Skip to main content

A New Age in Acoustics

by Joseph Chapline
Default

 

Back in the 19th century, two great scientific figures wrote books on the science of sound. The earlier was Hermann Helmholtz with his On the Sensations of Tone, 1863; the later was Lord Rayleigh in his The Theory of Sound, 1877. Both books are large and heavy tomes. These scientists were both highly skilled and thorough in their investigations. Indeed, these works are for most of us, formidable. Much theory, much mathematics, and much ponderous discussion. Nevertheless, they both set forth a theory of sound that has stood the test of time. As with any such intricate disquisition, the public has taken from the work of these two men what they want and, in a sense, "simplified" the principles. Since those books were written, the science of acoustics has made several substantial and significant advances.

 

Over the last several years, I have encountered two presentations of simple acoustic theory under somewhat formal circumstances: one was a lecture given at the convention of American Institute of Organbuilders held in Virginia, October 1997. The other is in a fine book of the popular press, Music, the Brain and Ecstacy, by Robert Jourdain (Avon). This book is well written and in its later pages examines deeply and interestingly the psychology of the musical experience. But in the earlier pages it gives an explanation of sound, like the speaker at the convention of organbuilders, that reads completely from the old theories.

In brief, the older and still popular theory says that all sound can be analyzed into component harmonics. All the harmonics in this composite sound are integral multiples of the bass frequency. Thus, given an A=440 hertz (cycles per second), its harmonics are 2x440=880, 3x440=1320, 4x440=1760, and so forth. Furthermore, these harmonics, like a pharmacist's compound, are added at various dynamic levels: the second harmonic is, say, 42% of the fundamental, the third harmonic is, say, 86% of the fundamental,and so forth. In other words, if you were to compound a given group of harmonics in their proper proportions to the fundamental, you will, perforce, re-create the original sound.

 Here is the basis on which Hammond constructed his now famous organ. Little sliders above the keyboards--there are nine of them--can be drawn out to one of 8 different positions to represent the various intensities of each harmonic and--voila--there you have the oboe, the violin, or whatever other sound your mind can dream up. Anyone who has played around with a Hammond knows that no such miracle takes place. Rather, the instrument produces some sterile sounds that can beguile briefly but ultimately do not imitate anything but a Hammond organ. The Hammond has been used extensively in the field of popular music. It is portable and not too expensive. And Hammonds do last a long time! Their basic sound-producing mechanism is a whirling shaft--spinning at a constant speed to keep the frequencies constant--with many notched wheels (one for each frequency); electromagnetic pickup heads pointed at each wheel feed the signal from the wheels through the sliders into an amplifier and eventually the loudspeakers. Another fact about the Hammond is that the harmonics are borrowed from the tempered scale of the bass frequencies. Therefore, the pitches of the nonunison "harmonics" are not in tune with the fundamental--not true harmonics--and therefore they cannot form composite sounds because they will beat with the fundamental.

The idea of compounding harmonics to produce composite tones is not new. The major chord is nothing more than the first, third, and fifth harmonics of the basic key note. Intricate harmonies such as in the Bach chorales or the barbershop quartet are merely other combinations of harmonic pitches to make a composite sound. In fact, the major and minor scales we use for our music are composed of the harmonics of a fundamental note. (The C-major scale, by the way, is based on the harmonics of F!) All the notes of the C-major scale can be played or sung simultaneously without producing any beats provided the notes are accurately tuned as harmonics of the frequency of the generating tone, F. The common theory of sound believes that by properly proportioning harmonics, one can make a human being think he hears the strident blare of the trumpet or the soothing coo of the flute. But later research and better understanding of acoustic phenomena have altered these earlier theories.

One of my colleagues, Ralph Showers, at the University of Pennsylvania, way back in 1943, was preparing a master's thesis on sound. I talked with him about synthesizing tones by the old theory. He laughed at me. I exclaimed, "You mean you can't put the proper proportions of harmonics together and recreate sounds of violins, oboes, and others?" He told me that in analyzing the sound spectra of the various instruments, he could find no clearly singular spectrum for any one instrument. "They went all over the place! The spectrum of the violin looks like the spectrum of the oboe; the clarinet looks like a trumpet," he said. I was crushed; I thought it was all so simple and neat. Further conversation with Ralph only made things worse; the whole idea of synthesizing tones by adding proportions of harmonics was nice in theory, but not in practice.

The harmonic synthesis principle, even if true, leaves a whole class of musical sounds out of the "equation." What about the struck instruments, the bell, the cymbal, the drum, the glockenspiel? These are all enharmonic instruments that do not obey the "harmonic" law at all.

Then I took a graduate course in acoustics and learned a fuller approach to the theory of sound. Its premise is that all elements that produce sound vibrate because they have been temporarily deformed. The restoring forces of the deformed bodies are due to one or the other of two forces: tension, or stiffness. The violin string is deformed by contact with the moving resin-laden bow and pushed from its normal position until the restoring force of tension in the string exceeds the grip of the resin on the string, at which point the string flips back. Continued bowing thereby sets the string into vibration. The triangle is struck with a little rod and is thus deformed, as with the violin string, but it returns to normal by virtue of the stiffness in the structure of the triangle. Unlike the violin, whose tone can be maintained as long as the bow keeps moving, the tone of the triangle gradually falls off as the energy of the initial blow is gradually dissipated into the air and the metal of the triangle. All instruments of music are governed by one or the other of the two restoring forces: tension or stiffness.

In order to study these phenomena, the physicist, in his formal mathematical way, writes down a differential equation that says: the vibration of a body is proportional to the sum of two restoring forces, tension and stiffness, as a function of time. Fortunately, the physicist finds that the musical instruments fall into either one or the other class: tension or stiffness, but rarely both (see pianoforte later). The equation is then simplified by dropping either the term for tension or the term for stiffness. If tension is the dominant restoring force, the equation reduces to the harmonic series of integral multiples of the bass frequency: one times, two times, three times, the fundamental frequency. The various frequencies are sometimes called upper partials, a good general term. But they can also be called, quite specifically, harmonics.

The class of harmonic instruments is large. The typical tension instruments are all the bowed string instruments, also the guitars, zithers, clavichords, harpsichords and other plucked instruments (the pianoforte is not included here; it's in a class by itself!). Also, it turns out that the wind instruments function also in the harmonic system because a column of air acts like a string under tension. Thus, all the wind instruments are also harmonic devices: the oboe, the flute, the trumpet, the human voice, the french horn, and the organ pipe, for example.

When stiffness is the dominant restoring force, the equation leads to another set of equations known as Bessel Functions. (Friedrich Bessel was a Prussian astronomer, 1784-1846, who developed a series of equations that have been named for him and which are much like the trigonometric equations.) Without going further into the abstruse, the Bessel equations describe the higher frequencies that form the upper partials of the sounds of stiffness-dominated instruments. The frequencies of these upper partials are not integral multiples of the fundamental; the Bessel multipliers are called transcendental numbers. These multipliers are long decimal numbers that have an infinite number of decimal places. They are not harmonic! They should properly be called overtones. These sounds do not blend quietly into the mélange of the harmonic orchestral sounds of the tension-dominated instrumental sounds.

The class of stiffness-dominated instruments is not as large as the tension-dominated. They include the triangle, the chime, the bell, the glockenspiel, the xylophone, the celesta, all the drums, the cymbals, and other struck-type instruments. The triangle with its single ting! sounds out clearly over the entire symphony orchestra. What is the loudest instrument in the football band? Not the trumpets. No, it's the glockenspiel, that brightly plated, lyre-shaped instrument that is played with a little mallet. Its ting sings out over everything else. It is nonharmonic and therefore does not get lost in the rest of the sounds.

So, we can summarize: All instruments are divided into two main classes--harmonic (tension-dominated) and nonharmonic (stiffness-dominated).

Now a special note on the pianoforte. Pianos, as they are commonly called, used to be in almost every American home. Acoustically, the piano is a total hybrid. Did you ever try to replace a piano string? Quite unlikely. But I assure you it is far from easy. All the strings in a piano are stiff and difficult to handle. They are unwieldy in their stiffness. And they must be wrapped around a tuning pin that is about 1/4≤ in diameter! Unlike the thin, delicate strings of the harpsichord, the piano string is definitely a thing of stiffness. And have you heard of the tremendous tension that exists in a piano when it is all strung up and tuned? There are many tons of tension between the tuning block in the front and the terminals at the rear of the cast-iron frame that holds all the strings. With these two facts, yes, the piano carefully sits astride the stiffness-tension systems. It is not quite either; it is both. Thus the piano--like the triangle--can, in a concerto, quite dominate the orchestral scene. At the same time, the pianoforte is not a member of the symphony orchestra. Often one sees pianos as part of high-school orchestras, but these pianos are used to fill in the parts of missing instruments.

Let's change gears rather abruptly. There have been two significant experiments performed in the last 30 years that have made us reconsider the old gospel significantly. One of these experiments might seem to have nothing to do with music. It has to do with language. (But isn't music a language?) A branch of the U.S. military service was curious about the limitations of frequency range on radio communication through earphones. What would the absence of certain frequencies in the communicating system do to the accuracy with which the serviceman would hear the messages? How accurately do the pilots hear the messages through the radios and earphones that guide them?

A test was carried out at MIT in which they had three rooms. Listeners were placed in rooms A and C. An articulator--a person who spoke English clearly--was placed in room B. Room B was connected to room A through an amplifier that passed only frequencies of 400 cycles per second and lower. (The unit, cycles per second, has been replaced with the single word hertz.) Room C was connected to room B by a similar amplifier that passed only frequencies of 400 hertz and higher. The decision on 400 hertz was to separate vowels from consonants. Realize that the vowels, though spoken, are pronounced as if they were sung. Vowels are sustainable; they can be made into continuous sound. These are the tones one makes when singing; they are, for a man's voice, below 400 hertz. The high A of the tenor is 440 hertz. But the fricative sounds--the s's and sh's, the explosives, p's and t's--are all in the upper frequencies, frequencies above 400 hertz.

 This test setup neatly divided the English language into vowels in room A and consonants in room C. The articulator in room B then read a list of words while the listeners in the other two rooms wrote down what they heard. Results showed that room A, with its vowels, heard about 20% of the words correctly; room C, with its consonants, heard 80% of the words correctly. In other words, 80% of the intelligibility of language lies in the consonants, not the vowels. Choruses and singers in general find it difficult to make the words they are singing intelligible to the listener because they sing mainly on vowels. However, there are a few singers, notably Rosemary Clooney and Bing Crosby, who do (did) an incredible job of pronouncing their consonants so distinctly as they sing that we can all understand what they are singing about.

