The Tonal Structure of Organ Reeds
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 The Tonal Structure of Organ Reed Stops 

 

by Colin Pykett

 

Posted: 5 January 2011

Last revised: 22 December 2011

Copyright © C E Pykett  2011

   

"A Village Voluntary fills the air
And ceases suddenly as it began,
Save for one oboe faintly humming on"

 

 From "Sunday Afternoon Service in St Enodoc's Church, Cornwall" by John Betjeman

 

(by kind permission of John Murray Publishers)

 

 

Abstract.  This article surveys a range of reed stops having either conical and cylindrical resonators in terms of their different acoustical physics and tonal characteristics.  Some important aspects are emphasised, including the fact that half-length conical resonators do not enhance the fundamental frequency at all, yet often this is scarcely noticeable to the ear.  To prove this, audio clips are included showing that even the complete removal of the fundamental in the sound of a reed pipe does not necessarily affect the way it sounds, and it explains why half-length pedal reeds can be so effective.

 

The fractional-length cylindrical resonators used in stops such as the vox humana are also discussed in detail.  Development of this stop over several centuries has been driven by a desire to imitate the human voice, and this was investigated to see if an objective basis for the attempt could be found.  An analysis of the sounds produced by a Wurlitzer vox humana rank shows that it possesses a relatively constant formant frequency over the considerable range of four octaves centred on middle C.  This frequency lies between the second formant of a child singer and the ‘singer’s formant’ of an adult male.  Therefore it is possible this Wurlitzer formant does indeed contribute to a similarity which the best stops of the genre are said (by some) to possess. 

 

 

Contents

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

 

 

Note on keyboard notation

 

Introduction

 

Summary of reed pipe physics

 

Reed pipes with conical resonators

 

Examples of conical reed pipes

Trumpets

Pedal reeds

The mystery of the missing fundamental

Oboes

 

Reed pipes with cylindrical resonators

 

Examples of cylindrical reed pipes

Clarinets

Oohs and Aahs - the Vox Humana

 

Conclusions

 

Notes and References

 

 

Note on keyboard notation

 

In this article notes on the keyboard are identified thus:

 

The bottom note on both manual and pedal keyboards is denoted C1, the octave above it C2, etc.  Thus middle C is C3 on both manuals and pedals.  Intermediate notes follow a similar convention, thus F#3 is the F sharp above middle C, etc.

 

 

 

Introduction

 

This article continues the series which examines why organ pipes sound as they do, and in this case we will now look at reed stops.  Five previous articles have considered flue pipes (references [1] - [5]), and more recently (2009) a sixth set the scene for this one by describing the physics of the reed pipe in simplified terms [6].  The present article now goes further by investigating some aural aspects of the reed pipe sounds we hear in organs today.  Only beating reeds are considered, those in which a curved piece of thin metal (the reed tongue) vibrates against a fixed aperture (the shallot).  Free reeds, as found in instruments such as the harmonium, are rare in pipe organs and they will not be discussed.  Likewise the diaphone or valvular reed invented by Robert Hope-Jones is also not covered, even though it was used by other builders such as Compton and was frequently found in theatre organs.  These omissions were necessary to keep the scope of the article within reasonable limits.

 

Classifying reed stops is difficult if only because of the number of ways one can do it.  An obvious approach is to consider their names, but the sheer variety of labels applied to stops which are actually similar means this is doomed from the outset.  Another line of attack is to use the shapes and sizes of the pipes, but this can be bewildering because external appearance is not always a reliable indicator of the tone to be expected.  Although this works reasonably for flue pipes, whose length, diameter and visible mouth dimensions correlate quite well with their tone, the pitch and tone of reeds also depend strongly on other factors. This is because the sound in a reed pipe is produced by a mechanical vibrator rather than by vibrations induced in the wind itself, as in the case of a flue pipe.  And, unlike the mouth of a flue pipe where the vibrations are set up, the properties of the vibrator in a reed (tongue dimensions, shallot size and shape, etc) are not discernible without taking the pipe to pieces because it is hidden away in the boot.  Moreover the tone is also influenced considerably by invisible parameters such as wind pressure.  In view of these difficulties, we shall only assign reed stops to one of two broad classes in this article depending on whether they have conical or cylindrical resonators, because the type of resonating tube (flared or not) influences the tone profoundly regardless of all the other factors.

 

As with the previous ones dealing with flutes [2] and principals [3], this article concentrates on the acoustics underlying the sounds of the various stops and why we perceive them as we do, rather than on matters such as the constructional details of their pipes which are easily obtained elsewhere.  This is because, in the last analysis, we listen to their sounds rather than just staring at the silent pipes.  Therefore topics such as the harmonic structures of the tones are discussed in some depth, and some audio clips are also included to illustrate particular points.  This approach renders the article distinct from most other treatments found elsewhere in the literature.  It is also worth pointing out that a considerable investment in time and equipment (and therefore in money also) is necessary to record organ pipes in sundry churches and other buildings and then to analyse their sounds, so it is understandable that others who have done this are reluctant to broadcast their results for all to see [7].  For this reason also, articles like this one are rare.

 

 

Summary of reed pipe physics

 

A detailed description of the physics involved in reed pipes is available in the article already referred to [6].  However the main processes are summarised briefly here for convenience and completeness.

