The Vox Humana at Weingarten Abbey
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  The Vox Humana stop on the Gabler organ at Weingarten Abbey  

 

Colin Pykett

 

"Of all the stops of the Organ, the Vox Humana is the one to which distance lends the greatest charm"

G A Audsley

 

"The well-voiced Vox Humana can give points to many a modern vocalist who could do with a little revoicing on his own account"

N A Bonavia-Hunt

 

Posted: 28 October 2018

Revised: 27 November 2018

Copyright C E Pykett 2018

 

Abstract.  Joseph Gabler's remarkable organ of 1750 at Weingarten Abbey incorporated a Vox Humana stop considered so lifelike that its origins quickly became rooted in legend. It remains celebrated today, thus prompting this article. Its pipes were found to have a high frequency formant ascending from 1.8 kHz to 4.4 kHz over the note range analysed (tenor C# to top A nearly three octaves higher). Hence the formant frequencies vary by a factor of only 2.4 for a note frequency ratio of 6.4, following a logarithmic law across this range. Thus the similarities to the 'singer's formant' present in the voice of a trained adult male singer were striking. This occupies a band around 2 - 3 kHz and, as with the Vox Humana, its frequency is relatively static compared with the tessitura of the singer. The formants of both the Vox Humana and singers also lie within the frequency band in which the ear is most sensitive, endowing them with similar penetrating abilities.

 

It is further shown how the formant arises from the fractional-length resonating tubes used across the rank, and how its frequency for a given pipe can be deliberately selected by promoting a coincidence between a specific harmonic of the vibrating reed and a specific natural resonance of the tube. Thus it is likely that Gabler had learnt how to precisely select and maximise the loudness of his chosen formant for each pipe through careful tuning of the tube relative to the reed just by using his ears. The Q-factors of some formant resonances were surprisingly high, resulting in SPL enhancements of several tens of decibels relative to the local mean levels in the spectra. It is a tribute to Gabler's obvious skill and an exquisitely keen ear that he was able to achieve this outcome. His Vox Humana at Weingarten does indeed have characteristics objectively similar to those of the human singing voice, even though it seems to have taken nearly 270 years to prove it.

 

These results are comparable with those from a previous analysis of the Vox Humana rank on a Wurlitzer theatre organ from the 1930s, also discussed in the article. This too is a striking example of the genre, and it makes one wonder whether and how the insights of master organ builders of the baroque era such as Gabler might have been handed down in some way through the craft to their successors some two centuries later.

 

 

Contents

(click on the headings below to access the desired section)

 

 

Note on keyboard nomenclature

 

Introduction

 

Fundamentals of reed pipes and phonetics

 

Formants

 

Travelling and static formants

 

Construction of the Vox Humana stop

 

How the Vox Humana works

 

Discussion of results

 

Concluding remarks

 

Notes and References

 


Note on keyboard nomenclature

 

The Weingarten organ has a four-octave key compass starting at 8 foot C. In this article notes on the keyboard are identified by their name and serial number as follows: 

The lowest C is denoted by C1 and the digit increments by one for each ascending semitone. Thus the octave above it (tenor C) is C13 and the octave above that (middle C) C25 etc. Following the usual tuners' convention the black keys are called sharps and the white keys naturals regardless of temperament and their musical context. Thus D#4 is the same as the lowest E flat and so on.

 

 

Introduction

 

Joseph Gabler's spectacular organ of 1750 at Weingarten Abbey needs no introduction. It incorporates several celebrated stops, one of which, the Vox Humana, was reputed to be so lifelike when first heard that its genesis quickly became rooted in legend [3]. Partly for this reason I decided to apply a bit of physics to the sound of this stop to see if its secrets would yield to analysis. They did, and the results are described in this article.