Another experiment--this in music directly--was performed with only two rooms. Room A contained a number of experienced musicians; room B contained a number of familiar sound sources such as violins, trumpets, oboes, and singers. Room A was connected to room B by a fine, high-fidelity sound system. In this experiment, the various sound sources in room B played notes. In room A, the auditors wrote down what they thought was the source of the various sounds they heard. Their answers were nearly all correct.

Then they did a second phase of the experiment. In each case, now, the microphone was turned off until the source had already started its sound and the microphone was turned off before the sound had stopped. In other words, the auditors in room A heard only the steady-state sound without any initial or terminal transients. The "consonants" were excluded and only the "vowels" were sent to room A. The results were nearly all in error. Experienced musicians could not tell the "vowel-sound" of the oboe from that of the violin! In other words, in music as in language, it is the consonants of the "language" that make for intelligibility, not the vowels. As we grow older, our ears lose their high frequency sensitivity; we drop off the consonants so that we fail to understand what other people are saying.

The significance of these two experiments cannot be overstated. Notice now that the entire sound of those "loudest" instruments--triangle, glockenspiel--lead to an idea that sounds silly when posed, yet is not frivolous. Why does a composer use ties to sustain notes across a bar? One might answer unwittingly; "In order to make the note longer." But wait! May it not be that he wishes to avoid a new transient at that moment? Syncopation is another example; by not accenting the beat and accenting the offbeat note, one achieves syncopation. The force of the syncopation is enhanced by the transient sounding powerfully on the offbeat!

The articulation--the breaking up of the music into its parts and pieces by the presence of transients--is the way to understand the details of a work. Mozart used the trumpet--much to the trumpeter's distress because it made Mozart's trumpets parts so simple‚ largely as a source of juicy transients. The ta-ta-ta-tah of the trumpet is really a percussion effect. The trumpet has long been the alarm, the tocsin, that brings us all to attention. The wonderful cackle of the oboe is the source of its joy and rhythm. The breathy concomitant sounds with the flute are its own joy.

Once I was demonstrating a new organ to a group of curious people. While I was bubbling about the wonderful tones of the new instrument, I picked one stop and put my finger on a single note and held it. I continued to rhapsodize about the beauty of the tone as I held the note ever longer. Suddenly, one of the listeners burst out, "Play it again!" He wanted another transient to savor again the "tone" of the pipe, not listen just to the steady-state tone.

Jazz, the great American music, is known for its rhythm and especially its syncopation. What are the instruments most useful to jazz? The trumpet, the saxophone--which has some wonderful transients--the trombone, the clarinet. Notice, the violins are missing. Why? Because the violins and their cousins have weak transients. Listen to a violinist trying to play jazz and you will hear a musician with an instrument that has weak transients doing his best. He will employ every device known to music to overcome his lack. He will play late (agogic accent), he will play off pitch, he will play with vibrato. These are the devices also used by vocalists, who also have weak transients. How often have you heard a jazz singer arrive at the last note singing well flat of the note and then, as he/she sustains the note, gradually begins to add vibrato and slide up to the pitch? A string quartet is, at best, inept at jazz.

Bach's favorite instrument was the clavichord; he also liked the harpsichord. The sounds of both these instruments consist largely of transients. In fact, they are noted for their lack of sustained sound. The distinctive ting of both these instruments makes the counterpoint brilliantly clear. When Silbermann showed Bach his latest pianoforte, Bach is said to have made some remarks that apparently caused a falling-out between these two men. Perhaps Bach's comments had to do with the less pronounced transients of the new pianoforte compared with those of the clavichord and the harpsichord. The counterpoint was not as easily heard as on the earlier instrument. So too, the "chiff" of the unnicked organ pipe provides a transient that also helps to make the counterpoint clear.

One must conclude from these experiments and from personal experience tha the definition of musical tone and its place within the fabric of music is more dependent on the opening and closing transients of the sounds than on the old theories of composite tone that consists of harmonics or overtones in varying proportions. Yes, there are harmonics; yes, there are overtones; yes, they are there in varying quantities. But between the actual music and the laboratory analysis, there is a long distance. We live on transients for most of our interest in music. Many of us may think that the pear-shaped tones are the sine qua non of music. Certainly, the mellifluous sustained tones of a great choir of strings in an orchestra, or the sustained sound of a large chorus of human voices is a stirring sound, but both are sounds that need to be ventilated frequently with consonants to make them totally meaningful.

We must modify the old credo of sound to bring in these new understandings. Transients form the intelligence in music. Music must have transients to be interesting. It is the consonants, not the vowels, that make for articulate, intelligible, and moving music. Otherwise, we have ululation!

Related Content

On Teaching

Gavin Black

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;.

Files
Default

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.

 

An Acoustic Basis for Organ Specificiation and Registration

by Robert Huestis
Default

Introduction

The modern "orgelbewegung" organ revival has cultivated as a norm the German neo-Baroque organ, using stopped or partly stopped flutes as foundations at 8' and 16' pitch in small instruments. This practice has been given such authority that many organists do not question it; but this type of organ is only one style among many. Neither it nor any other design ought to be raised to the level of dogmatic acceptance. The multiple foundation stops found in the best nineteenth-century organs  represent the continuation of a tradition which had been already established in the Baroque period. A perception of the history of the organ which does not ignore the nineteenth century should lead us to see that multiple foundation stops in the manuals are consistent with eighteenth-century practice and not the exception.

In this paper, the presence of such stops in important examples is noted and described. It is observed that some organs of the eighteenth- and nineteenth-century have an extraordinarily cohesive blend of stops in various combinations. An acoustic theory is put forward to explain the reason for this blend or its absence. This theory states that stops are able to blend when harmonics are present in the unison tone which duplicate the fundamentals of the upper pitches. It is also observed that stopped pipes used as foundations cannot provide these harmonics.

A most important application of this point of view is that the pedal of a small organ may be based upon a 16' open subbass, not the traditional stopped bourdon. Several organs are cited which demonstrate this practice, from the eighteenth, nineteenth, and twentieth centuries. It is noted that in the manual divisions the Italian organs used 8' open pipes as foundations through their entire history; however, the Italian organ has generally been ignored as a model for small instruments. It is concluded that the exclusive use of stopped pipes as fundamentals in small organs should be reconsidered. The extensive use of stopped flutes represents a restricted, national style which ought not assume the role of a universal model. Open pipes blend better and make the tone more cohesive. We should question accepted norms of "organ design" and revise them in favor of those traditions which include the use of open pipes to provide the fundamental tone. This will allow organs in churches to be most effective at their primary role, to provide a foundation for congregational singing.

Historical Background

With the neo-Baroque organ revival, organ scholarship blossomed and has resulted in the construction of new instruments re-creating stop lists that belong to specific national or regional styles of organ building. These instruments reflect earlier times and their respective literatures. These trends were transmitted remarkably quickly to North America. This was accomplished primarily by North American scholars studying abroad and by European specialists teaching in North America. Some years later these same trends appeared in other English-speaking countries such as Australia. This organ revival filled a particularly heartfelt need resulting from a discontinuity of the traditions of organ building which was most evident in the "orchestral" and theatre organs of the 1920s.

It is not a simple matter to establish exactly why traditional concepts of organ building were abandoned, but if any one cause is to singled out, it must be that certain types of electric action made possible the use of the same pipes at two or more pitches (unification) or on two or more keyboards (duplexing)1. These purely technical devices of organ design, made in the interests of a certain type of economy, made it impossible to voice the organ so that its stops could blend. This break with the traditional concepts of organ voicing set the stage for rediscovery of older traditions, rather than allowing a normal evolution of organ design. When it became obvious that something had been lost through neglect, there had to be a "revival" so that whatever it was that had been lost could be reinstated.

Unification and duplexing destroyed the blending ensemble so thoroughly that, despite the effects of the organ revival movement, we have not yet recovered the consciousness that the stops of an organ must truly blend together. The result is a genuine anachronism: the separate stops of many modern organs refuse to blend, while there still exist a few forgotten nineteenth-century instruments, the best from their time, which preserve the ability of every one of their stops to blend with every other. While the "revival" organs do not have unification or duplexing, often they show an indifference to blend that can be traced to the disastrous lapse of sensitivity in voicing that unification and duplexing have left as their aftermath.

New Organs in North American and Australia

One result of the organ revival has been the crystallization of the neo-Baroque stoplist into a norm for the construction of new organs. But because a "revival" resurrects an older stratum of the culture which has already passed away, the organ revival reflects the specific requirements of a style of organ playing which is no longer in an active phase of development. The "revival" organ often reflects the general requirements of eighteenth-century organ playing and the specific demands of German Lutheran organ literature. It is now customarily imposed upon English-speaking regions of the world, regions which possess traditions and literatures vastly different from those of an eighteenth-century culture. This neo-eighteenth-century norm presents itself virtually as a doctrinal system, often assuming a degree of authority that is insisted upon in the same way that a theological principle may be insisted upon.

The North American adoption of the neo-Baroque organ design was a "marriage of convenience" to aid the recovery from the theatre organ debacle and its after-effects. It has persisted quite a bit too long. Now we are being called to take up once again the historical evolution of the instrument.

The objective of the author is to develop a theory of organ registration and specification that does not reflect the demands of any national or regional style. Instead, it is a theory of organ specification which proceeds from an acoustic basis. It is intended to fulfill the needs which we find in English-speaking churches at the end of the twentieth century. Like the ancient eclectic philosopher, we have selected such doctrines as please us from every school. Our music borrows freely from many sources, and is not exclusive to any one tradition.

The Nineteenth-Century Contribution

In Australia, New Zealand, Canada, the United States and Europe, there still exist nineteenth-century organs virtually untouched or relatively intact, preserving a tradition of organ building which has largely been lost in the major population centers. A number of these organs are being rehabilitated and it is no longer fashionable to take away their original characteristics. Restorations, not rebuilds, are becoming more common. An example is the organ formerly of St. Stephen's Roman Catholic Cathedral, Brisbane, built about 1880.2 This old instrument survived the rebuilders because of the happy circumstances of benign neglect. Fortunately, there was not enough money available to replace or "modernize" it.

This organ features tracker action, low wind pressure, bright reeds, and clear but not loud upper work. Everything rests upon a foundation of several unison stops and all reasonable combinations of two or more stops can be depended upon to combine into a blend of great cohesion. These factors suggest that this organ represents an evolution of the traditions of organ building which had been current during the century before. Though the sound is quite different from a Baroque organ, there is no radical departure from the eighteenth-century traditions, but rather a continuity with them. The result is that the music of both Bach and Brahms sounds very comfortable on this instrument.

