The Sound of Gottfried Silbermann, Part 2

Michael McNeil

Michael McNeil has designed, constructed, voiced, and researched pipe organs since 1973. Stimulating work as a research engineer in magnetic recording paid the bills. He is working on his Opus 5, which explores how an understanding of the human sensitivity to the changes in sound can be used to increase emotional impact. Opus 5 includes double expression, a controllable wind dynamic, chorus phase shifting, and meantone tuning. Stay tuned.

Editor’s note: The Diapason offers here a feature at our digital edition—three sound clips. Any subscriber can access this by logging into our website (thediapason.com), click on Magazine, then this issue, View Digital Edition, scroll to this page, and click on each <soundclip> in the text.

Part 2 of this article is found here.

Deductive logic is tautological; there is no way to get a new truth out if it, and it manipulates false statements as readily as true ones. If you fail to remember this, it can trip you—with perfect logic. . . . Inductive logic is much more difficult—but can produce new truths.¹

 

The late Peter Williams, pipe organ scholar extraordinaire, occasionally remarked to John Brombaugh that he most favored the sound of Gottfried Silbermann. Brombaugh thought this was perhaps a contrarian view, a position Williams often took in their conversations.² Silbermann’s sound is indeed both deeply admired and controversial.

The sound of an organ is the sum of its scaling, voicing, temperament, windchest design, action, layout, wind system, wind pressure, position in the room, and room acoustics. Among these factors, only the art of voicing is perceived as the elite province of a select and gifted few, shrouded in mystery. But as Reiner Janke has so ably demonstrated, voicing can be understood by anyone willing to commit the effort.³

Pipe organ literature abounds with subjective opinions of organ sound and the received wisdom of voicing recipes. These often contain a kernel of truth, but they can sometimes lead us down perilous paths. We will use data and inductive logic to give us insight into Silbermann’s voicing. And in Part 2 of this article we will use those insights to gain a wider perspective on voicing in general by comparing Silbermann’s voicing with a wide range of other styles. In the process we will see what makes Gottfried Silbermann’s sound so interesting.

Fundamentals of scaling and voicing

A quick overview of the features of organ pipes, scaling, and voicing may help readers unfamiliar with these terms. Figure 1 shows the basic features of an organ pipe and the terms used in this article.

Scaling and wind pressure determine the maximum power of a pipe. Scaling includes the diameter of a pipe’s resonator and the width of its mouth. Wider resonators and wider mouths will produce more power, as will higher wind pressure. Scaling also affects the vowel sound, or timbre, of a pipe, ranging from the “ah” of wider scales to the “ee” of narrower scales. The “ah” consists of the fundamental that increases in power in wider resonators. Narrower resonators will emphasize the power of higher harmonics with a brighter timbre.

In Figure 1 we see that the flueway of a pipe is the slit formed by the lower lip and the languid, the horizontal plate soldered on top of the pipe’s foot. The wind from the chest enters through the toe hole into the pipe’s foot and exits through the flueway slit. The languid’s edge turns the sheet of wind formed by the flueway into a spinning vortex. The upper lip cuts the vortex, creating pulsations of pressure that will drive the resonator to sound if the conditions are right.

The vortex spins fastest at the languid edge and spins slower as it expands towards the upper lip. If the height, or “cutup,” of the mouth’s upper lip cuts the vortex where it pulsates at the same frequency that the resonator is tuned, the pipe will speak very quickly.⁴ Lower cutups create higher frequency pulsations where the vortex spins faster. The resonator has more difficulty with faster pulsations, and the speech is both slower to form and brighter with more powerful harmonics. Keep lowering the cutup, and at some point the resonator cannot “resonate” with the vortex at the fundamental, and an open pipe will overblow to the octave, its second harmonic. More pressure or more wind from a larger toe will make the vortex spin faster with more energy, and the cutup will have to rise.

Voicing begins by adjusting the flueway depth and/or the diameter of the toe to control the power (this is also known as “regulation”). More wind from larger toes and deeper flueways produces more power.

A voicer will raise the height of the cutup by degrees to adjust the timbre, making the sound continuously less bright and more like a flute as cutup is increased. Cutup is by far the most sensitive aspect of voicing—very small changes in cutup will make big changes in timbre. While toe areas, flueway areas, and wind pressure have proportional effects on a pipe’s power, its cutup has an exponential effect on its timbre; Ising showed that it is a cube function!

When we say that an organ is voiced in a Germanic or French style, what does this mean? Received wisdom relates that Germanic voicing leaves the toe wide open and closes the flueway to regulate power, while French voicing emphasizes a deeply open flueway and closes the toe to regulate power. Does this make a difference? Charles Fisk thought it made a great difference, and he wrote with passion about the musicality of deeper flueways in 1975.⁵ Subjective impressions suggest that deeper flueways result in a warmer fundamental with less percussive speech when power is regulated with closed toes. Physics tells us that the pressure in the foot and the velocity of air in the flueway will be lower as the toe area decreases and the flueway area increases, and the vortex will spin more slowly.

The musical range of flueway depths spans the very deep flueways of romantic voicing to the more closed flueways exemplified by the work of organ builders like D. A. Flentrop. The received wisdom of Germanic voicing often assumes the sole use of closed flueways to regulate power, but the reality is more complex. How do we know this?

The minimum required data

Typical organ documentation lists pipe diameters, mouth widths, and cutups, but ignores the crucial voicing data of flueway depths and toe diameters, and this unfortunately tells us little about the sound. For example, without the toe and flueway data we do not know if the cutup data imply a softer and smoother sound with more closed toes and flueways or a powerful, brighter sound with more open toes and flueways. As Ising has shown, cutups and the timbre they control are extremely sensitive to changes in pressure and the flow of wind in toes and flueways.

While voicing data of most organbuilders, including Arp Schnitger, are exceedingly rare, our knowledge of Gottfried Silbermann is made possible by the work of Frank-Harald Greß and his documentation of voicing for several of Silbermann’s organs.^{6, 7, 8} To make matters far worse in our quest to understand historic voicing, many organs have been revoiced, repitched, retuned in new temperaments, and their wind pressures raised or lowered during their restorations, often on multiple occasions. We will have great difficulty discovering the original sound of most older organs. We owe a great debt to F.-H. Greß, who has documented the changes made to each of Silbermann’s surviving organs.

Early influences

Gottfried Silbermann was born in 1683 in Kleinbobritzsch, Saxony, the son of a carpenter. His older brother, Andreas, “left home in great haste to avoid military conscription” and worked for Eugenio Casparini on the Görlitz organ before settling in Strasbourg, Alsace, as an independent organbuilder.⁹ Andreas spent the years 1704–1706 learning French organbuilding from François Thierry in Paris. Andreas was at first rebuffed in Paris, but found a willing mentor in Thierry, who would later build the organ we now see in Notre Dame de Paris. Little is known of Gottfried’s youth, but we know that he joined Andreas in Strasbourg in 1702, earned his title as a master organbuilder, and returned to Saxony with two journeymen and an apprentice. He built his first organ in Frauenstein in 1709 and 1710 and spent the rest of his life building nearly all of his organs in Saxony. Gottfried died late one night in August of 1753 while voicing the organ in the Dresden Hofkirche.¹⁰

Gottfried “was accustomed to throw his cane on the floor when he wanted to judge the acoustics in a church.”¹¹ This shrewd test creates a broad range of frequencies which will decay at different rates, informing Silbermann of the room’s different absorption of sound from bass to treble. This is very similar to what acousticians do today with a blank gunshot. He notoriously refused to build organs in churches whose acoustics were poor, and he would likely be appalled at the acoustics of most American churches.¹²

Scaling

Gottfried Silbermann’s scaling, voicing, and stoplists were extremely consistent. He had three sets of principal chorus scales, wider to narrower, which he used to differentiate the timbre of his different divisions. He also used one of the narrower scales for his mixtures.¹³ More wind pressure was employed to fill larger or less efficient acoustics. Unlike most other organbuilders, he never found the need to experiment with different sounds.

Silbermann’s layouts were well engineered and featured easy access, which probably has much to do with the longevity of his organs. He has been criticized for the regularity of his tonal schemes, but this regularity helps us understand how he achieved that sound by comparing his least modified surviving organs. Silbermann became relatively wealthy as an organbuilder, an impossible achievement for modern organbuilders who design their classically inspired organs as completely unique creations.

We will use graphs presented in Normal Scales to understand Silbermann’s sound. Tables of raw numbers do not convey the underlying intent of the organbuilder, and Normal Scales allow us to make easy visual comparisons. These Normal Scales were published in the author’s article, “1863 E. & G. G. Hook Opus 322: Church of the Immaculate Conception, Boston, Massachusetts, Part 1,” The Diapason, July 2017, page 18. Those who want actual measurements can use those tables to convert the Normal Scale data in this article into raw data.¹⁴

Diameter scales of the 1714 Freiberg Dom Hauptwerk principal chorus are shown in Figure 4. The mid-range scales are narrower, emphasizing less power and more harmonic brightness. In Figure 5 we see the mouth widths. Normal Scale mouth widths are based on mouths which are ¼ of the pipe circumference. Silbermann’s mouths are wider, a very unusual practice. The figure captions describe Silbermann’s scaling in more detail.

Influence of French voicing

The roots of Gottfried Silbermann’s sound lie in French voicing, and an essential feature of classical French voicing is a deeply open flueway. Figure 2 shows an image taken by Reiner Janke of Andreas Silbermann’s voicing. We are looking down into the mouth of a tenor G pipe from the Hauptwerk 4′ Prestant in the 1709 organ at Marmoutier. Note the deep 0.7 mm flueway, the absence of ears, and the alternating deeper and shallower nicks on the languid edge. To put this flueway into perspective, Figure 3 shows an image of a modern, “neo-Baroque” pipe of a similar pitch with a low cutup, a flueway of 0.27 mm depth, and ears. The flueway in Figure 3 is the thin black line.

Divergence from French influence

Gottfried Silbermann designed his organs for exceptional power, even by modern standards. While the sound of Gottfried Silbermann is based on the deep flueways of French voicing, it differs from French voicing in specific ways to get that power.

French flueways tend to be very deep, pushing the maximum limits of musicality, and this might lead us to think that these pipes are very powerful. But classical French voicing uses more closed pipe toes to limit the wind for a more restrained power. We will see in Part 2 that Gottfried’s toes are more open than typical French voicing, and they feed wider mouths.

Mouth widths range from about 2⁄7 to 1⁄7 of the circumference of a pipe. Wider mouths on the same resonator will have more wind flow and proportionally more power. Very small mouths will have a delicate effect. Classical French scaling does not trend toward the maximum limits in mouth widths, but the scaling of Gottfried Silbermann’s principal chorus does exactly that. The combination of very wide mouths, deep flueways, and more open toes is the source of Silbermann’s power. To get a sense of his wind pressures, Andreas Silbermann’s 1709 organ at Marmoutier is voiced on 69 mm, Gottfried’s organ at the Rötha Georgenkirche is voiced on 76 mm, and Gottfried’s Freiberg Dom organ originally had pressures of 97 mm in the manuals and 109 mm in the pedal.¹⁵

Unusual pipe construction

Figure 6 shows the basic features of Gottfried Silbermann’s pipework as recreated by C. B. Fisk, Inc. The bottom image in Figure 6 shows a generous flueway and very fine nicking. The 2⁄7 mouth width is evident here, the maximum practical width. The image at top shows a vertical counterbevel (also called a “counterface”) on the languid and a very high position of the languid; you can see the bottom edge of the languid rising just above the top edge of the lower lip. Such a languid position will move the windsheet outwards, and to compensate for this, Fisk has moved the upper lip outwards by extending the side walls of the pipe. There are no added ears. These are the hallmarks of Gottfried Silbermann’s pipes. The pipe in Figure 2 by Andreas Silbermann shares the deep flueway, counterbevel, and nicking, but it does not have the extended upper lip, high languid, and wider mouth.

The sound

At the 1980 American Institute of Organbuilders convention Charles Fisk demonstrated the voicing of a pipe constructed in the style of Gottfried Silbermann. This pipe produced a sound with very prompt and articulate speech of great power and intensity, which I measured at 90 dB at a distance of one meter.¹⁶ The mouth of this pipe is shown in Figure 7.

In voicing this pipe Fisk first set the toe diameter and the flueway depth. He then raised the cutup by degrees and added nicks by degrees to reduce harmonic brightness, while adjusting the languid height for prompt speech. He set the languid high as a consequence of the outward extension of the side walls and upper lip.¹⁷ To hear the sound of this pipe, listen to a soundclip of Bach’s Duetto I in E Minor, BWV 802, on Silbermann’s nearly original Principal at the Rötha Georgenkirche. <soundclip 1>

Zacharias Hildebrandt apprenticed to Gottfried Silbermann in 1714. He and Silbermann soon became bitter rivals, but upon Silbermann’s death in 1753, Hildebrandt was given the task of finishing Silbermann’s last organ in the Dresden Hofkirche. The sound of Hildebrandt’s 1746 organ at Naumburg is reminiscent of Silbermann’s deep flueways, but I do not have data to confirm this. Like Silbermann, Hildebrandt used different scales of principals to give his divisions a different character. Here is a soundclip of the Naumburg principals, played in contrast to each other in Bach’s Concerto in D Minor after Vivaldi, BWV 596. <soundclip 2>

The voicing

Voicing data for the Freiberg Dom Hauptwerk are shown in Figure 8, Toe Constants, Figure 9, Flueway Depths, Figure 10, Mouth Heights (cutups), and Figure 11, Ratios of Toe Areas to Flueway Areas. See the figure captions for descriptions of these voicing parameters; their derivations can be found in the author’s book.¹⁸ In the simplest terms, toe and flueway areas control power, cutups control timbre, and the ratio of the toe area and flueway area affects speech articulation (also known as “chiff”). The crucial takeaway is that Silbermann’s toes and flueways were extremely regular and not treated as free variables. The free variable for Silbermann was cutup.

The regularity of Silbermann’s voicing is remarkable, and it suggests that he calculated his flueway depths and toe diameters prior to voicing. In Part 2 we will see that this regularity is consistent with other organs voiced on similar wind pressures and built at very different times. The regularity of his tonal designs, scaling, and voicing is evidence that he approached organ design from a set of inductively-derived design rules based on very early experimentation. As we will see in Part 2, the design rules for Silbermann’s toes and flueways were different for lower wind pressures.

Greß’s voicing data encompass several of Silbermann organs in acoustics ranging from smaller and more intimate to spacious and grand.¹⁹ Silbermann used higher wind pressure for more power, and at higher pressure a pipe is also brighter. Higher cutups will restore a pipe’s timbre at a higher power.²⁰ In Figure 12 we see mouth heights (cutups) plotted in Normal Scale halftones against pitch. The data in the orange line show the higher cutups of powerful principal pipes voiced on 90 mm pressure at Großhartmannsdorf; the data in the light blue line show the lower cutups of less powerful principal pipes voiced on 70 mm pressure at Reinhardtsgrimma; the timbres are similar.

Gottfried Silbermann used cutups to differentiate the timbre of his flutes and principals at the same pressure. In Figure 13 we see that Silbermann cut his 8′ Bordon pipes at the Freiberg Dom (data in the blue line) far higher than his principals (Figure 12 data in the orange line). This is why a Silbermann Bordon is extremely smooth and his principal has harmonic bite. It is also why they have similar power and can be played against each other. If the flueways had been closed to make the Bordon less bright, it would have had far less power than the principal. Listen to a soundclip at the Rötha Georgenkirche of Bach’s O Mensch, bewein’ dein Sünde Groß, BWV 622, where the Bordon holds its own against the powerful principal. <soundclip 3>

The striking feature of Silbermann’s voicing is that he used only cutup as a free variable during voicing to achieve his sound. The regularity of his toe diameters and flueway depths is virtually unique, and that regularity strongly implies that they were calculated.

In Part 2 we will take a much deeper dive into these voicing parameters and compare Silbermann’s voicing to the work of other organbuilders. Some of the data may challenge conventional assumptions and yield surprising and very useful insights.

To be continued.

Uncredited images reside in the collection of the author. Fr. Thomas Carroll, S.J., graciously suggested clarifications in the prose of this article.

Notes

1. Robert A. Heinlein, The Notebooks of Lazarus Long (New York: G. P. Putnam’s Sons, 1973).

2. John Brombaugh. Personal communication, used by permission via telecommunication of June 2, 2021.

3. Reiner Janke, Copy and Intonation: The tacit knowledge of Reiner Janke, Universität Göttingen, 2018, Youtube video: youtube.com/watch?v=isEWba9rLRY&feature=youtu.be. Figure 2 image is at 9:47. In this video Janke skillfully demonstrates a recreation of the Andreas Silbermann pipe in Figure 2 and its exact voicing. You will not find a better tutorial on voicing. Here are Janke’s instructions to the pipemaker (translated from German), with my notes in brackets [ ]. Pitch: g° Prestant 4′. Wind pressure: 69 mm. Alloy of resonator: 85% tin. Alloy of foot and languid: 10% tin. Inside diameter: 36.5 mm [-2.5 HT]. Mouth width: 29 mm (¼ of circumference) inscribed straight and only lightly pressed [-2.5 HT]. Mouth height (cutup): 8–8.5 mm, upper lip not beveled [arched 0 to +1.5 HT]. Resonator wall thickness: 0.8 mm. Foot wall thickness: 0.9 mm. Foot length: 200 mm. Resonator length: 426 mm. Languid face: 50° with a small counter bevel, 90° to the languid underside. Toe hole: 6 mm [0.97 toe constant and 1.4 toe/flueway ratio]. Flueway depth: 3⁄4 metal thickness [0.68 mm]. Soft, intense, warm onset. Soft attack without harshness, set slightly fast. (“Weich, intensiv, warmer Strich. Weiche Ansprache ohne Härten, etwas zu schnell eingestellt.”)

4. Michael McNeil, The Sound of Pipe Organs (CC&A, amazon.com, 2014). When the pipe speaks most quickly, John Coltman would say that the impedances match and Hartmut Ising would say that I = 2; for more detailed descriptions see pages 64–67 and 77–80. Coltman dealt only with the fundamental harmonic, but Ising’s equation shows the crucial relationships between pressure, flueway depth, and cutup on timbre. For descriptions of toe diameters see pages 43–47. The toe constant equation: diameter of the toe = √(toe constant * 4 * mouth width fraction * pipe diameter). A full graphical analysis of the Isnard organ at Saint Maximin on pages 159–190 can be compared to the Silbermann data at Freiberg.

5. Charles B. Fisk, “Pipe Flueways,” Music: The AGO and RCCCO Magazine, December 1975, page 45. A reprint of the article can be found on the website of C. B. Fisk, Inc., www.cbfisk.com/writing/pipe-flueways/.

