On Teaching

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

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

but rather something like this:

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

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 is director of the Princeton Early Keyboard Center in Princeton, New Jersey. He can be reached by e-mail at <A HREF="mailto:[email protected]">[email protected]</A&gt;.

Intervals, tuning, and temperament, part 1

In this series of columns, I want to share a few ideas about how to introduce aspects of tuning and temperament to students. In so doing I will unavoidably simplify a very complicated subject. My hope is not to oversimplify, but to simplify in a way that completely avoids inaccuracy.
Most organists do not have to do any tuning as such, or at least can do without tuning if they prefer. However, it is very convenient indeed for any organist to be able to touch up a tuning, or to help out with tuning, or to do a bit of tuning of a chamber organ. And of course anyone who plays harpsichord has to expect to do all or most of their own tuning. Beyond that, however, it is very useful and enlightening for any organist to understand the role of tuning, temperament, and the nature of different intervals in the esthetics of organ and harpsichord sound and repertoire, and in the history of that repertoire.

Tuning is one of those areas that many people—including, especially, beginning students—tend to find intimidating. It certainly can be complicated, and can, in particular, involve a lot of math, some of it rather arcane (the 12th root of 2 can be involved, for example, or the ratio between 27 and 1.512). However, the concepts are straightforward, if not exactly simple. I will start from the very basic here—indeed with the question of what a musical sound is, since everything about tuning arises out of that. I myself, who have tuned constantly for over thirty years, still find it useful to revisit the most basic notions about tuning.

What is a musical sound?

Sound travels in waves, and those waves have peaks and valleys spaced at regular intervals. When the peaks and valleys of a sound wave traveling through the air arrive at a solid material they will tend to make it vibrate. Some materials vibrate inefficiently (a block of granite, for example, or a piece of fabric); some, like an eardrum or the diaphragm of a microphone, vibrate very efficiently indeed. In any case, a sound wave will tend to make a solid vibrate at a speed that corresponds to how often—how frequently—the peaks and valleys of that wave arrive at the solid. This is what we call the frequency of the sound: a very common-sense term. The wavelength of a sound wave is the distance between two successive peaks. The longer this is, the less frequently those waves will arrive at a given object (say, an eardrum), the more slowly they will make that object vibrate, and the lower the frequency of that sound will be. The shorter the wavelength is, the more frequently the peaks will arrive, the faster the vibrations will be, and the higher the frequency will be. This assumes that these two waves are traveling at the same speed as each other. It is also true that the peaks of any given sound wave will arrive at a given place more frequently if that wave happens to be traveling more quickly and less frequently if that wave is traveling more slowly. (This is an important point to remember in connection with the practical side of organ tuning, as I will mention later on.)

It is the frequency of a sound that humans interpret as pitch. A sound wave that makes our eardrums vibrate faster we describe as “higher” in pitch than one that makes our eardrums vibrate more slowly. We do not hear wavelength directly: we hear frequency. (This is also an important point for organ tuning.) Frequency, being a measurement of how often a particular thing happens, is described in terms of how often that thing (vibration) happens per second. This is, of course, just a convention: it could have been per minute, or per year, or per millisecond.

Sounds that we tend to experience as “music” have wavelengths and frequencies that are consistent and well organized. Other sounds have frequencies and wavelengths that are in many respects random. This is actually a distinction that—even absent oversimplification—cannot be defined perfectly or in a cut-and-dried manner. It is not just scientific, it is also partly psychological and partly cultural. However, for the (also cultural) purpose of thinking about tuning musical sounds, it is enough to describe those sounds as follows: a musical sound is one made up of sound waves with a frequency that remains constant long enough for a human ear to hear it, which may be joined by other sound waves with frequencies that are multiples of the frequency of that first wave. A conglomeration of sound waves in which the peaks are spaced irregularly will not be heard as music. To put arbitrary numbers to it, a musical sound might have a wave with a frequency of 220 vibrations per second, joined by waves that cause vibrations of 440, 660, 880, 1100, and 1320 per second. (Vibrations per second or cycles per second are abbreviated Hz.) In a musical sound, the lowest (slowest, largest wavelength) part of the sound (220 Hz, above) is called the fundamental, and the other components of the sound (440 Hz, etc.) are called overtones or upper partial tones—upper partials for short. A sound consisting of only one frequency with no overtones will be heard as a musical sound; however, this is very rare in non-computer-generated music. Essentially every device for producing music produces overtones, some (oboes, for example) more than others (flutes). (By convention we usually label or describe or discuss a musical sound by referring only to its fundamental, but that never implies that there are no overtones.)