The Great manual of this organ corresponds almost exactly to the Baroque ideal in the plan of the stops and their assignment at various pitches. The character of the stops has changed according to the styles of the period, but the essential design of the ensemble is preserved. As a model for comparison the specification of the Great manual is given from the Löfsta Bruk organ of 1728 by the Swedish builder Cahman,3

It is apparent from nineteenth-century examples (for instance, by E.&G.G. Hook and others in Canada and the United States), that tracker action, low wind pressure, bright reeds, upper work and mixtures were all elements of organ building that had been carried over into the nineteenth century from the eighteenth century. What about the multiple unison stops? Do these represent a "Romantic" tradition only, or are they an element that was being carried over from the Baroque period into the Romantic era? In both organs cited above, there is an open 8' to serve as the foundation for the ensemble, a wide-scaled flute to give it depth, and a third 8' stop to contribute the harmonics necessary to bind the ensemble together. In the eighteenth century, these harmonics were provided by the Quintadena, meant to act together with the Principal 8'. In the nineteenth century the Diapason had a wider scale than the eighteenth-century Principal. Therefore the third 8' stop, which must contribute the binding harmonics to the ensemble, is the Gamba, a string-toned stop of such wide scale in this organ that it is very much like a narrow-scaled Violin Diapason.

If we emphasize the similarity of the two stop lists rather than their differences, we can obtain a better view looking back at the eighteenth century and also looking forward to the twentieth century. It is possible to theorize on specifications which can accommodate not only the music of Buxtehude and Bach, but also the other portions of the literature, such as that by Dupré or the French symphonists, which have grown out of the traditions of the nineteenth century.

The Difference between "Registration" and "Specification"

Organ specification is not the same thing as organ registration. A specification is a list of the various stops of which a particular instrument is composed. Registration is the setting down of certain combinations of stops in order to produce a desired effect. In a given organ, there is a specification of stops which should combine together to give the instrument a distinctive musical formulation, which we call "ensemble", all the parts of which match together and harmonize. From this specification, an indeterminate number of registrations may be drawn, which express various facets of that distinctive musical ensemble. The full organ registration should be equivalent to the specification of the instrument less certain stops intended for special effects.

The specification of an organ should be built up, not to make combinations, but rather to provide for maximum blending of stops. Blending stops may be pursued in two directions--vertically (8', 4,' 22/3', 2' etc.) and horizontally (8' + 8', 4' + 4'). The 8' and 4' accompaniment stops, which are flutes, should blend horizontally with the principal chorus. How often have students been admonished not to combine stops of the same pitch, because of tuning problems! In nineteenth-century organs, the 4' flute was usually open or harmonic and combined naturally with a 4' principal, rather than beating against it. Both the Brisbane organ and the Löfsta Bruk organ present an open 4' flute capable of combining with a 4' principal. This is not a new characteristic making its first appearance in the nineteenth century.

The reed stops should blend horizontally with both flutes and principals. There ought to be maximum harmonic reinforcement between the reeds and flues--that is, there should be no sour off-harmonics in the reeds. Therefore, full-length reeds are to be preferred to half-length reeds, which have a peculiar harmonic series with flat ninths and so on.

Finally, at least one mixture stop may contain a tierce, in order to assist in the blend with the reeds. This characteristic occurs in both the Brisbane and the Löfsta Bruk organs. We can see from the above, that specification is the organ builder's art. Specifications should not be made up to encompass the most possible registrations. Rather, the various registrations should be derived from each organ's individual specification. The specification of a particular instrument should be set up to secure the maximum possible blend, both in the horizontal and vertical directions. From a specification may be derived two contrasting types of classes of registrations: blending registrations and non-blending registrations. These are defined and discussed below.

The Harmonic Overtones of Open and Stopped Pipes

It is well known that all organ pipes produce composite tones consisting of various harmonic partials.4 The partials of 8' open pipes which concern the present theory of registration are these:

First partial = Fundamental

Second partial = Octave = Fundamental of 4' stops

Third partial = Quint = Fundamental of 22/3' stop

Fourth partial = Double octave = Fundamental of 2' stop

Fifth partial = Tierce = Fundamental of 13/5' stop

The fundamentals of the 4', 22/3', 2' and 13/5' stops all reinforce harmonics already present in tone of the open 8' stops. Therefore the 4', 22/3', 2' or 13/5' stops will blend acoustically with the open 8' stops.

The stopped pipes, in contrast, behave very differently. They emphasize only the odd partials. Those partials of stopped pipes which characterize their tone are these:

First partial = Fundamental

Third partial = Quint = Fundamental of 22/3'stop

Fifth partial = Tierce = Fundamental of 13/5' stop

These stopped pipes form strong blends with mutation stops, but not with the octave-sounding registers of the principal chorus.

"Blending "and "Non-Blending" Registrations

"Blending" registrations are defined here as those registrations which consist of stops arranged in such a manner that the harmonic overtones of the lower stops duplicate the fundamental tones of the higher stops.

Examples:          Open 8' (Principal)        +              open or stopped 4'

                  Open or stopped 8' (Principal or Quintadena)                  +             22/3' Quint

"Non-blending" registrations may be defined as combinations of stops arranged in such a manner that the harmonic overtones of the lower stops do not duplicate the fundamentals of the higher stops.

Examples:          Stopped 8'         +               stopped 2' or open 2'

                  Stopped 8'         +              stopped 4' or open 4'

Blending registrations are used for music which demands the full chorus attribute of the organ. Non-blending registrations should be used where the music is to stress the maximum independence of line, such as in the typical bicinium type of chorale prelude.5

Some compositions may feasibly use either a chorus type of registration or a contrasting non-blending registration which stresses independence of line. Hence the dividing line between the two types is not clear. To express this ambiguity of intention, hybrid registrations are useful. Some of the stops blend with each other, while some do not.

Examples:           Open 8'                +              stopped 4'          +              open 2'

                  Stopped 8'         +              open 4'                 +              open 2'

In the first example, the open 8' combines with both the stopped 4' and open 2,' but the open 2' cannot combine with the stopped 4' because there is no 2' partial in the stopped 4'. In the second example, the stopped 8' can combine with the open 4', but not with the open 2'; also the open 4' and open 2' can combine with each other. For both examples, the character is not clearly either "blending" or "non-blending." Registrations with this property might be best used in music which has three or four voices where both the cohesion of the lines and their independence are to be stressed simultaneously.

These observations lead to the conclusion that successively higher pitches in a registration should be more open acoustically.

Example: Stopped 8' + partially open 4' (Koppelflute or Rohrflute) + open 2.

Single stops can also exhibit this hybrid characteristic. For example, the bottom octave may be stopped, the next octave partially stopped, and the treble fully open.

Composite Solo Registrations

The foundation 8' flutes should contain the 4,' 22/3', 2' and 13/5' partials, so that the mutation stops can join with them acoustically. The 4' flutes should contain prominent quint partials, if there is a Larigot or quint at 11/3' above. A conclusion which follows from this type of design is that the stop which determines the musical quality of a Cornet V is the 8' flute that supports it, rather than the mutations of which the Cornet itself is composed.

Solo registrations involving reed stops may be either blending or non-blending. It is interesting to contrast the combination Oboe 8' + flute 4' with the combination Clarinet 8' + flute 4'. The action of the flute in each case is different. There is, however, a little of every harmonic to be found even in the hollow-sounding reeds such as the Clarinet and the Krummhorn, because the reed itself produces a full series of partials.

If we contrast the registration Oboe 8' + quint 22/3' with Clarinet 8' + quint 22/3' we find that the adhesion of the quint to the Clarinet is stronger than the cohesion of the quint with the Oboe. This happens because the quint harmonic (22/3') is much stronger in the Clarinet than it is in the Oboe. A composite solo registration may be used with either a blending or a non-blending accompaniment registration, depending upon the character of the accompanying voices.

Conclusive Statement of Theory

This present theory of registration is easy to apply. If a stop at a lower pitch contains a harmonic that can bind with the fundamental of a stop at a higher pitch, then those two stops are capable of a good blend. If not, they will be limited in their capability of blending, or prevented from it altogether. An ensemble composed from a "non-blending" specification (such as is found in small neo-Baroque "revival" organs) comes out in layers, rather than producing a blended, cohesive, and "blooming" sound.

Specification of Foundation Stops at 8' and 16' Pitches

A practice which flows from the acoustic analysis of specification is the placement of open and partially stopped flutes at the 8' pitch in the manuals and at the 16' pitch in the pedal organ. This is much in contrast to the idea of placing them exclusively at the 4' pitch and higher in the manuals and only from the 8' pitch upward in the pedal. In the manual divisions, the economy of the organ and the space it requires are not greatly affected, since in most cases the bottom octave of open flutes at the 8' pitch is stopped and made of wood to assure quickness of speech. The provision of a narrow-scale open subbass in the pedal requires room overhead and this stop is expensive; but this expense should be more than offset by the fact that such a pedal division is more versatile and blends so much better than the alternative. The organ can be made a stop or two smaller than might otherwise be planned. The expense of the open 16' stop is more than recovered because a smaller pedal organ will actually sound better and more compelling.

When the pedal is based upon a 16' open flue, producing a relatively quiet tone--about the same intensity as a normally stopped Subbass 16'--there is an exquisite blend of harmonics. The upper partials of the soft open 16' are able to combine with the fundamental tone of the various members of the chorus above, particularly the 8' Principal.

This is the design of the pedal organ specification which is found in the Cahman organ of Löfsta Bruk.

Öppen Subbas 16'

Principal 8'

Gedackt 8'

Kvinta 51/3'

Oktava 4'

Rauschkvint II

Mixtur IV

Basun 16'

Trumpet 8'

Trumpet 4'

It is exceedingly rare. Cahman also did another interesting thing. The combination Gedackt 8' , Quintadena 8' and Quint 22/3' is repeated both in the Great and Positive organs. Are we to realize from this repetition that Cahman provided the Quintadena 8' in each case to secure an acoustical, harmonic "locking in" with the quint 22/3' above it? Most modern specifications would have omitted the Quintadena, probably on both manuals, and supplied a stopped 16' to the pedal, substituting for the Open Subbass 16' a louder Principal 16'. The particular quality which sets this Cahman organ apart as a gem among artistic instruments would be destroyed.

The Open Subbass of the Löfsta Bruk organ is made of wood and has a fairly narrow scale. In the published photographs of the organ, the end of the largest pipe can be seen behind the 8' Prestant of the pedal organ. The lowest pipe is approximately seven inches square. If this principle of specification and voicing is to be retained in an organ large enough to offer both an open and stopped 16' flue in the pedal, it is important that the open stop be of narrow scale and voiced quietly so as to support the chorus above. When 16' open flues are scaled and voiced loudly, so as to "add power", their harmonic development is much reduced and their ability to contribute to a unified chorus ensemble is lost. Therefore the 16' open flue stop should be planned to be no louder than any stopped 16' open flue which may accompany it in the pedal.