6. Heimo Reinitzer, Die Arp Schnitger-Orgel der Hauptkirche St. Jacobi in Hamburg (1995). This is one of only three publications known to the author to include complete data for understanding the sound of an organ, i.e., its pipework, windchests, wind system, temperament, action, and layout. The other examples can be found in the author’s “The 1755 John Snetzler Organ, Clare College, Cambridge, restored by William Drake, Ltd., Joost de Boer, Director,” The Diapason, September 2019, pages 17–21, and “The 1864 William A. Johnson Opus 161, Piru Community United Methodist Church, Piru, California,” The Diapason, August 2018, pages 16–20, September 2018, pages 20–25, October 2018, pages 26–28, and November 2018, pages 20–24.

7. Frank-Harald Greß, Die Klanggestalt der Orgeln Gottfried Silbermanns (Wiesbaden: Breitkopf & Härtel, 1989). Regrettably, this crucially important book is not easy to find.

8. Frank-Harald Greß, Die Orgeln Gottfried Silbermanns (Dresden: Sandstein Verlag, 2007), pages 36, 52. Greß carefully documents the modern changes to Silbermann’s organs, e.g., wind pressures, temperament, voicing, pitch, etc.

9. Poul-Gerhard Andersen, Organ Building and Design (London: George Allen and Unwin, 1969), page 192.

10. Ibid, pages 193, 200.

11. Ibid, page 26.

12. The architectural standard of -60dB for the measurement of reverberation length has a solid basis in physics, but it creates vast confusion and disappointment. At -60dB reverberation is 1/1000 or 0.1% of its original power, the lowest level of sound perceptible to (young) human ears. We do not even remotely hear such sounds in the context of music and singing. Reverberation that is audible during singing and organ performance will be louder than about -26dB, or 5% of its original level. The -60dB standard is not relevant to human perception in the context of music. Now you know why your architect will guarantee you three seconds of reverberation in your new church, but you are aghast when you first walk into the new room and find the reverberation barely audible. The residual of sound for reverberation length should be specified at no less than -26dB to architects and acousticians, a request that will make them quite aghast, too, but your music will come alive.

13. Greß, Die Klanggestalt der Orgeln Gottfried Silbermanns.

14. An Excel analysis of diameters, mouth widths, mouth heights, toe diameters, and flueway depths of the Freiberg Dom Hauptwerk, Oberwerk, and Pedal can be obtained from the author by emailing [email protected]. Wind pressures on the Freiberg Dom organ have been lowered. The 85 mm pressure noted in Figures 4 and 5 is the current pressure; the original pressure according to Greß was 97 mm.

15. Greß, Die Orgeln Gottfried Silbermanns, page 36.

16. Specifications of Fisk’s pipe: Inside diameter 24.5 mm [-2.5 HT]. Pitch 4′ middle e, about 659 Hz. Very thin and stiff 0.36 mm wall of 90% hammered tin. Mouth width 19.6 mm [-2 HT]. Toe 7.7 mm [2.35 toe constant] with 65 mm pressure. An upper lip extension approximately equal to the wall thickness. Cutup 6.6 mm [+5 HT]. Languid counterbevel 90 degrees with five fine nicks alternating with four extremely fine nicks. Flueway depth 0.8 mm [2.9 toe/flueway area ratio].

17. I attended the featured voicing demonstration by Charles Fisk. Our conversation afterward turned to the dynamics of the wind system, and with a common analytical approach to such problems, we became deeply engaged in this subject. Fisk started looking for a place where we could have a conversation without interruption. He found a janitor’s closet with folding metal chairs and shut the door. He gave me the pipe in Figure 7 and offered me the chance to work for a few months in his shop, and to this day I regret not taking him up on that offer; he died three years later.

18. McNeil, The Sound of Pipe Organs.

19. Greß, Die Klanggestalt der Orgeln Gottfried Silbermanns.

20. McNeil, The Sound of Pipe Organs, pages 64–80.

 

Soundclips

1. [00:18] Johann Sebastian Bach, Duetto I in E Minor, BWV 802 (Clavierübung III), Gottfried Silbermann, St. Georgenkirche 1718, Rötha, Johannes Unger, GEMA VKJK 0111 (2001), © Verlag Klaus-Jürgen Kamprad 2001.

2. [00:27] Johann Sebastian Bach, “Grave,” Concerto in D Minor after Vivaldi, BWV 596, Zacharias Hildebrandt, Wenzelskirche, 1746, Naumburg, Robert Clark, Calcante CAL CD041, © Calcante Recordings, Ltd. 2001.

3. [00:35] Johann Sebastian Bach, O Mensch, bewein’ dein Sünde Groß, BWV 622, Gottfried Silbermann, St. Georgenkirche 1718, Rötha, Johannes Unger, GEMA VKJK 0111 (2001), © Verlag Klaus-Jürgen Kamprad 2001.

Michael McNeil

Michael McNeil has designed, constructed, voiced, and researched pipe organs since 1973. Stimulating work as a research engineer in magnetic recording paid the bills. He is working on his Opus 5, which explores how an understanding of the human sensitivity to the changes in sound can be used to increase emotional impact. Opus 5 includes double expression, a controllable wind dynamic, chorus phase shifting, and meantone. Stay tuned.

Editor’s note: The Diapason offers here a feature at our digital edition—four sound clips. Any subscriber can access this by logging into our website (thediapason.com), click on Magazine, then this issue, View Digital Edition, scroll to this page, and click on each <soundclip> in the text.

Many American organists have traveled to Europe and heard the sounds of older organs that make Bach a revelation. American organ building was for much of its history rooted in the Anglican tradition and the Romantic sounds of organbuilders like Ernest M. Skinner, and neither of those great art forms are an ideal medium for Bach. Tentative steps in the Anglican tradition were made as early as the 1930s to recreate this European sound, but they did not amount to a revelation. The revelation occurred with a British-born virtuoso, E. Power Biggs, who brought a sound to America that would convincingly play Bach in the form of an organ built by D. A. Flentrop. Biggs paid for this organ out of his own pocket and in 1958 found a home for it in the very reverberant acoustics of what was known at the time as the Busch Reisinger Museum.¹ His recordings of this Flentrop energized the budding Organ Reform Movement in the United States and inspired many American organbuilders. Listen to the end of the Fugue in A Minor, BWV 543ii <Soundclip 1>.

Dirk Andries Flentrop (1910–2003) worked in his father’s organbuilding shop and with Theodor Frobenius in Denmark, eventually taking over his father’s business. He was intensely interested in classical organ design, and he gave a lecture at a very young age in 1927 in which he promoted the use of mechanical action and slider windchests.² A conversation with Flentrop in the 1970s turned to his earlier career, and he recalled that he was traveling on a streetcar in Rotterdam when bombs started falling on that city in World War II. Everyone on the streetcar agreed there was no point in getting off, and they continued traveling to their destinations as bombs fell. The date was May 10, 1940, the year he took over his father’s business. I sailed with my parents on the SS Rotterdam in 1964 and still remember the shock of seeing upturned docks as we approached the harbor at Rotterdam and whole city blocks of uncleared rubble decades after the bombing.

Flentrop’s sound

The sound of pipe organs can be described subjectively and objectively. Subjectively, the sound of D. A. Flentrop is bright and “instrumental,” where individual pipes in the principal chorus have rich harmonic content. This is very different from what is today called vocale voicing, which emphasizes less harmonic power. Flentrop’s richly harmonic sound creates a scintillating principal chorus with clarity of pitch.

A key component of this sound, and a strong departure from the Romantic and Anglican traditions, is the expression of “chiff.” E. Power Biggs described chiff as the articulate “ictus” of a sound, adding clarity to rhythm and contrapuntal harmony. Chiff is not just percussive noise. It consists of higher natural harmonics to which the human ear is very sensitive, quickly defining the pitch. Flentrop was a master of this percussive speech, and it was always musical and fast. Chiff can be modulated with a sensitive mechanical action and low wind pressures (i.e., with little or no key pluck). Biggs was adept at this on his Flentrop, easing the pallets open for a smooth treble line while crisply opening the pallets to delineate inner voices with more chiff.

Later expressions of this articulation in what became known as neo-Baroque voicing are often heard as a slow, gulping sound. You never hear slow, gulping speech in a Flentrop organ, and as the data will show, Flentrop’s voicing exhibits no relationship to neo-Baroque voicing recipes.³

There is ample evidence that much of D. A. Flentrop’s sound is based on examination of the work of Arp Schnitger, and Schnitger’s sound is much more instrumental in character than modern vocale voicing. The similarity to Schnitger extends also to the design of the reeds, whose basses are the source of a smooth and powerful fundamental.

Flentrop organs have considerable presence, due in large part to the shallowness of the casework found in all of his organs. Flentrop related that the maximum depth of a case should be no deeper than the reach of an arm from the back doors of the case to its façade pipes. Deep cases and chambers will tend to absorb sound, especially the higher harmonics that create the sense of presence. I find it interesting that unaltered manual divisions of Cavaillé-Coll organs, while using higher pressures with Romantic scaling and voicing, almost never exceeded twelve stops and always used slider chests with mechanical action, reflecting some of the important design features of Flentrop organs.

The generosity of D. A. Flentrop

D. A. Flentrop was secure in his knowledge and very willing to share it. I was the recipient of his generosity on several occasions when he toured the United States with his senior voicer, Sijmen “Siem” Doot, to maintain and tune his organs. Doot, born in 1924, entered Flentrop’s service in 1939 and retired in 1988. Ed Lustig at Flentrop Orgelbouw confirmed that Franz Rietsch, Rob Oudejans, Johannes Steketee, and Doot assembled the Flentrop organ in Saint Mark’s Episcopal Cathedral, Seattle, Washington, in 1965, while Steketee and Doot remained to voice the organ. The voicing data in this article is a testament to their skill. I was introduced to Flentrop by Albert Campbell in 1971. After scouring the literature and finding mostly subjective opinions with very little data, I quickly discovered that Flentrop was genuinely interested in answering the detailed questions of a budding organbuilder. When I asked him if he would grant me permission to take measurements of his organs, he replied, “imitation is the finest form of flattery. Your ears will be different than mine, and you will use your observations to find your own sound.” He was right, but it took quite some time before I began to understand some of those observations, and the data continues to generate insights.

I again met Flentrop in the Campbell home after completion of my Opus 1, and by that time I had learned enough to ask deeper questions. Flentrop had nearly completed the tuning of his organ at the University of California, Santa Barbara, and in a further gesture of generosity, Flentrop said, “If you finish the cone tuning of the Hoofdwerk Mixtuur, we can answer your questions.” I agreed to finish the tuning work on the Flentrop organ, and both he and Mr. Doot spent the whole day answering my questions.

Flentrop slider windchests

D. A. Flentrop organs have exclusively featured mechanical key action and slider windchests since 1949. Stop actions were mechanical, as well, and only in his larger organs do we find electric slider motors and combination actions. Organbuilders who looked to the literature for the design principles of slider chests in the 1970s often found the effort frustrating. Flentrop willingly shared a great deal of his design practice. In Figure 1 we see a drawing made by the author from notes of a conversation with Flentrop regarding channel design. Flentrop recommended that the cross-sectional area of the key channel should have about 20–30% more area than the combined areas of all of the pipe toes it would need to wind. A small vent hole at the end of the channel served two functions—to prevent ciphering and to dampen resonances in the channel that would interfere with reeds. Reeds that are equal in length to the channel that feeds wind to them may get much louder, and those not quite equal to that length may get much weaker and more dull in timbre from channel resonance. I noted that the bottom of the key channels in the Flentrop organ at the University of California, Santa Barbara, were covered in a thick paper that had pin pricks in a few channels in various positions, likely done to reduce channel resonance.

Flentrop stated that pallets did not need to exceed 200 millimeters (about eight inches) in length, but I have found much longer pallets in Hook organs. I did not ask how to trade off key channel widths and heights for a given area, nor the flow areas of the pallets, and these tradeoffs can be complex. Suffice it to say that the flow area of a pallet is the length of its opening times the distance the pallet is pulled open by the key (an open pallet has a triangle of flow at each side, and when combined, these triangles make a rectangle). It is also interesting to note that a pallet will not flow significantly more wind to a channel when its pull is more than half of the channel width (think about the height of those triangles that flow wind relative to the width of the channel). For a given pallet pull and a key channel width that is twice the pull, only a longer pallet will flow more wind to the channel.

The 1863 Hook organ at the former Church of the Immaculate Conception in Boston, Massachusetts, has roughly 460-millimeters-long pallets feeding 406-millimeters-long flue and reed channel openings in the Great bass octave (there are two pallets per note). The Romantic voicing of the Hook organ requires a very large volume of wind to feed its very deep flueways and very widely opened toes, which are much larger than Flentrop’s. At Saint Mark’s, Flentrop likewise used two pallets for the six bass notes of the Hoofdwerk, with pallet opening lengths of 155 millimeters, flue and reed channel widths of 21 millimeters and 17 millimeters, respectively, and a channel height of 79 millimeters. Readers who are interested in comparing the differences in the voicing of Flentrop and Hook organs can find the Hook data in The Diapason.⁴

Flentrop’s patented slider

Slider windchests in ancient organs often suffered from the advent of central heating. Topboard bearers are shimmed with layers of paper for a close fit between the slider, the windchest table on which it rests, and the topboard above it. With central heating and the resulting low humidity, shrinking wood caused these sliders to leak wind and impair the tuning. Many different forms of slider seals were invented in the twentieth century, most of which worked quite well. Flentrop’s system is patented and rather complex, but it is extremely reliable. Flentrop used two sliders, separated by springs with a leather-faced conduit for the wind between the two sliders. Figure 2 (see page 15) shows this slider seal mechanism in relation to the pallets, key channels, and topboards.

An objective approach to Flentrop’s sound

If you want to discover how to achieve a certain sound, it is often educational to closely observe the organs you like and those you do not. The objective differences will teach you what matters. Readers who want some perspective on the following Flentrop data will find a description of the voicing of several historic organs in The Diapason.⁵

The absolute minimum data needed to understand the sound of an organ is:

• pipe diameters (inside);

• mouth widths;

• toe diameters;

• mouth heights (also known as “cutups”)

• flueway depths.

Complete descriptions of these parameters can be found in the article mentioned above.⁶ In a nutshell, larger pipe diameters, wider mouth widths, larger toe diameters, and deeper flueways yield more power. Mouth heights control timbre, and higher mouths reduce harmonic power and brightness. Flutes typically have much higher mouths than more harmonically rich principals.

Wider scales produce an “ah” timbre, and narrower scales will progress towards an “ee” timbre, emphasizing higher harmonics. Flentrop stated that he used a constant scale of pipe diameters and mouth widths for the principal chorus in most environments and acoustics, which meant that he wanted a specific vowel timbre for all of the pipes at the same pitch and a specific power balance across the range of frequencies from bass to treble.

For different acoustics Flentrop used different pressures and voicing, adjusting the toe diameters and cutups. Ascending trebles were achieved in the toe diameters. Figure 3 shows Flentrop’s chorus scaling written in his own hand in 1971 with numerical values he had memorized.

Flentrop reeds were often made by the firm of Giesecke to Flentrop’s specifications. A description of the data needed to understand the sound of a reed can be found in an article in The Diapason.⁷ The author’s measurements of the Saint Mark’s reeds were not taken in sufficient detail to merit showing them. Flentrop reed designs are very similar to Schnitger’s and use tin-lead plates with restricted openings soldered to wide, lightly tapered, and deeply cut shallots for powerful, smooth basses. These typically transition to open, parallel shallots without plates in the tenor.

Taking the data at Saint Mark’s

I have been fortunate that many of those who are a gate to the access to some important organs have granted me permission to measure them. In 1972 that good fortune allowed me to take measurements of Flentrop’s organ at Saint Mark’s Episcopal Cathedral, Seattle, Washington, the organ Flentrop considered his largest by virtue of its 32′ façade pipes. The stoplist of the Saint Mark’s organ is easily found on the internet.⁸

The cathedral measures an estimated 150 feet in length and width, with a flat, wooden ceiling about 90 feet high. The walls are very thick concrete, yielding an acoustical reverberation of about five plainly audible seconds in the soprano range.⁹ The reverberation drops dramatically in the tenor and bass as a consequence of the very large windows, through which the lower frequencies easily pass.

Richard Frickmann, a life-long friend, and I drove over a thousand miles to visit this organ, and upon arrival in the early morning we sat in the pews in the empty cathedral, looking back at the organ. Glenn White, who maintained the organ, noticed our interest in this magnificent Flentrop and struck up a conversation. Learning that we were eager to find scaling data of the pipes, he questioned us for about five minutes and admitted that no one had taken the time to measure the pipework. He took us to the office and gave us the keys to the Flentrop casework, the organ loft, and the cathedral, asking that we return them when we were done. This was a stunning opportunity and one rarely offered. Mr. Frickmann and I took over fifty pages of data, interspersed with trips to the local twenty-four-hour pancake house to refuel with food and coffee. I had brought with me copies of scaling sheets and measuring tools, and Mr. Frickmann wrote down the numbers as I called them out from the walkways behind the windchests. After about twenty-four continuous hours of work, we handed in the keys to the office.

A word of caution on the data is in order. I took this data in 1972, very early in my career. I had experience with Flentrop’s organ at the University of California at Santa Barbara, and I understood basic scaling and data collection. But what I did not yet appreciate at the time was the importance of measuring the depth of the flueway. My general observations of the flueways of the Saint Mark’s organ were that “they tend to be consistent throughout the organ relative to pitch, much wider than current neo-Baroque work, but narrower than the voicing of the early American builders like Johnson and the Hooks.” Later measurements of Flentrop flueways provided a generalized model of the flueways for the Saint Mark’s organ. Please be aware that these are probably in the ballpark, but they are assumptions.

I was very careful in the handling of the pipes and making sure that their mouths faced in their original directions (this affects tuning on larger pipes whose mouths can be close to other pipes and shaded by them, lowering their pitch). The measurements of these pipes will have some inaccuracy from the time constraints. For larger pipes the measurements are likely better than +/- 1 millimeter, and for the very smallest pipes, about +/- 0.2 millimeter. The data is presented in halftone deviations from Normal Scale to make the relationships clear, as tables of numbers do not easily convey their meaning. These Normal Scales were published in the author’s article, “1863 E. & G. G. Hook Opus 322: Church of the Immaculate Conception, Boston, Massachusetts,” Part 1.¹⁰ Those who want actual measurements can use those tables to convert the Normal Scale data into dimensions, or they can email the author for a copy of the Excel spreadsheet with the more accurate raw dimensional data.¹¹

The Hoofdwerk

Larger pipe diameters generate more power, and smaller diameters generate a brighter timbre. Flentrop’s principal chorus scales combine these factors into the sound he wanted. His scaling model in Figure 3 is seen as a dashed blue line in Figure 4. The model generally follows the Saint Mark’s data. As Flentrop noted, the mixtures are narrower. Flutes trend much wider as the pitch ascends.