 

The reed tongue vibrating against the shallot produces a periodic (cyclically repeating) air pressure waveform which emerges from the narrow shallot tube, and this then drives the air in resonator sitting on top of the shallot.  The resonator itself also modifies the driving waveform to a limited extent through an acoustic feedback mechanism, though the coupling between driver and resonator is not as strong nor as intimate as it is for flue pipes. The characteristics of the drive waveform in terms of its harmonic structure are critical in defining the tone ultimately radiated into the auditorium by the pipe from the top of its resonator.  Such structure is defined by factors such as wind pressure, the size and shape of the shallot aperture and tongue curvature.  However it is the radiated sound which we hear of course, not the driving waveform emerging directly from the shallot, and the two waveforms differ considerably.  This is because of the modifications imposed by the resonator by virtue of its ability to enhance or attenuate particular harmonics in the sound presented to it from the shallot.  For example, the driving waveform produced at the shallot of any reed pipe always contains a complete retinue of both the even-numbered and odd-numbered harmonics, whereas the even ones can be partially suppressed by certain types of resonator tube.  This is a necessary and important property of such resonators for stops such as the clarinet.

 

The resonator also performs a second important function called impedance matching, and in this respect it is an acoustic transformer.  It takes the high acoustic output impedance of the reed/shallot assembly and transforms it into a lower impedance more suitable for radiating the sound into the auditorium.  This function is explained at length in [6] and it is particularly important for loud reeds such as trumpets, trombones and tubas.  The transformer action is less pronounced nor needed for the quieter and more delicate ‘colour’ reeds such as clarinets, where subtleties of tone quality are more significant than raw power.  In these cases, the modification of the driving harmonic spectrum by the resonator is the critical feature.

 

As with flue pipes, the resonating tubes of reeds are not always close to a half-wavelength in length for the fundamental frequency of the sound being radiated.  If this was so, then the longest pipe of an 8 foot reed would always be close to 8 feet long.  As with some flue stops such as the harmonic flute, the so-called harmonic principle is often employed in which the resonators are twice as long as would be expected.  Sometimes triple or even quadruple length tubes are found.  This technique is used when it is desired to enhance the power in the treble part of the compass for loud stops, and in these cases they often have names such as harmonic trumpet.  Another acoustic analogue with flues also exists in that some reed stops have half-length resonators which work in a similar manner to those of stopped flue pipes.  The clarinet is one example.  However, unlike flues, this practice can also be employed without changing the pitch of the pipe - one can cut a reed resonator in half without affecting the musical pitch of the pipe very much, yet this would be impossible with a flue pipe.  Such half-length tubes are used frequently for quieter stops such as contra fagottos, or in the bass register of 16 and 32 foot pedal reeds of moderate power.  This is possible for reeds because the acoustic coupling (in terms of feedback) between the driver and resonator is weaker than it is for flues.  Indeed, a resonator is not actually essential at all for a naked reed to emit sound, as can be heard when an oboist tests the reed by ‘crowing’ it before inserting it into the instrument.

 

 

Reed pipes with conical resonators

 

There is a huge variety of reed stops whose pipes have conical resonators.  A partial list of names includes the trumpets (military trumpets, fanfare trumpets, trompettes, clarions, just plain trumpets, trombas and tubas) and the oboes (cor anglais, hautboys, schalmeys and plain old oboes).  Along the way we also get cornopeans, posaunes, trombones, horns, ophicleides and even serpents.  They exist at several pitches ranging from 32 to 4 feet, occasionally higher or lower as well, and in a vast range of powers.  Now you can see why I abandoned any attempt to classify reeds by stop name!  And because all of them have resonator shapes which differ in detail, sometimes to an idiosyncratic or downright bizarre degree, external appearance is likewise taxonomically inefficient.

 

However the unifying feature is that all these stops have pipes whose resonators are conical - they increase in diameter linearly towards the top.  This enables the resonator to act as a transformer which couples the radiated sound more efficiently into the auditorium and, like a megaphone, it therefore makes the pipe sound louder.  It was also explained in [6] that a flared tube resonates or enhances the sound generated by the shallot at all harmonic frequencies, though the degree of enhancement varies for each harmonic.  This variation is important because it enables the resonator to act as a selective filter to tailor the sound to that intended by the organ builder - the tube applies a filtering action or frequency taper to the sound emitted from the shallot.  With a flue pipe, a narrow tube allows the upper harmonics to retain more power than a wide one, thereby making it sound ‘stringy’ rather than ‘fluty’.  Similarly, a narrow reed pipe resonator is used for ‘keen’ colour reeds such as orchestral oboes.  Conversely, a wider tube is used for more rounded trumpet-type tones where the lower harmonics resonate more strongly than the upper ones.  The reason for this behaviour in both flue and reed pipes resides in the way the natural non-harmonic partials of the tube coincide (or not) with the exact harmonics generated by the oscillating reed itself. In turn, this is due to the end correction of the pipe and the way it varies with frequency and with pipe scale.

 

Examples of conical reed pipes

 

Trumpets

 

Mainly for convenience we shall define the trumpet family as a large one, ranging in power from the ear-splitting post horn found on American theatre organs (not dissimilar to the very high pressure military trumpets on a few British cathedral organs) to quiet bassoons and fagottos.  The middle ground is populated by stops such as the cornopean [8], horn and the familiar trumpet stop itself.  Usually somewhat louder than these are the tubas, posaunes and trombas.  Any of them can be continued downwards in pitch to produce pedal reeds such as the trombone and contra trombone, though often under other names.  Higher pitches attract names such as clarion. 