 

 

The organ at Weingarten Abbey by Joseph Gabler, 1750

 

 

 

Some of the Vox Humana pipes at Weingarten Abbey

( Martin Doering - www.die-orgelseite.de)

 

It is well known that striving for a stop which sounds like a human voice has been associated with the organ since at least the sixteenth century, though it may be less well known that it was just a part of the wider post-Renaissance fascination with humanoid automata that remains with us today in the shape of AI and robotics. Thus other contemporary avenues were also being pursued, such as Wolfgang von Kempelen's speaking machine which astonished the world towards the end of the eighteenth century and which used techniques borrowed from organ building. Prior to that he had also astonished the world with a chess-playing automaton which revealed him as a fraudster of no mean ability. It was a pity that he degraded himself thus because he made genuine headway in purely mechanical speech synthesis which repays a study of the apparatus. Perhaps this unfortunate episode contributed to the lack of esteem in which the Vox Humana is still held by some, such as Audsley [1] whose aim was obviously to get as far away from it as he could. At the opposite pole Bonavia-Hunt [2] maintained that it could assist singers to develop their tone (see the quotations at the top of the page). I can only assume those he had in mind must have been pretty dreadful. Nevertheless, the Vox Humana has survived and it still graces organs today. Its development straddles three main epochs - that leading to the baroque era and beyond, its use by romantic composers in the 19th century and into the 20th, and its subsequent evolution into a characteristic voice of the theatre organ. The Weingarten specimen has long been regarded as so fine that it has been copied and incorporated into other instruments such as that at the Stadtkirche in Waltershausen, Thuringia. So let us see why Gabler's stop has exerted such a fascination for so long

 

 

Fundamentals of reed pipes and phonetics

 

Two earlier articles on the site cover sound production in organ reed pipes so the material will not be repeated here. One covers the field at a generic level [4] while the other discusses the sounds of particular stops in more detail, including the Vox Humana [5]. This will now be used as the springboard from which to analyse the Weingarten stop.

 

Given that organ pipes are only able to emit sustained notes of relatively long duration, they are limited to simulating the vowel sounds in speech or singing rather than fleeting transient components such as consonants. So we need a basic understanding of vowels if we are to comprehend the acoustic architecture of the Vox Humana and the factors which have driven its development. Whether one likes the stop or not, it is remarkable that even some old examples do seem to possess humanoid qualities of a sort, ranging from a struggling tenor to a baby's cry depending on where it is played across the key compass. Between these extremes one can sometimes detect in the middle of the keyboard a passing likeness to a child's or woman's soprano voice. I consider these correspondences to be worth investigating, given that this old pipework was made at a time when virtually nothing was known about acoustics, phonetics and the physics of music compared with our understanding of these matters today. Apart from anything else, they remain a testament to the aural acuity and insightful skills of the pipe makers and voicers whose achievements have come down to us across the centuries.

 

 

Figure 1. Generator-resonator sound production model

 

Functionally, the human vocal tract and the organ reed pipe are similar at the level of the basic physical model in Figure 1. Both consist of a sound generator energised by compressed air which supplies an acoustic pressure waveform, rich in harmonics, to a resonant system. In today's jargon this is an example of subtractive tonal synthesis in which an unrefined harmonic retinue is sculpted by filters to produce the desired sounds. The vocal chords constitute the generator in the case of the vocal tract, and for the organ reed pipe it is the reed-plus-shallot assembly. The resonator system of the vocal tract consists of several cavities such as the mouth, thus there are various corresponding resonant modes which are adjusted rapidly by the brain during speech or when singing. The reed pipe is much simpler in that it consists of only one resonating chamber, the tube driven by the reed, whose characteristics remain fixed once the pipe has been made and put on speech [6]. In both cases the resonator system dramatically modifies the harmonic structure of the sound generated initially by the vocal chords or the pipe reed to produce a quite different effect at the listener's ears. This can be appreciated from the difference between a reed pipe sounding with and without its resonator, the latter revealing simply the thin squawk of the naked reed. Similar differences occur with the orchestral reeded woodwinds such as the oboe in that the sound when the player 'crows' the reed before inserting it into the bore has none of the beauty we expect of the instrument itself. An example of the hugely different spectra produced by a reed pipe (from a Cornopean stop speaking middle C) with and without its resonating tube is shown in Figure 2. The harmonic retinue of the naked reed (blue bars) extends as far as the 40th though it obviously continues well beyond this. In contrast, the filtering action of the tube not only shapes the spectrum but it reduces the number of harmonics to about 17 as shown by the red bars. So here we see the major effect of the resonator on the sound produced by the reed, and we shall later investigate the Vox Humana in the same way since there are some important differences.