Sound clips of the Saint Mark’s Flentrop in the digital edition of this article allow one to hear these power and timbre balances. They were derived from 1981 recordings of James Welch, organist, another life-long friend. The recording engineer, Dave Wilson, was known as one of the world’s best, and he recorded Welch on Flentrop organs. I was present in 1981 for the Saint Mark’s recordings, mostly to help with touching up the tuning of the reeds. I also made suggestions for stop registrations that ran counter to the prevailing wisdom of the time, dictating a minimal use of foundations to aid in clarity of pitch. This was not necessary on a Flentrop, whose foundations can be combined to any degree and still maintain clarity of pitch. Amassing foundations, as any Romantic organist knows well, is a source of rich chorus depth, and it is heard to great effect in Charles-Marie Widor’s “Andante cantabile” from Symphonie IV in <Soundclip 2>.

We made many experiments with microphone placement. The proper power balances of the different Flentrop divisions were finally achieved by placing microphones on very tall stands about twenty to thirty feet in front of the Rugwerk, the division that has the most presence for the congregation. Having been accustomed to the practice of using fast tempos in dry acoustics, Welch and I discussed appropriate tempos for the reverberant acoustic of Saint Mark’s. Borrowing headphones from the recording engineer to hear what the sound was like in the room at the microphones, he arrived at the tempo we hear in C. P. E. Bach’s Toccata and Fugue in D Minor, which takes full advantage of Saint Mark’s long reverberation <Soundclip 3>.

Late in the all-night recording session a note went dead in the Rugwerk. The organ had been in service for only sixteen years at this time, and a failure was unexpected. I pulled up the floor panels in the choir loft, which gave access to the Rugwerk trackers, and the culprit was a torn piece of weak leather that connected a long horizontal tracker at a suspension point. None of the other connectors showed the slightest sign of wear. I made a temporary fix, adjusted the action, and we continued recording well into the next morning.

Figure 5 shows the scales of the mouth widths, and these generally imitate the diameter scales. Normal Scale mouth widths are based on 1⁄4 of the circumferences of Normal Scale diameters, and as Flentrop almost exclusively used 1⁄4 mouths, we would expect a similarity to the diameter scales. Some of these mouth widths appear to be a bit wider than 1⁄4 of the circumference, and this may indicate that the pipes were slightly tapered, something I did not measure, and which is not uncommon. Inside diameters were measured at the top of the pipes. If the pipes have a slight taper, the true diameter scales at the bottom will be larger and will more closely match the Flentrop model in Figure 4, as well as the mouth scales in Figure 5.

Figure 6 shows mouth heights, or what is more commonly known as “cutups.” The cutup controls timbre. A higher mouth will reduce the harmonic content, and smooth flutes have higher cutups. These can be clearly seen in the lofty cutups of the 8′ Roerfluit. Normal Scale mouth heights are calculated as 1⁄4 of the Normal Scale Mouth Width, a common recipe in neo-Baroque voicing. In Figure 6 we see that Flentrop did not use this recipe. The Saint Mark’s cutups are much higher, and they have no relationship to the mouth width scales. They are also highly variable as a free voicing parameter. Flentrop raised the cutup until the desired timbre was achieved and the speech was fast. This is why you do not hear slow, gulping speech in a Flentrop organ.

The soaring cutups of the Roerfluit

The soaring cutups of the 8′ Roerfluit illustrate how Flentrop achieved a rich harmonic timbre in his principal chorus and a smoother, warmer timbre in the flutes. While Flentrop is noted for a brighter, “instrumental” timbre, which strongly implies lower cutups, Figure 6 clearly shows that his cutups were much higher than the neo-Baroque recipe. As an example, the cutup of the 8′ Roerfluit tenor C pipe in Figure 6 is +5 halftones, while its mouth width in Figure 5 is -5 halftones, revealing a cutup that is a stunning 10 halftones higher than the neo-Baroque recipe.

Figure 7 (see page 18) shows the relative flow of wind in the pipe toes. Larger pipe toes will flow more wind and yield more power. Received wisdom relates that Flentrop used “open toe” voicing, but Flentrop toes are in most cases quite restricted. Much more open toes can be found in Hook organs. Hook toe diameters also have high variability at a specific pitch, very unlike the more regular wind flow patterns we see with D. A. Flentrop and Gottfried Silbermann.¹³

The values in Figure 7 are toe constants, a number that represents relative flow. Flentrop suggested to me that a reasonable starting point for a toe diameter is the square root of its resonator diameter. The area of that closed toe represents a constant of “1,” and as you can see in Figure 7, Flentrop converged on that number at about 1′ pitch and increased the flow in both deeper and higher pitches. The area of the toe is proportional to the toe constant, i.e., a toe constant of “2” has twice the area of a toe with a constant of “1.” One added feature is that the toe constant compensates for mouths that are wider or narrower than the Normal Scale mouth of 1⁄4 of the circumference. For Flentrop this does not matter, because he used 1⁄4 mouths, but for a builder like Gottfried Silbermann who used 2⁄7 mouths, or Ernest M. Skinner who used 1⁄5 mouths, this compensation is critical, because wider mouths need more wind and narrower mouths need less. The toe constant allows us to compare the relative flow of wind in pipes with different diameters and different mouth widths. A good example in Figure 7 is the 8′ Roerfluit, which has slightly more wind than the 8′ Octaaf. Although it has a much smoother timbre, the 8′ Roerfluit’s slightly more powerful fundamental adds chorus depth to the much brighter 8′ Octaaf.

Toes control power, and in Flentrop organs designed for smaller acoustics I have found toe constants of 0.6 in the lowest mixture pitches, and this is a very restricted toe. A fully open toe has a toe constant of about 4, which we see in the highest pitches of the 2′ Octaaf and III Scherp in Figure 7.

Note the consistency of wind flow in the Flentrop principal chorus pipes at a given pitch, with a minimum flow of wind at about 1′ in pitch and much more flow in the bass and treble. This represents a voicing model for the Saint Mark’s acoustic. Similar patterns of wind flow exist in the 1692 Schnitger organ in the Hamburg Jacobikirche.¹⁴

The wind flow of the 4′ Speelfluit in Figure 7 is very instructive. Its lower cutups, relative to the 8′ Roerfluit, are explained by its more restricted toes. Closing the toe has the tonal effect of raising the cutup for a much warmer timbre at a lower power. The Speelfluit adds color to the more powerful Roerfluit, while restraining the power of the combined flutes as accompanimental stops.

Figure 8 data are estimated flueway depths based on observation of other work by Flentrop. In 1972 I did not have tapered wedges for measuring flueway depths. Wooden wedges are the safest material for documentation, but for a voicer, brass or steel wedges will last longer.¹⁵ The important feature of Flentrop flueways is that they are not used as a primary means of controlling power. Flentrop flueways do vary, but they vary within a restricted range at a given pitch. Neo-Baroque voicing emphasized a cutup recipe set to 1⁄4 of the mouth width with “open toes.” The result was that a voicer was often forced to use very narrow flueways to regulate both power and timbre, and the resulting sound was typically thin in fundamental warmth with a slow, gulping speech on the verge of overblowing. Flentrop used wind pressures and toes to control power, not the flueways, and he adjusted the cutup to achieve the desired timbres with fast speech.

In both modern and ancient work we will find an enormous variation in flueway depths. Although it is very rarely measured, flueway depth is of critical importance in understanding the different sounds of pipe organs. As the flueway deepens, more breathiness is heard in the sound. This is corrected by an increasing amount and boldness of nicking as the flueway depth increases. This is one of the reasons you will find many bold nicks in deep Romantic flueways. Flentrop’s voicing finds the flueway depth that will yield a tolerable breathiness with a minimum degree of nicking, and this is the optimum point for chiff. This is not a deep flueway, but it is much deeper than the razor-thin neo-Baroque flueways that resulted from arbitrarily low cutups. Both Andreas and Gottfried Silbermann used much deeper flueways than Flentrop, and their milder chiff is the result of their bolder nicking. Readers can find the flueway depths for some important historical styles in The Diapason.¹⁶

Figure 9 shows what happens when we divide the area of the pipe toe (the radius of the toe, squared, times π) by the area of the flueway it feeds (the flueway depth times the mouth width). In Figure 9 we see this data as a ratio of those areas. This tells us a great deal about the speech onset of the pipes. If the pipe toe is closed to the point where its area is less than the flueway area, the pressure will drop in both the foot and the flueway.¹⁷ We often see this in organs with higher wind pressures where the toes are strongly reduced to control power. In this situation, however, not only does the pressure drop at the flueway, the buildup of pressure in the foot is slower, and this can lead to slower speech. This form of slower speech is not immediately obvious, but a chorus with ratios above 1.0 will have a prompt attack, while pipes with ratios of 0.5 will have a noticeably slower attack, as is often heard in the smooth solo voice of the classical French cornet.¹⁸ When we look at theatre organs with extremely high wind pressures and deep Romantic flueways, we also find extremely small toes that produce ratios well below 0.5. This is why the attack of theatre organ flue pipes is much slower than what we hear in a Flentrop.

Ultra-low area ratios also explain in part why theatre organ pipes never have chiff. A fast rise in pressure in the foot and flueway is essential to the production of chiff, and we hear this when Biggs crisply opens the pallets on his 1958 Flentrop. Ratios close to 1 or above will be conducive to a fast pressure rise and the production of chiff, and in Figure 9 we can see that no Flentrop pipes have values below 1, and most pipes have values well above 1. This is a feature of Flentrop voicing in all of his organs for which I have data, and it is a significant factor in Flentrop’s fast, articulate voicing. Flentrop flueways are not deep in the Romantic style, and their areas are relatively small, with the result that even Flentrop’s more restricted toes still supply much more wind than the flueways need, and the fast pressure rise produces chiff.

Chiff can be eliminated in any ratio of toe and flueway areas by simply applying many bold nicks, but Flentrop used nicking sparingly, and when it is used, it is typically very fine in nature. Hook voicing also features relatively high area ratios, but the voicers used many bold nicks on every pipe, and no chiff is audible in their voicing. Theatre organs combine ultra-low area ratios with very bold nicking and unsurprisingly never exhibit chiff.

Figure 10 shows the mouth of a Flentrop pipe from about 1980, which is articulate, even with its two bolder nicks. The finest nicking in the center of the languid is more typical of the Saint Mark’s organ. Note that the flueway, while not deeply open in the Romantic style, is much deeper than typical neo- Baroque voicing.

The Pedaal

Figure 11 shows the diameter scales of the Pedaal. The scales of the larger pipes are consistent with the Flentrop model in Figure 3, and the diameters of the larger pipes were measured at the bottom. The Mixtuur is also consistent with the model notes. Like the Hoofdwerk, the flutes trend much wider as the pitch ascends.

The wind pressure of the Hoofdwerk is 80 millimeters, which is interestingly the same pressure found in the restored 1692 Hamburg Jacobikirche Schnitger. All other divisions at Saint Mark’s are winded on a very modest 68 millimeters of pressure, including the Pedaal. Flentrop once commented that wind pressure in a pipe organ is analogous to the tension of strings on a violin, with similar effects in the sound.

When I visited in 1972, the 32′ Prestant featured large ears at the sides of the mouths, and a few years later I observed that large wooden rollers had been added between the ears. This was perhaps an effort to make the 32′ sound more audible, as human hearing is very poor in the deep bass. At about 20 cycles per second we feel sound as much as we hear it, and a 32′ pipe resonates at 16 cycles per second. The addition of the rollers increases audible harmonic power to the sound, just as they add harmonic power to very narrow string pipes. Joseph Gabler found an elegant solution to this problem in his organ of 1750 at Weingarten: drawing the 32′ stop also draws the 16′ stop at the same time, making the sound both felt and more easily heard.

Tin was very expensive when Saint Mark’s Flentrop was constructed, the result of a powerful tin mining cartel. Many Flentrop organs utilized copper for larger façade pipes during this time as an alternative to zinc. The colorful patina on Flentrop copper pipes exhibits reddish earth tones and subtle greens. I asked Flentrop how he achieved this, and he laughed. The process was the result of long experimentation, and it involved strongly heating the pipes and applying the urine of cows to the heated metal. Flentrop smiled when he said that the smell in the shop was not at all pleasant. The lovely pastel colors of those copper pipes enhance the deep reds of the mahogany used in the casework, which Flentrop carefully selected from his supplier in Africa.

The full principal chorus of Flentrop’s magnum opus in its 1981 configuration is electrifying in the Praeludium in E Major by Vincent Lübeck <Soundclip 4>. The organ today features some wonderful additions by the shop of Paul Fritts.¹⁹

Paul Fritts and Company Organ Builders

Additions and changes to pipe organs can result in irreparable harm to the original sound. The additions and changes by the Fritts shop, however, are sympathetic to Flentrop’s original concept. They are exceedingly well executed, and Flentrop’s original voicing was left unchanged.²⁰

In 1991 the console action was replaced with a suspended action. Germanic reeds were added at 16′ and 8′ to the Hoofdwerk, and the horizontal reeds were replaced at their original pitches with designs based on the 1762 work of the Iberian organbuilder Jordi Bosch. The original Flentrop reeds have been carefully packed and stored. The addition of a 32′ Pedaal Bazuin on the back wall to the rear of the Pedaal casework is a welcome one in a room whose large windows consume a great deal of bass sound. These alterations will hopefully diminish future appetites for changes to Flentrop’s historic magnum opus.

The precarious life of historic sounds

D. A. Flentrop’s organs are probably a very good representation of the sound of Arp Schnitger, which has very rarely if ever survived in its original form. Between 1953 and 1955 Flentrop undertook a major restoration of the 1720 Schnitger organ at Saint Michael’s Kerk in Zwolle to return it to its original condition, and Biggs recorded that magnificent sound in the 1960s.²¹ History teaches us that original sounds only survive in the very rarest of circumstances, and these are often found in depressed economies where there is no funding for restorations. Historically important sounds quickly disappear with the good intentions of restorers who change wind pressures, temperaments, pitch, and voicing to suit their own ears.²² This is why early documentation is so important, and it can expose later changes.

This article features a sample of scaling and voicing data from D. A. Flentrop’s magnum opus taken in its original form in 1972.²³ It has hopefully provided readers with a better appreciation of the sound of D. A. Flentrop. Astute readers will also no doubt notice that fifty-one years elapsed before I carefully analyzed this data. I should have done this long ago. Tempus fugit, carpe diem.

Notes and references

All images are found in the collection of the author unless otherwise noted.

1. Barbara Owen, E. Power Biggs: Concert Organist (Bloomington, Indiana: Indiana University Press, 1987), pages 128–133.

2. wikiwand.com/en/Dirk_Andries_Flentrop, accessed July 6, 2023. From their reference: Kerala J. Snyder (Spring 2005), Symposium in Honor of Dirk A. Flentrop, Resonance.

3. Michael McNeil, “The Sound of Gottfried Silbermann,” Part 2, The Diapason, January 2023, pages 13–19.

4. Michael McNeil, “1863 E. & G. G. Hook, Opus 322, Church of the Immaculate Conception, Boston, Massachusetts,” The Diapason, Part 1, July 2017, pages 17–19, and Part 2, August 2017, pages 18–21.

5. McNeil, “The Sound of Gottfried Silbermann,” Part 2.

6. McNeil, “The Sound of Gottfried Silbermann,” Part 2.

7. Michael McNeil, “Designing an Historic Reed,” The Diapason, June 2023, pages 14–20.

8. saintmarks.org/music-arts/organs/the-flentrop-organ/ accessed July 12, 2023.

9. “Plainly audible” reverberation is measured at about -26 dB. The -60 dB architectural standard does not take into account the audibility of reverberation in the context of music, and it is also a source of grave disappointment for musicians and organbuilders. The standard needs to be revised for music.

10. Michael McNeil, “1863 E. & G. G. Hook Opus 322: Church of the Immaculate Conception, Boston, Massachusetts,” Part 1, The Diapason, July 2017, page 18.

11. Email the author for Excel files with the Saint Mark’s Flentrop data and/or the Jacobikirche Schnitger data at no charge at: [email protected]. The Schnitger data is derived and graphed from: Heimo Reinitzer, Die Arp Schnitger-Orgel der Hauptkirche St. Jacobi in Hamburg (Hamburg: Christians Verlag, 1995), with restoration by Jürgen Ahrend and data measurements by Cor Edskes.

12. Ibid.

13. McNeil, “The Sound of Gottfried Silbermann,” Part 2; McNeil, “1863 E. & G. G. Hook, Opus 322, Church of the Immaculate Conception, Boston, Massachusetts,” Part 1.

14. Email the author for Excel files with the Saint Mark’s Flentrop data and/or the Jakobikirche Schnitger data at no charge at: [email protected]

15. Michael McNeil, “The Sound of Gottfried Silbermann,” Part 2, The Diapason, January 2023, see Figure 15 on page 14 for an illustration of a wedge for measuring flueway depth.

16. McNeil, “The Sound of Gottfried Silbermann,” Part 2.

17. Email the author for Excel files with the Saint Mark’s Flentrop data and/or the Jacobikirche Schnitger data at no charge at: [email protected]. The Schnitger data is derived and graphed from: Heimo Reinitzer, Die Arp Schnitger-Orgel der Hauptkirche St. Jacobi in Hamburg, (Hamburg: Christians Verlag, 1995), with restoration by Jürgen Ahrend and data measurements by Cor Edskes.

18. McNeil, “The Sound of Gottfried Silbermann,” Part 2.

19. saintmarks.org/music-arts/organs/the-flentrop-organ/.

20. saintmarks.org/music-arts/organs/the-flentrop-organ/.

21. E. Power Biggs, The Organ in Sight and Sound, Columbia Masterworks, KS 7263, ca. 1969. Many examples of Schnitger organs are included in this landmark recording. D. A. Flentrop wrote a primer on classical organ design for the twenty-eight-page book included with this vinyl recording.

22. Flentrop was right when he remarked that I would use my observations of his work to find my own sound. The temptation to modify organs to the taste of the restorer is very strong, and I have regrettably succumbed to that temptation, too. I carefully documented a Wm. A. Johnson organ and described the changes I made to it in these articles, “The 1864 William A. Johnson Opus 161: Piru Community United Methodist Church, Piru, California,” The Diapason, Part 1, August 2018, pages 16–20; Part 2, September, 2018, pages 20–25; Part 3, October, 2018, pages 26–28; and Part 4, November 2018, pages 20–24.

23. Email the author for Excel files with the Saint Mark’s Flentrop data and/or the Jakobikirche Schnitger data at no charge at: [email protected].

Sound clips

1. [00:34] Johann Sebastian Bach, Prelude and Fugue in A Minor, BWV 543, E. Power Biggs, Bach, the Great Preludes and Fugues, Volume 2, CBS Records, 42648, recorded in 1964 at the Busch Reisinger Museum, Harvard University, Cambridge, Massachusetts.

2. [00:30] Charles-Marie Widor, “Andante cantabile,” from Symphonie IV, opus 13, number 4 (1872), James Welch, Magnum Opus, Volume 2, Wilson Audiophile, WCD-8314, recorded in 1981 at Saint Mark’s Cathedral, Seattle, Washington.

