On Teaching

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;.

Registration and teaching—Part III

To all this was added the peculiar manner in which he combined the different stops of the organ with each other, or his mode of registration. It was so uncommon that many organ builders and organists were frightened when they saw him draw the stops. They believed that such a combination of stops could never sound well, but were much surprised when they afterwards perceived that the organ sounded best just so, and had now something peculiar and uncommon, which could never be produced by their mode of registration. This peculiar manner of using the stops was a consequence of his minute knowledge of the construction of the organ and of all the single stops.1

In the last two columns we have gone over, as carefully as possible, all of the aspects of the art of organ registration that are objective and systematic—that is, the meaning of the pitch designations given to stops, and the science of combining stops as it relates to the different pitch levels and to overtones. By devoting two whole columns to these matters and in the way I laid out all of their details, I have tried to make the case that students wanting to study registration should be encouraged to understand these things extraordinarily thoroughly at the very beginning of that study. This seems to me to be the necessary first step in achieving the “minute knowledge” attributed to Bach by Forkel (and his sources) in the famous account quoted above.
The next step in achieving the level of knowledge and understanding that permits freedom and confidence in registration—or, I should say, the next set of steps—involves beginning to explore the actual sounds of the stops: the thing that makes organ registration exciting and challenging, and that gives meaning and variety to the essentially infinite number of different combinations of stops that a mid-sized or large organ possesses. Let us begin with a few principles. These partly reflect my practical experience—they seem to me to provide a good foundation for an approach that clearly and simply works to help students to feel comfortable with registration and to achieve results with which they are happy. Partly, however, they reflect my belief—which I admit probably rises to the level of an ideology—that every musician ought to think for him- or herself and be willing or eager to achieve results that are different from anyone else’s. These principles are as follows:
1) The art of registration is fundamentally the art of really listening to every sound that you hear—also really hearing every sound that you listen to—and noting carefully and honestly your reaction to it.
2) The ideal approach to choosing a sound for a given piece or passage is to try it out with every available sound. This is almost always actually impossible (see last month’s column), but it is still an interesting and invigorating concept to keep in the back of one’s mind.
3) The names of the stops are only a general guide to what they sound like or how they should be used. These names can be very helpful for targeting which stops or combinations to try, given that it is impossible to try everything. However, they should never even tentatively override the evidence of your ears. (My teacher, the late Eugene Roan, used to say that the best Diapason on a certain older model of electronic organ was the stop marked “French Horn.” This may be an extreme case, but the principle always applies: it is the sound that matters, not the name.)
4) Relating the sound of any registration to a piece—that is, choosing stops for that piece—is part of the same interpretive process that includes choosing a tempo, making decisions about phrasing and articulation, making choices about rhythm, agogic accent, rubato, etc., etc.
5) Using stops that someone else—anyone else—has told you to use is not part of the art of registration. Rather, it is a choice not to practice that art in that particular case. There can be very good reasons for doing this, most of which have to do with respecting the wishes of composers, or of conductors or other performing colleagues, or occasionally of participants in an event such as a wedding or a funeral.
6) Learning how to respect the wishes of a composer when playing on an organ other than the one(s) that the composer knew, taking into account but not necessarily following literally any specific registrations that the composer may have given, is an art in itself. It requires both a real mastery of the art of registration as understood here, and thorough knowledge of the composer’s expectations and wishes.
The first three of these principles essentially lead to the conclusion that a student wanting to become adept at using organ sound should spend a lot of time listening to organs. This is, in a sense, a process that takes place away from, or even without the need for, a teacher. However, there are ways that a teacher can help with the process, and the rest of this column will be devoted to suggesting some of these.
The last three principles concern ways of relating registration to music, either in and of itself or in connection with various historical, musicological, or practical concerns. Next month’s column will offer suggestions for helping students think about these issues.
The first logical step in beginning to listen carefully and learn about organ sound is to listen to 8' stops. A student should find a short piece of music for manuals only that feels easy enough that it can be played without too much worry or too much need to concentrate. This can be a well-learned piece or passage, or a simple chord progression, or a hymn, or even just some scales. The student should play this music on any 8' stop a time or two, and then on another 8' stop, and then back to the first, listening for differences and similarities: louder, softer, darker, lighter, brighter, joyful, somber, open and clear, pungent and reedy, compelling, boring, with or without emotional content. Then he or she should continue the process, adding in another 8' stop, and then perhaps another, comparing them in pairs. (Any and all adjectives that the student uses to describe individual sounds or to clarify the comparison between sounds should probably remain in the student’s head. All such words are used completely differently by different people, and can’t usually convey anything meaningful from one person to another. In any case, the point here is for the student to listen, react, and think, not to convey anything to anyone else.)