An Example of the 16' Open as the Only Pedal Foundation Stop in a Modern Organ

The Casavant organ at the Dordt College chapel at Sioux Center, IA, was built under the supervision of the late Gerhard Brunzema. It is a 37-stop instrument which contains only principals and reeds in the pedal according to this disposition.6

Praestant 16'

Octaaf 8'

Octaaf 4'

Mixtuur VI

Bazuin 32'

Bazuin 16'

Trompet 8'

Cornet 2'

Since there is only one 16' flue stop, this stop also has to be able to fulfill the role normally taken by a stopped 16'. Therefore it must not be loud. But if the 16' foundation cannot be loud, how is power to be built up? The Sioux Center organ relies on its reeds rather than its flue stops for power in the pedal organ. This also happens in the Löfsta Bruk organ.

The Use of Mutation Stops to Support a Pedal 16' Flue Stop

The Löfsta Bruk organ builds power for its 16' flue both through its reeds and through a 51/3' pedal quint. This method of building power and clarity without overvoicing the 16' flue stop was followed regularly by the late Nils Hammarberg, a modern Swedish organbuilder of Göteborg. A stopped 8' pipe acquires definition though the reinforcement of its third partial, the 22/3' Quint. The Quint's fundamental is the same as the third partial. Cahman specified a Quint 51/3' in the pedal organ to complete the same harmonic function that the 22/3' Quint fulfills in the manual divisions. The combination of a soft open 16' together with a quint supporting its third partial gives the pedal organ a firmer foundation than any loud, wide-scaled diapason could ever provide.

The mutation stop must be narrowly scaled and gently voiced, and a true principal rather than a flute. This is also a prominent characteristic of the 22/3' and 2' stops in the Great organ of the nineteenth-century Brisbane instrument in Australia. Blending tone is aided by conservative scaling and gentle voicing, both of the fundamental tone and its corroborating harmonic.

Hammarberg continued this tradition with the provision of a pedal stop called "Aliqvot," a name which simply means "harmonics." It can refer to any useful combination of supporting harmonic partials. In his most recent work it consisted of the following 16' partials:

51/3' quint = third partial

31/5' tierce = fifth partial

22/3' quint = sixth partial

2' fifteenth = eighth partial

Hammarberg developed this idea because in Sweden, organs are placed in the gallery at the western end of the church and there is no headroom for open 16' pipes. It substitutes for the open 16' sound a resultant:

                  Alikvot                  51/3' C                  96 Hz

                  Principal               8' C        64 Hz

                  difference                               32 Hz = 16' C

He also provided the 32' resultant in the same way:

                  Kvinta 102/3' C               48 Hz

                  Principal               16' C     32 Hz

                  difference                               16 Hz = 32' C

Sometimes the Alikvot mixture has less than four ranks and sometimes more; Hammarberg sometimes built it in the following way:

51/3' quint = third partial sounding G

31/5' tierce = fifth partial E

22/7' flat seventh = seventh partial flat A#

17/9' ninth = ninth partial D

A typical specification for such a pedal organ is:

1. Subbas (wood, stopped) 16'

2. Kvinta 102/3'

3. Principalbas 8'

4. Gedacktbas 8'

5. Alikvot 51/3' + 31/5' + 22/3' + 2'

6. Bombard 16'

7. Trumpet 8'

8. Rörskalmeja 4'

9. Koralbas 4'

Hammarberg built this plan in conditions where headroom was restricted, from about 1981, and used the Alikvot mixture as well as the 102/3' plus 16' resultant in various instruments dating from the 1960s and 1970s. Examples of this work may be found in Mora, Boras, Göteborg, Falkenberg and Grebbestad, all in Sweden. In all of these organs, the presence of the Alikvot stop relieves the 16' from any obligation to attempt to produce power through volume, with the attendant deterioration of its tone.

Hammarberg's plan of pedal specification works well with gently voiced open 16' flue pipes, to develop a pedal organ of considerable power, while allowing the open 16' flue to remain as the only 16' flue stop in the division. Hammarberg's ideas combine well with Brunzema's plan (above) to give the following:

1. Subbass 16' wood, open narrow scale, about 7≤ CCC as at Löfsta Bruk

2. Quint 102/3'

3. Principal 8'

4. Gedacktbass 8'

5. Quint 51/3'

6. Coralbass 4'

7. Alikvot, composition as appropriate

8. Basun 16'

9. Trumpet 8'

10. Rohrshalmey 4'

Summary

The modern organ reform movement has given strong support to the exclusive use of gedackts and other stopped pipes at 16' and 8' pitch in small organs. This type of specification is derived from a "Neo-Baroque" Germanic tradition of organ building. Although these stopped pipes sometimes have narrow chimneys as in the Rohrflute, they nevertheless act as stopped pipes in the ensemble. This practice of specification leads to a form of non-blending registrations.

It is curious that the Italian organ, in which one always finds open pipes for foundation tone, is hardly built today, while the typical "reform movement" type of instrument, with a high percentage of stopped pipes, is commonly built. This is not merely a result of economic considerations, but rather a question of style and fashion.

Derived from this background is the practice of specifying a stopped Subbass as the pedal foundation stop. It provides the fundamental pitch in an undefined sound that blends with difficulty; and when pushed to provide greater volume, its tone deteriorates very quickly. A stopped Subbass has little blending power because it has no harmonic at the octave. This defeats the purpose for which it is intended. A 16' pedal stop should do more than supply a fundamental pitch; it should provide a harmonic series to support the chorus above.

We have examined pedal organ designs by builders who have not frozen their thinking into traditionally accepted ideas. The contemporary organs of Brunzema and Hammarberg take much of their design from the organ reform ideals, but also demonstrate innovative ideas which reinforce the true acoustical nature of the instrument. Let us turn to models such as these, rather than the typical "organ reform" prototypes, in order to construct organs of moderate size that do not lose our public for want of a good foundation for singing.

If we emphasize gently voiced open pipes as the natural source of fundamental tone, and obtain the power of the organ by means of harmonic reinforcement, we will assure that its sound has that live-giving warmth which will appeal to the musical public.8                

Appendix

The Löfsta Bruk Organ

by John Hamilton7

The sumptuous Löfsta Bruk organ was built in 1728 by Johan Niclas Cahman, a North German builder who had emigrated to Sweden. Of twenty-eight registers (two manuals, pedal), it was conservatively conceived; it is today Scandinavia's finest example of the sort of instrument known to the Praetorius/Scheidemann/Scheidt/Buxtehude school. The lavishness of conception is indicated in, for instance, the pedal's two full-compass full-length sixteen-foot registers, a Principal and a Posaune--in a church seating barely three hundred. The organ has largely escaped the periodic "modernizations" which have plagued many important old instruments. When nineteenth-century tastes called for a different sort of churchly music-making, the Ryggpositiv windchest and pipes were carefully removed and stored in the church's attic; Romantic tastes were satisfied by the two-manual-and-pedal reed organ which replaced the Ryggpositiv. A restoration in the early 1960s, by a Danish firm, was in the tradition of the best obtaining taste of that decade; it was well carried out but, alas, today's wind-supply is the mercilessly steady nineteenth-century norm, today's temperament is nineteenth-century equal, today's reed tongues are modern (the restorer discarded the old tongues without making measurements or metal analysis), and today's key action possibly is overly spring-loaded. Plans are afoot to correct these modern intrusions.

Tone is big, noble, unforced, in the north European historic tradition. Plenums admirably support the ardent congregational singing known to have characterized the eighteenth century: today's listener readily envisions vigorous hymn singing from strong-lunged Walloon ironwrights, who sat together in the church's most prestigious area. Of particular interest are the organ's mixtures, all of which contain third-sounding pipes contributing strength and color to the plenums. Individual Principal registers are among the most gloriously singing known to this listener.

Today's organists at Löfsta Bruk are Birgitta Olsson, the excellent parish organist, and Göran Blomberg of Uppsala University, who with a background in musicology, organ performance, and classical archaeology, is a strong summer presence. Blomberg's personal involvement with the instrument coincides with the period of its modern international reputation starting around 1980; his tireless, knowledgeable commitment to its becoming known have resulted in the organ's having become widely recognized even earlier than was the village itself. He has recorded an excellent selection of material by Buxtehude and Bach on an LP released by Bluebell-of-Sweden and is preparing digital recordings. Birgitta Olsson and Blomberg have organized a succession of summer "Cahman Days" forming an annual framework for presentation of the instrument; these included an international festival in August 1987, during the Buxtehude anniversary. And Blomberg offers numerous demonstration recitals on the instrument for groups of both lay and professional visitors.

In the wind...

John Bishop
Default

Where’s the fire?

Throughout my organbuilding career, I’ve owned and driven large vehicles. There was an interval when I tried a mini-van. It was a nice car with lots of space inside, but it was no truck. It only lasted 185,000 miles, by far the least of any car I’ve had. The transmission couldn’t take the loads.

The current job is a black Chevy Suburban—think presidential motorcades (Wendy thinks Tony Soprano!). It has a big V-8 engine and a 31-gallon gas tank. It’s a 5,800-pound carbon footprint. I know it’s environmentally irresponsible, but I justify it because of my work as an organbuilder. As often as not, the car is loaded with ranks of organ pipes, a reservoir or two, a windchest, or at least, five or six boxes and bags of tools and supplies. It’s also great for taking organ committees on field trips to visit our past projects. Three ranks of reeds or a six-member committee takes the GVW up to nearly 7,000 pounds!

Even though the car is big and heavy, that engine has power to spare. Trusting that there are not many state troopers reading The Diapason, I confess that I routinely drive close to 80 miles-per-hour. I know I’ve exceeded 90 going downhill and not paying attention, but I’ve never “maxed out” the speed. I’m pretty sure I could pass 95, maybe even 100—but I doubt I’ll
ever try.

 

How fast is too fast? 

When I joined the Organ Clearing House, I knew I was taking on a travel schedule that would preclude my work as a church musician, so after thirty years on the bench, I hung up my cassock. It’s been fifteen years since I played for worship. Of course I miss it, and I may go back to it someday. But in the meantime, it’s been fun to mix having free weekends (!) with hearing other people play for worship. 

The huge repertory of music for the organ is chock-full of fast passages, and any good organist is capable of sending salvos of notes across a room faster than a speeding bullet. And good bel canto singers can dazzle listeners with fast passages. But the ordinary person in the pew is comfortable at a slower pace. Though I’m not a trained singer, I think I do pretty well, and I’m certainly familiar with most of the hymns we sing, but still I find that sometimes I have trouble keeping up. And I’m uncomfortable when I’m not given enough time to breathe. It’s easy to tell if an organist is paying attention to the words, even singing them as he plays, because he needs time to breathe also.