3. [01:01] Carl Philipp Emanuel Bach (often attributed to Johann Sebastian Bach, BWV 565), Toccata and Fugue in D Minor, James Welch, Magnum Opus, Volume 1, Wilson Audiophile, WCD-8111, recorded in 1981 at Saint Mark’s Cathedral, Seattle, Washington. Exhaustive research by Michael Gailit has convincingly shown C. P. E. Bach as the most likely composer of this work. See “Exploring the unknown of BWV 565,” The Diapason, Part 1, June 2021, pages 18–19; Part 2, July 2021, pages 12–14; Part 3, December 2021, pages 16–18; Part 4, August 2022, pages 15–17; Part 5, September 2022, pages 19–21; and Part 6, October 2022, pages 15–17.

4. [00:40] Vincent Lübeck, Praeludium in E Major, James Welch, Magnum Opus, Volume 2, Wilson Audiophile, WCD-8314, recorded in 1981 at Saint Mark’s Cathedral, Seattle, Washington.

—It is strongly recommended to use Sony MDR 7506 headphones for the sound clips. Earbuds will not generate bass sound.

Saint Mark’s Episcopal Cathedral website: saintmarks.org.

Flentrop Orgelbouw website: flentrop.nl.

An analysis by Michael McNeil from data published in 2016 by William Drake, Ltd., Organbuilder

Michael McNeil

Michael McNeil has designed, constructed, and researched pipe organs since 1973. He was also a research engineer in the disk drive industry with twenty-seven patents. He has authored four hardbound books, among them The Sound of Pipe Organs, several e-publications, and many journal articles.

Editor’s note: The Diapason offers for the first time here a new feature at our digital edition—two sound clips. Any subscriber can access this by logging into our website (www.thediapason.com), click on Current Issue, View Digital Edition, scroll to this page, and click on <soundclip> in the text.

John Snetzler

By 1750 England had become a nation with a large middle class with an appetite for music and art performance. “It proved to be a magnet to foreigners such as Handel and J. C. Bach. It is no surprise at all to find a continental organbuilder making a substantial impact in England in the 1750s.”¹ John Snetzler, born in Schaffhausen, Switzerland, in 1710, may have arrived in London as early as 1740. His earliest known instruments date from 1742, one of them a chamber organ at Yale University, New Haven, Connecticut. According to Charles Burney, who knew Snetzler personally, he may have worked on Christian Müller’s famous organ at the Bavokerk in Haarlem, the Netherlands, during its construction in 1735 to 1738.² Although his stop nomenclature looks very much like normal English fare of the time, Snetzler’s sound is much bolder and brighter. This voicing style led to the development of true string tone in Snetzler’s Dulcianas.

Large contracts for English cathedrals eluded him, and Snetzler never achieved the fame of builders like Samuel Green. He produced many smaller chamber organs along with a few larger instruments. According to Bicknell, Snetzler may have been excluded by the remains of the Guild system.

“To claim that Snetzler cornered the market in chamber organs would be an exaggeration, although it is difficult to escape the conclusion that he led the field in re-establishing their popularity.”³ Bicknell was a gifted English writer, fully at ease in organbuilding technology, music theory, and historical context. His description of a chamber organ built by Snetzler in 1763 for Radburne Hall, Derbyshire, but now residing in Schaffhausen, Switzerland, gives a clear idea of Snetzler’s tonal concept:

A pedal raises and lowers the lid of the organ to provide a simple swelling device. In 1982 the organ was very clean and well preserved and still retained most of its original leather work. The pipes had been crudely torn to alter the tuning, but once repairs had been made it became clear that the instrument had been tuned in 1⁄4-comma meantone temperament or something very close to it. The effect, in the home keys, of the Fifteenth and the strong quint and tierce in the Sesquialtera and Cornet is astonishingly bold. The effect of playing a chord of C major, with the tutti very strongly coloured by dissonant intervals in the upperwork, is disconcerting. Moreover, the Stopped Diapason and Flute sound the unison rather weakly, with a very strong first harmonic (the octave quint). The result is that the notes of a G major triad are represented almost as strongly as those of C major. To analyse a chorus in this way is to challenge the very principles of organ tone, and it has to be accepted that the multiple dissonances and consonances found in a principal chorus actually produce a musical effect full of interest and colour. But here, with such a Spartan distribution of the harmonic components and heard at very close quarters the tonality of this or any other chord is highly ambiguous. However, as soon as it is put into musical context, all becomes clear, and the vigour and daring of Snetzler’s method is suddenly justified. The combination of boldly voiced mutations and shifting patters of consonance and dissonance (always a part of a performance on a keyboard instrument tuned to meantone temperament) highlights the harmonic structure of the composition played, and in particular emphasises modulations away from the home key. That home key will itself have its own colour, depending on how many sharps or flats it has. This tonal world is one that is almost completely unfamiliar to modern ears, despite the early music movement and interest in authentic performance: the insights it provides are well worth pursuing.⁴

Snetzler built a chamber organ in 1755 with one of his larger specifications, whose original provenance is unknown but today resides in Clare College, Cambridge, and has survived without significant alterations. The “vigour and daring of Snetzler’s method” can be heard in a Youtube recording of this organ (pre-restoration) of Bach’s Fugue in C Minor, BWV 575.⁵ <soundclip1 here> Although containing only one manual and no pedal, it extends in the English style of the time from GG, AA to f′′′, a compass that descends well into the 16′ octave. The performance of the fugue incorporates the use of this extended bass compass with revisions to the score to accommodate the original pedal line. The balances in the voicing allow all voices to be clearly heard and the emotional impact is startling.

Like other English builders of his time Snetzler used a form of meantone tuning (not heard in the Youtube recording), whose pure or nearly pure major thirds added significant gravity with their low resultants. The gravity of meantone tuning along with the extended manual bass compass goes a long way to explain why the lack of an independent pedal persisted in English organs well into the early nineteenth century.⁶ <soundclip2 here>

But what makes this particular organ most interesting is that it has been restored and documented in unprecedented detail by William Drake, Ltd., who have placed on their website descriptions, drawings, data, and photographs from which Snetzler’s work can be fully understood.⁷ This is no small achievement; organs are almost never documented in such detail.

Preface to the analysis

Good documentation of organs with enough pipe measurements to permit an analysis of both scaling and voicing is extremely rare. Pipe diameters, mouth widths, and mouth heights (cutups) may be found to some degree, but toe diameters and especially flueway depths are extremely rare. William Drake, Ltd.’s documentation of the 1755 Snetzler organ includes all of this and much more—detailed dimensions of the windchest and wind system that allow a full analysis of wind flow and wind dynamics, parameters having an enormous impact on the sound of an organ. A full narrative of the restoration in William Drake, Ltd’s. documentation includes the data that support the very few restorative changes made to the instrument, all of which were guided by carefully documented investigative work.

William Drake, Ltd., gives us a good model for documentation, where they have chosen to provide photographs and detailed hand drawings of the organ along with the important dimensions. While computer drawings are nice, most organbuilders do not have the time or funding to make them. If we want to see good documentation in print, we must also be willing to accept the lack of polish in hand drawings. The editorial staff of The Diapason has shown courage in their willingness to publish such drawings.

The data in this analysis are presented in normalized scales for inside pipe diameters, mouth widths, and mouth heights. Tables showing how raw data are converted into normalized scales may be found in the article on the E. & G. G. Hook Opus 322 published in The Diapason, July 2017, pages 17–19. The set of data and the Excel spreadsheet used to analyze the Snetzler may be obtained at no charge by emailing the author.⁸ Readers interested in a deeper understanding of the models used in the analysis may refer to the book The Sound of Pipe Organs.⁹

Pitch, temperament, wind pressure, and compass

The Snetzler organ is pitched at A = 422.5 Hz at 17.5 degrees Celsius. The current tuning is Young II temperament with indications of original meantone. The wind pressure, water column, is quite low at 51 mm (2 inches). The compass is GG, AA to f′′′. The organ has no pedal but derives bass tone from its extended manual compass, which with its lower pitch extends nearly a halftone below GG. The stops are divided bass and treble:

Bass, GG, AA to b

Sesquialtera (17–19–22)

Principal (4′, full compass)

Flute (4′)

Dulciana (8′, GG to F# grooved)

Diapason (8′)

 

Treble, c′ to f′′′

Hautbois (8′, expressive)

Cornett (8–12–17)

Fifteenth (2′, full compass)

Flute (4′)

Dulciana (8′)

Diapason (8′)

The wind system

The wind system can be modeled from two viewpoints: 1) the restriction of flow from the areas of the wind trunks, pallets, channels, and pipe toes, and 2) the dynamics of the wind. Wind dynamics are fully explained in The Sound of Pipe Organs and are a very important aspect of an organ’s ability to sustain a fast tempo with stability or enhance the grand cadences of historic literature. The superb data set on the Snetzler allows us to explore all of these characteristics. Figure 1 shows the Snetzler wind flow model.

In Figure 1 we see two lists of all of the stops with the pipe toe diameters for a note in each octave in the compass at the top and their calculated areas directly below. These toe areas are then added together (this is the first set of boxed values). The key channels must be sufficiently large to flow wind to these pipe toes, and the pallets activated by the keys must be sufficiently large to flow wind to the key channels.

A model for the total required wind flow of the full organ assumes a maximum of ten pallets (a ten-fingered chord) as described in the next line in the table, and the combined toe areas are multiplied by the number of these pallets played in each octave of the compass. Here we see that the sum of the flow of all of the pipe toes in the full organ (the next boxed value) is 2,982 mm².

Next in the table are values for the pallet opening lengths, the extent that the pallets are pulled open when a key is depressed (estimated from the ratios in the drawings), and the height and widths of the key channels that are fed wind by the pallets. These data allow us to calculate the relative wind flow of the channels (height times width), and we find that there are robust margins in the windflow from the channels to the pipe toes (see the boxed values of 201% at low GG to 549% at high c′′′).

Now we can calculate the flow of the pallets that feed the channels (the sum of the opening length and channel width times the pallet pull), and we find the ratio of the flow of the pallet openings to the channels (the next boxed values) is less robust and ranges from 88% in the bass to 187% in the high treble. The pallets still adequately flow wind to the bass pipes when we consider the more robust margins in channel flow. The estimate of the pallet pull may also be low. It is interesting to speculate that pallets that just barely flow the required wind to the channels may allow some degree of modulation of touch to the organist. Smaller pallets also require less force to open and are easier to play.

The next value, the area of the wind trunk, is 10,230 mm², and we see that the area of the wind trunk affords 3.4 times more wind than all of the pipe toes in the full organ, so much in fact that it does not function as an effective resistance in the system. Interestingly, the Isnard organ at St. Maximin uses the wind trunk as a strong resistor to dampen Helmholtz resonances in the wind system, and it has a ratio of wind trunk area to a plenum toe area of 1.07 for the coupled principal chorus of the Grand-Orgue and Positif (no reeds, flutes, or mutations). Helmholtz resonances are the source of what is normally called wind shake, and we might expect some mild wind shake with the Snetzler wind system with its large wind duct and low damping.

The underlying dynamics of a wind system are the result of its mass and volume. These factors produce a natural resonance that can enhance the grand cadences of literature with a long surge in the wind, or it can produce a nervous shake if it is too fast. A grand surge in the wind is characterized by a resonant frequency of less than 2Hz (cycles per second), and it is most often produced by a weighted wedge bellows. A nervous shake is characterized by much higher resonant frequencies, and it is produced by a sprung, vertical rise bellows with low mass. We correct the latter condition with small concussion bellows in modern organs, but the Snetzler wind system does not have such devices; instead, it features a weighted wedge bellows.

We can model the dynamic response of an organ by using its wind pressure, the area of the bellows plate, and the combined internal volume of its bellows, wind trunk, and pallet box. The model in Figure 2 shows the dynamic response of the Snetzler wind system at a relaxed 1.52 Hz, producing a wind surge of 0.66 seconds. William Drake, Ltd., found that the original wedge bellows had been modified to a vertical rise design, which the model shows would have resonated at about 2.26 Hz with 0.44 seconds surge, and they wisely restored the original design. The restorers found that with the wedge bellows, “The wind is lively but smooth and enhances the sound in a musically pleasing way.”⁷

The scaling

The Normal Scale of pipe diameters is a way to visualize relative power, where a flat line from bass to treble will produce relatively constant power. Pipes with data extending higher in the graph will produce more power. Each half tone on the vertical scale is worth 0.5 dB of power. Readers may refer to The Sound of Pipe Organs, pages 8–32, for a discussion of the underlying theory and principles. The Snetzler metal principal chorus pipes have a constant scale where all pipes of the same pitch have the same diameter regardless of the stops in which they appear. Snetzler mildly increased his treble scales from about 1⁄2′ in pitch in Figure 3, a reflection of the smaller acoustics of chamber organs and less need to compensate for distance losses. The flute has wider treble scales. The Snetzler Dulciana descends dramatically; it shares the bass with the Diapason. The scales of the wood pipes are represented by their diagonals, not their relative areas; this represents the true power capability of the standing wave in the pipe, as pointed out by John Nolte, and correctly relates to metal pipes. The GG compass is represented by notations on the pitch axis as “10, 5, 2.5,” indicating rough approximations of the length in feet for the extended bass compass.

The Normal Scale of mouth widths operates just like the pipe diameters, where a flat line from bass to treble will produce relatively constant power. Pipes extending higher in the graph will produce more power. Each half tone on the vertical scale is worth 0.5 dB of power.

Mouth widths are nearly always a better indicator than pipe diameters of power balances; this is because mouth widths can be designed to vary considerably within the same diameters of pipes. Narrower mouths will produce less power, other voicing parameters like flueways and toe diameters being equal.

In Figure 4 we see that Snetzler greatly reduced the mouth widths of the 8′ Diapason and the 4′ Flute. The mouth width reduction of the Diapason in Figure 4 reduces the power to blend seamlessly into the tenor of the Dulciana; it also makes the upperwork seem relatively much more powerful. This example of the seamless blend of the Snetzler mouth widths for the Diapason and the Dulciana shows why it is often advantageous to use mouth widths, not diameter scales, to understand the balances of power in a chorus. The Dulciana has very narrow mouths consistent with its role as a soft string stop.

The voicing

Mouth height, or “cutup” as it is commonly called by voicers, is the primary means of adjusting the timbre of a pipe. Low cutups will create a bright tone with many higher harmonics while high cutups will produce smoother tone. Readers may refer to The Sound of Pipe Organs, pages 68–80. It is not uncommon to find flute pipes cut as much as 12 half tones higher than principal pipes in classical pipe organs.

In the Normal Scale of mouth heights, a higher cutup value on the vertical scale will result in smoother tone. Cutups may be adjusted higher for two reasons: 1) the voicer wants a smoother timbre, or 2) the voicer wants more power at the same timbre. More power means more wind, and this means a larger toe or flueway opening to admit more wind. More wind will always produce a brighter tone, so the voicer can make a pipe louder and preserve the original timbre by opening the toe or flueway and raising the cutup until the timbre is restored.

Pipe toe diameters can be normalized (this is the “C” parameter in Figure 6) to the diameter of the pipe, the width of the mouth, and the depth of the flueway; larger values of “C” will admit more wind to the pipe. Readers may find the derivation of this normalization in The Sound of Pipe Organs, pages 43–47.

Now we can understand the Snetzler graphs. In Figure 5 we see exceptionally low cutups in the bass that are low even for the very modest 51 mm. pressure. Snetzler’s use of bold nicking on the languids of the bass and mid-range pipes stabilizes the speech with such low cutups. This is consistent with the “slower” speech of Snetzler’s voicing, where the languids are kept high and the resulting timbre is brighter (the speech is not actually slower, just brighter—the pipes are slower to overblow to the octave on higher pressure).¹⁰ Gottfried Silbermann took this concept to an extreme with upper lips constructed to extend far in front of the flueway; this virtually required the voicer to raise the languid well above the edge of the lower lip, with the consequence that the timbre became very bright. Snetzler was more moderate in his use of this voicing technique.

But lower mouth heights can also be explained by reduced toe diameters, and we see very consistent and greatly reduced toe diameters for the Snetzler upperwork in Figure 6 where only the wood pipes of the 8′ Diapason and 4′ Flute have generous toes. As we will see later, those wood pipes also have reduced flueways. The reduction in toe diameters in Figure 6 reduces the wind pressure at the mouth of those stops, allowing the use of lower cutups.

Of interest in Figure 6 are Snetzler’s very reduced toes on the 8′ Dulciana stop. This is consistent with the very low mouth heights of this stop in Figure 5, giving the stop low power with significant harmonic overtone structure; Snetzler used box beards to stabilize the speech of the Dulciana. Taken together, this is a very powerful demonstration of Snetzler’s skills in scaling and voicing where he achieves good balances with the metal chorus pipes and the common bass with the Dulciana.

Like the pipe toe, flueway depth controls the flow of wind and strongly correlates to the power and the speed of the speech of the pipe. Readers may refer to The Sound of Pipe Organs, pages 50–63 and 77–82.

In Figure 7 we see very generous flueways for the metal pipes of the Snetzler chorus, while the wood pipes and Dulciana have much more restrained flueways. In the chorus pipes Snetzler is controlling the power balances with scaling and toe diameters, not flueways, a technique more commonly found in classical French voicing. The reduced flueways of Snetzler’s wood Diapason and Flute are more typical of classical Germanic voicing, where power is controlled at the flueway rather than the toe. It is unusual to find a chorus with both voicing styles.

The languids are boldly nicked at an angle in the bass pipes progressing to finer nicks in the higher pitches and ultimately little or no nicking in the highest trebles. Ears are present on pipes up to 1-1⁄3′ pitch and absent at higher pitches. Upper lips are lightly skived to about one half of the metal thickness.

The flow of wind and power balances are controlled by the voicer at the toe and flueway of a pipe. The ratio of the area of the toe to the area of the flueway is important. If the area of the toe is less than the area of the flueway, which is a ratio less than “1,” the speech will be slower. “Slowness” in this instance does not refer to the voicer’s term (which reflects how the voicer adjusts the relative position of the languid and upper lip), but rather to the effect of resistances (toe and flueway areas) and capacitance (volume of the pipe foot) on the rate of the buildup of pressure at the mouth, which in turn affects the buildup of pipe speech to full power. Readers may refer to The Sound of Pipe Organs, pages 56–63 and 114–116, for a discussion of this very important musical characteristic. A well-knit chorus of pipes may have pipes that speak less promptly or pipes that speak more promptly, but never both; a chorus with both would have a confused and ill-defined attack. The effect here is subtle and measured in milliseconds, but the human ear is very sensitive to such fine variations.

The ratio is exactly “1” when the area of the toe and flueway are equal, and this is the normal lower limit for pipes with prompt speech; for example, the vast majority of the principal chorus pipes in the Isnard organ at St. Maximin in the range of 4′ to 1′ pitch exhibit a value of almost exactly “1,” with the highest pitches approaching a value of “3.”