After doing this for a while—reacting to the sounds on a spontaneous aesthetic level—the student should begin listening for structural characteristics of the sound. The most obvious of these is (usually) balance. If you play, say, a chord progression on a principal, then on a gedeckt, then on a salicional, there will be all sorts of aesthetic differences. Are there also differences in how well you can hear the bass? the treble? the inner voices? Is there a difference in how well your ears can follow lines, as opposed to just chords as such? If you arpeggiate the chords in various ways (faster, slower, up, down, random) does the effect of that arpeggiation seem different on one sound from another? If you play the same passage very legato and then lightly detached, is the texture different on one sound from another? (This latter might be easier to execute and to hear with a single line melody.) Do the several different sounds suggest varied tempos for the passage that you are playing?
(It is important that the teacher remind the student not to expect all such questions to have clear-cut or unchanging answers. The point is to listen and think, not to solve or decide.)
After playing around with a few 8' stops this way, start combining them. This should be done without reference to any assumptions about which combinations will “work” or which are sanctioned by common or historical practice. Again, the point is to listen, even to things that you might not like or ever use. For each combination of two 8' stops, the student can go through an exercise like that described above, asking the same questions. However, there are also other things to listen for. If you combine two 8' stops, does the resulting sound resemble one of them more than the other? Does it resemble neither? Does it seem louder than the separate stops? (Acoustically it always will be, psycho-acoustically it will not always seem to be.) Do the two stops in fact seem to blend into one sound, or does it seem that there are two sounds riding along together? If someone randomly removes one of the stops while you are playing, can you tell which one is left? Is the nature of the beginnings of notes (pipe speech or diction) different with the combined stops from either one by itself? Does it resemble one more than the other?
Another wrinkle on this exercise is this: choose one loud 8' stop, say a principal, and then make a separate combination of 8' stops to create a similar volume level, say a gedeckt plus a quintadena plus a rohrflute. How do those two different sounds compare to one another with respect to all of the questions asked above, or any others that you can think of? Here’s another: what is the very quietest 8' stop that can be heard alongside a (presumably fairly loud) 8' principal in playing a two-voiced passage on two manuals? Does this change depending on which hand is on which keyboard? Or this: if you play a two-voice passage on one keyboard (i.e., the same registration in each part), do the left hand and the right hand sound like they are using the same sonority, or do they sound different? Does this differ from one registration to another? (Every student and every teacher can make up many further questions, exercises, and tests such as these.)
The next step, of course, is to begin combining 8' sound with higher-pitched stops, and to listen in the same way and to ask the same kinds of questions. The student should choose one of the 8' stops, and add to it first one 4' stop, then another, then two or more together, then a 2-2/3' if there is one, then a 2', then a different 2', then a 4' and a 2' together, etc. In all of these cases, the first thing to listen for is whether the sounds really blend into one—like a section of a fine chamber choir—or just sort of straggle along together—like the voices at a party singing “Happy Birthday.” (Of course, these differences are really likely to be along a continuum, not “either/or.”) Next come any and all of the other questions, not forgetting the structural ones. The addition of a 4' or higher stop can change the structure of a sound significantly, often bringing out or suppressing inner voices or a particular part of the keyboard compass. A special case of this is the 2-2/3', which, as experienced organists know, often blends well with an 8' stop in the upper part of the compass of the keyboard, but separates out somewhere below middle c. It can be interesting to try the following experiment with an 8' + 2-2/3' combination: first play a bit of a melody remaining above middle c; then play a scale starting an octave or so above middle c and going down. Notice when the sound “splits” into what sound like parallel fifths (perhaps suddenly sounding vaguely medieval!). Then, play a few notes in that lower part of the compass—notes chosen as good roots for a chord progression, say c-f-g-G-c. (They will sound unsuccessfully blended.) Then play those very same notes, but with appropriate chords added above them. This will sound absolutely fine. Of course, it is even more interesting to try this with several different 8' + 2-2/3' combinations and see how similar or different the results are, and then to compare all of these results to those obtained with 8' + 4'+ 2-2/3' or 8' + 2-2/3' + 2'.
All of the above is a kind of systematic “goofing off,” first of all in that it should be fun—it should be one of the things that connects a student to the joy in the sensations of sound that is part of playing the organ—and also in that it shouldn’t be too well ordered. After all, it is impossible to hear/try/test all of the sounds, so the sample that one tries should be random enough to achieve good variety. Second, it is systematic in that it is important to do these exercises in an order that permits meaningful comparisons—more or less as described above—and also in that it is important, alongside a generous amount of pure aesthetic listening, to remember to ask questions about the more measurable or “structural” aspects of the various sounds.
Next month I will take up some aspects of the business of combining one’s awareness and understanding of organ sound with various external matters. These include the aesthetics of particular pieces, historical instruments and styles, and the wishes or intentions of composers.