There is categorically no such thing as an organ pipe or harpsichord string that produces a fundamental with no upper partials. (Though of course the mix and balance of upper partials can vary infinitely.) This fact is crucial in the science and art of tuning, and for the relationship between tuning and esthetic considerations.1

What is an interval?

Any two musical notes form some interval with each other. We are accustomed to identifying intervals by the notes’ linear distance from each other in the scale, and the terminology for common intervals (second, fifth, etc.) comes from that practice. However, in fact intervals arise out of the ratio between the frequencies of the fundamentals of two notes. The number of possible intervals that exist is infinite, since the number of possible frequencies is infinite. However, the common intervals in music are some of those in which the frequency ratios are simple: 1:1, 2:1, 3:2, 4:3, and a few others. And of course these are the intervals that have common names: 1:1 is the unison, 2:1 is the octave, 3:2 is the perfect fifth, 4:3 is the perfect fourth, and so on. To put it another way, if we say that two notes are a perfect fifth apart—as in, say, E above middle C and A below middle C—that means that the frequency of the higher note is in the ratio of 3:2 to the frequency of the lower note, or 1½ times that frequency. (A below middle C is often 220 Hz, so E above middle C should be 330 Hz.) If two notes are an octave apart, then the frequency of the higher one is twice the frequency of the lower one, for example middle C at 256 Hz and C above middle C at 512 Hz. The names—both of the notes and of the intervals—are arbitrary conventions, the existence of notes with these ratios a natural fact.

The question of why those particular intervals have been important enough to so many people that they have formed the basis of a whole system of music—indeed many different systems—is a complicated one that probably cannot be answered in full. It seems self-evident to people brought up listening to music based on fifths and thirds, etc., that those intervals “sound good” and that they should form the basis for harmony—itself in turn the basis for music. Explanations for this have been sought in the structure of the universe, in various mathematical models, and through neurological research. However, for the purpose of thinking about how to tune intervals on keyboard instruments, the interesting and important thing is that the intervals that we use in music and consider consonant are the intervals that are found in the overtone series described above, and in fact found amongst the lower and more easily audible partial tones. The octave (2:1) is the interval between the first upper partial and the fundamental. The perfect fifth (3:2) is the interval between the second and first upper partials. The perfect fourth (4:3) is the interval between the third and second upper partials. The major third (5:4) is the interval between the fourth and third upper partials. This may in fact explain some of the appeal of those harmonies: in a major triad, all of the notes other than the tonic are found in the overtone series of the tonic. (Of course this is only actually true if you accept the notion that notes an octave apart from one another are “the same” note. This appears to be a universal human perception, and has recently been found to be shared by other primates. Possible neurological sources of this perception have also recently been found.) For example, starting with the note C, the first few upper partials give the notes C, G, C again, E, G again. These are the notes of the C major triad.

What does it mean for an interval to be in tune?

If intervals are ratios, then there ought to be a simple definition of what it means for an interval to be in tune: the ratio of frequencies should actually be what the theoretical definition of the interval says it should be. Thus, if a given note has a frequency of (for example) 368.5 Hz, then the note a perfect fifth above it should have a frequency of 552.75 Hz. Or if a note has a frequency of 8.02 Hz then the note a major third above it should have a frequency of 10.025 Hz. Also, since these commonly used intervals are related to the overtone series, it makes sense to believe that their being really in tune this way is important: if they are not exactly in tune, then, presumably, they fail to correspond exactly to the overtones. And it may be this correspondence to overtones that gives those intervals their artistic meaning and power.
The very last statement above, however, is speculative and perhaps subjective—a proposed value judgment about the effect of a kind of sound. It is also quite possible that some interested parties—listeners, composers, performers, instrument builders—might happen to prefer the sound of a given interval in a tuning that is not theoretically correct. It is indeed very common for instruments on which intonation can be shaded in performance (that is, most non-keyboard instruments, including the voice) to be played with a kind of flexible intonation. Notes are moved a little bit up or down to express or intensify something about the melodic shape or the harmony. This is something that keyboard instruments, with limited exceptions on the clavichord, simply cannot do. However, it is an idea that can influence choices that are made in setting a keyboard tuning.