How loud is too loud?

Several years ago, Wendy and I attended a recital by a visiting European organist played on the Kotzschmar Organ in Portland, Maine’s City Hall. He came out on the stage to the customary applause. When he got to the bench, the audience went silent and the lights dimmed. The first chord he played was so furiously loud that we jumped, and I set my teeth against liking the rest of the program, which predictably continued in bombastic style.

My Facebook page regularly lights up with posts from organists who indignantly report to the community that a parishioner had the audacity to complain that “the organ was too loud.” No doubt, some are meant in fun—one exchange included the quip, “if they don’t like it, they can sit in the hallway.” Surely, no organist would say something like that in earnest. Would they? But I often read similar comments that I know are heartfelt.

No other musical instrument can approach the dynamic range of the pipe organ. Organbuilders tell an old joke: 

 

The voicer, seated at the console, cups his hands to his mouth and yells to his assistant in the distant chamber, 

“Is the Aeoline playing?” 

Barely audible, from the distance, “Yes.” 

“Make it softer!”

 

The Aeoline in the Echo is barely audible; with the box closed it’s but a heavenly whisper. And the full organ is mighty roar—a hurricane of sound to be used with discretion.

Of the hundreds (thousands?) of pipe organs I’ve heard and played, I’ve experienced only one that was so much too loud that there was no single stop soft enough to accompany a solo singer. There are many organs that are infamous for their power, but even they can be used with discretion. As organists, we have become inured to the mighty tones of our instruments. We sit on the bench, alone in a dark church, challenging the muses to our hearts’ content, in the thrall of the power of the tone. For many congregants, not so much.

I have to admit that when sitting in the pews, I often feel that the organ is too loud. I wonder how many of you would simmer down your registrations if you had the chance to sing to someone else’s hymn playing a couple times a year. Besides, if you’re always playing “with the pedal to the metal,” you’re making organbuilders look bad. We’re supposed to provide instruments that can challenge the Gates of Hell once in a while, but thank heaven we’re not always facing the Gates of Hell.

 

What’s your job?

I often ride the train between Boston and New York. It’s a beautiful route along the Connecticut coast, passing tidal inlets loaded with osprey, egrets, and herons. There’s a wonderful sensation as those trains leave a station. I’m daydreaming, gazing out the window, and suddenly realize the train is moving. There’s no sound of locomotion, or clanking as links between cars take up slack. My imagination goes next to the expert bus driver and his ability to operate the vehicle smoothly. His foot on the brake pedal is feather-light, his speed through turns is just right, and his passengers are free to enjoy the ride, knowing that they’ll arrive safely and promptly at their destination.

I know, I know, that may be a fictional driver. The New York to Boston route is crowded with budget bus companies that have terrible safety records. That’s why I take the train. But I like the image and compare it to the “hymn driver” at church. He goes fast enough that the words make sense, but not so fast that the average congregant can’t keep up.

When an organist is really focused on the words of a hymn, both pace and registration follow. The other night, Wendy and I attended a service of Evensong, and the devil made an appearance in a middle verse. The organist led us to safety, acknowledging Satan’s presence with a growling registration for those few bars, and returning to something more soothing. There’s the majesty of the organ, painting pictures with tone color.

 

A happy little cloud

Bob Ross (1942–95) was a teacher of painting who famously hosted a series on PBS called The Joy of Painting. He had a goofy way of chattering as he painted that I think was intended to make aspiring painters feel at ease. Make a little mistake, a slip of the brush? No problem, make it into a bird. It’s a bird now! His brush strokes were quick and easy, and he often suggested dropping in “a happy little cloud.”

The pipe organ has a greater expressive range and wider variety of tone colors than any other musical instrument, and the expressive musician uses those characteristics like a brilliant painter with a lovely palette of colors. Think of the landscapes of Meindert Hobbema (1638–1709) with those magical patches of sunlight glowing through the trees. How did he do that? I think he always included trees just so he could do his sunlight trick. I love it when the organist gives me glimpses of sunlight through the trees, or happy little clouds. If you play through all the verses of a hymn on full registrations, loud, louder, loudest, you deprive the listener/singer of the beauty of it all.

You can use your palette like sunshine and clouds, and you can use it like an arsenal. The arsenal is fine with me at the right moment—that powerful Tuba giving the melody in the tenor is an awesome effect, but I don’t want to hear it in every hymn. 

Many of us are inclined to characterize the pipe organ as a keyboard instrument, as if it is common with the piano or harpsichord. In the matter of tone production, the organ has more in common with a trumpet or flute, the piano has more in common with a xylophone, and the harpsichord has more in common with a guitar. I consider the organ first to be a wind instrument. Making organ music happen is about managing air. This, simply, is why the organ is ideal for leadership of our singing—both the organ and the human voice are wind instruments. We circulate the same air molecules through the organ’s pipes and through our voices in sympathy. We’re all in it together.

 

You can’t play a tune on a Mixture.

Since the revival of classic organbuilding in the mid-twentieth century, many of us have had love affairs with Mixtures. They provide brilliance and clarity in polyphonic music, and their harmonic structures blend wonderfully with choruses of stops. I say this assuming that the Mixtures on your organ are well planned, well voiced, and balanced with the other voices. In my days as a student, I was organist at a church in Cleveland that had an aging Austin organ. Originally, there was no Mixture, and one had been added not long before I got there. But even in my brash youth, steeped in the ethic of Northern European classic organs, I couldn’t bear to use the thing. It was just too loud, and had nothing to do with the rest of the Great division.

Mixtures in pipe organs are harmonic tricks. The typical Great Mixture comprises four ranks, meaning four pipes are speaking on every note. My organbuilding colleagues know that I’m leaving out a lot of exceptions and variations as I describe Mixtures generally, but it’s enough to say here that those four pipes each speak a different harmonic, and the harmonics “break back” each octave. It’s formulaic. At low C, those four pipes typically speak at 11⁄3–12⁄31⁄2′, which are logical additions to “Principals, 8-4-2”. At tenor C, they jump back a notch: 2–11⁄3 –12⁄3. The 22⁄3 pitch enters at middle C; 4 pitch enters at “soprano” C. In the top octave, some builders omit the scratchy 51⁄3 and jump directly to 8.

Follow me carefully. A 4pitch at soprano C is the same note as 1pitch at tenor C. A 11⁄3 pitch at low C is the same note as 51⁄3 pitch at middle C. Think this through, and you’ll realize that an ordinary Mixture has pipes at soprano C that speak the same, and even lower pitches than at tenor C. Sounds like a muddle, doesn’t it? Well friends, use it wrong, and it is a muddle. Just for fun, play the melody of a hymn on Mixture alone, especially a hymn whose tune passes out of the middle octave past soprano C. Doesn’t make much sense, does it?

Now play all four voices of the same hymn on Mixture alone. Wacky. Absolutely wacky. Imagine that as a tool for teaching a tune to someone for the first time. Now play the same hymn on 8Principal alone. That’s better. What’s my point? Be sure that every hymn registration includes enough fundamental tone that the tune is easily recognizable when playing four-part harmony.

If you’re playing on a large organ, you likely have more than one Mixture on each keyboard. Listen to each one carefully, octave by octave, and try to analyze what pitches are actually playing? Use that to inform how you use them. A Principal Chorus with Mixture(s) is ideal for playing a fugue, because the graduated harmonics of the Mixture help project inner and lower voices of the polyphony. Mixtures are great with Reed Choruses, because they emphasize the rich harmonics of the Reeds. But Mixtures are like icing on a cake—they enhance, even decorate, but substance is in the batter. All icing, and your teeth will hurt. Do I sound like the parishioner who says the organ is shrill? Maybe it is. The math says so.

 

It’s all in the numbers.

Here are some pipe organ facts for nothing. The reason reeds sound more brilliant than flutes or Principals is that reeds have richer development of overtones—those secondary pitches present in every musical tone. 

Pythagoras (571 BC–495 BC) was the first to understand overtones. He proved that they follow the simple formula of 1:2, 2:3, 3:4, 4:5, etc. That simple progression was later defined by Leonardo Bonacci (c. 1170–c. 1250) as the Fibonacci series. Google that, and you’ll find terrific articles that show how the Fibonacci series describes the shell of the Nautilus, pineapples, artichokes, pine cones, and magically, the Romanesco broccoli, which I think is one of the most beautiful and delectable vegetables.

 

Break a head of Romanesco apart into florets, toss them in olive oil and salt, and roast them at 400° for 40 minutes (or less if want to keep some “tooth”), maybe sprinkle a little lemon juice and parmesan.

 

What does all this have to do with playing hymns? Pythagoras’s overtones can be defined this way. Play low C on an 8-foot organ stop, and you’ll be producing the following pitches: 8, 4, 22⁄3, 2, 13⁄5, 11⁄3, 11⁄7. Recognize those? It’s nothing but a list of the most common pipe organ pitches. Accident? I don’t think so. You may find these hard to hear, and as a practical matter, lots of them are inaudible, but they’re there. 

I demonstrate this at the console using voices like Oboes or Clarinets. They have especially rich “second overtones,” which is the equivalent of 22⁄3 pitch. Play and hold tenor C on the Clarinet. Then, on another keyboard, tap third G on an 8 stop. (That’s the equivalent of 22⁄3 pitch at tenor C.) That should enhance your ability to hear the 22⁄3 pitch present in the Clarinet note. Move around to different notes, and you’ll likely hear that overtone a little better in some notes than others. Then, play and hold tenor C on the Clarinet, and on your second keyboard, tap fourth E of an 8 stop. That’s the equivalent of 13⁄5 pitch, and you should be able to hear the Tierce independently in the Clarinet note.

Have you ever wondered why a Nazard and a Tierce sound so good with a Clarinet or Cromorne? It’s because the Clarinet and Cromorne (those two stops are very similar in construction) both have prominent 22⁄3 and 13⁄5overtones. That explains the origin of the French registrations Cornet (8, 4, 22⁄3, 2, 13⁄5), and by extension, Grand Jeu (Trompette 8, Octave 4, Cornet). Accident? I don’t think so.

Because of this, it’s often easiest to tune high mutations to reeds, assuming that the reeds are trustworthy, because the harmonics of the reed pipes are so clear. Draw 4 Principal and 13⁄5Tierce, and play up the top octaves of the keyboard. Substitute a Clarinet for the Principal, and do it again. I’ll bet a tuning fork that you hear the pitch of the Tierce more clearly with the Clarinet.

Why is a Rohrflute brighter than a Gedeckt? Because the hole in the cap with the little chimney emphasizes the second harmonic, which is 22⁄3 pitch. 

