried on, primarily in the Veneto and Marche regions, by a number of organbuilders: in Venice by Giacomo Bazzani, a former worker in his shop, and by his successors; in Padova and its province, among others, by Gregorio Malvestio, a priest (1760-1845), by his nephew Domenico, by Domenico's son Giuseppe and grandson Domenico. The closing down of this shop originated the beginning of the Ruffatti firm.28

In the Marche region Callido had a number of followers including Vincenzo Montecucchi from Ancona, Sebastiano Vici (Montecarotto, 1755-about 1830), Vincenzo Paci (Ascoli Piceno, 1811-1886) and others, who in some cases produced organs so close to Callido's techniques that sometimes their identification as non-Callido instruments requires an expert examination.29                   

Notes

                        1.                  His real name was Peter Nakic, born in Bulic, near Skradin, north of Sibenik, in present Croatia, a former territory of the Republic of Venice. As was customary during the time, his name was "Italianized" and became Pietro Nacchini.

                        2.                  The Republic of Venice during the eight-eenth century was a large State, including parts of Slovenja and Croatia and the present Italian regions of Veneto, Friuli Venezia Giulia and eastern portions of Lombardy.

                        3.                  See Studi e Documenti di Storia Organaria Veneta by Renato Lunelli. Ed. Olschki, Florence, 1973, and also Gli organi di Callido nelle Marche by Ferrante--Quarchioni, Ed Villa Maina, 1989.

                        4.                  Opus numbers 13, 185 and 393 were built for churches in Istambul and opus number 424 for Izmir, Turkey.

                        5.                  The original list or catalogue of organs built by Gaetano Callido survives. It consists of three panels made of canvas on which the opus number, year of construction and location of the instruments were marked in India ink by the builder. Although water damage washed away the names of 88 of his instruments, between the years 1789-91 and 1794-98, it still gives accurate information about 342 organs manufactured in his factory. The last opus number is 430, built in 1806, after which the list was discontinued. In recent years many of the "lost" instruments have been identified.

                        6.                  Only at the turn of the nineteenth century, when Callido's sons Antonio and Agostino were active in the factory, a limited number of "variations" were introduced, in the form of new reed stops (but still of the commonly used "regal" type) and flutes. Times were changing in Italy and a more "orchestral" style of sound, requiring highly characterized solo stops, was being introduced in churches, in the wave of the predominant influence of opera even in the music composed for organ.

                        7.                  This exceptional instrument, built in 1767 (opus numbers 37 and 38) and restored in 1979-80 by Fratelli Ruffatti of Padova, is practically equal in size to another organ, built for the Parish church of Candide (Belluno).

                        8.                  The Great keyboard of the Feltre organ is extended by one octave at the bass . This "counter-octave" as it is commonly called, consists of a short octave (C-D-E-F-G-A-Bb-B) of which only the notes from F up are real, the preceding ones activating the corresponding notes of the higher octave. In essence therefore the Principal starts in this case at 12'F, the Octave at 6', the Fifteenth at 3', etc.

                        9.                  This is the normal system used in Italy to designate not the pitch but the position on the keyboard. F3 for instance designates the note F of the third octave of the keyboard.

                        10.              Due to the absence of the "beards," which makes tuning adjustments possible when the caps are soldered, it is quite obvious that Callido must have had a very precise scale for cutting the resonators of these flutes to length before soldering the caps. Minimal tuning adjustments were however still possible through cone tuning of the chimneys.

                        11.              i.e.,  without the addition of lead, as reported in the specifications for the new organ to be built for the Madonna della Salute Church in Venice, dated September 19, 1776.

                        12.              Same, as above. In other contracts he chooses different alloy compositions for the internal pipes, as in the case of the contract with the Parish Church of Borgo Valsugana, November 8, 1780, where a 15% tin content is specified.

                        13.              The walnut from Feltre (Belluno) was traditionally of the highest quality, dense, dark and almost redish in colour.

                       14.              The short octave, or "broken" octave as it is often called in Italy, consists of 8 keys: C-D-E-F-G-A-Bb-B. The key arrangement is different from normal: basically, it looks like an octave starting from note E, where E plays C, F# plays D, G# plays E and all other notes are in the right place.

                        15.              This is the case of the organ in the convent Church of S. Anna in Corinaldo (Ancona), where Callido's daughter was a nun. The instrument, which is presently under restoration at the Fratelli Ruffatti shop, was found in remarkably good condition, still with the original hand-pumped bellows in good working condition. Since Callido was rightfully considered a master, his work was highly respected over the years by other organbuilders and for this reason the voicing of his instruments was often never altered in spite of the changes in musical taste.

                        16.              It is the case of the Callido organ at the Chiesa della Croce in Senigallia (Ancona), restored by Fratelli Ruffatti in 1993, where the original hinged bellows and their carved stone weights were found. Probably due to the unusually dry acoustics of the church, whose walls and ceiling are literally covered with elaborate wood ornaments and canvas paintings, the pressure was originally set at 60mm at the water column. Another example is the Callido opus 69, 1771 in the church of the Agostinian Fathers, Civitanova Marche. The instrument, restored in 1987 by Pier Paolo Donati, shows an original wind pressure of 64 mm (information courtesy of Dr. Massimo Nigi, honorary Inspector for the "Soprintendenza per i Beni Artistici e Storici" of Florence, a governmental agency in charge of supervising the preservation of Italian ancient works of art).