 

 

A generic trumpet-type pipe is shown in Figure 1.  The resonator shown in the diagram has an open top, so it is sometimes turned sideways by mitreing the pipe to prevent dust and dirt falling into the reed.  Frequently the resonator is about a half-wavelength long, meaning that it would approximate to 8 feet for the bottom note of a stop of that pitch.  However half-length tubes are sometimes used in the bass and/or double-length ones in the treble for the reasons already mentioned.  Resonator scale, the degree of flare for a tube of given length, affects the tone considerably, with narrower tubes encouraging the development of the upper harmonics relative to the lower ones.  This is because a narrow tube brings more of its natural upper partials closer in frequency to the corresponding forced harmonics generated at the shallot.  Conversely, wider tubes preferentially enhance the fundamental and lower harmonics by increasing the divergence between the natural partials and the forced harmonics at higher frequencies.

 

The other main way of controlling the harmonic development of the tone is by shaping the shallot aperture in conjunction with the curve applied to the vibrating reed tongue.  The so-called open (French) shallot has a rectangular opening over its full length, and these generate the most extensive harmonic series.  Since many of the upper harmonics are grossly dissonant with others in the ‘discordant interval’ sense, these pipes can sound excessively coarse and rough to some ears, especially when played in chords.  They simply have too many harmonics.  Suppressing these extreme harmonics by using so-called closed shallots (those with truncated and/or specially shaped apertures) leads to smoother tones with less harmonic development, of which the horn is probably the ultimate example.  All of these topics are discussed in more detail in [6].

 

Examples of the waveform and the harmonic spectrum of a trumpet stop were given in Figures 7 and 8 of reference [6], and in the audio clip below you can now hear what it sounded like as it was being sampled.  It was recorded on the splendid Rushworth and Dreaper organ at Malvern Priory before the 2004 rebuild by Nicholson, and it was the middle F# pipe of the 8 foot trumpet stop on the swell organ.  The prominent blower noise was a defect which Nicholson’s could not (and did not) overlook! [9].

 

 Trumpet 8' F#3, Swell organ, Malvern Priory (100 KB/10s)

 

 

 

Figure 2. Trumpet 8' spectrum (F#3, swell organ, Malvern Priory, Rushworth & Dreaper, 1927)

 

The corresponding frequency spectrum is shown again here in Figure 2 [10].  There are about 11 harmonics visible, the majority of which seem to be standing in a field of long grass.  This is the noise from the blower and leaky winding system, the hisses and rumbles of which become even more prominent at the lowest frequencies below the fundamental, as can be seen from the spectrum plot.

 

Pedal reeds

 

Although 16 and 32 foot pedal reeds with names such as ‘trombone’ are really just low-pitched trumpets, there are some aspects worth emphasising.  Constructionally, they sometimes have half-length resonators for the lowest notes, though this affects the tone less than might be thought in favourable circumstances (e.g. if the stop only needs to be of medium power for a small or moderate-sized building).  Nevertheless, the retinue of natural partials in half-length tubes is incomplete compared to the harmonics of the reed itself, and in particular there is no resonance or partial corresponding to the fundamental frequency of the reed.  This does not prevent the reed vibrating at the fundamental frequency and transferring its energy to the resonator, but the fundamental emitted at the top of a half-length reed pipe will clearly be weaker because it cannot be enhanced by a tube resonance.  Also the impedance match at the top of the tube, and thus its radiation efficiency, will be worse than for a full-length pipe at the fundamental frequency because its cross-sectional area at the open end is smaller.  This means that the overall sound will be less loud than if the tube was of full length.

 

So why can organ builders get away with half-length pedal reeds so frequently?  One answer was given above, in that a reed of low to medium power does not need the higher radiation efficiency which a louder one would require.  Another reason depends on a subtle psycho-acoustic property of our auditory mechanisms, and this will now be explained and demonstrated in some detail.

 

The mystery of the missing fundamental

   

 

Figure 3. Trombone 16' spectrum (C2, St George's, Dunster, Hill, Norman & Beard, 1962)

 

First let us look at the harmonic spectrum emitted by a trombone pipe.  An example is shown in Figure 3, derived from a recording of the Hill, Norman and Beard organ built in the early 1960’s at St George’s church, Dunster (and recently rebuilt in 2010).  In passing we can observe that the blower of this organ was much quieter than that formerly at Malvern Priory - there is no ‘grass’ in this plot!  The note in question was CC, an octave above bottom CCC on the pedals, and as this was a 16 foot stop this means the fundamental frequency was about 65 Hz.  The large number of harmonics, at least 75, is noteworthy, continuing up to the 5 kHz display limit of the diagram.  Many reed pipes, regardless of pitch, seem to exhibit similar behaviour in that the harmonic series does not disappear until 5 kHz or so.  Thus it also applies to the Rushworth and Dreaper swell trumpet whose spectrum is shown in Figure 2, though because of the higher pitch of the latter pipe (370 Hz approximately), far fewer harmonics can be accommodated within the 5 kHz frequency span. 

 

The interesting psycho-acoustic property of our ears and brains, mentioned above, is that it matters not whether the fundamental frequency is actually present at all in this sample.  This is a relatively well known phenomenon, though it might surprise those who have not come across it before.  Therefore the following audio clips will demonstrate the effect, and it is thought to be the first time it has been presented in the public domain for anyone to hear.