What does all this have to do with playing hymns? It tells us that higher-pitched stops are secondary to fundamental pitch. What is fundamental pitch? Eight-foot tone. It’s that simple. If your hymn registrations favor higher pitches, you’re back at that exercise of playing a hymn on a Mixture alone. Awareness of all this is at the heart of good pipe organ registration.

You can’t play a tune on a Mixture. It’s confusing to the singer, especially if that singer doesn’t know the tune. Suggestion? Introduce the tune on a simpler registration, and bring in bigger sounds as appropriate. If you have a variety of lovely solo sounds, use them. Play one verse on Trumpets alone. Play another with Principals but no Mixtures. Just be sure they can hear the tune. And be sure that your choice of sounds supports the words. There’s more to hymn playing than a blur of harmonics.

Gentle on the accelerator and the brakes, paint beautiful colorful pictures, “ . . . and the wheels on the bus go round and round . . .”

On Teaching

Gavin Black

Gavin Black is director of the Princeton Early Keyboard Center in Princeton, New Jersey. He welcomes feedback by e-mail at <[email protected]>. Expanded versions of these columns with references and links can be found at <http://www.pekc.org&gt;.

Default

Registration and teaching—Part II
In last month’s column, I emphasized the usefulness of starting off the teaching of registration with a clear explanation of the meaning of the foot-designation of organ stops and with a set of demonstrations of that meaning. This is a necessary foundation for understanding everything about combining stops and about choosing organ sounds for music. Once a student clearly understands the meaning of all the numbers on the stop knobs, it is time for that student to begin exploring the art of combining stops. This starts with developing an awareness of what the stop pitch levels imply about the structure of stop combinations, and continues with the development of an ear for the aesthetic nature of different sounds, and then with the acquisition of knowledge about registration practices in different schools of organ composition or in the work of specific composers.
The concept that it is OK to combine stops that are not at the same pitch level as one another, and that the resulting sound will be (or at least can be) a coherent musical sound at a coherent pitch level, is not self-evident. In fact, it is counterintuitive to most people who have not already become well versed in organ registration. It seems, if anything, self-evident that this kind of mixing will result in obvious parallel octaves and fifths, and also in a generalized jumble of pitches, which would at a minimum make clarity impossible (because notes that you play in the tenor register, for example, would produce pitches proper to the treble register, etc.). Since the blending of stops at different pitch levels in fact can work the way it does because of the overtone series, it is useful to explain something about overtones to students. It is certainly not necessary to go into all of the scientific details—the physics of the creation of overtones, the reasons for inharmonicity of overtones in certain situations, or even what the notes of the overtone series are, above the first few. However, it is a good idea to review the basics:
1) Almost all musical sounds produced acoustically have many frequencies blended together. (It usually takes a computer to produce a sound at exactly one frequency.)
2) These frequencies are (usually) a) a given frequency and b) other frequencies that are multiples of that first frequency. (Of course we use the lowest frequency to identify the note, as in “A 440.”)
3) These multiples produce sounds that are related to the lowest frequency by common musical intervals: octave, octave-and-a-fifth, two octaves, two-octaves-and-a-third, etc.
On most organs it is possible to find individual notes on some stops in which some specific overtones can be heard as separate pitches. These can be used to demonstrate the existence of overtones and the pitch levels of some of them. Gedeckts, flutes, and quintadenas are often the most fruitful for this, and notes in the octave and a half or so below middle c are the most promising, because they are the easiest to hear. Usually it is possible to find a pipe or two in which the twelfth is clear (quiet, perhaps, but clear), others in which the seventeenth is, and others in which the octaves are. To someone who has never tried to listen to overtones before, these sounds are usually hard to hear at first, but then suddenly “come in.” The teacher can help with this, first by making sure to zero in on the pipes with the clearest individual overtones, and then by briefly playing, singing, or whistling the actual note corresponding to the overtone that you wish to help the student to hear. This will attune the student’s expectation to that pitch, and it will probably only be necessary for the first few notes.
(A further exercise in listening to overtones is this: play a simple melody on one stop. Try to hear and follow the counter-melody created by the clearest and most noticeable overtones. For example, consider the notes of the fugue subject of Bach’s E-flat major fugue:
b-flat – g – c – b-flat –
e-flat – e-flat – d – e-flat
Depending on what the overtones of each pipe happen to be doing, a counter melody could arise that went like this:
d – d – g – d – g – g – f# – g
or that went like this:
f – b – e – f – b-flat –
b-flat – f# – b-flat
or any number of other possibilities. It will be different for each different stop on which you play the melody. The “extra” melody will be quiet, and usually it will range from one to three octaves above the “official” melody. It is quite possible that these inherent counter-melodies are one source of the human invention of counterpoint. This is all a bit of a detour from learning techniques of registration as such, but it is a useful exercise both for learning to listen carefully to sound and for remembering that sounds themselves are complex and interesting, often doing more than we might at first expect.)
Once a student understands the basic concept of overtones (and believes in them!), it is easy for him or her to understand the blending of stops of different pitches: a 4? stop blends with and reinforces the first upper partial of an 8? stop, a 22?3? stop the second upper partial, a 2? stop the third, etc. One advantage of going through all of this quite systematically is that it answers the question of how in the world it can make sense to combine stops that don’t even produce the same letter-name notes as one another. This is certainly the thing that seems the least intuitive and the most questionable about registration to many of those who are not yet experienced with the organ.
(This can be true especially if someone stops to think about all of the pitches that are present in a thick texture. For example, a G-major 7th chord played on a registration that includes a 22?3? stop includes the pitches g, a, b, c, d, f, f#. If you throw in a tierce you add a d#. That this would be acceptable makes a lot more sense if you know that all of those “extra” pitches are present anyway as overtones.)
So the most basic description of the structure of the art of combining organ stops, and the most useful as a starting point, goes something like this: that, as long as you have one or more 8? stops present in your combination of stops, anything and everything higher than 8? pitch has the potential to blend with the 8? sound. In so doing, it will change the nature of the sound by changing the overall balance of the overtones, and by changing the volume, but it will not upset the pitch identification of the notes that you play.
A simple exercise to demonstrate this would be as follows:
1) choose a keyboard that has more than one 8? stop and several higher-pitched stops.
2) draw the louder (loudest) 8? stop.
3) play a simple passage—a chord progression or a bit of a hymn is good—adding and taking away various 4? and higher stops at random.
4) after a while, remove the 8? stop. The student will hear the music suddenly jump up in pitch.
5) repeat all of this with a softer 8? stop.
Anyone performing or listening to this exercise will certainly notice that not all of the combinations work equally well. Some of the sounds that could blend in theory will not seem to blend very well in practice, perhaps because a 4? or higher stop is too loud or too bright (or for that matter out of tune) or because a given 8? stop is too thin or weak or has something about its intrinsic overtone development that conflicts with rather than supports the addition of higher-pitched stops. These considerations are extremely important. They are also subjective and in the end belong to the realm of artistic judgment or discretion. A student listening to or trying out this exercise should be encouraged to notice aesthetic aspects of each sound. However, the main point for the moment is that the dropping of the 8? pitch makes a sound that is utterly different in kind from the adding or dropping of any higher-pitched stops.
Of course, it might occur to a student, or a teacher might want to mention for completeness if nothing else, that it is perfectly possible to use sounds that omit 8? stops, for some special reason or in some special way. The simplest of these is the use of a 4? or higher sound to play the music at an octave or more higher than the written pitch. Also fairly common is the use of a non-8? registration accompanied by the moving of the hands to a different position on the keyboard to bring the pitch in line with original expectations. These are useful things to bear in mind as a performing organist, but they are special cases that can best be thought about at a slightly later stage in learning, and that should certainly not distract a student from developing the most thorough possible understanding of “normal” stop combination and registration. The same can be said about the use of 16? sound in multi-voiced or chordal manual playing. This, in theory, just transposes the music down an octave, but often doesn’t—for some psychoacoustic or just plain acoustic reasons—quite sound like that.
So far we have developed a rather scientific approach—perhaps too scientific for some people’s taste—to the teaching or learning of registration. We have asked students to think very clearly about the pitch designations of stops, about overtones, about what overtones imply about the use of different pitches of stops, and about how to make sure that a sound is grounded in unison pitch. We have not yet talked about either how to choose registrations that “sound good” (or “beautiful” or “appropriate” or anything else) or about how to respect composers’ wishes or any other way to tailor sounds to pieces. We have also barely mentioned stop names, or even names of important categories of stops, diapasons, flutes, reeds, and so on. Nor have we mentioned any rules or even ideas about how or whether to combine stops of different types, or for that matter of the same type.
Organs have lots and lots of sounds. For example, by my calculations, allowing only for sounds that include 8? pitch and leaving cornets and “céleste” stops out of any ensemble, but taking into account couplers, the Grand Orgue of the Mander organ at St. Ignatius Loyola in New York—a well-known, recent, large but not gargantuan organ—commands 121,889,158,594,564 different sounds. A hypothetical medium-sized organ in which three manuals have 25 to 30 stops would have about 200 million to about a billion 8?-based sounds available in the manual divisions. If the pedal division of such an organ had eight stops, then, assuming normal couplers, the pedals would have a quarter of a trillion different sounds available.
Harpsichords, on the other hand, have rather few sounds. Most large harpsichords have seven to ten different available sonorities all together. Many very fine and versatile harpsichords have only three. In planning registration for a piece on the harpsichord, it is always possible to use what I consider to be the soundest and most artistically thorough approach: simply trying the piece out on every possible sound, listening carefully and with attention, and deciding which sound you like best.
This approach is almost always impossible on the organ. It is always impossible on any organ but the very smallest. However, it seems to me that it is still—albeit only in an underlying theoretical way—the best approach, and the right concept to have in the back of one’s mind when working out registrations. That this is true can, I think, be almost proven logically. If you are using a given registration, whether it comes from an editor, or from your teacher, or from something that you jotted down in your copy years before, or from any other source, but there is in fact a different registration that you would like better if only you heard it, then you should in theory be using that other registration. Therefore, ideally, one would always hear every registration before making a final choice.
(I am not right now dealing with the extra-musical quasi-ethical considerations of authenticity that arise when a specific registration comes from the composer. I will address that at least briefly next month.)
The purpose of taking a student very systematically through what I described above as a scientific approach to the technique of registration—the feet, the overtones, the combinations at different pitch levels—is to allow the student then to feel free to try anything and everything (again, knowing that there won’t really be time for everything!) without fear of doing something that really, in some concrete way, doesn’t and can’t work. This will enable the student to be relatively independent of outside guidelines, and increase the chance that the student will contribute something new and interesting to the world of the organ. It will also almost certainly provide the student with a great measure of out-and-out fun, and keep the job of practicing as interesting as it can be.
Next month I will talk about ways to practice listening to the more subjective, sound-quality-oriented aspects of the blending and combining of stops. I will also talk about helping students to begin to relate sound to other aspects of their concept of a piece of music, and to both structural and historical considerations.?