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

Intervals, tuning, and temperament, part 1

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

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

What is a musical sound?

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

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

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

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

What is an interval?

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

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

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

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

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

What is the problem with keyboards?

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

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

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

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

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;.

Registration and teaching, part I
I was first drawn to organ and harpsichord back in the late ’60s—not too long after I turned ten—by the sonorities of those instruments. I remember being particularly entranced by the reed sound that E. Power Biggs used for the fugue subject in his recording of the shorter Bach Prelude and Fugue in c minor on the Schnitger organ at Zwolle. Later I discovered the sounds of the small organ at St. Jakobi Church in Lübeck as recorded in 1947 by Helmut Walcha, and the sound of the so-called Ahaus Ruckers harpsichord, recorded, in music of Froberger among others, by Gustav Leonhardt. Later still I was captivated by the sounds of Messiaen’s Cavaillé-Coll organ at La Trinité through the composer’s own recordings there. In all of these cases and many others, it was the sounds themselves that most interested me, not the repertoire or the performances. A desire to be involved more and more closely with these sounds was the first and most essential reason that I decided to study organ and harpsichord and later to make a career out of those instruments. Of course an interest in much of the repertoire, in the act of performance itself, and, especially, in teaching, followed fairly quickly. But it was the sounds that got me hooked.
I think that this is a fairly common experience among people who end up studying organ or harpsichord. All of the many rather different instruments that have been accepted as “organs” over several centuries, and all harpsichords and harpsichord-like instruments, have in common that the actual sonorities are determined in advance of any playing of the instrument. These sounds are created by the combined work of builders, metalworkers, voicers, tuners, acousticians, and so on. The player can make only very subtle changes in the sound itself, if any, while playing. Therefore, it has always been important that builders create sounds that are in some way compelling, beautiful, interesting, even perhaps disturbing, but in any case worth hearing—important in and of themselves to someone who hears them. So it is natural that these sounds would form a large part of the reason that some people become interested in these instruments.
This has implications for the teaching of registration, or, more accurately and more interestingly, for the interaction between registration and teaching. For most students, the sonorities of the instrument are a source of fun and interest. Therefore the whole business of trying out sounds and getting to know sounds can be fun, can be highly interesting, and can both relieve and enliven the painstaking, difficult work of becoming more adept at the technical side of playing. The practicing of any simple—and therefore potentially tedious—exercise can be made more interesting or even very interesting by also using it as an opportunity to pay attention to the sound and to try out different sounds. The difficult and intense practicing of difficult and intense passages can be leavened by occasional breaks during which the student uses any easier or more accessible musical material—simple or already-learned passages, scales and chords, folk songs, improvisation, whatever—to try out different sounds, and to listen to those sounds carefully. And even a beginning student can learn right away to make registration choices that are interesting and appropriate for the music and the situation, and that, often, are different from the choices that the teacher or any other player would have made. This can be a source of encouragement and can help to create a feeling of connectedness to the real art of music making.
This column and next month’s will consist mostly of suggestions for ways of introducing students to the art of registration: that is, explaining to them what it is, demystifying it as much as possible, offering them ways of exploring and practicing it, and helping them to relate sounds to particular kinds of music and particular pieces. It is very important that students be given a way to learn registration from within, that is, by understanding how it works, and not just through formulas or (even very sound) principles. Only in this way will students learn to be able to create registrations on their own. Also, only this way will they be able to understand registration formulas or suggested registrations that they might encounter, and to be able to figure out when to apply such things and when to modify or ignore them. These suggestions are aimed in the first instance at students who are beginners or who are at least fairly new to the organ. However, some of the ideas should also be helpful to more experienced students who happen, for any reason, to feel uncomfortable with their approach to registration or who want to rethink it or perhaps simplify it a bit.
Registration is simply the act of choosing stops—choosing sounds—for pieces or passages of music. If there are no stops drawn, the music will not be of much use to the listeners: it will be silent. This is something that can be said more or less as a joke, but indeed some students come to the organ not quite realizing it. (After all, we are not born knowing something that seems so basic to practicing organists!) In choosing what particular stops to use in a given situation, we normally take into account at least some of the following:
1) What the sound is like subjectively—loud, soft, dark, bright, smooth, clear, reedy, warm, piercing, hollow, thick, thin, haunting, and so on—and how this relates to our sense, again subjective, of what the piece is like or should be like. (Everyone uses adjectives differently, however. They are useful for listing the kinds of qualities that a sound might have. They are also useful for helping one person, in his or her own mind, to characterize and remember what a sound is like. They are normally not particularly useful in conveying a sense of what a sound is like from one person to another.)