 

The sound samples in the mp3 file below were prepared digitally using the process of additive synthesis applied to the trombone spectrum shown in Figure 3.  This means the sample was built up by adding 70-odd sine waves (the harmonics) together, each with the frequency and amplitude indicated by the spectrum.  The signal processing system used to implement this procedure is described in detail elsewhere on this website [11].  The clip consists of two sections separated by a short audible gap in the middle: the first section is the waveform obtained using all harmonics in the spectrum, but half way through the clip the second section continues with a different waveform obtained when the fundamental was suppressed.  The interesting feature is that there is no difference in the perceived tone quality (timbre) of the sound when the fundamental is absent.

   

Trombone 16' C2, St George's, Dunster - fundamental removed (162 KB/10s)

I have repeated this experiment many times on different pedal reed tones, and the same result was usually obtained.  For instance, it also works for the lowest note (CCC) of this trombone stop.  However this example was not used here because its very low fundamental frequency, at about 33 Hz, might not reproduce well on the headphones or audio systems of some listeners.  In these cases, the fact that the listener would not be able to hear this frequency in any event would confuse the issue.  Therefore the CC pipe was chosen for the experiment here, so that its higher fundamental frequency (about 65 Hz) should be less likely to present this difficulty.

 

Just as interesting is that one can hear a difference in the two sounds if the second harmonic rather than the fundamental is removed.  This is demonstrated in the clip below, which was otherwise prepared in the same way as above:

 

Trombone 16' C2, St George's, Dunster - 2nd harmonic removed (162 KB/10s)   

An audible difference is also perceptible if other harmonics, such as the third, are removed instead.

 

It is interesting to speculate on how these results suggest the brain might be processing the information in the sound wave picked up by the ear.  It is related to the phenomenon of masking but further discussion would be too much of a digression here.  For present purposes we need only note that the brain has no difficulty in assigning the correct musical pitch and timbre to a reed pipe whose fundamental is completely absent.  This is a remarkable aural illusion.  In other words the brain does, in effect, reinsert a weak or missing fundamental in certain circumstances.  In turn, this explains why pipes with half-length  resonators can be surprisingly effective as pedal reeds.  Nevertheless the effect does depend on the amplitude of the fundamental relative to the rest of the spectrum.  In this case the spectrum (Figure 3) shows that it is much weaker (36 dB) than the second harmonic (56 dB) to start with, which means it only has one tenth of its amplitude.  Therefore one could argue that it is not surprising such a relatively weak component of the total sound cannot be heard even when it is present.  Against this is the fact that removal of the fundamental is still unnoticeable even when one increases its amplitude four-fold, i.e. if it is boosted by 12 dB to 48 dB.  This experiment can also be done easily using the same digital processing system as before.  Beyond this level it does begin to become perceptible as a separate aural entity, and it then starts to become noticeable when it is removed.  But it is even more remarkable that when boosted, a fundamental only 8 dB (a factor of 2.5) lower than the second harmonic can still be removed without affecting the sound.  This does not apply to harmonics above the fundamental, whose presence is critical to the perceived timbre as demonstrated above.

 

It is also important to note that the effect is only obtained when an extensive harmonic series is present, as it always is for pedal reeds.  If only a few harmonics exist, as with large flue basses which frequently have less than ten, a missing fundamental is obvious - the ear does not reinsert it in these cases.  This is why ‘resultant bass’ 32 foot stops are so unsatisfactory (see note [12] for more details).

 

 

Oboes

   

 

Figure 4. Oboe and Cor Anglais pipes

 

One of the quieter group of reeds, the oboe family has comparatively thin conical resonating tubes sometimes crowned by a bell or flare as in Figure 4. Presumably these are intended to approximate more exactly the tone of the orchestral cor anglais or oboe respectively by aping their construction.  However since there is often little resemblance between the tone of organ oboes and their orchestral counterparts in practice, perhaps one can be forgiven for concluding that there is little justification for the considerable extra trouble (and therefore cost) in making the pipes that way.

 

Nevertheless, a few examples exist which show that a skilled voicer can coax a closer imitation than that which we get with the general run of organ oboes.  In these cases it is likely that he has hit on an optimum harmonic recipe of the driving waveform emerging from the shallot.  He will have achieved this largely by carefully shaping the shallot aperture, by meticulous attention to the tongue curvature and by adjustments to the wind pressure.  He will also have used a tube which has the optimum flare so that the correct frequency taper is applied to the harmonic spectrum generated at the shallot.  Regardless of whether this occasional happy state of affairs arises by accident or design, there is little wonder that the most successful reed voicers keep their secrets very much to themselves!

   

 

Figure 5.  Oboe 8' spectrum (F#3, swell organ, St Mary's, Ponsbourne, Walker, 1858)

 

The harmonic spectrum of a quiet Victorian organ oboe, recorded on the 1858 Walker organ at St Mary’s, Ponsbourne near Hatfield [13], is shown in Figure 5.  There are about 9 harmonics within a frequency span of 3 kHz, rather less than one observes with the general run of trumpets.

                       

 

Figure 6.  Orchestral Oboe 8' spectrum (F#3, St Albans music museum, Wurlitzer, 1933 )

 

At the other extreme one gets the orchestral oboe, a penetrating and thin-toned stop supposedly imitative of the woodwind instrument.  A spectrum of such a pipe is shown in Figure 6, recorded on the Wurlitzer theatre organ now in the St Albans music museum.  Originally this instrument was installed in 1933 in the Empire cinema, Edmonton on the northern fringes of London.  There are about 18 harmonics within a 7 kHz frequency range, more than most trumpets and considerably more than the quieter swell oboe illustrated above.  As at Malvern Priory this organ, too, had rather noisy wind at the time the recording was made, and again this is reflected in the appearance of the spectrum.