The wood pipes of the 8′ Diapason and 4′ Flute in Figure 8 have ratios far in excess of “1,” and this is another way of looking at Snetzler’s technique for pushing these pipes harder with their narrower mouth widths and narrower flueways. In stark contrast, the Snetzler metal pipes have ratios trending at or well below a value of “1,” suggesting that they speak a bit less promptly. The recording made by Anne Page prior to the restoration demonstrates the full chorus and supports this conclusion. Slightly slower speech is not necessarily a defect, and it can be used to dramatic advantage.

Very rarely do we find anything in the organ literature about voicing, and very rarely do we find documentation with enough data to analyze the voicing of an organ. With William Drake, Ltd.’s data we can understand Snetzler’s voicing and tonal concepts in depth.

Further paths

This short essay cannot begin to do justice to the documentation done by William Drake, Ltd., on the Snetzler organ. Readers are encouraged to visit their website to view their wonderful PDF files.⁷ The casual reader can simply peruse the photos and notes to see what the inside of an eighteenth-century organ looks like. The motivated organbuilder can fully recreate the Snetzler sound from these notes. This is a gold standard of documentation.

Notes

1. Stephen Bicknell, The History of the English Organ, Cambridge University Press, 1996, Cambridge, p. 174.

2. Ibid, p. 174.

3. Ibid, pp. 203–204.

4. Ibid, pp. 204–206.

5. Anne Page, Fugue in C minor, BWV 575, www.youtube.com/watch?v=slgjVr97FLY. This is a pre-restoration recording made during the 2011–2012 time frame. The volume is set very low in this recording and should be turned up. It is important to keep in mind that the tuning has been modified from its original meantone to something much closer to modern equal temperament.

6. The gravity induced by meantone must be heard to be appreciated. The 1739 Clicquot organ at Houdan is tuned in meantone and may be heard to advantage in the superb new recording reviewed in The Diapason, July 2018, p. 15, Magnificat 1739, Regis Allard, available from www.editionshortus.com. This organ has no 16′ stops, but 16′ tone is strongly evident in the resultants of the pure major thirds.

7. William Drake, Ltd., The Restoration of the 1755 John Snetzler Organ at Clare College, Cambridge, PDF documents accessed August 16, 2016, www.williamdrake.co.uk/portfolio-items/clare-college-cambridge/.

8. The author’s email address is: [email protected].

9. Michael McNeil, The Sound of Pipe Organs, CC&A, 2012, Mead, 191 pp., Organ Historical Society and Amazon.com.

10. The History of the English Organ, p. 178, “Snetzler’s chorus consists of ranks all made to the same scale and voiced at the same power . . . . The speech of the individual pipes is significantly slower than that of earlier generations, and this encourages brightness (as well as facilitating the development of the new string-toned stops). Any tendency of the pipes to spit or scream is controlled by the consistent use of firm, slanted nicking on the languids of the pipes—a hallmark of Snetzler material.” Joost de Boer, the director of William Drake, Ltd., confirmed the use of higher languids and slower speech on the Snetzler pipes in a personal communication in 2018.

Michael McNeil

Michael McNeil has designed, constructed, and researched pipe organs since 1973. He was also a research engineer in the disk drive industry with twenty-seven patents. He has authored four hardbound books, among them The Sound of Pipe Organs, several e-publications, and many journal articles.

Very few organs survive the depredations of time. Some are the victims of wars and fires, but most are the victims of the good intentions and interventions driven by changing tastes in sound. Those few that have survived such calamities usually have something special about them in their sound or their visual impact. The 1750 Joseph Gabler organ at Weingarten, Germany, is special on both counts—its dramatic chorus makes music come alive, and the architecture of its casework and façade is a stunning tour de force.

The Gabler organ has been criticized since almost the time it was built for its lack of power, having almost a chamber instrument quality. But the Gabler organ has a dramatic flair and musicality that sets it apart from most pipe organs, perhaps teaching us some valuable lessons in tonal design.

Human sensory perception takes notice only of changes. The old joke about cooking a live frog has more than a grain of truth to it. Place a frog in hot water, and it jumps out; raise the temperature of the water slowly, and the frog will take no notice and become dinner. It is the same with sounds. If a sound does not change, we do not notice it or we lose interest. Gabler was a master of the control of change in sound, and this is the heart of the drama in his organ. By way of example, Johann Sebastian Bach’s early composition, the Toccata in E major, BWV 566, requires an organ with a dramatic sound to pull it off, not just a loud organ. Peter Stadtmüller’s 1975 recording of BWV 566 on the Gabler organ takes us to new emotional dimensions <soundclip1>.¹ The Gabler organ’s lessons go to the heart of musicality.

In 1986 Friedrich Jakob and the organbuilding firm of Kuhn published a wonderful book on the Gabler organ at Weingarten. Die Grosse Orgel der Basilika zu Weingarten is available from Orgelbau Kuhn AG, Männedorf, Switzerland.² We are very fortunate that Jakob and Orgelbau Kuhn took the time to write this book and publish it. In an effort to better understand the sound of this instrument, I translated some of its passages with Google Translate, edited the translation as an organbuilder would understand it, and then graphically analyzed the data from the appendix of this book. This is but a very small part of what this book has to offer, and those seriously interested in this organ should purchase this wonderful book.

The current basic specifications of the organ after the restoration by Kuhn are:

Manuals: compass C to c′′′, 49 notes; pitch a′ = 419 Hz at 15 degrees Celsius; wind pressure = 70 mm water column.

Pedal: compass C to d′, 27 notes (originally C to g); pitch a′ = 419 Hz at 15 degrees Celsius; wind pressure = 70 mm water column.

Orgelbau Kuhn restored the Gabler organ between 1981 and 1983. The work was carried out partly in Männedorf, partly in Weingarten, and was summarized as follows:  

A. Static remedial measures:

• Renovation of the gallery floor, partial replacement of supporting beams. 

• Improvement of the Kronpositiv position. 

• Improved support for the bracing of the Positive chest.

B. Removal of added features:

• Demolition of the additional works built in 1954.

• Rebuilding of the Barker machine and restoration of the continuous direct mechanics.

• Rebuilding of the electric trackers for the Kronpositiv, reconnection to the Oberwerk by means of the original conductor blocks.

• Rebuilding of the numerous bellows as well as the newer wind ducts and blower system.

• A reconstructed wind system with six wedge bellows.

C. Normal cleaning and restoration work.

• Make the whole organ wind-tight again.

• Treatment against wood pests. 

• Reworking of all mechanical parts, in particular the axle points. 

• Repair and reconstruction work on the pipework. 

• Tuning in an unequal temperament.³  

Pipework repair

Orgelbau Kuhn performed the normal repairs on pipes that would be expected from centuries of tuning damage. Split pipe seams and loose languids were resoldered, deformed pipe bodies were rounded, and new sections were added to the tops of damaged pipes. 

The effect of the wind system on sound dynamics

The dynamic response of the Gabler wind system is one of most important aspects of its dramatic sound. While measurement data of the wind system is lacking, Orgelbau Kuhn carefully described what they found and what they changed:

The Gabler wind supply in the north tower had already been replaced for the first time in the work of 1861/62. In place of the six original wedge bellows, there were ten box bellows of a new design. Probably in 1912 during the installation of an electric blower the wind system was again modernized by the construction of a large, so-called double-rise bellows.

In the course of the restoration, six wedge bellows were again set up, however, according to practical requirements, with motor operation. The old beams of the bellows chamber did not allow any definite conclusions as to the former position of these six bellows, so free assumptions had to be made.

The original wind duct system, in so far as this had not been done earlier, was practically completely expanded in 1954 and replaced by a new version with cardboard pipes. On the basis of a large number of traces (cut-outs on the casework, color traces on the walls, cut-outs on the beams and on the grids, as well as on the original windchest connections), the course as well as the dimensioning of the Gabler wind duct system could be known.

In three places, where it was obviously not possible to expand, some of the original ducts were preserved. On the one hand, these are the supply ducts to the two Rückpositives under the floor, on the other by a section of the connecting channel above the façade middle flat. This remainder was of particular importance. This is a double channel (57 x 17.5 cm outer dimensions) with a middle wall. The upper part of the duct is marked with “Manual” and the lower part with “Pedal” with a weakly readable red pencil. This was the proof of the actual execution of the wind separation for manual and pedal, which was already required in the contract.⁴

Data on the size of the bellows, ducts, and pallet boxes would allow a calculation of the capacitance (volume) and the inductance (mass, or weight on the bellows) of the wind system. From this data the resonant frequency could be calculated, giving insight into the slow, dramatic risetime of this wind system on full demand. What we do know from the elegant layout drawings of the Gabler organ by Orgelbau Kuhn is that the wind ducts were very long, and the cardboard ducting from 1954 (heard in the 1975 recording by Peter Stadtmüller) was apparently larger in cross section. (“In three places, where it was obviously not possible to expand, some of the original ducts were preserved.”⁴) This means that the internal volume of the wind ducts was larger in 1975, and the sheer length of the ducting indicates a very large internal volume for the entire wind system.

In the 1975 recording we hear a very long, slow surge in the sound of the full pleno driven by a very low resonant frequency in the wind system, and this is a large part of the dramatic sound of the instrument. Such a slow wind system obviously forces a slower tempo, and that is how Stadtmüller interpreted the Toccata in E Major in the glorious acoustics of the basilica. From this we see an essential component of dramatic change: a slow buildup of power when the full organ is played and the wind system is forced to work hard <soundclip2>.¹ The current sound of the organ post-restoration still retains a very dramatic sound, but it is slightly faster, and may be the consequence of the smaller ducting cross sections with less capacitance.¹⁵ When asked about the pipe organ, Igor Stravinsky is reported to have said, “The monster doesn’t breathe.” Although it may have been unintended, Gabler’s gift to us is that he makes the organ breathe.

To put this into perspective, the author took careful measurements in 1996 of the J.-E. & J. Isnard wind system on their organ at St. Maximin, France, and calculated its resonant frequency to be 1.2 cycles per second, a value that correlated very well with actual measurements of the slow, grand surge of this wind system.⁵ Although it is not as long a surge as what we hear in the Gabler organ, the J.-E. & J. Isnard organ at St. Maximin also features a dramatic buildup in power on full organ, the result of high capacitance and high mass in the wind system.

Famous organs with dramatic chorus effects, e.g., the Isnard at St. Maximin, tend to exhibit a purposeful starving of the wind supply where the total area of the toes that can be played in a full plenum are roughly equal to or even greater than the cross section of the wind duct that feeds them. Gabler’s reduction of ranks in the Kronpositiv to alleviate wind starvation, as noted by Orgelbau Kuhn, does indeed suggest that Gabler restricted the cross sections in his ducting. To more fully understand the wind flow of this organ we need measurements of the ducting, pallet openings, channels, and pipe toe diameters for each division.

The effect of the mixture designs on sound dynamics

Pipes are very effective sources of change in sound when they are out of tune (think of the richness of a celeste). We also hear complex dynamic changes in the sound when the speech transients of many pipes combine to form a complex onset of speech in the attack of a chord. The most obvious sources of tonal change are Gabler’s immense mixtures that contain as many as twelve ranks in a single stop. His Sequialters are also constructed of many ranks, and they are scaled exactly like the mixtures. The combination of the Hauptwerk Mixtur, Cymbalum, and Sesquialter contains a vast number of pipes that, as Jakob nicely phrased it, have the effect of a “string choir.”

Multiple ranks at the same pitch do not produce significantly more power (the power increase of doubling the pipes at a single pitch is the square root of 2, or 1.4 times the power). The significant effect is in the depth of the chorus, which is heard as subtle celesting (mistuning) in sustained chords, and which is also heard in the attack of a chord where many pipes speaking together have subtle differences in the speed of their speech and their harmonic content. To some degree these effects are mitigated by the “pulling” effect; pipes of the same pitch placed closely together on the same channel will tend to “pull” each other into tune. But the Gabler chorus has not only many duplicated pitches in a single mixture, it has three such mixtures on the Hauptwerk with limitless possibilities for subtle mistuning effects. The upper pitch ceiling in Gabler’s mixtures is a 1⁄8′ pipe. The preponderance of mixture tone resides in the region from 1⁄2′ to 1⁄8′ pitch, precisely the frequencies to which human ears are most sensitive.

Understanding the sound of the Gabler organ

The appendix of the book contains wonderful data on pipe diameters, mouth widths, and mouth heights (cutups). No data exists on the diameters of the toe openings or the depths of the pipe flueways. This data would allow us to understand the very high cutups of the pipework in this organ. Furthermore, the ratio of the areas of toes to flueways plays a large role in the speech of these pipes. We can only hope that this data will someday be made available. The very useful reed pipe scales in the appendix would benefit from additional data on shallot opening widths, tongue lengths from the tuning wire, tongue widths, and tongue thicknesses, all of which would help us to better understand the sound, especially the very effective Pedal 16′ Bombarde.

Orgelbau Kuhn addressed the low power of the Gabler organ in their description of its scaling and voicing.

The sound of the Gabler organ was already felt as comparatively weak, often as too weak. From the construction period, there were no complaints, because the deadlines and costs were too much in the foreground. Even so, the sound development must have been perceived as partially deficient. This is borne out by the various supplementary technical measures taken by Gabler to increase the sound: the lifting of the roofs by means of cable mechanics, the opening of the side walls of the Oberwerk and the Pedal. All these changes, however, did not benefit much. The reason lay deeper . . . .

The weak sound of the Gabler organ . . . finally led to the construction of auxiliary works, along with stylistic considerations as a result of the altered sound tastes of the time. This resulted in 1912 in the construction of the Seraphonwerk with seven high-pressure registers (150 mm water column) as well as the supplementation of the Kronpositiv by a Cymbal.

What is the source of the relatively weak sound, or rather the relatively low decibel performance of this organ? According to our findings, there are essentially four. The scales of the pipework by Gabler, the sometimes precarious wind conditions, the inhibited sound egress due to Gabler’s compact design, and finally the throttling by the narrowing of the toeholes of the pipes. The number of nicks is irrelevant in this context.

Orgelbau Kuhn pointed to the casework as a source for the low power of the organ.

A[nother] reason for the relative weakness of the sound is to be found in the comparatively small openings for egress of the sound . . . . The big façade pipes are very closely spaced. Apart from the triangle openings around the pipe feet only very narrow slots between the pipes are available for the egress of sound.

Interestingly, images of the façade show that Gabler added carved ornaments between the feet of the façade pipes, further blocking the egress of sound.

Massive, unperforated pipe shades also reduce the egress of sound. While the three problems of scaling, wind supply, and compact construction were already present, the fourth problem only arose as the organ aged: the narrowing of the toe holes due to the very steep angles of the toeboard bore chamfers on which they sat. Last but not least, it was also due to late maintenance. This secondary damage was discovered and corrected in the course of the restoration, while the other characteristics of the Gabler style, of course, remain untouched.⁶

Scaling

The scaling of the Gabler organ is unusually narrow for such a large acoustical space. And unlike the French who scaled their foundations wide but kept the upperwork stop scales narrow, Gabler uses a constant scale, which is narrow in both the foundations and upperwork. Why would Gabler do this? The answer may lie in the layout of his unusual principal chorus, which with its enormous mixtures looks more like an ancient Blockwerk than a typical chorus of his time. Here is Orgelbau Kuhn’s description of the problem:

We can only confirm: Gabler had difficulty with the scales. It is not only in the strings, but in general, that the composition of the scaling is quite narrow. Obviously, he looked at the size of the scales as an absolute one, whereas in reality they were dependent on space. For the giant room of the Weingartner Basilica, respectable distance considerations were appropriate. As a result of these under-nourishing scales, the principal is already near the strings, while the strings are already struggling against the frontier, where a clean, precise, and reliable approach to the fundamental tone is scarcely possible.

That is why Gabler also had to make extensive use of voicing aids, not only of nicking, but also of other voicing aids such as front and box beards. By making use of these aids, at least, all the pipes were able to speak in the fundamental, but a development of the power of the organ was not possible.

Gabler sought to compensate for this scaling deficit through numerous double-ranked and multiple-ranked voices. In the mixture voices, Gabler goes much further. In the Hauptwerk, for example, he built the Mixtur 2′ with ten ranks, the Cimbel 1′ with twelve ranks, and the Sesquialter with nine ranks. Through these chorus effects, Gabler sought to achieve sound power, a power that was not due to the too narrow scales. As we have seen in the Kronpostiv, but also in the Mixturbass, he had wanted to go further in this direction of multiple ranks, but he was, to a certain extent, overtaken by the second evil: he came to the limits of the wind supply. The long wind trunks made an inadequate supply, so that in the course of the work he was forced to cut back on the number of ranks (in the Kronpositiv, for example, a reduction from 18 to 2 ranks).

This struggle for sound and wind is clearly visible to the expert on the evidence in the construction. This desperate wrestling resulted in a great success. But it is clearly a struggle and not a virtuosic play with the principles of organbuilding. The result is a result of the struggle and not artistic design.⁶

The wonderful scaling data in this book was entered into a spreadsheet that normalized the measurements into Normal Scales for pipe diameters, mouth widths, and mouth heights (or “cutups” to a voicer). This graphical presentation allows a much easier interpretation of the data. A set of graphs of the Hauptwerk (Figures 7, 8, and 9) and Pedal (Figures 10, 11, and 12), with commentary, are presented at the end of this article.

The graphs of the pipe diameters (Figure 7) corroborate Orgelbau Kuhn’s assertion that much of the low power was due to narrow scaling. Mouth widths are usually a better indication of relative balances of power, but Gabler used mouth widths that were generally very close to the normalized mouth width scale (one fourth of the pipe circumference), and as such, the normalized mouth width scales (Figure 8) are very similar to the normalized pipe diameters.

The normalized mouth height (or cutup) scales (Figure 9) are remarkable. Gabler’s mouth heights are generally fairly low in the bass increasing to extremely high values in the trebles, so high in fact, that 1⁄8′ pipes are cut up roughly 40% of their mouth widths. The relatively high mouths would suggest pipes with very open toes and flueways, although this data is unfortunately not tabulated. 

Gabler knew how to use very wide scales, but he only used them in his flutes (see the graph of the Hauptwerk, Figure 7). Is Gabler showing us what a Gothic chorus would look like? The chorus effects of these multiple-ranked mixtures are astounding, unique, and very musical. Chorus dynamics, not power, may have been his objective. The subtle imperfections of tuning in these ranks produce subtle celesting on a grand scale. Subtle differences in voicing will produce a rich chorus effect resulting from random differences in the speech onset of the pipes in these mixtures. Gabler may have aimed at the grand sound of a Gothic Blockwerk, not loud, but rich in texture and chorus effects.

Few unmolested pipes remain from the Gothic period, much less complete organs, but one example stands out: the 1475 organ by da Prato in the Basilica of San Petronio, in Bologna, Italy. As recent research shows, this organ is largely original and serves as an elegant example of a Gothic chorus.⁷ The author graphed and combined the data for both the Gabler and da Prato organs. In Figure 1 we see data for normalized pipe diameters, and in Figure 2 we see normalized mouth widths. The data for the da Prato chorus extends to 24′ low F; the 32′ value is a straight-line extrapolation of the 16′ and 24′ da Prato data.8 The Gabler chorus includes the Hauptwerk and Pedal pipes, which extend to 32′.