                        17.              This is not an obvious observation, since a great number of slider chests built in the 17th and 18th centuries in central and southern Italy were built with sliders non-parallel and of decreasing thickness. This feature was intended to avoid the sticking of the sliders. When in the "on" position, the sliders were pushed in and no space was left between the sliders and the other wooden surfaces; on the contrary, when pulled out (stop in the "off" position) the sliders, due to the decreasing thickness and width, could move freely.

                        18.              One might say that, during Callido's time, the problem of artificial heating of churches did not exist, thus making this procedure possible. It is to be noted on this subject that the very high number of strictly philological restorations on these organs by Fratelli Ruffatti and other restorers in Italy, performed without the introduction of any non-original elements for the sealing of the sliders, proves that the original system of windchest construction well withstands changes in heat and humidity level of the air.

                        19.              For a scale drawing of a Callido windchest see L'Organo Callido della Cattedrale di Feltre by Oscar Mischiati. Ed. Pàtron, Bologna, 1981.

                        20.              In this case the key pushes down a wooden tracker which in turn pushes down the rollerboard tracker placed under the keyboard. At the opposite end of the roller the pallet is pulled open by means of a brass wire.

                        21.              In some cases, where the original bellows were replaced in the nineteenth century by the more "modern" multi-fold parallel bellow with pumps, activated by means of a wooden lever or a wheel, the local governmental authorities designated to supervise the preservation of ancient instruments may choose not to have the system rebuilt as a replica of the original but to keep the already "historical" substitute.

                        22.              Born in Castelfranco Veneto (Padova) in 1709, he studied at the University of Padova and became a famous mathematician, architect, expert in hydraulics and music. He was the author of an interesting temperament, which became famous at the time, used by many organbuilders especially in the Venetian area. It was surely used in his later works by Nacchini and possibly by Callido as well.

                        23.              See Patrizio Barbieri, Acustica Accordatura e Temperamento nell'Illuminismo Veneto, Ed Torre d'Orfeo, Roma 1987.

                        24.              See Patrizio Barbieri, Acustica Accordatura e Temperamento nell'Illuminismo Veneto, Ed Torre d'Orfeo, Roma 1987.

                        25.              The result of studies conducted during restorations show that a variety of similar temperaments, which can be defined as variations of the above Riccati and Vallotti temperaments, were used in normal practice.

                        26. The Vallotti temperament in the slightly corrected version by the contribution of Barca, was intended to simplify the Riccati, and consists of a series of six consecutive quint intervals, from F-C to E-B tuned flat by 1/6 comma, and the six remaining quint intervals practically pure (flat by an imperceptible 1/66 comma). The value in cents of semitones of its quint and tierce intervals follow:

Quint intervals cents

F - C        698.4                              C - G      698.4      G - D      698.1                              D - A      698.6                              A - E       698.4                              E - B       698.4                              B - F#    701.7                              F# - C#                        701.5                              C# - G#                      701.6                              Ab - Eb                       701.7                              Eb - Bb                       701.6                              Bb - F    701.6                                                     

Tierce intervals                      cents      

C - E       393.5

F - A       393.5

G - B      393.5

Bb - D  396.5

D - F#   397.1

A - C#  400

Eb - G   400

E - G#   403.2

Ab - C  403.3

F# - A#                       406.4

Db - F   406.5

B - D#  406.5

                       

Keeping in mind that the value of the pure quint is 702 cts and the value of the quint in the equal temperament is 700 (narrow by 2 cts), by analysing the quint intervals of this temperament it is easy to see that they are basically divided in two categories, narrow (but more moderate than, for example, in the 1/4 comma mean tone, which shows a value of 696.5 cts.) and almost pure. As to the tierce intervals (pure tierce = 386 cts, tierce in equal temperament = 400 cts) although no pure intervals are present, five of them are "better" or more in tune than the corresponding ones in the equal temperament, and two more show the same value of 400 cts. It is also to be considered that no tierce reaches extreme values. The absence of really unusable keys and the relatively easy application in practical terms by the tuner have determined the success of this temperament during its time.

                        27.              The Tai temperament includes two "wolf" quint intervals, at the opposite ends of the "circle of quints," one wide (G#-Eb) and one narrow (A-E) and six very good tierce intervals. This system is of particular significance primarily because it shows how far from equal temperament this organ was tuned so late in Callido's history.

                        28.              See Renato Lunelli, Studi e Documenti di Storia Organaria Veneta, Ed. Leo Olschki, 1973, p. 200.

                        29.              Information about Callido's followers in the Marche region are the courtesy of Mauro Ferrante, honorary Inspector for the preservation of ancient organs in the Marche region, appointed by the "Soprintendenza per i Beni Artistici e Storici" of Urbino.