 

 

Reed Pipes with Cylindrical Resonators

 

The effect of using a cylindrical rather than a conical resonator is discussed in detail in [6].  In some respects it acts like an upside-down stopped flue pipe because the point at which the resonator meets the shallot is deliberately made to have an acoustic impedance mismatch, and this is analogous to the stopper in a flue pipe.  A further mismatch occurs at the open end because the tube is not flared to act as an acoustic transformer, and this is similar to the mismatch which occurs at the mouth of a flue pipe.  Together with the half-length resonator, the result is that the even-numbered harmonics generated by the reed are partially suppressed, just as in a flue pipe and for similar reasons.  It is a common misconception that a reed pipe has to be cylindrical for this to happen, whereas the only requirement is that its cross-section must not vary.  Therefore square or rectangular resonators would work just as well, as they do with stopped flue pipes.  Such a pipe would merely be more difficult to make in metal and join to the shallot, which is why cylinders are used more frequently for reeds.  The important point is that the tube must not flare, otherwise the impedance discontinuities at the ends which are so essential to its working would not be pronounced enough.

 

Examples of cylindrical reed pipes

 

Clarinets

 

Because of the significant impedance mismatch at the top of a cylindrical pipe where it has to radiate power into the auditorium, all such stops cannot be anything other than fairly quiet.  Raw power can only be obtained from flared resonators.  For this reason stops with cylindrical tubes exist as various ‘colour reeds’, either for solo use or for adding a subtle piquancy to the fluework, and in this respect they are similar to the quiet conical reeds such as oboes.  However any similarity ends there, because the ‘hollow’ tone of cylindrical stops is quite different on account of the even-numbered harmonics of lower power.  The clarinet is one of the commonest examples, and as it also exists in the form of a number of minor tonal variants with different names, we can loosely treat such stops as forming the clarinet family as was done above when discussing the oboes.

   

 

Figure 7. Clarinet pipe

 

Figure 7 illustrates a typical clarinet reed pipe with its conical resonator and slotted tuning cap, and the frequency spectrum of a similar pipe, a Corno di Bassetto from the stop of that name in the organ at Malvern Priory, was given in [6]. 

   

 

Figure 8.   Krummhorn 8' spectrum (C3, swell organ, St George's, Dunster, Hill, Norman & Beard, 1962)

 

Yet another stop from the clarinet family is the Krummhorn, and the spectrum of such a pipe (middle C) from a modern stop is at Figure 8.  This was derived from recordings made on the HNB organ at St George’s, Dunster.  Often the Krummhorn will sound somewhat thinner and more plaintive than the clarinet, partly because it has more harmonics, and this example also shows the suppressed even-numbered harmonics very nicely.

 

Oohs and Aahs - the Vox Humana

 

The vox humana has existed for centuries.  As made today its pipes are broadly similar in appearance to those of a clarinet, except that the resonators are much smaller.  Typically they are only about one eighth as long as those of the clarinet which means they exert far less control over the tone emitted from the shallot, though their resonant frequencies are still essential to the tone-forming process.  The stop remained popular in romantic organs of the nineteenth century and into the twentieth, and (for instance) César Franck called for it explicitly in his Choral number 1 in E where he specified “Voix Humaine et Tremblant” at several points.  It was given a considerable shot in the arm during the heyday of the theatre organ, and this still continues to nurture interest in it today.

 

For the purposes of this article it is useful to recast the musical value of the stop on a theatre organ in acoustic terms, and it is mainly related to the way it blends so happily with the tibias.  This is because the tibia has weak even-numbered harmonics [2], as do some examples of the vox humana itself.  When present, this latter property is of course the result of the vestigial cylindrical resonator in the same way as for the clarinet.  A favourite combination is to use the vox humana at 8 foot pitch and a tibia at 4 foot, and when one does this an entirely different composite sound emerges on a good instrument.  It is almost impossible to emulate this satisfactorily other than on a theatre organ because it is only this type of instrument which has both tibias and vox humanas at various pitches.  Particularly when tremulated, this sound is one of the hallmarks of the theatre organ, and it derives its unique character from the fact that the strong odd harmonics of the octave tibia reinforce the even harmonics of the vox humana in a subtle manner.  It is subtle because not all of the vox humana’s even harmonics are reinforced in the same way - the 2nd, 6th, 10th, etc are reinforced strongly but the 4th, 8th, 12th, etc are only reinforced weakly.  This arises because of the octave separation of the two tones.  The resulting spectrum is completely different to either of the constituent ones, giving a novel and synthetic flavour to the sound which cannot be obtained from any single stop on any type of organ.  In the days before electronic synthesisers one can see why the theatre organ became so popular for such reasons.

 

Given these eulogies, it is all the more extraordinary that the vox humana on its own sounds so weak and pathetic.  Percy Scholes likened it to the sound of a discouraged goat, presumably emboldened by the greater Dr Burney who thought it resembled an old woman of ninety or Mr Punch singing through a comb [14].  However, it is telling that the attempts by these gentlemen to discredit the vox humana as an imitation of the vocal utterances in higher mammals relied on the non sequitur that they agreed it did resemble the vocal utterances of higher mammals.  Few seem to have directed a more objective gaze on this centuries-old attempt to imitate the human voice, yet more than one musician of my acquaintance whose judgements and ears I respect have persuaded me that the best examples do have a certain je ne sais quoi about their tone which sometimes does have a flavour of a nasally-challenged person trying to sing.  One of these musicians plays the theatre organ among other instruments, and he once complimented me (I think) on an attempt to simulate a Wurlitzer vox humana digitally by saying that it had “something of the ‘oohs’ and ‘aahs’ of the real thing”.  Therefore this led me to study the matter in a little more detail, on the basis that there must be something in it if the well-honed ears of at least some highly trained musicians think so.