Scaling data are intrinsically noisy; variations from the intended scale are produced both by the pipemaker and by the person who measures a pipe. Variations of +/- a halftone are normal. The data are remarkable because both sets of data converge on the same intended diameter and mouth scale. We do not know if Gabler imitated the da Prato scales or any other Gothic design, but the similarity of the Gabler and da Prato scales is unquestionable. The dotted black line represents the approximate intended scale, the red lines represent the actual Gabler pipes, and the blue lines represent the actual da Prato pipes.

Gothic pipework (Figure 3) from an organ by an unknown builder in Ostönnen, Germany, exhibits an unusual design characteristic also seen on the façade pipes of the Gabler organ (Figure 4). Figure 3 shows an extension of the upper lip at the sides of the mouth (red arrow), making the mouth width slightly narrower than the width of the flueway.⁹ We do not know if Gabler was taking his cue from a Gothic model, but the comparison is interesting.

Voicing

The minimum data set to understand the voicing of an organ includes the mouth height (“cutup”), toe diameters, flueway depths, treatment of the languids (bevel angles and types of nicking), and presence or absence of ears and other such devices. Like the da Prato organ of 1475, the Gabler organ exhibits no ears on the façade pipes and presumably none on the internal pipes of the principal chorus. Orgelbau Kuhn provides data on cutups, but not on toe diameters or flueway depths. Voicers adjust toe diameters and flueway depths to affect the flow of wind for more or less power. Voicers raise cutups to make the pipe tone smoother with less harmonic bite. More wind, from either the toe or flueway, will increase power and make the tone brighter with more harmonic bite. A more powerful and brighter timbre can be made smoother again with higher cutup. Hence, it is important that we know all three variables—cutups, toe diameters, and flueway depths—if we are to understand the voicing. We have only mouth height data. 

A common precept of neo-Baroque voicing was the rule that the mouth height should be 1⁄4 of the width of the mouth. There is, of course, no basis for this in historic work, nor is there any theoretical basis, and it produces a rather strident timbre in most pipework. The normalized mouth heights of the Gabler organ, seen in Figure 5, are remarkable. Only in the bass do they approach a value which produces a height 1⁄4 of the mouth width (this occurs when the normalized mouth height scale in halftones is the same as the normalized mouth width scale in halftones). But as the pitch ascends for the Gabler pipes, so do their normalized mouth heights, until at the highest 1⁄8′ pitches the mouths are very high, about 40% of their mouth widths. Also of note is that the treble mouth heights of the principal chorus are almost as large as the mouth heights of the very wide flutes in the Hauptwerk. The same trend is seen in Figure 6 of the da Prato mouth heights, but the typical da Prato values are lower, a reflection of that organ’s lower wind pressure. The highest mouths in the da Prato graph are also those of its flutes. Gabler’s treatment of mouth height looks very much like the Gothic work of da Prato, adjusted for higher wind pressure.

Reiner Janke sent the author photos of pipe mouths from the 1743 choir organ at Weingarten, also built by Gabler. These photos show very generous flueway depths and deep, fine nicking. Although we do not have toe diameters to confirm this, it may be reasonable to assume that Gabler’s high mouth heights in the treble reflect a desire for a more ascending treble.

Orgelbau Kuhn limited their analysis of the voicing to the presence of nicking and the method of tuning:

While ‘tuning’ means the mere regulation of the pitch, the ‘voicing’ includes the processing of all partial aspects of a musical tone, including the loudness, the tone color, the tone accent, or the transient response. This eminently artistic work is generally performed only when a new organ is being built, or when a major rebuilding is carried out.

A restoration, especially if it also includes changes or regressions in the wind supply system (bellows and wind duct system), also causes a new voicing of the pipework. It is necessary to think philosophically about the original Gabler voicing, and it would be wrong to assert that it had remained intact, for the intervening interventions were too great. Of course, we did studies on other Gabler organs, but also on instruments of other South German masters such as Holzhay and Höss, but there were no exact models for the voicing in the Weingarten types, one simply had to work with the existing pipe material. The technical procedure can be easily rewritten. First, the pipes were normalized and repaired where necessary (open solder seams and loose languids soldered). The languids were then carefully placed in the correct position for an optimal response to the pipe in the fundamental. In the rest, as little as possible was changed.

Gabler has made extensive use of nicking. This can be seen in the non-speaking but voiced façade pipes c′–d′ of the Kronpositiv, which are completely unchanged. In addition to the original nicking of Gabler, the main body of the pipes also contains nicking of other handwork. It turned out to be impossible to assign only the newer nicking, but to leave the Gabler nicking unmarked. So it was decided not to work the languids; the insertion of new languids was not considered at all . . . .

The labial bass pipes are provided with cleanly inscribed tuning slots proportioned to the pipe diameter up to the 2′ position. Attempts have shown that stops without these tuning slots could not be tuned over the entire range of octaves. These tuning slots are therefore to be regarded as original. In contrast to later practices, however, these tuning slots are only scribed and not fully enrolled.

Tuning 

The absolute pitch is A = 419 Hz at 15 degrees Celsius. The original temperament was very similar to Gottfried Silbermann’s meantone. It was characterized by eight not pure, but good, major thirds, eleven tempered fifths, and one large Wolf fifth on D-sharp to G-sharp. It had an equal temperament fifth at C, extending to -12 cents at G-sharp and extending to +5 cents at D-sharp.

The current milder tuning deviates from the original meantone and has an equal temperament fifth at C, extending to -9 cents at G-sharp and extending to +1 cent at D-sharp.10 It is not known if the Musical Heritage Society recording of 1975 reflects Gabler’s original tuning or something closer to the present tuning.1 Like Gottfried Silbermann, Gabler uses high cutups in his voicing for a less strident timbre, and this works well with meantone temperaments, mitigating the harshness of the more dissonant intervals.

Reflections

Friedrich Jakob reflected on the sound of the Gabler organ:

How is the sound of the Gabler organ to be characterized? We are confronted with the general problem of describing sound with words. With features such as warm, round, pointed, sonorous, bright, and so on, no exact statements are possible. Still, be tempted.

The Gabler organ is certainly not a forceful organ. Power and brilliance are missing in comparison to the normal large organ. The sound is somewhat reserved, veiled, poetic, and pastel colored. The tremendous multiple ranks of the mixtures give the effect of a string orchestra. Minimal deviations of the individual voices do not result in any false tone, but a larger range of the right one. It was very important to leave the organ intimate in character with the chamber music and not to have a wrong symphonic influence. But since everything is wind-tight again, and every pipe is speaking the fundamental, the organ sounds a little more powerful than before.¹¹

The claim has been made that Gabler did not understand the principles of scaling as they relate to larger rooms, and Jakob describes very convincing evidence that Gabler struggled with the power. But the inflection point of Gabler’s constant scale at 1⁄2′ demonstrates that Gabler had a good grasp on the effect of distance on the sound absorption of higher frequencies. Tones extending from the deep bass up to the pitch of a 1⁄2′ pipe will carry very effectively over long distances, but pitches above that point will lose energy in their interaction with the atmosphere, so much so that the sound of a 1⁄8′ pipe will lose 5 dB in power at 500 feet.¹² One halftone of scaling is equivalent to 0.5 dB of power, so this means that 10 halftones of wider scaling must be used at 1⁄8′ to compensate for the atmospheric losses at 500 feet. Gabler widened his mixture pipes by 8 halftones from 1⁄2′ pitch to 1⁄8′ pitch. The length of the Basilica of Saint Martin and Saint Oswald at Weingarten is 102 meters, or 335 feet. Gabler has compensated very well for the distance losses. The absolute values of these scales are indeed much narrower than what we would typically find in rooms of this size, but the mathematics show that Gabler was cognizant of the effects of large distances. But Jakob also convincingly demonstrates that Gabler was not satisfied with the power, went to some trouble to correct it, and ultimately failed in the effort.

Figures 7 and 8 show the diameter and mouth width scales of the Hauptwerk. Note how much wider Gabler scales his flutes relative to the principal chorus. These flutes are quite powerful and provide an extremely effective contrast to the mixture plenum. A wonderful example of this contrast can be heard in Ton Koopman’s interpretation of the Bach Concerto in A Minor after Vivaldi, “Allegro,” BWV 593 <soundclip3>.¹⁵ Here Koopman demonstrates that Gabler’s flutes can cut through the principal chorus. While typical interpretations of this concerto use contrasting principal choruses, Koopman’s performance gives a clarity and beauty to this concerto that can only be heard with Gabler’s tonal balances. Gabler’s organ, if it is not powerful, is extremely musical, and we can learn much from his example, all of it applicable to organs with more power.

To summarize, some of Gabler’s musicality derives from the intense chorus effects of the mixtures with their many ranks, the many duplicated pitches, and the subtle depth created by the mistuning of those multiple ranks. Multiple ranks do not significantly increase power, but they do increase the sense of chorus.

Another aspect of the musicality of the organ resides in its very slow wind response, which takes the form of a dramatic surge to full power when the organ is playing a full pleno. Another effect that produces a slower wind is a high resistance in the wind system, and Jakob mentions this in his description of the Kronpositiv ducting, which was so restrictive that Gabler was forced to remove a large number of ranks on that chest. Many classical organs feature wind trunks that were purposely designed with smaller cross sections to barely flow the required wind, or even starved the wind to a degree.¹³  

Finally, Gabler employed very large scales in the deep bass of the Pedal. Along with the robust Bombarde 16′, the Pedal produces a tactile effect underpinning the modest power of the manual pleno. The overall effect of the Gabler organ is intensely dramatic without being at all overbearing. To reduce this to a basic philosophy, Gabler was a master of designing for a sense of change in the sound, both aural and tactile. The acoustician R. Murray Schafer observed that “. . . a sound initiated before our birth, continued unabated and unchanging throughout our lifetime and extended beyond our death, would be perceived by us as—silence.”¹⁴ His point was that for a sound to have drama, to grab our attention, it must change: change in pitch with the subtle mis-tunings of his multiple-ranked mixtures, and change in power with the slow rise in the pressure of the wind. The organ at Weingarten is the singular achievement of a master, and even if by today’s standards the overall power seems modest, we can use Gabler’s lessons to great advantage.

 

Excellent recordings exist of the restored Gabler organ.¹⁵ See also Youtube for a cut from this CD: Präludium & Fuga C Moll, BWV 549: www.youtube.com/watch?v=hWWtpS-yvKI.

 

The following normalized graphical data for the Hauptwerk and Pedal were constructed from Jakob’s data. Email the author for a copy of the original Excel file with the data and normalizations, which also includes the Oberwerk: [email protected]. Readers interested in the theory behind these normalizations may refer to The Sound of Pipe Organs.¹²

Hauptwerk data (see Figures 7–9)

Jakob’s claim that narrow scaling is responsible for much of the low power of this organ is amply supported by the normalized pipe diameter data. Gabler is using a “constant scale,” where all pipes speaking the same pitch are the same scale, regardless in which stop they appear or in which part of the keyboard compass they appear. This constant scale averages -7 halftones from 16′ to 1⁄2′ pitches, then increases rather linearly to +1 halftone at 1⁄8′ pitch. The normalized mouth widths seen in the next graph follow a similar trend because Gabler scaled his mouth widths very close to 1⁄4 of the pipe’s circumference, the basis of the normal mouth width scale.

Gabler’s normalized mouth heights are remarkable in their deviation from the pipe diameter and mouth width Normal Scales, and they tell us something about Gabler’s intentions in power balance from the bass to treble. High mouths are a tool of the voicer to achieve a smoother, less bright tone, or alternatively, a more powerful tone when the pipe is winded with larger toes or larger flueways. Gabler uses the mouth height as an independent variable, perhaps to achieve an ascending treble power in the plenum. Data on the toe diameters and flueway depths would give us a deeper understanding.

The diameter and mouth scales of the Hauptwerk 8′ and 2′ flutes are very wide. The Gabler flutes are very smooth and liquid in tone and have very high mouths when plotted on the Normal Scale, but those mouth cutups would appear low when looking at the actual pipes because the diameter and mouth scales are very wide. Gabler knew how to use very wide scales, but he only applied such scales to the flutes, perhaps suggesting that his narrow principal chorus scales were an intended result, even in this large acoustic.

Pedal data (see Figures 10–12)

In Gabler’s Pedal we also see a constant scale, but it has a different shape, averaging about +3 halftones at 32′ pitch, descending linearly to about -7 halftones at 2′ pitch, and thereafter remaining roughly flat at that scale up to 1⁄2′ pitch. These wide scales in the deep bass are the source of the tactile effect in Gabler’s sound. Human hearing becomes dramatically less efficient in the bass; at about 20 Hz we hear and feel a sound at about the same level. Below that frequency we tend to only feel the sound. The frequency of a 32′ pipe is 16 Hz and is much more felt than heard. Note the very wide scales of the 16′ Octavbass. It is powerful enough to achieve a strong tactile effect; also note its very high cutups, which imply full wind at the toes and flueways. 

Like the Hauptwerk, the Pedal mouth widths are similar in normalized scaling to the pipe diameters and tell a similar story. Also like the Hauptwerk, the Pedal mouth heights dramatically ascend with higher pitch. 

The Pedal Bombarde is full length with rectangular wooden resonators. The effective scale of a wooden resonator is its diagonal measurement, i.e., the width of its standing wave, and this reed measures a very generous 240 mm at low C. Combined with the tactile character of the deep bass flue pipes, the Bombarde is a very strong component of the drama achieved by the Gabler chorus.

Notes:

1. Peter Stadtmüller, Toccata in E major, BWV 566, J. S. Bach, Musical Heritage Society MHS 3195, Gabler organ, Basilica of Saint Martin and Saint Oswald at Weingarten.

2. Friedrich Jakob, Die Grosse Orgel der Basilika zu Weingarten, Geschichte und Restaurierung der Gabler-Orgel, Verlag Orgelbau Kuhn, Männedorf, Switzerland, 1986, 146 pages. The book and shipping totaled 73.00 Swiss Francs. At this time Kuhn is only able to receive funds wired to their account, which makes the book rather expensive to those of us who live across the Atlantic Ocean. Email Orgelbau Kuhn AG: [email protected]. Website: www.orgelbau.ch.

3. Ibid., pp. 40–43.

4. Ibid., pp. 55–56.

5. My statement of the “. . .motions of the bellows plates. . . to be ≈ 1.25 Hz” for the Isnard wind system in The Sound of Pipe Organs, page 108, has errors that I missed as a result of the closeness of the calculated resonance in Hz and the measured period of the response in seconds. My measurement of the bellows response at 1.25 seconds represented three motions of the bellows, down-up-down, which is 1.5 times the period of the wind surge. Therefore, the correct period, one cycle of two motions, down-up, is 1.25 / 1.5 = 0.83 seconds. Inverting that (1 / 0.83 seconds) gives us 1.20 Hz, or cycles per second, which perfectly correlates to the correctly calculated resonant frequency of the system.

6. Die Grosse Orgel der Basilika zu Weingarten, pp. 72–79.

7. Oscar Mischiati and Luigi Ferdinando Tagliavini, Gli Organi della Basilica di San Petronio in Bologna, Pàtron Editore, Bologna, 2013, 577 pp.

8. Michael McNeil, A Comparative Analysis of the Scaling and Voicing of Gothic and Baroque Organs from Bologna and St. Maximin, e-publication, PDF, Mead, Colorado, 2016. Email the author for free copy:
[email protected].

9. See Youtube video of the organ at Ostönnen: www.youtube.com/watch?v=YxmsZ5ksaVY. Also see the Youtube panoramic video of the Gabler organ in which you can zoom in to see the same treatment of the façade pipe mouths: www.panorama-rundblick.de/gabler-orgel-weingarten. Click on the red arrow to move to the front of the console to see the 32′ façade.

10. Die Grosse Orgel der Basilika zu Weingarten, p. 78.

11. Ibid., p. 79.

12. The Sound of Pipe Organs, pp. 13–14.

13. Ibid., pp. 119–127. See the example of the wind flow calculations for the Isnard organ at St. Maximin.

14. R. Murray Schafer, The Tuning of the World, Alfred A. Knopf, New York, 1977, p. 262.

15. Ton Koopman, J. S. Bach Orgelwerke II, Gabler-Orgel, Basilika Weingarten, Novalis CD, 150 020-2, 1988.

 

Photo: The 1750 Joseph Gabler organ, Basilica of Saint Martin and Saint Oswald, Weingarten, Germany (photo credit: Thomas Keller; see the source in Note 9)

Michael McNeil

Michael McNeil has designed, constructed, and researched pipe organs since 1973. He was also a research engineer in the disk drive industry with twenty-seven patents. He has authored four hardbound books, among them The Sound of Pipe Organs, several e-publications, and many journal articles.

C. B. Fisk, Inc., Opus 133

The C. B. Fisk, Inc., shop, located near sea level in Gloucester, Massachusetts, had to carefully consider the delivery of their Opus 133 to an altitude of 2,127 meters (6,978 feet) at First Presbyterian Church, Santa Fe, New Mexico. Would that affect its sound? With 74% of the world’s population living below an altitude of 500 meters (1,640 feet), the effects are unnoticed, and we rarely have to deal with this.¹ Others have addressed this problem, and we can find excellent guidance in an article by James W. Toevs using Fisk’s Opus 133 as an example, where he noted that altitude had no effect on “basic intonation” (here meaning “pitch,” not “voicing”), but had a “significant effect [on] . . . pre-voicing and voicing.”² I am a voicer, I live at 5,000 feet altitude, and I want to understand how altitude affects the sound and the voicing. We can find answers with Hartmut Ising, a man who thought very deeply about voicing.

Toevs explains that at higher altitudes air will be less dense, and at sea level the voicing must be done at a higher pressure than the intended pressure at altitude. The compensation is simple: find the ratio of the air density at the workshop to the air density at altitude, and then multiply it by the desired pressure at altitude to find the correct pressure for voicing in the shop. In the example of Fisk’s Opus 133, the air density at Santa Fe is 77% of that at sea level, and we get a ratio of 1 / 0.77 = 1.3. Fisk’s desired pressure at altitude was 76 mm water column, so at sea level the pressure needed for voicing was 76 mm x 1.3 = 99 mm. As any voicer knows, that is a big change in wind pressure and a lot more power!

Hartmut Ising and Johan Liljencrants

The Fisk example shows us how to compensate for voicing at different altitudes, but if we want to understand how the voicing and sound is affected, it might help to explain the need to adjust wind pressure.

In a 1971 internal publication of the Walcker firm, Hartmut Ising proposed an equation to show how the timbre of a pipe (a primary goal of voicing) is affected by its pitch, the height of its mouth (also known to voicers as “cutup”), the depth of its flueway, and the velocity of air (this last term was transformed by Johan Liljencrants into air density and wind pressure).³ For those not familiar with these terms, Figure 1 illustrates the front, side, and cross-section views of an organ pipe, showing its mouth height H and its flueway depth D. This equation is rarely seen, but it gives profound insight into many aspects of voicing.