 

 

Figure 2. Spectrum of a Cornopean reed pipe with and without its resonating tube

 

 

Formants

 

The concept of formants is applied widely in phonetics and musical acoustics. If there are one or more camel-like humps visible in the frequency spectrum of a sound, then these are called formants more often than not. Often (though not always) the humps arise as the result of the vocal tract or organ pipe resonances we spoke of earlier, so it is convenient to run with this definition here. Such a spectrum is sketched generically in Figure 3.

 

 

Figure 3. Diagrammatic representation of two formants

 

This picture does not represent any particular or real situation as the intention is only to put across the essentials of the concept. It shows the frequency spectrum of a hypothetical sound which might be emitted either by the vocal tract or an organ reed pipe. Only 18 harmonics are shown whereas in practice there might be considerably more, or sometimes less, in either case. In this example the respective resonator system (the vocal tract cavities or the tube of the reed pipe) has imposed a double-humped envelope on the emerging sound, and these are often referred to as formants. In the case of the human voice there are sometimes more than two formants because there are more than two resonating cavities, and reed pipes also have several because their tubes resonate at more than one frequency. The latter are termed the natural frequencies or modes of the tube, and an important feature is that they are anharmonic (not exactly harmonically related) owing to the end effect of the tube and its variation with frequency. The Cornopean spectrum shown by the red bars in Figure 2 only seems to have one broad formant, but in fact the several tube resonances here have merged into the same overall envelope because the tube was tuned to resonate at the first harmonic or fundamental frequency (i.e. that at the origin of the plot). Therefore the resonances are relatively close together in frequency. For the same reason the formant envelope has been slid leftwards towards the first harmonic so we only see the higher-frequency half of its hump. The resonating tubes of most reed pipes are tuned in this way, that is they are tuned to their lowest frequency, though the Vox Humana is not and we shall return to this difference later. When analysing the spectra of organ pipes one has to be careful not to assign too much importance to apparent resonance effects which might have no connection with sound generation in the pipe itself, and this requires some experience [7]. At the other extreme, some formants are difficult to identify visually in a spectrum plot yet they can dominate the subjective tone colour of an organ pipe. An example is the subtle low-level formant structure of a typical Cor Anglais imitative reed pipe, which is quite obvious to the ear yet frequently invisible to the eye. As in the orchestral instrument, it arises from the bell at the end of the resonating tube.

 

 

Travelling and static formants

 

The term 'travelling formant' was introduced by Harald Bode to describe those which travel along the frequency axis as the pitch of a musical note varies. Most organ stops have travelling formants because the lengths of their resonating tubes vary with the note played and therefore with pitch. This follows because the tubes of reed pipes are usually tuned to their fundamental frequency, which of course varies with position across the key compass. Consequently the formant frequencies of each pipe, which depend on pipe dimensions, also vary from note to note in much the same ratio as their variations in pitch (though the correspondence is usually not numerically exact for reasons we shall not go into here). This helps to preserve the characteristic tone colour of an organ stop over a very wide frequency range which, in the case of a five octave keyboard, varies by a factor of 32.

 

This is quite different to the behaviour of many orchestral instruments. In these, the resonant frequency bands revealed by formants are set up by static physical artefacts such as the bells at the end of woodwinds or the body structures of stringed instruments. Because these are obviously invariant, the formants also remain substantially static and centred on absolute frequencies rather than being relative to the fundamental as with organ pipes, even though the player can vary the pitch of the note widely. Consequently the formants affect different harmonics depending on the note being played, and this leads to the marked timbral changes associated with orchestral instruments when they are played in different registers. An example is the orchestral clarinet which has three distinct tonal registers which can be exploited by a skilled player.