2) How loud or soft the sound is in relation to other things that are going on. In particular, how two sounds balance when they are being used together (i.e., in a two-manual or manual and pedal piece) or when they follow one another, as in sections of a piece or verses of a hymn; also, if it’s relevant, how the volume of sound relates to things beyond the organ, such as singers or other instruments. All of these considerations are more objective than those in 1), but not entirely so except at the extremes when one sound actually threatens to drown out another.
3) What is known, if anything, about composers’ intentions. This can range from a general sense of what kind of instrument a composer knew—or even just what was prevalent in a given composer’s era and approximate geographic area—to precise, meaningful, and specific registration instructions from a composer about registration. Some of the data in this area is essentially objective or even beyond dispute. However, its application to a given situation often requires flexibility and judgment, as when a particular organ doesn’t have the stops specifically suggested by the composer, or when the acoustics of the room, or the specific sound qualities of stops with a particular name are different from what a composer knew. (This is the case more often than not.) Also non-objective and subject to different philosophies and judgments is the basic question of whether and how much it matters what a composer wanted or expected.
Registration is the art of choosing sounds, and, on the organ and the harpsichord, most available sounds are combinations of other sounds. (This, again, is something so basic that an experienced player might not notice that it is not self-evident to a beginner.) The first step in learning how to combine sounds is developing a sense of what the sounds are like on their own. I tend to define a “stop” to a new student as “a set of pipes, one per key, all of which make more or less the same sound as one another, and each of which plays the right note for its key.” (This is just a starting point. Mixtures can be explained separately, perhaps simply as several stops that are operated by one control for convenience and that function as one sound. The technicalities of breaks and changing numbers of ranks can certainly be discussed with a student who is eager to understand such things, but that can wait, since it is not necessary to know this in order to learn how to begin to use them in stop combinations.)
Each stop typically has two parts to the label that describes it: a number and a word. The number—8', 4', etc.—is one of the very few things in the world of the arts that has a clear meaning that never changes and is not subject to interpretation. However, as with some of the other basic points that I have mentioned above, students often don’t know what that meaning is. In fact, if you ask a beginning student what those numbers mean, he or she will more often than not say “Isn’t it something about how long the pipes are?” (I certainly mean no criticism of those students! No one knows something that they haven’t yet learned. My point is just that it is easy for us to take it for granted that everyone would know something that seems so basic to an experienced organist.) So it is important to start by explaining very simply what the numbers mean: 8' means “at unison pitch,” 4' means “an octave above unison pitch,” and so on. It is a good idea to demonstrate that every 4' stop is at the same pitch as every other—though the sounds may be very different—and the same for 2 2/3', 16', and all the other numbers/pitch-levels. I would suggest doing this with something like the following routine:
Draw two stops, on two different keyboards. One should be an 8' stop, the other a 4', and they should be as similar as possible in tone. Play two keys, one on each keyboard and thus one on each of the two stops, which are ostensibly the same note. (They should be near the middle of the keyboard, middle c or close.) Invite the student to hear that these notes are clearly an octave apart. Make sure that the student really gets this: the concept of an octave, especially when listening to a new kind of sound, can be elusive. (The first time that I ever tried to tune a harpsichord, I broke several 4' strings because I was trying to tune them an octave high! I just couldn’t hear the octave placement of the notes amongst all the strong harmonics of the bright sound.) This should be repeated with several different “8', 4', similar sound” pairs, and also 4', 2' pairs. Then, with the same various pairs of stops, demonstrate that (for example) the f below middle c on the 4' stop and the f above middle c on the 8' stop are clearly the same pitch, and so on with other appropriate pairs of stops, or that the scale from tenor c to middle c on the 4' stop is clearly at the same pitch as the scale going up from middle c on the 8' stop.
Next, draw pairs of 8' stops that are noticeably different in tone: a gedeckt on one keyboard, an oboe on another, for example, or anything like that. Then compare notes from one to the other, making sure that the student hears that in this instance keys that ostensibly represent the same note actually produce the same pitch. This can be done with single notes—again starting around the middle of the keyboard since that region is the easiest to hear—then with short scale passages and perhaps chord progressions. Then the same sort of comparison can be done with 4'stops and so on, even including mutations, if there are multiple examples of the same ones on the particular instrument.
This procedure is very simple and may even seem simplistic. Again, however, I want to emphasize that these things are not known to beginners. They are also not always absolutely clear even to people who have sat at a console and done some organ playing, but have not yet had any systematic study. It is not uncommon, for example, for someone to know by experience that a 2' stop is kind of bright, but not to know anything about the stop’s pitch level, or about how the brightness is achieved. An unshakably clear grasp of the meaning of the pitch designations is the first step in understanding how organ stops can be fruitfully combined with one another: that is, really understanding it in a way that permits one to do it without formulas and without assistance, on a familiar or an unfamiliar instrument. We will move on to this in next month’s column.

