Stephen Hammer

Toward a sensible keyboard temperament for Baroque orchestras

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Over the years I have been asked many times to recommend a tuning recipe for ensemble keyboards, or else to tune them myself. Choosing a tuning system has always been problematic—the symmetrical sixth-comma temperaments that are so prevalent these days (Vallotti, Young, etc) have never been very satisfying, for several reasons. Firstly, they aren't historical (both were published long after the Baroque era); secondly they are boring (a lot of the keys sound the same); and thirdly they create a number of ensemble problems, making it difficult for orchestra members to lock in to a resonance and pitch center.

The ubiquitous "Vallotti" temperament, published in 1779 by the Padua composer, theorist and organist Francesco Antonio Vallotti, has become the default tuning for many of today's Baroque musicians who feel obliged to play in some kind of unequal temperament. It is simple, consisting of six adjacent pure fifths and six adjacent fifths that are tempered by 1/6 comma, and it is therefore easy to remember. It is circular, meaning that in principle it can be used in all keys. And Baroque string players like the fact that their open string intervals are all tempered the same amount.

But the Vallotti tuning, in my experience, has for decades been a persistent source of intonation problems for Baroque instrumental ensembles, creating uncertainties for the bass instruments that find their way into the rest of the group. Essentially, what tends to happen is that the flat side of the tuning ends up being the highest notes in the scale, so that notes like F, Bb and Eb seem to float and nobody in the group knows quite where they are supposed to be; since these notes often serve as the roots of chords in a lot of Baroque music one can be left with a distinctly queasy sensation—consider, for example, the first two Eb-major chords of "He Was Despised"—how often do they sound in tune?

Some ensembles have attempted to improve on Vallotti by using the "Young #1" tuning, another theoretical temperament, described by the English physician and polymath Thomas Young in 1799.  While slightly less problematic, Young retains the aggressively high Eb, Bb and F pitches that make ensemble tuning difficult in flat keys and make chords such as F# major unusable.

For a while when people asked about temperaments I would give up and say "just tune it equal" (which after all IS a historical tuning, described in the early 17th century and favored by Rameau among others) but this wasn't totally satisfactory either, and provoked more than one raised eyebrow from the authenticity police. Then I became aware of the work of Bradley Lehman, who makes a very convincing case that Sebastian Bach's preferred keyboard tuning was one that he apparently describes in a diagram on the cover of Das Wohltemperirte Clavier. Click here for more information about Lehman and his work on this subject. While still a sixth-comma tuning Bach/Lehman distributes the pure fifths somewhat differently from a symmetrical system like Vallotti, and addresses some of its most thorny problems. In ensembles where Bach/Lehman has been used, tuning has been much less problematic in my experience, and resonances easier to find.

We should remember, though, that Bach's diagram was associated with a volume of solo keyboard music, a tuning intended to be listened to rather than played with. For ensembles, and especially for orchestras of mixed strings and winds, I believe it is possible to improve on Bach/Lehman in one significant way—by making F-C and Bb-F pure intervals, one can make the often-majestic music written in those keys sound very resonant indeed, and also make ensemble tuning in flat keys in general more predictable for bass players.

Further research revealed that a slightly tamer version of this tuning was actually published in 1724 by Johann Georg Neidhardt, Kapellmeister at Königsberg in Prussia, this retains the pure fifths from F-C and Bb-F but less bright in the sharp tonalities, making it especially useful for trumpet music in D, for example. It is known variously today as "Neidhardt 1" or "Neidhardt 3" although at the time he called it the "Dorf" or village temperament—interestingly Neidhardt recommended a different tuning for large cities, and 12th-comma meantone (i.e. equal temperament!) for court use.

In any event here is my recipe, along with approximate comparisons with Bach/Lehman, Neidhardt Dorf, Vallotti, and Young #1, written in whole cents deviation from equal temperament for ease of use with an electronic tuner. If you are tuning by ear, similar results can be achieved by making sure that C-F and F-Bb are tuned pure, and distributing the other enharmonic fifths ad libitum.

  C G D A E B F# C# G# Eb Bb F
Hammer +6 +4 +2 0 -2  0 +2 +2 +2 +2 +2 +4
Bach/Lehman +6 +4 +2 0 -2  0 +2 +4 +4 +4 +4 +8
Neidhardt "Dorf" +6 +4 +2 0 -2 -2 -2  0  0 +2 +2 +4
Vallotti +6 +4 +2 0 -2 -4 -2  0 +2 +4 +6 +8
Young #1 +6 +4 +2 0 -2 -2 -2 0 +2 +4 +6 +6

Note that the sixth-comma tempered intervals between the "open string" notes are identical in all five tunings. Bach/Lehman places pure fifths from E-B and B-F#, creating a distinctly brighter character as you migrate toward sharp keys; it also places a mild wolf fifth from Bb to F—interesting indeed, and it sounds great in solo keyboard music from Bach to Chopin, but is perhaps too gnarly for an orchestra. My revision, with even twelfth-comma fifths between all the enharmonic notes, is easier for instrumentalists to cope with, and as noted above, creates wonderfully resonant fifths in F and Bb. Neidhardt goes a step further, by tempering E-B and B-F# slightly the G-major, D-major and A-major sonorities are rendered less bright. Choice of temperament is, of course, a matter of personal taste, but I would propose that choosing Bach/Lehman, Neidhardt Dorf, or my formula instead of Vallotti or Young will contribute substantially to tuning stability in an instrumental ensemble while retaining the character and variety of a non-equal temperament.