 

The human vocal tract lies between these two extremes. Its formants do not 'travel' with driving frequency to the extent seen in most organ stops, yet nor are they static. Although its formant frequencies vary somewhat across the frequency band of speech or the tessitura of a singer, they do not vary as much as the frequency of the vocal chords themselves. This is why vowels remain recognisable to a listener even though the pitch of different speakers can vary over several octaves, from an adult male voice to that of a toddler learning to talk. Therefore it is clearly desirable for the behaviour of the formants in a Vox Humana stop to imitate those of the human voice as pitch varies, and this means that the formant frequencies should vary somewhat with pitch, though not by as much as the notes themselves. Thus the formant frequencies should not 'travel' across the key compass nearly as much as those of regular reed stops such as the Trumpet. It is remarkable that this insight apparently dawned on some organ builders such as Gabler hundreds of years ago when the concepts considered here were barely understood. They could not have known anything about formants and the other matters discussed above in terms of physics. Their achievements were solely the result of the most exquisitely sensitive ears, honed by years of patient empirical observation only made possible by their superb craftsmanship.

 

 

Construction of the Vox Humana stop

 

Some of the Vox Humana pipes at Weingarten Abbey were pictured earlier, and although details might differ they are broadly similar to those made by many builders both before and since. The pipes are similar to those of the organ Clarinet but with one important difference - their resonating tubes are much shorter. To appreciate the implications of this it is necessary first of all to briefly review how the Clarinet pipe works. Sketched in Figure 4, it consists of a boot which encloses the reed and shallot assembly to which the wind is admitted. The reed is tuned by adjusting the wire protruding externally. The shallot feeds the sound generated by the reed firstly into a short conical section and then into a longer cylindrical resonating tube (though Gabler seems to have given some of his Vox Humana tubes a slight flare, which would have increased the levels of the even-numbered natural resonances of the tube relative to the odds). The tubes of both stops are tuneable independently of the reed. For the Clarinet pipe in Figure 4 this is achieved by means of an adjustable slide at the top, though other ways exist for performing this function. Gabler seems to have tuned his Vox Humana tubes by adjusting the area of an aperture at the top. This would have been a difficult procedure requiring great skill and patience, though it would have had the advantage that the tuning, once set, would have remained pretty stable over long periods. Presumably this is one reason why the stop probably still sounds today much as it did over two centuries ago - lesser organ builders may well have been wary of tampering with the tube resonances lightly because of the sheer difficulty of doing it (and because, if they went too far, it would have been next to impossible to go back again). For the Clarinet the tube is tuned so that it resonates at or close to the fundamental frequency of the reed. As explained in reference [4], the resonator is about half the length of the flared ones used for stops such as the Trumpet and acoustically it is similar to a stopped flue pipe in this respect. Also like the stopped pipe, it attenuates the even-numbered harmonics relative to the odds, though they still exist albeit at lower amplitudes.

 

 

Figure 4.  Clarinet pipe

 

The much shorter tubes of the Vox Humana mean that it resonates at correspondingly higher frequencies. There are no rules or common practice prescribing the length reduction, thus half, third, quarter or eighth-length tubes are found relative to the Clarinet, and at times other lengths as well. Sometimes the reduction ratio varies across the compass of the same stop. This variability might embolden the cynic to suggest that organ builders have little idea how the stop is supposed to sound, and even less as to how it works in an acoustic sense. Although the criticism is probably unfair if applied across the board, it does help to explain why there has been such a wide variation in the acceptability of the result across the centuries, a phenomenon which continues today. However, if we grant that the Vox Humana at Weingarten rises above the tediousness of most run-of-the-mill examples, then one might perhaps assume that Gabler had hit on a recipe which is worth exploring further. This we shall now try to do.