In the wind . . .

John Bishop

John Bishop is executive director of the Organ Clearing House

Default

Appreciating depreciation
When a business owner purchases a machine, it becomes an asset of the company, and its value is spread out over a period of years of tax returns. In some cases, the value of a machine is spread out across the cost of doing business. For example, most pipe organ builders own a table saw. A table saw is a piece of stationary equipment with a circular saw blade that’s ten, twelve, fourteen, or maybe sixteen inches in diameter, depending on the size of the machine. There are saws with bigger diameter blades, but they are not so common, and they can be pretty scary.
The blade is mounted on an arbor (shaft) turned by an electric motor. The name of the machine is derived from the milled iron table through which the saw blade emerges. The accuracy of the machine depends on the exact relationship of the blade to the table. Most of the time the blade is set at 90º to the table, so the cut edge of a board is perfectly square to the face that was against the table. The angle of the blade is adjustable in most table saws, so when you want the edge of the board to be 30º off square, you turn a crank that swivels the internal works—motor, arbor, and blade all move together.
There’s a sliding fence that is square to the table and parallel to the blade. The woodworker sets the distance between the blade and the fence to set the width of the board he’s cutting.
The table saw is running a lot in a busy organ shop. Nearly every piece of wood in the organ—from the tallest supports of pedal towers to the tiniest trackers—goes across that machine.
The cost of the machine is depreciated on the company’s tax returns, but the use of the table saw is not usually billed directly against the cost of the organ. It’s part of the cost of doing business. The other basic machines are the cut-off saw (which cuts boards to length), jointer (with a drum-shaped blade that planes one surface smooth and then another smooth face that’s square to the first one), and thickness planer (that works off the jointed face of a board to bring the opposite face parallel and flat). A piece of wood is typically jointed first so an edge and a face are both flat and square to each other, run through the thickness planer so the two faces are parallel and the board is the correct thickness, and passed through the table saw so the two edges are parallel and square to the faces and the board is the correct width. With all that done, the true and square board is cut to length. It takes four machines to cut one board.
A workshop adage is measure twice, cut once. The first person to invent a machine that will lengthen a board is going to be rich and famous, just like the inventor of the magnet that will pick up a brass screw.

$400 an hour for man and machine
You need to put a bell in a church tower, so you hire a rigging company. They show up with the bell strapped on the back of flatbed truck and a big mobile crane. Sometimes you see these cranes on the highway heading to a job. They’re huge and have ten or twelve wheels. They’re very heavy to provide a stable platform for heavy lifting. The steering gears are fascinating—maybe the front three axles are involved in steering. You might think that turning the steering wheel would move all the wheels the same, but if that were the case the machine would hop around corners and eventually break itself apart because the paths of the different axles actually need to be concentric circles. In fact, each axle turns a different amount to allow those concentric circles. Once you know that you can see it easily. It takes some pretty fancy figuring at the drawing board to get it right.
I don’t know actual figures, but I’ll take a stab at the cost of such a machine. Let’s say the machine cost $600,000. The tires are worth $3,000 each. The company bills the customer $400 an hour. Maybe $100 of that is the cost of the operator and the operation—fuel, insurance, excise taxes, maintenance. So $300 an hour is applied to the cost of the machine. At that rate, the machine is paid for in 2,000 hours. There are 2,000 hours in a working year. But the owner of the machine probably can’t keep the machine busy with billable hours all the time. Maybe it takes three or four years to make 2,000 billable hours. After that, every hour billed for the use of the machine is clear money for the owner.
When I was in high school, my home church commissioned a new organ from one of the premiere builders of mechanical-action instruments. It had twelve stops with preparation for six more. The preparation meant that toeboards and rackboards were in place with center holes marked, there was space on all the stop-action rails for additional actions, and there were plugged holes on the console for additional knobs. The original cost of the organ was $36,000. The additional stops were added about ten years later—they cost nearly as much as the original organ. Today, the same organ with eighteen stops would cost $500,000 or more. And this is a relatively small organ.
After looking at those figures, it’s easy to see that a three-manual organ with 50 stops is going to cost more than a million dollars. A million dollars for a pipe organ—the organbuilder must be making a killing. But when the contract is signed, the organbuilder buys ten tons of exotic hardwoods and fancy metals, and commits 10,000 person-hours to the project. He’s paying income tax, payroll taxes, liability insurance, worker’s compensation insurance. He’s spending a lot of time researching, planning, designing, and drawing. And he’s operating a workshop with all those machines and enough (heated) space to handle the instrument. It’s not easy to make ends meet.
So the organ is installed. It cost a million dollars. I wonder if we can pay for it with a concert series. Let’s say there are 500 seats in the church, and let’s charge $20 a seat. That’s box office revenue of $10,000 for each concert. It only takes 100 concerts to pay for the organ. But wait. How often have you seen a 500-seat church filled to capacity for an organ recital? And who’s going to pay $20?
Say $10 then, and 100 people at each recital. Now it takes 1,000 recitals to pay for the organ. And we haven’t heated the building, tuned the organ, paid for electricity to run the blower and light the church, paid the recitalists, or even bought the cider and doughnuts for intermission. And if we’re doing ten concerts a year we’re talking about 100 years. We’ll have to releather the organ at least once—and 60 years from now that will probably cost close to the organ’s original price.
It’s a terrible business plan. You’ll never get your money back out of it. You’re better off buying a crane.

What’s missing?
Meeting with the vestry or board of trustees of a church to discuss an organ project, I have often heard a question that sounds like this: “We’ve got a furnace to replace, a parking lot to pave, a roof to repair, and the city says we have to put in an elevator and bunch of ramps. What’s this unit going to cost?”
I don’t like to think of a pipe organ as a unit. And I don’t think the organ belongs on the list with the potholes in the parking lot or shingles on the roof. It goes on the list with communion silver and stained glass windows. It’s an expression of our faith. It enhances our worship. It raises our spirits. It facilitates our communal singing. Where else in our society do we sing together so regularly and with such purpose?
Our music has evolved from natural laws. On a sunny afternoon in 540 BC on the island of Samos in the Ionian Sea, 30-year-old Pythagoras was walking past a blacksmith shop. There were several smithies at work inside, and our friend Thagos noticed that the hammer blows were producing different pitches. He went inside and watched for a while. At first he thought that a heavier hammer made a lower pitch and a lighter hammer made a higher pitch, but after a little while he noticed that the pitch was determined by the anvil, not the hammer. An anvil would produce the same pitch whether struck with a heavy or a light hammer.
The bell in the temple works the same way—it produces the same pitch when hit with a sledge hammer or a soda can.
With this information in mind, Thagos noticed that there were secondary pitches audible in the tone of an anvil or bell. He set up a cord under adjustable tension that would produce a variety of tones and duplicated the various sounds he was hearing in a single tone. He realized that each different “overtone” represented a ratio to the original pitch: 2:1 (octave) was the first one, 3:2 (fifth) was the second, 4:3 was the third (fourth), etc. And he realized that a series of 13 consecutive fifths would take him back to the original pitch displaced by octaves. These formulas are easy enough to understand, but the original discovery was amazing.
Here’s another example of an extraordinary mathematical observation. A perfect cone is one in which the height of the cone and diameter of its base are equal. The cool fact is that a perfect cone is half the volume of the sphere with the same diameter.
All through his life, Pythagoras worked on these theories, developing systems of altering, or tempering, the intervals to increase the consonance. In simple words, he messed with the math to make it sound better.
The concept of the interval came from the physical world. Next, musicians thought it would sound great to sing in two or more parallel parts using a given interval, and using the scale of notes that had been derived from the natural overtones. It’s easy to imagine the moment when a couple singers, either by design or by error, sang in opposite directions rather than parallel motion. (I think it was by mistake!) They started with a fifth. One went up a note while the other went down a note and they were singing a third. It reminds me of a television ad campaign featuring a collision between a truck carrying peanut butter and one carrying chocolate.
Did it take 1,000 years to get from Thagos’s blacksmith shop to a couple monks messing up while singing in parallel motion? If so it took another 1,500 years to evolve the rules of four-part harmony through Bach’s 371 Chorales, Mozart’s symphonies, Mendelssohn’s oratorios, and Saint-Saëns’ piano concertos. Enter Debussy, Stravinsky, and Alban Berg.
With all that development of the theory of music came the development of the panoply of musical instruments. The physics of each instrument represents another exploitation of the overtone series. Change a pitch by doubling or halving the number of cycles-per-second and you jump an octave. Change by a factor of 3:2 and you jump a fifth. Hit a string and you get one tone. Stroke a string and you get another. Blow into a tube, blow through a reed, etc., etc. It all started with the hammer and anvil.
By the way, thinking about the evolution of music, I think that Debussy discovered the whole-tone scale in church. The interiors of most pipe organs are arranged in whole tones. The proof of that is the symmetry of most organ cases. Low C is on one side of the case, C# on the other, D is next to C, D# is next to C#, and so on. Among other things, this distributes the weight of the organ evenly from side to side. The organ tuner goes up one side first, then the other side—otherwise he’d be jumping back and forth across the organ for each new note.
It sounds like this: C-next, D-next, E-next, F#-next, G#-next, A#-next, etc. Claude D. walked along the river bank, got a good impression noticing Claude M. painting pictures of the same cathedral day after day, went into the cathedral to hear the organ playing scales in whole tones—another good impression. Bet it was Aristide Cavaillé-Coll tuning the organ. Did you know he was the inventor of the circular saw blade?
In the fourteenth century AD, the organ was among the most complicated devices built by mankind. In the early twentieth century, organbuilders were creating the first user-programmable binary computers. They were bulky, made of wood, leather, and metal, ran on electro-pneumatic power, and had memories of about .001KB. But the user could program them. Amazing. Push a button with your thumb and you have the registration for verse three. The organ is the most mechanical of all musical instruments—an oxymoron, a conundrum.
Organbuilder Charles Fisk talked about the magic of all that air being turned into musical sound. Think of the air as fuel. Burn some air and you get a toccata. Or burn some air and you play a hymn. Share the air around the room, and the organ and the congregation can do the same hymn.
All of that Samian observation, all of that math, all of that experimentation brought us to that million-dollar organ. It all comes from natural laws interpreted by a healthy dose of human reason, wonder, trial, and error. The organ may be the most mechanical of all musical instruments, but it’s not a machine. It’s not a unit. It’s a gift. It’s the gift that keeps on giving until it needs to be releathered. You can’t pay for it by selling its use by the hour. You can’t justify it as a business expense. It’s not practical, it’s not even necessary. But it feeds the soul. It’s just that simple. 