 

The main difficulty in analysing the harmonic structure of the vox humana is its extreme variability, not only between the stops of different organ builders but among the pipes of a given stop.  For example, one pipe might exhibit even-numbered harmonics which are weaker than the odd-numbered ones, yet an adjacent one might not.  It was therefore difficult to draw general conclusions, apart from one feature which emerged during the study.  An artefact which appears frequently is the presence of a strong harmonic in the spectrum which is well separated from the fundamental.  This harmonic often stands out to the eye in a spectrum plot because it is appreciably stronger than adjacent ones, and its absolute frequency does not deviate much regardless of note over a span of several octaves.  It can be seen clearly in the spectrum of the middle F# pipe of the 8 foot vox humana stop on the Wurlitzer organ at St Albans, shown in Figure 9.

   

 

Figure 9.  Vox Humana 8' spectrum (F#3, St Albans music museum, Wurlitzer, 1933 )

 

For this note the prominent harmonic is the fifth, which lies at a frequency of 1850 Hz.  The frequency of the dominant harmonic was also measured for all other C and F# notes in the first four octaves of the keyboard.  Note that it is the absolute frequency which remains fairly constant, not the serial number of the prominent harmonic.  Thus for bottom C the twentieth harmonic is the dominant one, whereas for F# in the middle octave (shown in Figure 9) it is the fifth. The results are shown as the pink line in Figure 10.  Also plotted as the blue line are the fundamental frequencies (pitch) of each note.

   

 

Figure 10. Vox Humana formant frequency variation (St Albans music museum, Wurlitzer, 1933)

 

Since the frequency scale on the vertical axis is logarithmic, the blue points lie exactly on a straight line.  This is because the pitch frequency of any keyboard instrument always varies logarithmically note by note across the compass, and plotting any logarithmic quantities using a log scale results in a straight line.  The interesting aspect is that the frequencies of the dominant harmonic also lie pretty much on a straight line, but the variation across the compass is much smaller.  These frequencies only vary by a factor of 2.4 over the four octaves whereas the pitch frequency variation is a factor of 16.  In fact the absolute frequency of the dominant harmonic over the middle two octaves from F#2 to F#4, where it is musically most important, deviates only about 18% from the mean frequency in this region.

 

Therefore one can reasonably assume that the effective lengths of the vox humana tubes were adjusted, pipe by pipe, to resonate at this frequency (about 1850 Hz) by the voicer.  One can further assume that tube length does not (indeed, should not) change as rapidly over the compass as does that of an ordinary stop so that the relative constancy of the dominant frequency can be maintained.  Because it is so short, the first natural resonance of the tube can only emphasise a frequency well above the fundamental frequency emitted from the shallot.  Except for the topmost notes it is far too short to resonate at the fundamental itself, which is why this frequency is almost absent from the spectrum in Figure 9. 

 

In musical acoustics this feature is called a formant frequency, one which does not vary much even though the note being played or sung does.  Formants characterise the sounds of virtually all melodic instruments and the human voice itself.  Being a tad charitable, the most obvious conclusion one can draw from the evidence above is that this stop was probably intended to resonate at the so-called ‘singer’s formant’ [15].  This is a special frequency band which occurs only in the singing voice of a trained adult male singer; it is not seen in normal speech nor in women or child singers.  However the singer's formant is in the frequency region 2500 - 3000 Hz, somewhat higher than the formant frequency at about 1850 Hz measured for the Wurlitzer stop in this study.  The fact that the frequencies do not correspond very well is actually of little account, because using a slightly shorter resonating tube would bring them closer.  Were it deemed desirable, this could be probably be done by no more than a careful readjustment of this stop at the resonators by an expert voicer.

 

An alternative, though perhaps less compelling, interpretation of this formant is possible if we consider the acoustic properties of the human voice in a little more detail.  The vocal tract of all people, not just singers, exhibits four formant bands which characterise the resonant cavities within it.  Under the control of the brain they are continuously variable over certain frequency bands during articulation, and the first two having the lowest frequencies are the most prominent.  As an example, for a child singing ‘ah’ (as in ‘father’) the first two formant frequencies are around 875 and 1375 Hz [15].  With a minor stretch of the imagination one might therefore postulate a correlation between the second ‘child’ formant at 1375 Hz and the vox humana formant identified here at 1850 Hz.  As with the singer’s formant, changing the length of the resonating tube (but making it slightly longer this time) would bring them closer. 

 

Because human vocal formants are continuously variable and because of the random variability of vox humana sounds mentioned earlier, it is not appropriate to pursue these analogies too far.  However there is clear evidence that this Wurlitzer vox humana stop does have a formant frequency, and maybe it is this which endows the stop with its peculiar humanoid qualia. Therefore, although the similarities do not transcend those of the Tweety Pie variety, maybe the best examples do indeed have their ‘oohs and aahs’ as my musician friend insisted.