 

 

How the Vox Humana works

 

Few examples exist in the literature describing the acoustic characteristics of the Vox Humana, and even fewer attempt an explanation of its physics. There seems to be a tacit assumption in some quarters that it simulates (or should simulate) the human speaking voice, with various authors seizing on what they see as low frequency speech-related formants of a few hundred Hertz or so in the pipe spectra which they then compare with those of the vocal tract. I suggest this is misguided. Surely something whose sole function is to contribute to the melodic and harmonic texture of music is better judged against the singing rather than the speaking voice? So if we proceed from this position instead, a more promising avenue emerges. It is well known that a trained adult male singer can be heard above a full orchestra because of his so-called 'singer's formant' which plays no part in normal speech. This formant gives a pronounced 'ring' to the voice and it manifests itself in the unusually high frequency region of 2 - 3 kHz, occupying the lower half-octave over which human hearing is most sensitive (2 - 4 kHz). This explains its ability to penetrate through other sounds. The restrained tone of the Vox Humana certainly needs the assistance of something comparable if it is to be heard at all in the vastness of a cathedral, especially against the sonic backdrop of other stops sounding at the same time. So does it have an analogue of the singer's formant?

 

The short answer to the question is yes, it definitely does. The Weingarten Vox Humana has a high frequency formant which appears consistently in the sound of every pipe I have analysed, and moreover it is relatively static in that its frequency does not change across the compass nearly as much as the note frequencies themselves. This mimics the approximately static behaviour of the singer's formant frequency in the vocal tract. Pipe sounds were analysed between tenor C sharp (C#14) and top A (A46) inclusive, thus covering most of the upper three octaves of the key compass. Over this range the formant frequencies varied by a ratio of about 2.4, whereas the corresponding note frequencies varied by the much greater factor of 6.4. Over the same range the formants (1.8 - 4.4 kHz) also overlapped the same frequency band as the singer's formant (2 - 3 kHz). As just pointed out, the Weingarten formant band over the top three octaves coincides almost exactly with the most sensitive region of the ear (2 - 4 kHz). This remarkable behaviour is illustrated graphically in Figure 5 - it is remarkable because Gabler could not possibly have known very much about most of the physics discussed here. Did his ears detect the singer's formant in tenors' voices, and did his experience and intuition suggest how to encourage similar qualities in a reed stop? Or was it more the result of serendipity, perhaps arrived at after much patient experimentation on a trial and error basis?

 

 

Figure 5. Weingarten Abbey Vox Humana - variations in note and formant frequencies 


Across a keyboard the note frequencies (their pitch) vary logarithmically from one key to the next, so on a linear frequency scale they would lie on a curve. However in this diagram the vertical frequency axis is logarithmic so they lie on a straight line instead (the blue one). Plotted this way it can be seen that the measured formant frequencies also lie substantially on a straight line (the pink one), allowing for the inevitable scatter from pipe to pipe. This behaviour is not surprising as the formants are tuned to various harmonics which themselves vary logarithmically from note to note. Observe how the slopes of the two lines differ, confirming that the formant frequencies vary over a smaller range than those of the notes themselves. However the slope chosen was under Gabler's control as it depended on how rapidly he allowed the formant frequencies to vary across the key compass. It is possible that an optimum choice of this parameter (i.e. the line slope) contributes to the success of the better Vox Humana stops, something which Gabler might well have grasped intuitively.

 

For some notes the formant in question resonates so sharply that it affects just a single harmonic in the spectrum, as in the case of tenor F whose spectrum is shown in Figure 6.

 

 

Figure 6. Weingarten Abbey Vox Humana - spectrum of the tenor F pipe

 

Here the formant is glaringly obvious at the 10th harmonic (1750 Hz). For some other pipes the formants are broader, affecting groups of harmonics rather than individual ones, thus forming the spectral humps of Figure 3 referred to earlier. This behaviour reflects variations in the Q-factors of the formant resonances. They are centred at various harmonics across the note range analysed, starting from the 13th harmonic at tenor C# and progressively descending (with some jitter from pipe to pipe) to the 5th at top A nearly three octaves higher.