I am going to take a great risk here by showing the somewhat intimidating Ising equation (in its form by Liljencrants). This is where readers will normally storm for the exits, but bear with me, I will do all the math for you in Excel, and I will show you what it can teach us:

[Ising equation]

I is the timbre of a pipe—the German word for “voicing” is Intonation. An I value of 1 is the timbre of a smooth flute. A value of 2 is an optimal state for the “shortest duration between the opening of the pipe valve and reaching the steady pipe sound (fundamental plus overtones).”⁴ In this state the timbre of a pipe also has more power in its harmonics, i.e., it is more like a principal and brighter. A value of 3 is the point where the harmonics have become so strident and powerful relative to the fundamental that the pipe overblows to the octave (strings can operate in this region with help from devices like roller beards to prevent overblowing). Most organ pipes are voiced in a range of values from about 0.8 (a very smooth flute with delicate harmonics) to about 2.3 (a principal with very well-developed harmonics and brightness).⁵

F is the frequency of the pitch in Hz.

D is the depth of the flueway in meters.

H is the height of the mouth in meters.

P is the wind pressure in Pascals, or N/m². Organ pressure is measured by the height of a water column, and 1 mm of pressure = 9.80665 Pascals. This is the term we will vary to see how it affects the timbre of the pipe I.

ρ is the density of air in kg/m³, which is 1.2 kg/m³ under standard conditions at sea level. This is the term we will adjust for different altitudes.

The beauty of Ising’s equation is that it lets us “hear” the changes to the timbre of a pipe’s voicing when we change its altitude or its pressure. Let’s see what it can show us.

Air density at different altitudes is a subject with complex compensations that include temperature and humidity. Figure 2 shows online data that yielded air densities ρ in very close agreement with Toev’s example.⁶

We are now ready to create the Excel table shown in Figure 3, and we will begin with a sea level air density ρ of 1.20 in the last column. A full range of pipes from 16′ to 1⁄8′ are shown in column 1, and the frequencies F of the pitches of those pipes are seen in column 3. The flueway depths D in column 4 are typical of the principal chorus voicing of the Isnards at Saint-Maximin, and the mouth heights H in column 5 are all Normal Scale.⁷ In column 6 the pressure P in the foot of the pipes is adjusted to 35 mm (343.2 Pascals). The Ising equation now calculates timbre values I of 2.21, shown by the red arrow in column 2.

The flueway depths D were fine-tuned to get the same I values for all pitches (with minor rounding variations). This is probably in the ballpark for the Isnard sound. The bellows pressure of the Isnard organ is 83 mm, but the toes of the flue pipes are closed and the actual pressure in their feet is far lower.⁸ Figure 3 represents voicing at sea level.

Now we are ready to see what happens if we adjust our altitude to 1,500 meters by changing the air density ρ from a value of 1.20 to 1.00 in the last column in Figure 4. We are not changing the sea level voicing in the flueways, mouth heights, or wind pressure. The change to the timbre I is a revelation.

The timbre I increases to a value of 2.42 for all pitches. This is a much brighter and more powerful sound, and it is not what the voicer intended at sea level! While I do not recommend this as a solution (it would involve a great deal of work), we could raise the mouth heights (cutups) on all of the pipes to restore the timbre of the original sound. For example, in Figure 5 we see the new mouth heights H (in red font) that would restore the timbre of the pipes at 1,500 meters altitude to an I value of 2.21.

The mouth heights and flueways in this table are noted in meters, so the mouth height on the 16′ pipe is 54.5 mm, and so on for the other pitches. You can compare these heights (cutups) to the table in Figure 4—very small changes in mouth height make big changes in the timbre. The point of this example is to show that mouth height can be adjusted to keep a constant timbre at different levels of power.⁹

The much better solution for moving an organ to a higher altitude, just as Toevs suggests, is to lower the wind pressure. For our new example, we find the ratio of the air densities at 1,500 meters altitude and sea level: 1.0 / 1.2 = 0.83. Using this ratio, our new lower wind pressure is 0.83 x 35 mm = 29.1 mm. Figure 6 demonstrates our original sea-level voicing, but the air density ρ is 1.00 for 1,500 meters altitude in the last column, and our new lower wind pressure P of 29.1 mm (285.4 Pascals) is shown by the red arrows at the right). Figure 6 now calculates an I timbre value of 2.21 at 1,500 meters altitude, the exact timbre we had at sea level on the higher pressure with our original voicing!

Higher altitude brightens the timbre

The Ising equation confirms the Fisk method of altitude compensation with wind pressure, and it shows why we have to compensate for it—while we might be gasping for breath at higher altitudes, the sound of a pipe organ gets brighter. If we reduce the wind pressure in the bellows with higher altitude, we can keep the same timbre at any altitude with the same voicing. This is a key insight from Ising, and his equation works in the real world of voicing.⁹

The final piece of the puzzle

We might correctly surmise from the Ising equation that the power of both the fundamental and the harmonics increases with altitude, and the power of the harmonics will increase faster than the fundamental, making the sound brighter. Adjusting our wind pressure lower corrects both the timbre and the power. But there is one more crucial effect at play here: the intensity of sound decreases in rough proportion with the air density.¹⁰ This means that power will drop with altitude.

And this is why Fisk chose a target pressure for their normal power at altitude and raised that pressure at sea level for pre-voicing. They simply voiced the pipes at sea level with normal timbre and more power on higher pressure. Then, when the pressure was reduced at altitude, the normal timbre was maintained and the power dropped to normal as well. Now we know how the sound and voicing of organ pipes are affected by altitude and why the Fisk method works.

What this means for the organ builder

The bottom line here is very important. Once an organ is voiced at a desired power level, timbre, and pressure at a specific altitude, it cannot maintain both its timbre and its power at a different elevation with the same voicing.

Pressure can be adjusted lower if the organ is moved to a higher elevation to keep the timbre the same, but the power will be lower. If the original pressure is maintained, the power will be the same, but the timbre will be much brighter (requiring higher cutups to restore the timbre).

Pressure can be adjusted higher if the organ is moved to a lower elevation to keep the timbre the same, but the power will be higher. If the original pressure is maintained, the power will be the same, but the timbre will be much duller (and cutups are not easily lowered).

A graph for altitude compensation

If you are able to plan ahead for a change in altitude, I have used the Ising equation and the air densities from Figure 2 to do the calculations for you in the graph in Figure 7. This graph will give a constant timbre and power for flue pipes spanning a range of altitudes from sea level to 2,500 meters (8,202 feet). See Figure 7 for instructions on its use and a worked example.

The graph in a nutshell

Voicing at a lower altitude for delivery to a higher altitude: Adjust the pressure higher than normal and voice for higher power with normal timbre; drop to the target pressure at higher altitude. The timbre and power will be normal. Voicing at a higher altitude for delivery to a lower altitude: Adjust the pressure lower than normal and voice for lower power with normal timbre; raise to the target pressure at lower altitude. The timbre and power will be normal.

Notes & References

1. Joel E. Cohen and Christopher Small, “Hypsographic demography: The distribution of human population by altitude,” Proceedings of the National Academy of Sciences of the United States of America, November 24, 1998, 95 (24), pp. 14009–14014.

2. James W. Toevs, “Organ Acoustics at High Altitudes,” The Diapason, October 2009, p. 31.

3. Hartmut Ising, “Erforschung und Planung des Orgelklanges,” Walcker Hausmitteilung, no 42, Juni 1971, pp. 38–57. Johan Liljencrants shows a form of this equation on the website www.fonema.se, accessed on October 18, 2020, which contains not only Liljencrant’s work but also the original Ising article. On this website we see that Liljencrants modified Ising’s original equation to use pressure and air density rather than velocity, making the equation more easily used by the organbuilder. Here is his transformation of Ising’s equation:

4. Personal communication from Dr. Hartmut Ising, October 2020. Previous literature has translated I = 2 as an optimal state for the fundamental, but did not define what was optimal about it. Dr. Ising continued to clarify this: “for I = 2 the transient of the sound is optimal (Einschwingvorgang).”

5. John Nolte, “Scaling Pipes in Wood,” ISO Journal, no. 36, December 2010, pp. 8–19. The original website referenced in this article by Nolte that posted the English translation of Ising’s equation by Liljencrants and his description of the range of values for I has disappeared. The website, www.fonema.se, contains much of this information. See also note 4 above.

6. www.engineeringtoolbox.com/air-altitude-density-volume-d_195.html, accessed August 25, 2020. The baseline at sea level assumes 20 deg C temperature, 40% humidity, and standard pressure.

7. Michael McNeil, The Sound of Pipe Organs, CC&A, 2014, Amazon.com, pp. 68–72. This chapter explains the derivation and use of the Normal Scale for cutups and displays a chart for all pitches from 32′ to 1⁄8′.

8. The scintillating Isnard reeds have far more open toes and their thicker tongues are more effective with the higher bellows pressure. The higher pressure also compensates for pressure losses in the tubing to the many offset pipes, which have much more open toes than the pipes on the windchests. Open toe voicing of flue pipes on even modest wind pressures requires compensation in the flueway depths, just as we find in neo-Baroque voicing. The warmth of French Classical voicing resides in its open flueways.

9. The Sound of Pipe Organs, pp. 77–84. A spectral analysis of a pipe’s sound measures the power of its harmonics and objectively quantifies its timbre. This chapter uses Ising’s equation to show how timbre, pressure, and cutup are related, using examples of spectral data from organ pipes taken with a state-of-the-art (in 1975) spectrum analyzer.

10. www.physics.stackexchange.com/questions/672/what-is-the-relation-of-sound-propagation-to-air-pressure, accessed October 3, 2020. Sound intensity is roughly proportional to the air density.

The equation for sound intensity is   I = ξ2 ω2 c ρ,  and I here represents intensity, not Ising’s I for timbre.

I = intensity

ξ = particle displacement

ω = frequency

c = speed of sound

ρ = density of air

Michael McNeil

Michael McNeil has designed, constructed, voiced, and researched pipe organs since 1973. He was also a research engineer in magnetic recording with 27 awarded patents. He has authored four books, among them The Sound of Pipe Organs, which explores the scaling and voicing of organ pipes, the effects of wind system dynamics on musicality, and the relationship of temperaments to tonal design.

Editor’s note: The Diapason offers a feature at our digital edition—two sound clips. Any subscriber can access this by logging into our website (thediapason.com), click on Magazine, then this issue, View Digital Edition, scroll to this page, and click on each <soundclip> in the text.

This article was written after the author received reed pipes built to specifications in this article by Aug. Laukhuff GmbH. A victim of the economic retraction during the pandemic of 2020 and 2021, Aug. Laukhuff GmbH closed its doors in June of 2021. Established in 1823, it served the needs of organbuilders worldwide. Its unimaginable loss is catastrophic to the profession, not only in the unique products it provided, but also in the centuries-old expertise of its managers and employees. Making an historic reed with the necessary detail will be a challenge.

The sound of an historic reed chorus may strike us like an emotional thunderclap and leave us with the wish that we might make such reeds today. I had one such experience with the sound of the reed chorus from the 1754 Joseph Riepp organ at Dole. Those reeds were a later addition in 1787 by the French builder François Callinet. You can get a sense of the drama of these reeds from a performance by the late Michel Chapuis <soundclip1>.¹ The great Romantic organbuilder Cavaillé-Coll often preserved Callinet reeds in the organs he rebuilt.

The sheer complexity of reed construction is daunting, but we might begin to understand reeds by trying to recreate one we like. Although one of my dear colleagues rejoiced that I did not tackle the subject of reeds in my recent book on the sound of pipe organs, this article takes a deep dive into the subject. An exact copy would be prohibitively expensive, but we can capture the sound using the resources available to us from modern suppliers. For this example we used the resources of Aug. Laukhuff GmbH, Weikersheim, Germany, as they described their capabilities in great detail on their website. 

There are hurdles to clear before we can reproduce such a reed, and perhaps the greatest of these is sufficient documentation. The detailed data required to really understand a reed is extremely rare, and the greatest practitioner of data collection was Pierre Chéron. We owe him a great debt for the complete measurements of every pipe in the 1774 Isnard organ at St. Maximin.²

The data

Sufficiently complete measurements of the reeds at Dole are unknown to the author, but a wonderful book gives just enough data to get a feel for the scaling of the entire reed chorus of that organ.^{3, 9}
Although we lack sufficient data for the Dole reeds, it is our great fortune that Chéron’s data for the 1st Trompette from the 1790 Callinet organ at Auxonne has been published in exquisite detail by Laurent Plet.4 The complete data from the Callinet reed at Auxonne and the limited data from Dole correlate very well. Chéron took the Auxonne reed data in 1990 prior to the restoration of the organ by Laurent Plet, and you will find a wealth of data and photos on Plet’s website for this organ.⁵ The complete table may be seen in Figure 25.

Chéron’s table has lettered data columns that are made clear by the drawing of a reed pipe in Figure 1 and the detail of a shallot in Figure 2. Chéron’s dimensions are in millimeters except thicknesses of the tongues, which are in hundredths of a millimeter. Here are descriptions of Chéron’s lettered columns:

Description of the Chéron data

Diameters

A is the name of the note (there is no bass C-sharp)

B is the inside top diameter of the resonator

C is the thickness of the resonator at the top

E is the inside bottom diameter of the resonator

F is the thickness of the resonator at the bottom

Lengths

G is the length of the shallot from the block, or “nut” 

H is the height of the block, or “nut”

K is the length of the resonator from the block to the top 

L is the total tuned length of the reed (there are no tuning slots)

Shallots

M is the outside diameter of the shallot

N is the outside depth of the shallot at the block

O is the outside depth of the shallot at the end

P is the inside diameter of the shallot

Q is the wall thickness of the shallot

R is width of the shallot face (the slot opening width is R-2Q)

S is the total shallot length, including the section inserted into the block

Tongues

T is the width of the tongue

U is the thickness of the tongue under the wedge

V is the thickness of the tongue under the tuning wire

W is the thickness of the tongue at the free end

X is the vibrating length of the tongue

Y is the extension of the tongue beyond the end of the shallot

Boots

AA is the diameter of the toe hole in the boot.

This seems like a lot of detail, but as you will see, Chéron recorded exactly what is needed to understand a reed.

Diameters 

Let’s start with the top diameters in the table in Figure 3, which control power. The amplitude of a standing wave in a resonator gets larger with larger resonator diameters, and Callinet’s diameters are very robust. In Figure 3, column 1 we see the raw values of the Callinet diameters. 

We will use an Excel spreadsheet to analyze the Callinet reed, and we will start by graphing the raw diameters. The beauty of the Excel spreadsheet is that a simple click of the mouse on the graph finds the equation of the line that best fits those diameters. That exponential equation is shown in the graph in Figure 4.
We can use that equation in Excel to calculate the smoothed data we see in Figure 3, column 2, which now fills in all of the missing gaps! Note that there are many missing pipes in the original data. The diameters in Figure 3, column 2 are placed into an Excel table, Figure 5, which will be the basis for the new design.

The diameter of the bottom tip of the resonator is usually not less than the inside diameter of the shallot, and it is often larger. Reiner Janke relates that Cavaillé-Coll used a ratio of approximately 8 for top to bottom diameters.⁶ The Callinet data shows ratios changing from 10.9 in the bass to 9.3 in the treble. These bottom diameters are narrower than Cavaillé-Coll would have specified (larger ratios yield smaller bottom resonator diameters), but as we will see, Callinet carefully designed the bottom inside resonator diameters to be about one millimeter wider than the inside diameters of his shallots, making a smooth transition from the bore of the shallot to the bore of the resonator. 

Using these Callinet ratios we let Excel calculate the inside bottom diameters of the resonators. Callinet tapers the thickness of his resonators in the bass, making them thicker at the bottom for added strength. These thicknesses are entered in the Excel file, and we have the specifications for the resonators. We also added a note to make the resonators of 75% polished tin, the highest tin alloy Laukhuff offered. Figure 5 shows the first steps in this table for the low octave. We will show the entire table when it is complete.

Lengths

Resonators will be longer with a lower temperature, lower pitch, higher wind pressure, and the flat-tuned intervals in an unequal temperament. For this exercise we will specify temperature at 20 degrees Celsius, wind pressure at 85 mm (the original Callinet pressure), pitch at A = 440 Hz, and Pietro Aaron’s 1⁄4-comma meantone temperament.¹⁵

Lengths obviously relate to the pitch, but they also strongly influence the timbre. Resonators voiced to the maximum lengths will have a strong “Bourdon” fundamental in the tone, and resonators voiced shorter will have less fundamental and stronger harmonic fire. The goal in the total tuned length is a resonator where the “flip” or “Bourdon” point preserves considerable fundamental in the tone while not sacrificing harmonic fire. The Bourdon point can be modified to some degree with the curve of the tongue and the diameter of the foot hole during voicing. An article by Reiner Janke has an excellent discussion of the Bourdon point.^{6, 10} Those interested in the math of the effect of temperature on pitch can refer to a very useful website (www.sengpielaudio.com/calculator-pitchchange.htm). The calculator on this website indicates that pitch changes a full halftone from 32 to 92 degrees Fahrenheit. 

As we can see, resonator length is very important, and it is doubly so if we are designing resonators with no tuning slots—like most classical, “dead-length” French resonators. Tuning slots are often used to tune reeds to changing temperatures, and while this maintains the timbre of the reed, such tuning slots nearly always end up molested thus that the pipes become extremely uneven in voicing. The lack of tuning slots in French pipes has preserved the intent of their voicers; the reeds are tuned “on the wire.”

Although we have been talking about resonator lengths, the important length in a reed is its total tuned length, and this includes the length of the resonator, the block to which the resonator attaches, and the extension of the shallot below the block. This total length is what really determines the pitch and timbre of the pipe. Chéron gives us the total tuned length in column L of his data. The original pitch of the Callinet organ was A = 415 Hz, and Plet displays a table for these pipes with the estimated total tuned lengths they would have had at their original pitch.⁷ The current lengths of the pipes in the Chéron table reflect a pitch closer to A = 440 Hz, and as this pitch is the goal of our new reed, we will use those lengths with the understanding that there is uncertainty in Callinet’s intended pitch of the Bourdon point. 

We can enter the total lengths of the Callinet pipes into Excel and fit a curve. Figure 6 shows a table with the raw total tuned length data in column 1. Figure 7 graphs that data for the actual Callinet tuned lengths and shows a fitted curve with its exponential equation. The very high R2 value indicates a close fit to the data.¹⁶ With this equation we can fill in the missing gaps with the fitted data in Figure 6, column 2. 