 

As it is, this particular Wurlitzer stop lies somewhere between the two types of voice (child and adult male) in terms of its formant frequency, though whether this reflects accident or design is impossible to say.  However it is fitting to pay tribute to the pipe maker and voicer of this Wurlitzer rank who obviously succeeded in maintaining its acoustic properties so uniform across the compass, using an impressive blend of experience and the voicer’s ‘ear’.  It is perhaps not surprising that Walter Strony considers the Wurlitzer vox humana to be the most successful of its genre [16].  Beyond this however, the complete absence of any indication in the literature as to what, if anything, guides organ builders in making their vox humanas renders it pointless trying to read much into the design and construction of the stops they turn out.  This is unlikely to change in view of the perceived unimportance and therefore the rarity of the stop in modern organs.

 

The results just presented are thought to be original, at least in the sense they do not seem to have appeared in the public domain before.  However attempts have been made to simulate the vox humana stop since the earliest electronic organs appeared, and these are briefly discussed below in reference [17].  So, speaking of electronic organs, you might as well hear what my simulated Wurlitzer vox humana sounds like, using samples recorded on the one discussed above at the St Albans music museum.  The clip below is a short extract from Franck's piece already mentioned, his Choral No 1 in E major, played on my Prog Organ simulation of the St Albans Wurlitzer.  At bar 47 he asks for “Voix Humaine et Tremblant”, though whether he meant this literally is open to debate.  Most players use a quiet 8 foot flute as well, such as the cor de nuit often included on the récit division of Cavaillé-Coll organs where the vox might also be found.  However I have not done this so that the vox humana can be heard on its own.  The tremulant here is not dissimilar to the fluttery ones sometimes made by Cavaillé-Coll, such as that on his organ at St Sernin, Toulouse.

 

Extract from Choral No 1 in E (César Franck) - 674 KB/43s

 

(Wot, Franck on a Wurlitzer, and a digital one at that?  Whatever next).

 

 

Conclusions

 

This survey of a range of reed stops having both conical and cylindrical resonators has included the different acoustical physics and tonal characteristics of the two varieties.  Conical resonators enable a stop to sound more powerful on account of its acoustic transforming or impedance matching action between the shallot and the listening environment.  Full-length resonators also enhance to some extent all the frequencies generated by the vibrating reed, but the enhancement is not uniform because at higher frequencies there is a divergence between the anharmonic natural partials of the tube and the exact harmonics of the reed waveform.  The degree of divergence varies according to the scale of the pipe, with narrower pipes enhancing the higher harmonics more than wider ones. 

 

Half-length conical resonators do not enhance the fundamental at all yet, surprisingly, this is scarcely noticeable to the ear.  To prove this, audio clips were included showing that the complete removal of the fundamental in the sound of a reed pipe does not necessarily affect the way it sounds.  It is thought to be the first time that this effect has been demonstrated in the public domain, and it explains in terms of their acoustics why half-length pedal reeds can be so effective.

 

The cylindrical resonators of fractional length used in stops such as the vox humana were discussed in detail.  Development of this stop over several centuries has been driven by a desire to imitate the human voice, and this was investigated to see if an objective basis for the attempt could be found.  An analysis of the sounds produced by a Wurlitzer vox humana rank showed that it possessed a relatively constant formant frequency over a range of four octaves centred on middle C.  This frequency, at about 1850 Hz, lies between the second formant of a child’s voice when singing ‘ah’ and the so-called ‘singer’s formant’ of an adult male.  Therefore it is possible this formant does indeed contribute to a similarity which the best stops of the genre are said (by some) to possess.  These results are original and presented in the public domain for the first time.

 

 

Notes and References

 

1. “How the Flue Pipe speaks”, C E Pykett, 2001.  (read)

 

2. “The Tonal Structure of Organ Flute Stops”, C E Pykett, 2003. (read)

 

3. “The Tonal Structure of Organ Principal Stops”, C E Pykett, 2006. (read)

 

4. “The Aural Perception of Organ Tones”, C E Pykett, 2007. (read)

 

5. “Gottfried Silbermann’s Fluework”, C E Pykett, 2008 (read)

 

6. “How the Reed Pipe Speaks”, C E Pykett, 2009. (read)

 

7. Sometimes people complain that they have to pay for waveform samples recorded on pipe organs in public places and that their use is subject to licensing conditions, so a few words about the procedure might help to explain why.  Firstly one has to get permission to record the instrument and, if granted (which is by no means certain), this generally involves a fee.  The owner of the organ will sometimes also impose conditions as to how the samples may be used subsequently.  Then one has to get to the venue with a considerable amount of equipment, and usually stay in the area for at least one night.  This will be necessary because of the distance involved, and/or because the recording session itself has to be at night to reduce traffic noise etc.  Typically, the equipment will include at least two professional-grade microphones and stands, and at least two digital recorders so that a backup recording is available from the outset.  The recorders might be DAT or Minidisc machines or a laptop recording onto CD.  I find that ancillary equipment is also mandatory such as audio monitors, audio pre-processing modules such as highpass and lowpass filters, and possibly a small mixing desk.  The cost of all the leads is not insignificant (and woe betide you if you forget to take any of them).  Thus the up-front investment in equipment alone has already run into thousands of pounds.  An assistant is usually indispensable, and you will usually have to cover his/her services including accommodation and travel costs.  Liability insurance is also highly advisable in case you fall inside the organ and ruin hundreds of pipes, not to mention the effects on yourself or your assistant.  Then, having returned to base, the analysis programme begins ....

 

Had I not done all this in many locations over several decades, you would not be reading this article because it could not have been written.  And no, I am not one of those who asks you for a contribution for the privilege.  But maybe spare a thought for the hard-pressed sample set producer in future!