Gavin Black is director of the Princeton Early Keyboard Center in Princeton, New Jersey. He can be reached at .

Registration and teaching—Part IV
In this column—the last on registration for now—I will offer suggestions for ways in which teachers can help students choose sounds for particular pieces. This is, of course, the practical essence of registration. The main point of the systematic approach to understanding organ stops and becoming familiar with organ sounds that was outlined in the last three columns is to enable students to feel confident choosing sounds for pieces and to end up choosing sounds that they will be happy with. The discussion in this column assumes that the student has done some of the analysis, the thinking, and the listening practice described in the last three columns. This student will have a good understanding of what stops are likely to combine well with one another, and will also be open-minded about trying combinations that are unconventional and that might or might not work. He or she will also be in the habit of listening to sounds carefully, and will expect to have a reaction to sounds—an aesthetic and/or emotional reaction—and to give importance and respect to that reaction. A significant part of the process of choosing appropriate sounds for pieces consists of noting one’s aesthetic or emotional reactions to those pieces and allowing those reactions to suggest sounds that evoke similar, compatible, or complementary reactions. This will be the focus of this column. Another part of the process consists of learning about outside factors that might influence registration. The most important of these are any registration instructions that a composer may have given, along with any information about organs or types of organs that a composer knew. I will make a few comments about this below, but it will receive much more attention in future columns devoted to the (often vexing) subject of authenticity.
There are two principles that serve as a foundation for my thinking about the teaching of this phase of the art of registration. The first of these is that no registration is “right” or “wrong.” Rather, any registration has a whole host of things that can be said about it that are descriptive rather than judgmental. Some of these might be simple descriptions of the sounds, such as “loud,” “soft,” “bright,” “mellow,” “pungent,” “hollow,” “beautiful,” etc. Some might be more situational or practical, like: “louder than the previous piece,” or “so muddy that you can’t hear the inner voices,” or “not to our pastor’s taste.” Some might be musicological or historical, like: “not what the composer had in mind,” or “uncannily like the mid-17th-century plenum.” Any of these descriptions might be important to note, and might serve as a basis for choosing or rejecting a registration. However, none of them is the same as “good” or “bad.” Most of us (I emphatically do include myself in this!) have an instinct to call a registration “bad” or “wrong” when what we mean is that it is “not what I am used to” or “not what I would do myself” or, more simply, that “I do not like it.” It is of course absolutely fine and good—and inevitable—for each of us to have developed such tastes and preferences, especially if we recognize them as such. However, if we pass them on to our students as “right” and “wrong,” with the weight of our authority behind them, we are in great danger of limiting and constraining our students rather than liberating and empowering them. We are also in danger of making registration—which has the capacity to be tremendous out-and-out fun—into a source of anxiety: yet another opportunity to get something wrong, in a world that has too many such opportunities.
(Here’s an anecdote about the weight of authority. Many years ago, when I was still a student, I had a friendly but heartfelt argument with a fellow organ aficionado about what was the “right” registration for the long middle section of one of the Bach organ fugues. We both had all sorts of musical, musicological, analytical, even philosophical reasons to give in favor of our preferred sound. We were each convinced that the other’s sound was wrong. Of course it turned out that we were each simply advocating a sound just like the one used in the recording of the piece that each of us happened to have heard first and gotten used to!)