I have used this formula for music by Bach, Telemann, Handel, Rameau, Mozart, and many other eighteenth-century composers. It works! Try it sometime and send me your comments. Remember that the idea is to tune the keyboard to the temperament (since a temperament is by definition a set of decisions about which intervals the keyboard will play out of tune, and by how much) and then to try to play intervals in musical context that sound in tune which may not always be the same as matching the treble notes of the keyboard. Also bear in mind that some repertoire (especially French and early-Baroque music) permits the use of more irregular or non-circulating temperaments, allowing for more interesting sonorities.

A version of this article appeared in the Fall 2010 issue of Early Music America

For more discussion of the perils of tuning Baroque orchestras, see also
A Modest Proposal.

A discussion of Neidhardt's tuning philosophy and variety of temperaments, part of a very useful site on historical tuning by the piano-maker Paul Poletti can be found here

Technology and Live Performance

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I recently finished a fascinating book called Capturing Sound—How Technology has Changed Music by Mark Katz, who is a professor at the University of North Carolina at Chapel Hill. In a very thoughtful monograph, Katz traces the cultural effects of developments in sound reproducing technology from its origins in the late 19th century to the looping and sampling skills of today's rap artists and the virtuosity of the "turntablist" DJ's such as i.Emerge and Kentaro:

One of Katz's ongoing themes is that technology has had a profound influence on live performance itself. He notes that recorded performances by their nature are fixed and repeatable, and that this fact led to performances, even in jazz, where performances by groups such the Ellington band often replicated "improvised" solos from their recordings note-for-note when they played live. He discusses ways that recording artists learned to compensate for the lack of a visual component of their performances, and offers the fascinating theory that the rise of continuous string vibrato around 1920 was inspired by recording technology; as electrostatic microphones began to capture and reproduce imperfections of intonation and bow technique that could be inaudible or unnoticeable in the concert hall, vibrato may have been a strategy for hiding them. He also observes that much of classical music's development in America in the early 20th-century, including the founding of many orchestras during that time, came about as recordings of the classics were marketed as a positive cultural influence, promoting the idea that exposing people to "good music" would help them become better and more moral citizens, able to contribute more fully to their communities.

Katz doesn't get into technology's influence on the early-music field, but he could. In the "beginning" of the popular Baroque-instrument revival, which we can date to the late 1960's, recording helped in a several ways: first by allowing splicing to create expert performances that never existed, free of squeaks, scratches, and poor intonation; second by amplifying a performance and making it portable allowing audiences to hear an intimate and stylish harpsichord performance anywhere they chose at at any volume they chose; third by creating early-music "celebrities" by marketing millions of recordings by artists such as Brueggen, Leonhardt, Hogwood, Pinnock, Norrington, Christie, et al.  The popularity of these celebrities caused a trickle-down effect, creating a large audience for recordings of and live performances by groups of professional early-musicians.  I was fortunate enough to profit from this phenomenon for several decades, making a reasonable living playing concerts for large audiences in halls that were really too big for the music, which was the only way to make the enterprise cost-effective, and audiences were often satisfied possibly because of positive associations from recordings.

Lately, however, it seems that things have taken a bit of a turn.  The celebrity lions of the field are reaching retirement age or beyond--quick now, name a world-famous Baroque musician under 50--and again, it seems that technology has played a part in preventing younger musicians from reaching their exalted status. With the advent of cheap analog-to-digital converters,  hard-drive recording, and digital editing and mastering, making a beautiful and perfect-sounding record has become so easy that pretty much anyone can do it.  Technology has made it easier to learn historical styles too, one can hear a large number of excellent performances of pretty much any repertoire you can name. Many of these recordings are available online at little or no cost with a few clicks of the mouse. So while the supply of product has gone up exponentially, the number of people who can discern between a competent performance and a great one remains more or less constant (Mary Deissler once told me that the demographic of early music connoisseurs in Boston was about 400 people, interestingly, our typical crowd when the NY Collegium played there) As the supply/demand equation has grown more lopsided, the predictable outcome has been the disappearance of "in demand" celebrity directors and instrumental soloists who are household names. Also predictably, most professional free-lance musicians are working a lot less than they were ten or twenty years ago.

What is taking the place of traditional professional performance? Different, "diverse" kinds of music, finding new or inter-media takes on historical instruments (for an example see http://soreagroup.com). The programs are often heavily amplified, so just a few performers can have enough profile to capture the attention of a large crowd. And, interestingly, amateur performance at a very high level. Music schools all over the country are graduating annual classes of very competent performers; there are only so many chairs in full-time symphony orchestras and competition for jobs with even part-time modern or period groups is growing ever more intense. These musicians need to play somewhere, and in increasing numbers they are forming groups and self-presenting. I'm always interested to read in Gene Murrow's "Gotham Early Music Scene" e-mail newsletter the sheer number of concerts that are being presented in New York, most of them by artists who are organizing themselves and performing for the gate; they often spend a little money and take the time to produce their own CD's as well.

It seems that technology largely fueled the growth of the "Early Music Scene" in the last century, and is becoming an important part of its transformation in this one. What will happen next, I wonder? Comments welcome!