So another definition of what it might mean for an interval to be in tune is this: an interval is in tune if it sounds the way that a listener wants it to sound. Obviously, this is almost a parody of a subjective definition, but it also might be the closest to a true one. If the tuning of an interval does indeed fit some theoretical definition but the musician(s) hearing that interval want it to sound a different way then, as a matter of real musical practice, it probably should be that other way (that is, assuming careful and open-minded listening). This notion, and in general the interaction between certain kinds of theory and certain kinds of esthetic preferences, have also been important in the history of keyboard tuning.

What is the problem with keyboards?

The very premise of the existence of keyboard “tuning and temperament” as a subject is that there are special issues or problems with keyboard instruments from the point of view of tuning. Understanding clearly what these problems are is the prerequisite to understanding keyboard tuning systems themselves, to understanding the role of tuning in the history of keyboard repertoire and, should the occasion arise, to engaging successfully in the act of tuning itself.

The first issue or problem is simply that keyboard instruments must be tuned. That is, prior to playing anything on a keyboard instrument, a set of hard and fast choices must be made about what pitch each note will have. This is perhaps obvious, but still important to notice. Of course the instrument can be tuned differently for another occasion—more readily with a harpsichord or clavichord than with an organ. But at any moment of playing, each note and each interval is going to be whatever it has been set up to be.
The second problem is an extension of the first, and is the crucial issue in keyboard tuning. The number of keys on the keyboard is simply not enough to represent all of the notes that in theory exist. That is, the notion that, for example, c and b# or g# and a♭ are the same as one another is a fiction or, at the very best, an approximation. This is where the math of the so-called “circle of fifths” comes into play. We are all taught that, if you start at any note—say c—and keep moving up by a fifth, you will come back to the note at which you started: c–g–d–a–e–b–f#–c#–g#/a♭–d#/e♭–a#/b♭–f–c. This circle provides a good working description of the way that we use these notes, but it glosses over the fact that if the fifths are pure (theoretically correct) it simply doesn’t work: the circle is actually a spiral. Going one way (“up”) it looks like this:c–g–d–a–e–b–f#–c#–g#–d#–a#–e#–b#–f–c–g, etc. Going the other way (“down”) it looks like this: c–f–b♭–e♭–a♭–d♭–g♭–c♭–f♭–b������–e������–a������–d������–g������, etc. If each fifth is really in the ratio of 3:2—the frequency of the higher note is 1½ times the frequency of the lower note—then none of the enharmonic equivalents work. The b# will simply not be at the same frequency as the c, the g������ will not be the same as the f, and so on.2 This in turn means that it is impossible to tune all of the fifths on a keyboard instrument pure: not just difficult but literally impossible.

The third issue or problem of keyboard tuning also arises out of the first and exists in a kind of balance or conflict with the second. On keyboard instruments the tuning of one class of interval determines the tuning both of other intervals and of the scale as a melodic phenomenon. If you tune a keyboard instrument by fifths, then the thirds, sixths, etc. will be generated by those fifths. If you tune the fifths pure, the thirds will come out one way, if you tune the fifths something other than pure (as you must with at least some of them), the thirds will come out some different way. This is an esthetic matter rather than (like the second issue) a practical one.

These three issues have defined and determined the choices made in the realm of keyboard tuning over several centuries. Next month I will discuss what some of those choices have been and how they have arisen.

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.    

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/   

What are the questions?