 

So now we have to explain how these formants arise and how they are controlled in frequency so that they can be deliberately selected and tuned for each pipe by the organ builder. The key issue lies in the fact that the resonator tubes of the Vox Humana are of fractional length as mentioned previously. This enables them to resonate at frequencies well above the fundamental frequency to which the pipe reed itself is tuned. By way of example, the lowest resonant frequency of a properly tuned quarter-length tube (relative to that of the organ Clarinet pipe) would correspond to the 4th harmonic of the reed. However this number is too low to explain the harmonics associated with the Weingarten formants which, as just mentioned, vary from the 13th in the bass to the 5th in the treble. It would be impractical to cut the tubes down further to resonate in the usual way at such very short lengths, and they would not work anyway because their Q-factors would be too low (Q depends on the volume, and thus the mass, of the oscillating air within the tube). Therefore the only way to proceed is to develop the formants from higher-order tube resonances rather than those of lowest frequency.

 

Sound production in all organ pipes, both flues and reeds, is strongly influenced by a retinue of natural resonant frequencies associated with the air columns of their resonating tubes. These are entirely independent of the harmonics generated by the sound-producing part of the pipe (the reed in this case), indeed they can be revealed easily in a silent pipe by suitable experiments. However the interaction between the reed harmonics and the tube resonances is pivotal to an understanding of how the Vox Humana works. Figure 7 illustrates the situation for two types of reed pipe, a Trumpet and the Vox Humana.

 

 

Figure 7. Correspondences in frequency between reed harmonics and natural frequencies of the tube

 

This diagram depicts typical correspondences between the frequencies of the reed harmonics (black lines) and the tube's natural frequencies or resonances (red lines). Note that only frequency is of interest here, not amplitude, thus the heights of the lines are irrelevant. Only their positions on the horizontal frequency axes matter to the discussion. Figure 7(a) shows how the harmonics and the tube resonances correspond for an ordinary reed such as a Trumpet pipe. Nine reed harmonics are shown (in practice there would be many more) and they are always regularly spaced along the frequency axis, but the first seven tube resonances are not. They get progressively stretched out, a phenomenon caused by the end effect of the tube and its variation with frequency. (Although this diagram is only a sketch, the relative spacings of the natural frequencies reflect the real behaviour of a typical tube). In most reed pipes, including the Trumpet family, the reed's fundamental frequency or first harmonic is tuned to coincide with the lowest natural resonance of the tube as shown here, and this results in a pronounced amplification effect. However most (though not all) subsequent resonances get progressively more out of step with the reed's harmonics as shown, resulting in progressively less amplification of the higher-order ones. But note how the 6th and 7th harmonics generated by the reed lie close enough to the 5th and 6th tube resonances to be amplified. This explains why these harmonics are a prominent feature of Trumpet-type tone to endow it with a satisfying rounded 'clang'. Beyond this the harmonic amplitudes in the sound start to fall away, as in the spectrum of a real Cornopean pipe which is just a milder type of Trumpet (see Figure 2).

 

In contrast, the Vox Humana works differently. In Figure 7(b) a simulated singer's formant is introduced by selectively amplifying the 12th harmonic of the reed (in the Weingarten stop a formant at this frequency occurred low in the tenor octave). The diagram suggests one way in which this could be achieved. By cutting down the tube to about one third of its normal length relative to the Clarinet, all of its natural frequencies will be multiplied by about three. Therefore the lowest natural frequency will now lie close to the third harmonic of the reed as shown, instead of its fundamental as for the Trumpet. But by marginally adjusting the tuning of the tube, the diagram shows how its third natural frequency can be brought into exact coincidence with the 12th reed harmonic as required. By this means the 12th harmonic will be selectively amplified through a tube resonance in the same way that the 10th harmonic was emphasised in Figure 6. Note that it is preferable to select the odd-numbered tube resonances for the amplification role because they are stronger than the evens for a cylindrical tube, though Gabler's slightly flared tubes might have had stronger even-numbered resonances than usual. This might have given him more tuning flexibility in selecting his simulated singer's formants.