The second principle is this: that the primary purpose of a student’s actions in choosing a registration for a piece is not the attainment of a registration that the teacher likes, or that any other listener would like, or that the composer would have liked, or even that the student likes. The actual registration is not the goal at this stage. Rather the goal is for the process to move the student along towards being more comfortable, confident, and skillful at choosing registrations for pieces. Therefore the teacher, in guiding the student in this process, should be very hesitant about actually giving specific registrations. It is easy for a student to use the stops that a teacher has pulled out, and in so doing to play a piece with a registration that the teacher likes and that some other listeners will also like. It is unlikely that this kind of transaction will teach the student very much. (The same criticism also applies to a student’s using registrations that are found in a printed edition.) If, however, a student goes through a process of listening to stops, listening to combinations, and thinking about the aesthetic of a piece and about possible sounds, the student will always learn a great deal. This is true even if no listener likes the registrations that are found along the way. If he or she creates registrations that listeners do like, the student will also learn a great deal, all the more so if such a registration is significantly different from others that the student may have heard or heard about.
There is one caveat that applies to this second principle. There are times when someone who is still a student, and for whom the work of registration should indeed be mostly about learning and trying things, does indeed—for some practical reason—have to devise a registration that will be acceptable in a particular circumstance. This need will be more compelling the more the circumstance is extra-musical. For example, in a church service, or a funeral or wedding, the student has to use sounds that will enhance rather than disrupt anything that is being accompanied. Also, in these settings, a student might have to respect certain traditions or needs as to the role of music in the service, for example having to do with dynamic levels during communion. A teacher might have to step in and suggest solutions that fit these circumstances, if the student is not yet ready to come up with appropriate registrations directly. A somewhat more cynical practical reason might be this: that the student needs to prepare an audition, and the teacher knows how to help the student match the known tastes of those who will be judging the audition. These practical circumstances should be recognized as limited exceptions to the general principle that it is a better learning experience for students to work on coming up with their own sounds, and then to try those sounds out in performance and see how effective they are.
In an earlier column I mentioned “what I consider to be the soundest and most artistically thorough approach [to choosing stops for a piece]: simply trying the piece out on every possible sound, listening carefully and with attention, and deciding which sound you like best.” This is possible on the harpsichord, but almost never, just as a practical matter, on the organ. If the goal is to allow and encourage students to come as close as possible to this open and un-predetermined approach, the teacher can suggest something like the following procedure:
(This is essentially for pieces that do not have registration suggestions that come directly from the composer, and has to be modified for those that do.)
1) Try, while learning a new piece, either to stay away from recordings and other performances of the piece, or to listen to several, three at least.
2) During the earliest stages of learning a piece, begin to form a sense of what it seems like in mood or feeling, in a very basic way: calm, excited, jaunty, disturbing, anxious, jubilant, peaceful, “in your face,” mellow, etc. (As always with adjectives that describe a piece of music, these are probably best used within the mind of one person to help that person consolidate thoughts about the piece. Different people use adjectives so differently that they can easily be misleading in conveying anything in the aesthetic realm from one person to another.) Do not worry about whether you can prove these feelings or reactions to be correct. (You cannot.) Also, don’t be surprised if you later change them. If you honestly can’t come up with any such feelings about the piece at this stage, choose a concept for the piece at random. (This will probably work out just as well in the end for your performance of the work itself, and certainly will serve just as well as a learning experience.)
3) Remembering the fruits of all of your prior exploration of organ stops and combinations for their own sake, choose a sound that seems to match the mood or feeling that you are discerning in the piece—that is, concoct such a sound: it is not necessary or desirable to remember a specific sound from before—and play the piece with that sound.
4) Find another such sound. That is, a sound that also fits your basic sense about the mood or feeling, but that is easily distinguishable from the first sound. (An easy-to-describe example of this might be, in a quiet and gentle piece, first an 8? Gedeckt alone, then an 8? Dulciana alone; or in a loud, forthright piece, first a principal chorus-based combination, then a combination based on strong reeds; or for a pungent but quiet sound, first the quietest available reed, then a Quintadena.) Play the piece a few times with this second sound.