An old adage says that the more experience you have in a field, the more you realize how little you know. This thought lurks at the back of my mind, ready to spring forth without notice. You hear a teenager say, “that’s the best movie ever made,” and you wonder how someone so young can be so sure. Then, pain of pains, you are reminded of similar cocksure statements you made when you were young. I knew so much when I was 18, 20, 22 years old that it was hard to imagine there would be more to know. Thank goodness for the inexorable professors who really did know more than I, and for the mentors who encouraged me in what I did know and never failed to point out those that were still mysteries to me. Whispered aside: A colorful and I think underused word in the English language is moil. The American Heritage Dictionary (Houghton Mifflin Company, 2000) gives “intr.v. 1. To toil, slave. 2. To churn about continuously. n. 1. Toil, drudgery. 2. Confusion, turmoil. (Note that moil is part of turmoil—what do you suppose tur means?) With that definition in your minds: I’ve been toiling and moiling (churning, drudgery, confusion) in the organ business since my first lessons as a young teenager and my first experiences in a workshop. There are completed projects and past performances of which I am very proud, and at least as many (God help us there are not more) that I’d like to forget. But that brings us to another most valuable adage: we learn from our mistakes. So as much as we’d like to forget them, we owe it to ourselves to keep their memory fresh lest they be classified as wasted pain. As I work in my shop I hear little voices saying, “if you do that . . . ” When I fail to listen to those voices I cut my finger or break the piece I’m working on. My friends might chuckle and say, “of course he’s hearing little voices—we’ve known that for years.” But the fact is, I think those little voices are the younger me seeing the scar on my hand caused twenty years ago by exactly the same obtuse motion. Those little voices are not signs of going over the edge, but are pearls of wisdom—that elusive and unquantifiable commodity that comes only from experience. And aren’t some of our best learned lessons those that rise from the smoldering coals of our mistakes? The master watches the motions of the apprentice and reaches for the Band-Aids® minutes before they are needed. The parent wishes to be able to spare the child inevitable pain, realizes that advice will not be heard, and has the Kleenex® on the kitchen table an hour before the school bus arrives.
I started by noting that the more you know, the less you know. A cubist view of that statement says that experience in a field reveals more questions than answers. If you really understand the questions, then you are getting somewhere. Often as I write I suppose I’m giving answers, or at least relating my experiences and observations as actualities. This time, I thought I’d give some questions, try to put them in context, and invite you to cogitate and moil over them. As always, I invite your comments: .

1. Which is better, tracker or electric action?

I grew up in the heart of the famed Revival, immersed in both new and antique pipe organs, believing tracker action to be the root of all that is good. As a young adult I had wonderful opportunities to work on massive electro-pneumatic instruments and was exposed to brilliant players doing magical things with them. I was startled when I realized that I was preferring the flexibility of fancy registration gizmos and the orchestral possibilities of these wonderful organs. Now I know I’m interested in good organs. As long as an instrument is well-conceived and well-built, it doesn’t make a whit of difference what kind of action it has. What do you think?

2. Why do some historical styles of organs have developed pedalboards and pedal divisions while others don’t?

The organs of 17th- and 18th-century France have simple and awkward pedalboards in comparison to those of northern Europe, and the music written for them reflects that. François Couperin le Grand (1668–1733) and J. S. Bach (1685–1750) were contemporaries—a quick glance shows the difference—most of Couperin’s music is notated on two staves. I’ve written before about the reproduced engraving that hangs over my desk (from l’Art du Facteur d’Orgues, Dom Bedos de Celles, 1766). It depicts a large 18th-century French organ shown in cross-section, with an organist playing. He is wearing a powdered wig (good thing it was tracker action, think of that powder clogging up the keyboard contacts), a heavy formal coat with long tails and buttoned cuffs, an equally heavy vest under the coat, and a sword whose tip was right next to his feet on that primitive pedalboard. A sword? No wonder they didn’t use the pedals. One fast flourish and your feet would be bleeding. Imagine the teacher saying, “Go ahead, take a stab at it.” And, to protect himself from injury he was wearing heavy boots. No Capezios here.

3. How do historical styles evolve?

It’s relatively easy to identify and study the differences between, for example, 18th-century French and German organs, but what caused the development of those differences? Was it the wine? Was it the spätzel?

4. Where did the different pitches of organ stops come from?

There is a simple answer—8' is the fundamental tone, 4' is first pitch of the overtone series, 22?3' is the second, and so on through 2', 13?5', 11?3', 11?7'. 102?3' is two octaves below 22?3' so 102?3' is the second overtone of 32' pitch—that series continues with 8', 62?5', 51?3'etc. The overtone series was perhaps first heard clearly in the tone of a big bell. The experienced listener can hear fifths and thirds clearly in the tone of such organ stops as an Oboe, Clarinet, Krummhorn, or Trumpet—in fact, those stops get their color from those strong overtones. That’s why you can hear the pitch of a Tierce so much more clearly against a reed than against warm and fuzzy Gedackt. (When I’m tuning those stops I have the habit of humming and singing parallel intervals and arpeggios inspired by the overtones —another example of the little voices in my head.) But the real question is how the perception of those overtones in the sound of an organ pipe led the early builders to experiment with creating individual stops that doubled overtones.