We need to add one more wrinkle to the lengths—temperament. The intended 1⁄4-comma meantone temperament will give us an opportunity to show how to make length corrections (the original Callinet temperament with the missing bass C-sharp probably had major thirds of less purity than the Pietro Aaron meantone). We can approximate that correction by calculating an octave of frequencies for this temperament and finding the differences in the intervals as seen in Figure 8. For this type of meantone, pipes speaking C-sharp, E, F-sharp, G-sharp, and B will need to have resonators with lengths that are approximately 2⁄3 of the whole step in which they reside, not the typical half step of equal temperament. Figure 6, column 4 shows the total tuned meantone lengths of new pipes with adjusted lengths in blue font. The values in Figure 6, column 2 work well for equal temperament. 

We can now enter these total tuned length values into our Excel table in Figure 9. The estimated block height “H” values are placeholders that will be modified by the pipemaker to suit the Laukhuff blocks. The estimated shallot, from block, “G” values are likewise placeholders; the entered values are approximations based on the vibrating lengths of the tongues plus the necessary clearances of the tuning wires to the wedges. Once the values for “H” and “G” are known, the pipemaker will subtract them from the total tuned length “L” to give the estimated resonators “K,” i.e., K = L - (H + G). The values of the estimated resonator lengths in the table reflect that equation.  

It is important to note that the octave ratios of the lengths are 1.94, where the resonators are shorter than a pure doubling of length at the octave as they descend into the bass. This will be addressed in the comments on voicing.

Shallots

Shallots are usually made of brass, and they provide the surface and openings on which the tongues beat to make the sounds we hear. A variety of shallot and opening sizes and shapes gives us a vast range of power and timbres.¹⁷ Callinet shallots are parallel with parallel slot openings. It would be prohibitively expensive to make custom shallots for every pipe, so we will refer to Laukhuff’s selection of shallots to achieve a close approximation of Callinet’s ratios of resonator top diameters to shallot inside diameters. Figure 10 shows a portion of Laukhuff’s shallot selection for their Type II Clicquot shallots with rounded ends, which closely resemble the Callinet shallots in shape (all dimensions are in millimeters).

Callinet’s ratio of “12” for resonators to shallot inside diameters is a crucial part of his sound. Reiner Janke relates that Cavaillé-Coll’s ratio is approximately 11, and this means that Callinet’s shallots are slightly smaller and drive his wide resonators with slightly less energy.⁶ In the first three rows of our Excel table under the heading “Shallots” in Figure 11 we see the Laukhuff shallot number, the shallot inside diameter “P,” and ratio we are trying to achieve. The Excel file calculates the ratio for us. We cannot achieve exact ratios with the shallot sizes available to us, so we select shallots to get as close as we can to a ratio of 12, i.e., a range of about 11.5 to 12.5. We enter the Laukhuff wall thicknesses in the next row, and the table calculates the outside diameter “M” as simply the inside diameter plus two times the wall thickness. 

The slot opening width of the shallot, “CC” in Figure 12, is extremely important; wider slots yield more power and more harmonic fire. While Chéron did not measure this parameter directly, it is implied in his measurement of the face width “R” minus two times the wall thickness “Q,” a calculation that is accurate for shallots that are cut deeply and nearly fully open. The “face” is the surface of the shallot on which the tongue beats. Tables of reed data most often record the height of the cut of the shallot (Chéron’s data “N” and “O”), but this is a very indirect method of getting at the slot width, especially if the wall thickness is unknown. A more direct method is to simply specify that the shallots are cut until they yield the desired slot opening width, and these are the values you see in the next to last row of Figure 11, slot width “CC.” The last row is a calculation of the ratio of the slot width “CC” to the shallot inside diameter “P,” and while the Callinet data is somewhat noisy, it averages about 0.85, a very widely cut shallot. We adjust our slot widths to achieve that ratio. The pipemaker can now cut the shallots of a given Laukhuff number to the same height and slot widths.

Blocks

We specified Laukhuff’s French blocks for this reed. French boots extend well beyond the block, or the “nut” as it is often called, to support the resonator, a design that minimizes the collapse of the resonator above the block, a common problem in reeds. Bass resonators have a narrower taper, and to keep the boot from extending too far, a “ring” is inserted above the block on the resonators of those pipes. This ring is deleted when the resonator taper sufficiently widens. Figure 13 shows the two classical forms. We specified half-round teak wedges and tinned bronze tuning wires bent at the top at right angles for ease in tuning. The Callinet originals at Dole have wires bent in this manner.

Tongues

We specified Laukhuff’s tongues made of rolled, spring elastic brass. Laukhuff gave us the option of voiced or unvoiced reeds, and we specified voiced with French tongue curves. The art of reed voicing encompasses power, the Bourdon point and timbre, and the promptness of the speech. With a dead length resonator, the voicer adjusts the diameter of the toe opening in the boot to control the wind along with the stiffness and curve of the tongue.

Stiffness relates to wind pressure and the amount of curve that can be tolerated. With a large curve a thick tongue may speak slowly or not at all. If too thin, it will speak quickly but the sound will be weak in fundamental. A range of timbres can be coaxed from tongues with different curves. We will start by characterizing the Callinet tongues with their stiffness. The power of this method will be demonstrated, and it appears that to some degree Callinet thought in these terms as well.

The stiffness of a tongue, especially if it is a simple parallel tongue, may be understood with some very simple ideas. Stiffness is inversely proportional to length, meaning that a tongue of half the length will be twice as stiff. You can demonstrate this to yourself by taking a metal ruler, holding it down at the edge of a table, and letting a portion of the ruler extend beyond the edge of the table; pull up the ruler at the free end, let it go, and listen to the sound it makes. Now extend the ruler only half as far off the table and listen to the sound it makes—it will sound an octave higher with twice the stiffness. Tongues obviously come in different lengths, and the longer tongues beat at lower pitches. Tongues also come in different widths, and what is intuitively obvious is also correct—a tongue of half the width will have half the stiffness.

Tongues also come in different thicknesses, but our intuition may fail us here—the stiffness will be the cube of the thickness. For example, if we double the thickness of a tongue, its stiffness will be 23, and that means it will be eight times stiffer (23 = 8). That makes thickness by far the most sensitive parameter.

In Figure 14 we see a portion of Laukhuff’s thicknesses for tongue brass. These dimensions, like Chéron’s, are in hundredths of a millimeter, e.g., brass with a thickness of “25” is 0.25 mm thick.

Figure 15 shows a table compiled from Chéron’s data on tongues. Chéron gives us not only tongue thickness in column 6 and width in column 5, he also gives us the vibrating length of the tongue from the tuning wire to its end in column 4, a parameter that is very rarely seen in reed documentation. With this data we can make a calculation of the stiffness of the tongues. These stiffness values involve relatively complex calculations that are illustrated in Figure 24. You do not need to understand them in detail if the math is daunting, and they are already worked into the Excel spreadsheet available from the author.⁹

The real point of using stiffness values is that we get a method to adapt the tongues to our shallots and to available tongue thicknesses. The value of this may not at first be obvious, but bear with me. We will take it step by step.

We first take the raw values for vibrating lengths in Figure 15, column 4, graph the values, fit an equation, and calculate the smoothed and missing data in column 2. Figure 16 shows the raw data and fitted equation; the fit with an R2 value of 0.99 is quite reasonable. 

The next step is to calculate the stiffness of Callinet’s tongues.¹³ We use the raw data in Figure 15, columns 4, 5, and 6 to calculate the Callinet tongue stiffnesses shown in column 7. We graph those stiffnesses in Figure 17, and fit it to an equation. This data is quite noisy with a low R2 value.¹⁶ The new equation yields the smoothed stiffness data for all of the tongues in Figure 15, column 8.

This has been a long slog through data and calculations, but we are now very close to reaping the rewards. In our Excel table for tongues in Figure 18 we have entered the smoothed Callinet vibrating length data in the row for vibrating length “X” and the smoothed Callinet stiffness data in the row for target Callinet stiffness. With this data we can now design our tongues.

We make trial entries in the rows for “width” and “thickness,” and the Excel spreadsheet calculates the resulting stiffness in the row “stiffness.” The last row, “width of tongue-slot/2,” tells us when the width we have entered is so narrow that the tongue will literally fall into the slot opening of the shallot, i.e., when the value in this row is zero or less. Ideally, we would like to have a generous overhang of the tongue on the slot opening of the shallot, and this would be something like a minimum of 2 mm on each side of the bass shallot openings and at least 1 mm on each side of the treble openings. It does not matter if the tongue is significantly wider than the face of the shallot (the slot opening width plus the two shallot walls), but it cannot be less than the slot opening itself. 

Now look at the table in Figure 18. The first data column is low C followed by C-sharp, etc. We enter the thickness for low C at 0.47 mm, then we adjust the tongue width until the relative stiffness matches the target Callinet stiffness. A few iterations gives us a tongue width of 14.3 mm and produces a 2.5 mm overhang of the tongue (last row, “width of tongue – slot/2”). If we had selected Laukhuff’s 0.50 mm tongue thickness, we would need to significantly narrow the tongue to achieve the target stiffness, and while it would not fall into the slot, it would be dangerously narrow. This is all there is to it. Just keep doing this for all 49 tongues!

Callinet apparently thought of tongue design in similar terms, although his noisy stiffness data indicates that he was not at all rigorous about this.16 In the table in Figure 19 we see the first two rows of Chéron’s data for the low C and low D pipes. The columns for tongue thickness, “V” and “W,” show that the tongue for D is thinner than the tongue for C. But note in the column for tongue width, “T,” that the 13.0 mm tongue for D is wider than the 12.5 mm tongue for C. Remember that thickness is our most sensitive parameter (it is a cube function of stiffness), while width is simply proportional to stiffness. The thinner tongue for D would lack the necessary stiffness if it were narrower than the tongue for C, and Callinet has compensated by treating tongue widths as an independent variable; he does not care if the tongue is wider than the face of the shallot, and the math for stiffness explains why we should not care, either.

To summarize, we have reproduced Callinet’s stiffness of the tongues with this method. We have achieved this while accommodating the shallots and tongue thicknesses that were available to us from Laukhuff. Figure 20 shows the tongue thicknesses we selected to make the tongues wide enough to extend over the shallot faces, and Figure 21 shows the final adjustments we made to the tongue widths to achieve continuous stiffness. With careful voicing we should be able to reproduce Callinet’s sound <soundclip2>.¹⁴

Boot toe hole diameters 

Toe hole diameters may be used to control the pressure in the boot, and there is evidence that Callinet made extensive use of this. In the bass and tenor octaves the toe holes are narrower than the shallot inside diameters (the maximum flow of wind is limited by the shallot diameter and its opening). These toe hole diameters, Figure 22, are much narrower than those found in Chéron’s data for a Trompette of similar scales and wind pressure in the Isnard organ at St. Maximin.⁸ I have entered the fitted data of Callinet’s toe hole diameters in the last data row of Figures 23a and 23b. Like the stiffness data, the toe hole diameters are quite noisy with an R2 value of 0.49, indicating that Callinet used the toe holes as a voicing variable. There is a poor R2 correlation of 0.20 between the tongue stiffnesses and the toe hole diameters, perhaps indicating that Callinet used this variable to accommodate different tongue curves, thicknesses, and widths.

We can now see our completed table in Figures 23a and 23b (the bass and treble are shown separately to make the table more readable). This table specifies our reproduction of the Callinet 1st Trompette at Auxonne, France! The Excel file shown in this article took considerable time to create, and it is available at no charge from the author.⁹ It can be used as a template for other reeds.

Voicing 

Power balances are greatly affected by scaling and voicing, and Callinet’s data are instructive. Total tuned lengths will be approximately a ratio of 2 for each descending octave if bass power is strong relative to the treble, and we find octave ratios averaging 1.99 for the three Trompettes in the Raisonnance and Grand Orgue of the Isnard organ at Saint Maximin. The Callinet octave ratios are significantly smaller at 1.94, indicating shorter tuned lengths with descending octaves and reduced power in the bass. Reduced wind pressure and reduced power will result in shorter resonators at the same Bourdon point, i.e., at the same timbre.¹⁰ This observation is reinforced by the significantly reduced toe hole diameters in the bass and tenor of Callinet’s reeds. The Bourdon point is also affected by the curve of the tongue—a larger curve makes the sound more powerful, the timbre brighter, and moves the Bourdon point to a longer resonator. Larger curves require more pressure and larger toe holes for prompt speech.

We begin to get a feel for Callinet’s power balances: a restrained power in the bass with still brilliant timbre and fundamental warmth—or put another way, a more ascending treble. A smoother, more sonorous treble can be accentuated with a Bourdon point that is closer to the tuned point in the treble, farther in the bass. For example, Reiner Janke relates that Cavaillé-Coll voiced normal-length reeds close to their Bourdon point just before they transitioned to harmonic-length reeds.¹¹

We might also note that Callinet lets his tongues extend by a small and varying amount beyond the end of his shallots, a technique that subtly affects timbre in much the same manner as adding weights to the tongues. See Chéron’s data in column Y, Figure 25. 

Reed voicing is a complex subject with much subjective opinion. The goal in voicing this reed, and especially the curve of its tongues, is the scintillating French voicing of Callinet. I can think of no better source for understanding French reed voicing than the wonderful essay on this subject by Reiner Janke.⁶ I have translated this essay into English, and it is available by contacting him at [email protected]. He has a gift for finding the important variables in scaling and voicing; see the professional documentary in which he shows how to make and voice perfect copies of a Baroque Silbermann pipe and a Romantic Walcker pipe.¹²

Janke provides further guidance in the voicing of tongues.¹¹ Tongue brass is made by rolling sheets to the desired thickness. The process of rolling produces work-hardened surfaces, and the direction of rolling produces a grain with more stiffness in the direction of rolling. Tongues will be less stiff if they are cut from sheets where the grain is parallel to the width of the tongue. Baroque voicers also commonly filed their tongues to different thicknesses, and this removed the work-hardened surfaces, making their tongues less stiff. A thinner tongue will yield a more rounded timbre, and a thicker and stiffer tongue will be brighter in timbre. Narrowing the tongue will make it louder (it will be less stiff and can be curved more). These are all issues to keep in mind during the voicing process, and they probably account for most of the variability we see in the Callinet stiffnesses in Figure 17 and the toe holes in Figure 22. For those who want to experiment with different tongue configurations, you will need an assortment of reed brass of different thicknesses and a guillotine to cut tongues.

Reflections

This analysis of a Callinet Trompette helps us understand Callinet’s intentions. For those wishing to replicate the entire Callinet chorus at Dole, the Excel model described in this article may be useful as a template to help us interpret the more limited data available to us for the Dole organ.^{3, 9} The author ordered and received a Trompette from Laukhuff based on these specifications as part of a new organ to demonstrate the range of wind dynamics, among other things. This new organ will be fully described in a future issue of this journal with sound clips—stay tuned.

There are many ways to design a reed, and the varieties of reeds and their sounds are virtually limitless. This essay on reed design should not be understood as the only way to tackle this complex subject, but taken rather as a contribution to its discussion. When we hear a sound that commands our attention like the Callinet reeds at Dole, this article reminds us that a great deal of time and effort is required before we can understand those sounds. Callinet reeds are worth our time.

Notes & References

1. Michel Chapuis. Michel Chapuis joue la suite gothique à Dole, a Youtube video by Frederic Munoz, January 25, 2018 <soundclip1>. www.youtube.com/watch?v=oxWHMPS6Lp4.

2. Yves Cabourdin and Pierre Chéron. L’Orgue de Jean-Esprit et Joseph Isnard dans la Basilique de la Madeleine à Saint-Maximin. Nice: ARCAM, 1991, 208 pages, ISBN 2-906700-12-6. 

3. Pierre-Marie Gueritéy et al. L’orgue de Dole, Canevas Editeur, Frasne, France, 1995, 127 pages, ISBN 2-88382-058-9.

4. Laurent Plet. Restauration de l’orgue d’Auxonne, accessed January 11, 2019. lplet.org/orgues/auxonne/tuyaux/tgo_tr1c.htm.

5. Laurent Plet. Restauration de l’orgue d’Auxonne, accessed January 11, 2019. lplet.org/orgues/auxonne/auxonne.htm#sommaire.

6. Reiner Janke. See the article Grundzüge Zungenintonation, accessed January 3, 2019. www.orgel-info.de/. An English translation is also available. The Cavaillé-Coll ratios are general approximations and were reported to Janke by Pierre Chéron. 

7. Plet, Laurent. Restauration de l’orgue d’Auxonne, accessed January 11, 2019. lplet.org/orgues/auxonne/tuyaux/tgo_tr1.htm.

8. L’Orgue de Jean-Esprit et Joseph Isnard dans la Basilique de la Madeleine à Saint-Maximin, pages 139, 155, 156.

9. Michael McNeil. Designing an Historic Reed, Excel file, Mead, Colorado, 2019. Email the author for a free copy: [email protected]. This file also contains data on the Callinet reeds at Dole.

10. See also my discussion of the Bourdon or “flip” point in “1863 E. & G. G. Hook Opus 322, Church of the Immaculate Conception, Boston, Massachusetts, Part 3,” The Diapason, September 2017, pages 20–22.

11. Personal communications, January and March 2019.

12. Reiner Janke. Organ Voicing, Experiential Knowledge of Reiner Janke. www.youtube.com/watch?v=isEWba9rLRY&feature=youtu.be. This professionally produced video by the Universität Göttingen, April 26, 2018, is a revelation for those wishing to understand the voicing of flue pipes. The sound track is in English.

13. In Figure 24 we see the stiffness calculations of the tongues with proper physical units of Newtons of force and Newtons/meter of stiffness. While the force is admittedly applied uniformly over the surface of the tongue and not at the end as modeled in the equations, the resulting stiffness increases uniformly with pitch in the expected manner. See the website: www.tribology-abc.com/calculators/t14_9.htm.

14. Michel Chapuis. Beauvarlet à Dole avec Michel Chapuis, a Youtube video by Frederic Munoz, December 5, 2017
<soundclip2>. www.youtube.com/watch?v=T_wPdGUfuD8&feature=youtu.be.

15. This temperament is described in detail in the author’s article, “Exploring the Sound of Keyboard Tunings,” The Diapason, April 2016, pages 20–21.

16. The term “R2” or “R-squared” describes how closely the data fits to the equation on the graph. If all of the data points fall on the line, the R² is equal to “1” and the fit is perfect. If the R2 is zero, the data is just a scatterplot looking much like a shotgun blast with no correlation at all to the line described by the equation. A click of the mouse in Excel will show the R2 for any graphed data fitted to an equation. The noisy fit of R2 = 0.56 for the Callinet tongue stiffnesses in Figure 17 may very likely indicate that Callinet used stiffness as a variable during voicing.

17. Personal communication of March 2019. Janke points out that the shallot functions as a resonator which strongly affects the timbre of the sound. Extremely wide shallots, typical of North German Baroque practice, produce an “oo” vowel with strong harmonics in the range of 200 Hz; less wide shallots will produce an “ah” vowel with strong harmonics in the range of 400 Hz; French Baroque shallots are narrower and produce an “ee” vowel with strong harmonics in the range
of 600 Hz.