5) Go back to the first sound and listen to it with ears that have now been influenced by the second sound. Perhaps introduce a third and fourth sound and go back and forth among all of them. Listen for the differences and similarities. Has this exercise enabled you to refine your sense of what the piece is like? Do you prefer one of the sounds to another? If you initially chose your concept of the piece at random, do you now find that concept convincing? If not, how might you want to modify or replace it? If you chose your concept not at random, do you still find it convincing? If not, in what way has your concept changed? If it has changed, then you should follow the same procedure but with stop combinations that reflect your new concept of the piece.
One of the points of asking a student to go through a procedure like this is to make sure that registration does not happen by habituation, that is, that a student does not just come upon a registration more or less at random and then get used to it, the way my friend and I each got used to the registration that we had heard on the Bach fugue recordings, as mentioned above. It is fine to discover some registrations at random, but it is important to be systematic about listening to them, and to be committed to trying others as well.
Although it seems that choosing stops would be easier when the composer has provided a registration, this is often not true. Assuming that we accept the notion that it is right to play a piece the way the composer wanted it to be played, then the composer’s registration probably narrows down the choice of plausible sounds. In effect the composer’s registration does the work of step 2) above. However, it is important to remember that the exact stop names given by a composer do not usually correspond perfectly to the stops available on whatever organ the student is using. This is always true unless the student is playing the organ that the composer had in mind or one very much like it indeed. (Again, I will discuss the ramifications of this at great length in future columns about authenticity.) In trying to recreate the effect asked for by a composer, it is best to do something like the following:
1) Glean from the composer’s suggested registration, and of course from the notes of the piece, as much as you can about what the composer thought the piece was like aesthetically and emotionally. (Again, a student who had already spent a fair amount of time trying many different sounds and listening carefully will have a good notion about how to approach this.)
2) Try out registrations that your own sense of organ sound tells you will express that mood or feeling well. As much as possible you should favor, or at least start with, registrations that resemble what the composer has suggested—for example, for a quiet pungent sound, try a quiet reed first if the composer’s registration is a reed or try a Quintadena or string first if the composer’s registration is a Quintadena or string; or for a bright “tinkly” sound try an 8?+ 11?3? first if that’s what the composer suggested, or an 8?+ 2? first if that is. But all the while, listen to the sounds with the same alert ears that you would apply to any sound that you chose yourself. Do not use a sound unless it works: that is, unless the components of the sound blend properly, the various balances are right (between different sounds if there is more than one, among the different regions of the compass of the keyboard, between inner and outer voices, between melody and accompaniment—whatever is relevant), and the emotional/aesthetic impact of the sound strikes you as right for the piece. A sound is not right just because the stop names are right. Stop names are just a beginning wherever they come from, even the composer.
That is all for now. Since the subject of registration is so multifaceted, I have posted on the Princeton Early Keyboard Center website <www.pekc.org&gt; an annotated version of this column, with examples drawn from specific pieces, and further discussion.

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!

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

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

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

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

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

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

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

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

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

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