5. Is chiff a good thing?

During the aforementioned Revival many organbuilders experimented with “chiff, ” that characteristic chiffy consonant that starts the speech of an organ pipe. Every musical tone has some sort of attack that precedes the vowel of the note, and an organ pipe can be voiced to have lots of chiff or virtually no audible chiff. It’s a matter of personal preference, but if some people like it can it be all bad?

6. How does a modern church justify the cost of purchasing and maintaining a pipe organ?

Hardly an organ committee comes and goes without grappling with this one. A committee member asks, “with all the hunger and suffering in our community, why shouldn’t we use the money for a food pantry?” Our church buildings with their fancy windows, silver chalices, statuary, paintings, and pipe organs are expressions of our faith. Our culture is loaded with examples of historical expressions of faith through art—think of the liturgical music of Mozart and Bach, the sculptures of Michelangelo, the buildings designed by Bernini and Henry Vaughan. Are we better able to fund a soup kitchen from a building that makes obvious to our neighbors the strength of the bonds that tie us together as a community of faith?

7. How does a chestnut become a chestnut?

Given the production cycle of this publication, I am writing in mid-December, these few hours sequestered, escaping the tyranny of commercialized versions of our favorite Christmas carols.
Otherwise, I’m racing around the countryside tuning organs (plenty of opportunity to be humming arpeggios next to Krummhorns). Several of the churches I visit are presenting “Messiah Sings.” Handel’s masterpiece is a fantastic artwork. It’s easy to understand how it would filter down through generations as a perennial international favorite. But it’s very difficult music. The choir members in these churches have no idea how difficult it is. I’m sure they wouldn’t dream of tackling Handel’s Israel in Egypt, another masterwork that’s equally majestic and equally difficult to perform. Why is that?
Many parish organists will agree with my assertion that you could successfully plan and play a thousand weddings, fully pleasing all the families involved, with a repertory of ten pieces. We could all name the same list: Wagner, Mendelssohn, Schubert’s Ave, Jesu Joy, Clarke, Purcell, Stookey (“there is love . . . ”). You play through ten unfamiliar pieces for a bride and groom with no response, and they light up with the first six notes of Jesu Joy (boom-da-da dee-da-da . . . ). It doesn’t matter if you’re in Boston, Seattle, San Antonio, Milwaukee, or London. Why is that?
How many of us look forward to playing those wonderful sassy French noël variations—the ones with the non-existent pedal parts? I see volumes of Daquin and Balbastre on organ consoles all across New England. How many congregants recognize them as seasonal music? We erudite organists associate them with Christmas as readily as reindeer and O, Holy Night. Why is that?

8. Why did it take so long to develop equal temperament?

(Please do not interpret this as an indication of personal preference!)
Equal temperament is the most common system of tuning keyboard instruments and was not commonly used until at least the late nineteenth century. Pythagoras (6th century, BC) is credited with the development of the concept of tempering, of dividing the circle of fifths into the octave, a feat that is technically impossible. If you start on a single note and tune pure fifths around the circle of fifths, when you complete circle returning to C from F, you have nothing like a fifth. So over the centuries, various musicians, mathematicians, and theorists toiled and moiled developing systems that would divide that discrepancy over more and more of the intervals, allowing more of the twelve possible keys to be useful—or usable. The advent of Pythagorean tuning was natural, but I wonder why he or one of his contemporaries didn’t solve the problem by dividing the difference over all the intervals from the very beginning. That would have changed the development of music dramatically.
Some of these questions have real answers. Some of these questions have different answers, depending on whom you ask. I’ve given comments to introduce each of the questions that may lead a reader to deduce that I have an opinion. And those of you that know me personally may be able to read what you know to be my opinions, whether I know them or not. Why is that?
The questions frame the debate. If there’s a debate over a specific question, does it follow that there is no right or wrong answer?
Here’s an exercise that illustrates the elusiveness of correct answers. Take a well-known church building: St. Thomas Church, Fifth Avenue, New York. Consider two well-known and successful organbuilders, respected for the toil and moil of their respective careers: Ernest Skinner and Taylor & Boody. Imagine what each would consider the ideal organ for the space. Now tell me, who’s right?