 

This acoustic mechanism can sometimes result in the appearance of pseudo-formants at additional frequencies where serendipitous coincidences arise between certain other reed harmonics and natural frequencies of the resonating tube. This is illustrated by Figure 7(b) in which the 3rd reed harmonic happens to lie near to the first tube resonance. If the correspondence is close enough the 3rd harmonic might therefore be amplified, though this depends on the Q-factors (broadness or narrowness) of the tube resonances. A similar situation occurs for the 7th harmonic and the second resonance, and possibly others as well. Although Figure 7 is only a sketch, it nevertheless serves to illustrate the point. This phenomenon was observed for some of the Weingarten pipes which, at first sight, seemed to possess additional formant bands at frequencies below that of the simulated singer's formant. However they were not a feature of every pipe analysed, whereas the simulated singer's formant was. It is possible this type of behaviour might have led some authors to the belief that Vox Humana pipes have low frequency formants comparable to those of speech rather than singing in the human vocal tract. But if this were so one would have expected them to arise more often than they did across the rank of pipes at Weingarten, and with greater uniformity from pipe to pipe. It confirms that, when studying organ pipes, it can be misleading to draw conclusions from just one or two.

 

 

Discussion of results

 

The results summarised above were the outcome of a detailed data analysis exercise which, among other things, necessitated the use of specially-developed software. The sounds of a large number of pipes from the Weingarten stop were subjected to detailed scrutiny occupying many months, so it was not the sort of thing one can repeat often. Life is too short. However an earlier study some years ago (2011) had looked at a similar stop on a Wurlitzer theatre organ made in the 1930s in the same way, and the results are summarised in another article on the site [5]. In this case high frequency formants were also observed in the acoustic spectra of the pipes, though their frequencies differed somewhat from those reported here. At Weingarten the formant frequencies ascend from 1.8 kHz at tenor C# to 4.4 kHz for top A nearly three octaves higher. Thus they vary by a factor of 2.4 for a note frequency ratio of 6.4. For the Wurlitzer stop the formant at tenor C is at 1.7 kHz and three octaves higher it lies at 3.1 kHz, a ratio of 1.8 for a slightly greater note range. One would not expect the two sets of figures to be exactly the same, though they are not a million miles from each other. Therefore it seems that the builders of these two very different organs, separated by nearly two centuries, had understood the desirability of simulating the high frequency singer's formant in their respective Voces Humanae. Although their realisations differed to some extent at the level of bald numbers, it is clear that they also appreciated the need to maintain the formant frequencies reasonably static compared with the much greater variation in note frequencies across several octaves. So perhaps these features - namely a simulated high frequency singer's formant whose frequency does not vary too much across the compass - do indeed dupe the brain into assigning a distinctly humanoid quality to the better Vox Humana stops.

 

These results seem to me to be remarkable. Although both organs were built by masters of the craft their genres, separated by nearly two centuries and over 4000 miles, could scarcely be more different - it is not often that one can draw out positive relationships between a Bavarian baroque instrument and an American theatre organ from North Tonawanda. Yet they possess Vox Humana stops with strikingly similar features in terms of their physical acoustics. It is tempting to ask which is the better stop, though the question can only be hypothetical. If the Wurlitzer specimen with its pungent immediacy at relatively short range in the dry acoustic of a cinema were to be transplanted to Weingarten, would it sound similar to Gabler's in the vast reverberant listening space of the abbey? And have the insights of organ builders such as Gabler been handed down through the craft to their successors some two centuries later?

 

It might be argued that the results presented here were not achieved solely by Gabler. After all, he built the organ some 270 years ago and it is possible the remarkable physical insights and the meticulous tonal finishing implied by my analysis emerged subsequently at the hands of other organ builders who might have meddled with his work. However I regard this as unlikely, given the immediate fame and bizarre legends aroused by his Vox Humana stop during his lifetime. It is questionable whether this would have happened if the stop had been just one more mediocre example in a long line of many.