 

8. I often wonder why people seem so confused by the etymology of the word ‘cornopean’.  In fact it was in popular usage in early Victorian Britain, and (for instance) it appears in several places in Thomas Hughes’s novel Tom Brown’s Schooldays.  Looking beyond its priggishness, the book reflects some interesting social history and it is worth reading it to find the occurrences.  These suggest that the name referred to any sort of horn as used on stage coaches, as well as various other instruments of entertainment  to be found in diverse places, though mainly the bawdier ones.  Whether any of these were valved remains unclear, suggesting the assumption that the name is a corruption of ‘cornet à pistons’ might be one of those misapprehensions which has become part of organ folklore.  However, if it is not a misapprehension, then all I can say is that any cornopean stop I have ever heard sounds nothing like a cornet, pistons notwithstanding.  The organ cornopean is merely a milder version of the organ trumpet, quieter and with relatively stronger lower harmonics - nothing more, nothing less.

 

9. It is worth saying a few words about extraneous noises, particularly blower noise, in view of the frequent use of ‘sampled’ pipe organ sounds in digital organs.  Clearly one could not use directly in any digital organ the excessively noisy raw recorded waveform of the Malvern Priory trumpet stop, as in the sound clip above.  Apart from anything else, the noise would be present on all samples, and it would therefore build up in a ludicrous manner as more notes were played.  Therefore it is necessary to process (‘denoise’) the raw samples in some way before they can be used.  The denoising procedure can affect the sound markedly, and this means a digital organ using sampled waveforms might not correspond quite as closely to the original pipe organ as some manufacturers would have us believe.

 

10. The spectrum of the trumpet pipe shown here in Figure 2 is slightly different in detail to that which appears in Figure 8 of the article “How the Reed Pipe Speaks” [6], even though the two spectra were computed from the same recorded waveform.  The reason is that the short waveform segments used in the two cases were different, having been arbitrarily snipped out from different parts of the longer recording.  Therefore one is seeing an example of the small variations in harmonic amplitudes which take place as an organ pipe speaks a sustained note.

 

11. “Voicing Electronic Organs”, C E Pykett, 2003.  See Figures 11 and 12 in the section entitled ‘Software Tools’ (read)

 

12. One can remove the fundamental from the waveform of a large flue pipe, such as a 16 foot open wood, in the same way as for reed tones in the audio examples above.  However, unlike with a reed, it leaves an entirely different sound in which the deep bass vanishes, to leave the second and third harmonics prominent and easily identifiable.  These lie at the octave and twelfth respectively of the missing fundamental and they are therefore a fifth apart.  For the lowest notes one can also hear the suboctave beat frequency between them, which is numerically the same as that of the fundamental which has been removed.  However the point is that there is no acoustic power in a beat.  Thus the poor suboctave illusion created by a ‘resultant bass’ stop only occurs because the ear is able to follow the amplitude envelope, i.e. the slow beat frequency, of the two pipes to some extent.  This is not at all the same thing as reinserting the missing fundamental of a real 16 foot pipe.

 

The fact that no power is generated at the fundamental frequency by a beat explains why ‘resultant’, ‘acoustic’ or ‘quinted’ 32 foot tone using a pair of large flue pipes a fifth apart in the 16 foot octave is ineffective and disappointing, because one only hears the two generating waveforms.  At higher frequencies the beat becomes too fast for the ear to follow, and there is then no suboctave illusion at all.  Those who doubt this only need to play, say, middle C and the G above it on an 8 foot stop to discover that no vestige whatever of a resultant note at tenor C can be perceived.  Illusions are fine provided one does not confuse them with reality!

 

13. “Gleanings from the Cash Book: St Mary’s Hatfield: Church Expenses”, P Minchinton, Organists’ Review, May 1999.

 

This article described this interesting and historic little organ of 1858 by J W Walker, and thanks are also due to Mr Minchinton for having provided the samples from which the oboe spectrum in this article was derived.

 

14. “The Oxford Companion to Music”, Percy A Scholes, tenth edition, Oxford, 1970, p. 734.

 

15. “Fundamentals of Musical Acoustics”, A H Benade, second edition, Dover, New York, 1990, p. 360 et seq.

 

16. “The Secrets of Theatre Organ Registration”, Walter Strony, published privately, 1991.

 

17. The first commercially successful analogue electronic organ using subtractive tone synthesis was the Baldwin Model 5 which appeared in 1946.  It was invented by Winston Kock who had previously gained his PhD in Germany under the guidance of K W Wagner and others, and it was this group which first used the name ‘formant’ in their speech and music research.  From the outset the Baldwin organ featured a vox humana stop using a tone-forming circuit which was widely copied in other manufacturers’ products almost up to the turn of the millennium.  Even today some of those who use Moog or similar analogue synthesisers (or digital emulations of them) still use Kock’s vox humana circuit or variants of it.  A fuller account of Kock’s development of the Baldwin organ is available elsewhere on this website in the article “Winston Kock and the Baldwin Organ” (read).

 

Being commercially confidential, the technical background to Kock’s work was never published, and consequently his filter designs are still regarded as something of a black art in the electronic music community.  However they yield to analysis, and it is noteworthy that his vox humana circuit contained two resonant sections.  Examination of the circuit shows that they resonated at frequencies close to those of the two principal formants of a child singer.  With his then-recent technical background in Germany it is not surprising that he had access to such data, which were novel and not well known at the time.  Therefore it seems that Kock attempted to directly emulate the human vocal tract with its multiple formants, rather than emulating the vox humana stop of the organ which only has one, as my work above has shown.