In the wind . . .

John Bishop
Default

At arm’s length
In recent months I’ve read three books about the violin, violinists, and luthiers: Stradivari’s Genius by Toby Faber (Random House, 2004), Violin Dreams by Arnold Steinhardt (Houghton Mifflin, 2006), and The Violin Maker by John Marchese (Harper Collins, 2007). Faber is a publisher; he traces the history of six instruments made by Antonio Stradivari. Steinhardt is the first violinist of the Guarneri Quartet, writing about his lifelong quest for the perfect instrument. Marchese is a journalist and amateur musician writing about Sam Zygmuntowicz who is a revered luthier in Brooklyn, New York, and Eugene Drucker, a violinist in the Emerson Quartet, chronicling the process of the commissioning, creation, and delivery of a splendid instrument. I recommend any and all of these as excellent reads for anyone interested in musical instruments.
There is much overlap between the three books. Each includes a pilgrimage to Cremona, the Italian city where the world’s best violins were built by generations of Guarneris, one of whom taught Stradivari, the local boy who eclipsed all others by building close to 2,000 instruments in a 70-year career, some 600 of which are still in use. Each discusses and compares theories about what makes Stradivari’s instruments stand out. Each poignantly describes the intimate relationships between the player and his instrument with rich use of sexual and romantic metaphors.
Arnold Steinhardt gets right to the point. Five pages into his book he writes,

    When I hold the violin, my left arm stretches lovingly around its neck, my right hand draws the bow across the strings like a caress, and the violin itself is tucked under my chin, a place halfway between by my brain and my beating heart.

Lovely images, aren’t they? You can daydream about how the human musician and mechanical instrument become one. The organist and organbuilder in me delves into the possibilities. But wait! Steinhardt’s next sentence puts me in exile:

    Instruments that are played at arm’s length—the piano, the bassoon, the tympani—have a certain reserve built into the relationship. Touch me, hold me if you must, but don’t get too close, they seem to say.

He completes the exclusion:

    To play the violin, however, I must stroke its strings and embrace a delicate body with ample curves and a scroll like a perfect hairdo fresh from the beauty salon. This creature sings ardently to me day after day, year after year, as I embrace it.

My envy of Steinhardt’s relationship with his instrument is at least a little assuaged by the beauty-salon simile—I can picture a sticky, brittle, slightly singed concoction that smells of chemicals, or Madeleine Kahn as Lili von Shtupp in Mel Brooks’s riotous film, Blazing Saddles, rebuffing an advance saying, “not the lips.” Some intimacy. Harumph. And what about the risk of simply being jilted?
In The Violin Maker, Eugene Drucker speaks of his instrument “under my ear.” He uses the phrase a number of times, his reference to the immediacy of what the violinist hears. After all, the instrument is barely an inch from the player’s ear. I reflect on how powerful a violin’s sound can be, and wonder what long-term effect that has on the player’s hearing, but Drucker clearly considers it an advantage. In contrast, it’s common to hear an organist complain about the instrument being “in my face, the Zimbel in the Brustwerk is unbearable.” That Zimbel is intended to be heard from 50 feet away—not 30 inches; how we sacrifice for our art! A tuner will tell you that sitting inside a heavy-duty expression box tuning a high-pressure Tuba is not an experience of intimacy with music “under your ear.” Tuners, identify with me—it’s the worst when you stand up to tune the bass in octaves. When you get to bottom G, the three-foot tall tenor G is necessarily right in your ear. At least when you’re tuning a powerful reed en chamade, you can duck!
Come to think of it, the fact that the tuner climbs ladders inside the instrument somehow separates the organ from the violin!
An intimate friend
My violin trilogy refers continually to the intimacy between the builder and the player of a violin. They spend hours together discussing the ideal, and as the craftsman works on the new instrument, the client’s recordings are playing in his workshop. Given the business of organbuilding—committees, contracts, deadlines, and delays (Christmas of what year?), how often do organbuilders and organists truly work together to create exactly the work of art that will be the true vehicle for the player? If I had a nickel for each time I’ve told an organ committee that the organ should be built for the coming generations and not for the current organist, I’d have a lot of nickels.
How many organists tell of their relationships with their instruments in such colorful loving terms? Because organists cannot take their favored instruments along to distant gigs, they must make peace, love, war, or at least a truce with whatever organ they encounter.
As a church organist I have had two long-term relationships with single instruments. One was a 10-year stint with a terrible organ that seemed to want to stop me from everything I tried to do. I could hardly bear it. The other was more like 20 years with an adequate instrument, comprehensive stoplist, good reliability, and a few truly beautiful voices. It didn’t stand in the way of what I played, but neither did it offer much help. I have been fortunate enough to have several extra-organic affairs with instruments I love. These experiences have allowed me the knowledge of what it’s like to play often on an organ that’s truly wonderful. I’m willing to indulge in expanding Steinhardt’s metaphor to a monumental scale. Rather than tucking a loved one under my chin, I or my fellow organists can become one with a 10-ton instrument and with the room in which it stands.
Steeple chase
Ours is a picturesque seacoast town with 19th-century brick storefronts and several distinctive steeples. One of those, the white one on the top of the hill that can be seen from miles away, is leaning to the left (allowing jabs of political humor) and threatening to fall. Because the cost of rebuilding the steeple far outstrips the resources of the parish, townspeople have mounted a public save-the-steeple effort. We’d hate to have to see all those postcards reprinted. Last Sunday I participated in a benefit recital that featured the church’s lovely little William B. D. Simmons organ (1865?) played by six different organists. It was fascinating to hear how different the organ sounded as the occupant of the bench changed. Each player offered a favorite piece, each player placed different emphasis on different voices, and each had a different approach to the attack and release of notes. And by the way, the steeple fund was satisfactorily increased.
In a simple rural setting, it was clear to me that even though Steinhardt refers to arm’s-length relationships with instruments other than violins (and I suppose violas, though he doesn’t mention them), an organist can in fact have an artistic tryst with an instrument. But with the violin trilogy in mind, a comment made that day by one of my colleagues set me to thinking. Noting that only a few stops on the Swell have complete ranks (most start at eº), that the keydesk is a little awkward, and that there is very little bass tone, she commented that the organ is limiting. And she’s right—it is, but it’s perfect for the music its builder had in mind. If you meet the organ on its own terms, you’ll get along much better. We cannot and should not expect to be able to play the same music on every organ, and when we try, the results are less than artistic.
A place for everything, and everything in its place
In the weeks after Easter I participated in several events that involved different groups of organists. Holy Day post mortems dominated the conversations, and a common thread was how many of them had played “The Widor” for the postlude. I knew that most of these musicians play for churches that have 10- or 20-stop organs, and I reflected that playing the “The Widor” on any one of them would be a little like entering a Volkswagen in a Formula One race. Widor wrote his famous Toccata for his lifelong partner, the Cavaillé-Coll organ at St. Sulpice in Paris, a magnificent instrument with five manuals and a hundred stops—but more to the point, a huge instrument in a perfectly enormous building rife with arches, niches, and statues. (By the way, Widor’s was a common-law relationship with his instrument. According to Marcel Dupré’s memoir, he was appointed temporary organist at St. Sulpice in 1869 and was simply reappointed each year until his retirement in 1933. He served as temporary organist for 64 years!) The sound of the organ rolls around in that building like thunder in the mountains. In such a grand acoustic, the famous arpeggios of “The Widor” that cost organists’ forearm tendons 128 notes per measure are rolled into the grand and stately half-note rhythm that is in fact the motion of the piece. Eight half notes in two measures make a phrase of the melody. If you play it on a 15-stop organ in a church with 125 seats, your listeners hear 256 notes per musical phrase—an effect achieved by pouring buckets of marbles on a tin roof.
Proportion is an essential element to all art. Classic architecture follows classic proportions. A great painting or a great photograph is celebrated for the balance and proportion of its composition. A great piece of music is an architectural triumph with carefully balanced proportions. The best sculptors knew how to stretch the proportions of the human form so a monumental statue would seem in correct proportion when viewed from ground level. Leonardo da Vinci’s famous sketch Vitruvian Man is a vivid illustration of how an artist/scientist worked to understand natural proportion, and we print it on neckties and lunch boxes to prove how dedicated we are to correct proportions.
In modern suburban life we grow used to seeing McMansions—houses that belong on 40-acre estates—crammed together on cul-de-sacs. It’s really not the houses that are out of scale, it’s the fact that they are twice as wide as the distance between them that bothers us.
In my opinion, playing “The Widor” on ten stops is simply a violation of proportions and can hardly be a rich musical experience—and I have to admit that I’ve done it myself many times. Note my use of quotes. We refer to this chestnut as though dear Charles-Marie only wrote one piece, just as “Toccata and Fugue” means only one thing to many people—you don’t even have to name the key or the composer before your mind’s ear flashes a mordent on high A.
Trivializing the monumental
Recently one of my second cousins died in an auto accident. It’s a very large family, Nick was an extremely popular guy, and at his funeral my parents and I wound up in the last row of a long narrow sanctuary with a low ceiling. (Okay, I admit that my father and I were planning a quick escape to get to the Boston Red Sox Opening Day game—the Red Sox won!) The three-manual organ was in chancel chambers a very long way from us. But the organbuilders in all their wisdom had foreseen the difficulty and included a small exposed Antiphonal division at the rear of the church. I glanced at it and guessed the stoplist: Gedeckt 8', Octave 4', Mixture III. Logical enough—I’ve suggested the inclusion of just such a thing in many situations. A little organ sound from behind adds a lot to the support of congregational singing. During the prelude the organist used that Antiphonal Gedeckt as a solo voice accompanied by enclosed strings in the chancel. Trouble was, from where we were sitting, you couldn’t hear the strings—they were too far away. And when he launched “The Widor” as the postlude, the effect was downright silly. What we heard from our seat was that huge piece being played on three low-pressure chiffy stops with a subtle hint of a bass melody from far away. (By the way, the organist was a friend. He and I shared a wink when I went forward with my parents to receive Communion and we had a fun phone conversation a few days later, so I expect he’ll chuckle when he reads this!)
Arnold Steinhardt sees a bassoon “at arm’s length,” but think about it—one end of the bassoon is in the player’s mouth. You don’t have that kind of a relationship with a violin. I wonder what he thinks of the organ. I’d love to have that conversation with him. I’ve heard of orchestral conductors who claim the organ is expressionless because you can’t change the volume of a single note, but I’ve heard organ playing so expressive as to take your breath away. I look forward to hearing lots more organ music played with expression, chosen in proportion to the instrument and surroundings of the day. Join me, dear colleagues, in promoting the organ as the expressive instrument that envelops you and moves the masses with its powerful breath.

Current Issue