 

 

Concluding remarks

 

Joseph Gabler's remarkable organ of 1750 at Weingarten Abbey incorporates a Vox Humana stop considered so lifelike that its origins quickly became rooted in legend. It remains a celebrated feature of the instrument today, thus prompting this article which has examined some aspects of its physics in an attempt to discover why. By analysing the acoustic frequency spectra of many pipes comprising the stop it was found that they possessed a singular common feature, namely a high frequency formant ascending from 1.8 kHz at tenor C sharp to 4.4 kHz for top A nearly three octaves higher. Hence the formant frequencies varied by a factor of 2.4 over a note range whose fundamental frequency (pitch) ratio was 6.4. Aside from some expected jitter from note to note, the overall formant frequency variation was plainly deterministic and close to logarithmic across this range. Thus the similarities of this behaviour to the 'singer's formant' present in the voice of a trained adult male were evident in that the latter occupies a band around 2 - 3 kHz and, like the Vox Humana, it is relatively static relative to the tessitura of the singer. The formants of both the Vox Humana and male singers also lie within the frequency band in which the ear is most sensitive (2 - 4 kHz), endowing both of them with similar penetrating abilities.

It was further shown how the formant arises from the fractional length resonating tubes used across the rank, and how its frequency for a given pipe can be deliberately selected by encouraging a coincidence between a specific harmonic of the vibrating reed and a specific natural resonance of the tube. Thus it seems likely that, once the organ builder had chosen the length of a particular tube, he was then able to select and maximise the acoustic power of the preferred formant through careful tuning just by using his ears. The Q-factors of some of the formant resonances were surprisingly high, resulting in SPL enhancements of several tens of decibels relative to the local mean levels in the spectra. It is a tribute to Gabler's experience, intuition, skill set and an exquisitely acute ear that he was able to achieve this outcome. His Vox Humana at Weingarten does indeed have characteristics similar to those of the human voice, even though it has taken nearly 270 years to prove it.

These results are comparable, though not numerically identical, to a similar analysis applied to a Vox Humana rank on a theatre organ made by Wurlitzer in the 1930s. This too is an attractive example of the genre, and it leads one to wonder whether the insights of master organ builders such as Gabler have been handed down in some way through the craft to their successors some two centuries later.

 

 

Notes and references

 

1. "The Art of Organ Building", G A Audsley, Dodd, Mead & Co, New York 1905.

2. "The Modern British Organ", N A Bonavia-Hunt, Weekes, London 1947.

3. At the time of writing the Weingarten Vox Humana stop can be heard on YouTube at:

https://www.youtube.com/watch?v=3cHwsMWksSw (accessed 22 October 2018)

4. "How the reed pipe speaks", an article on this website, C E Pykett 2009

5. "The tonal structure of organ reed stops", an article on this website, C E Pykett 2011

6. Some maintain that the organ reed pipe has two resonant chambers - the tube which is driven by the reed and the much smaller shallot. However in view of the diminutive dimensions of the latter, if it resonates at all it would only do so at high frequencies way above the important natural resonant modes of the much larger pipe. I have not seen this assertion demonstrated convincingly either theoretically or in practice in the sense that the consequential effects of shallot resonance could be detected by a distant listener, and that is what actually matters. This is quite different to the main resonating tube whose effects are crucial to the sound of the pipe. The spectral characteristics (harmonic structure) of the sound pressure waveform supplied to the base of the tube (i.e. that which emerges from the shallot) are dominated instead by factors such as wind pressure, the size and shape of the shallot opening, where the opening is placed relative to the shallot body, and reed tongue curvature rather than by shallot resonance.

7. Multiple humps are frequently seen in reed pipe spectra, but often these have nothing to do with sound generation in the pipe itself. For obvious reasons, it is usually only possible to derive the spectra of pipe sounds while the pipes remain in place on the organ soundboards. In this situation noticeable but spurious structure is often imposed on the observed spectra owing to room effects (standing waves or modes). Such structure can appear as humps which therefore look like formants, or anomalous amplification or attenuation of particular harmonics is sometimes seen. These effects can be distinguished from the real structure characterising the pipe sound by observing how they change as the microphone is moved around in the room, as they are very sensitive to listening position. A better way to identify and remove them is, of course, to make the acoustic measurements in an anechoic chamber, though this is seldom possible for practical and financial reasons.