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The Tonal Structure of Organ String Stops
by Colin Pykett
Gamba, meaning 'leg', must rank as the daftest organ stop name ever. And it's up against some stiff competition.
Posted: 14 November 2012 Last revised: 19 January 2015 Copyright © C E Pykett 2012 - 2015
Abstract. This article surveys the physics of string toned organ pipes at a non-mathematical level but without omitting the important features. On the contrary, some original material is presented for the first time, including a description of the physics underlying the range of adjustments available to the pipe voicer rather than merely describing their effects on the pipe sounds. The effect of nicking is discussed in particular detail because its mechanism at a physical level is not treated elsewhere. Among other things it is shown how nicking induces turbulence in the air jet issuing from the flue, and the effects this has on pipe speech is also covered.
The tenuous subjective correspondence between the sounds of bowed string instruments and string toned organ pipes is examined, and it is shown that both have a large number of harmonics. In the case of the organ this can sometimes exceed the number exhibited by reeds in the case of a 'keen' imitative string pipe. Nevertheless the harmonic generation mechanisms are entirely different in the two cases, and it is shown that the oscillating air jet at the mouth of a string pipe can be treated as a pulse generator whose mark-space ratio can be adjusted by the voicer. This enables the number and distribution of harmonic amplitudes in the frequency spectrum of the driving waveform to the resonator to be varied.
The sound radiated by a keen-toned string pipe has a uniquely interesting frequency spectrum as far as the family of flue pipes is concerned, in that the first few harmonics almost always increase in amplitude before falling away thereafter. This is attributed to the relatively poor radiating efficiency of a small-scaled (narrow) pipe which attenuates the radiated power at lower frequencies.
Contents (click on the subject headings to access the desired section)
Several articles on this website deal at length with the production of sound by organ pipes. Two of them describe the basic physics of flue pipes [1] and reed pipes [2] without recourse to mathematics. Using these as a generic starting point, another three articles then go further into details peculiar to the sounds of flute stops [3], principals (or diapasons) [4] and reeds [5]. This one now considers organ strings in a similar manner, and as these are flue pipes frequent reference will be made to the broader description of how this type of pipe works [1]. For this reason it might help to open it in a separate window if you want to follow some of the arguments here in more detail.
These four classes of organ tone - flutes, principals, strings and reeds - have existed in the instrument for centuries. For instance, J F Wender incorporated all four in just one division (the Oberwerk) of his small two manual organ at the Neue Kirche, Arnstadt as long ago as 1703. This instrument remains famous as that which J S Bach tested and subsequently presided at while he was still a teenager. The string stop in this case was called a Viol di Gamb, a name which is interesting in itself. To the best of my knowledge it was spelt like this in Wender's original contract of 1699 which still survives [6], though in the present organ reconstructed in 1999 by Orgelbau Hoffmann [7] it appears as a Viola di Gamba [8]. But aside from such etymological minutiae, the main point of interest here is that attempts were obviously being made over three hundred years ago to create an impression in the organ of the sounds of a contemporary stringed instrument. Its name lets slip the clue as to why this was so in view of the fashionable Italian influence in music at that time, which presumably encouraged the drive towards such imitative effects.
This article is thought to be unique. It explains how string-like tones can arise from an instrument using wind rather than strings, and some of these details have not appeared previously in the public domain. It further explains how the main voicing practices applied to string toned organ pipes actually work at a physical level, including that most mysterious of techniques known as nicking. The article also completes the series dealing with the four main classes of organ tone (references [1] to [5] plus this one), which itself is the only one of its kind.
There is a considerable range of string toned stops in the organ with an equally considerable range of names, some of them not only fanciful but frankly silly. In these respects, therefore, organ strings are no different to the flutes, principals and reeds. Surely the ridiculously contracted name 'gamba' would not have been applied so widely had people thought for a moment what it actually means? String pipes are of either metal or wood, though the critical voicing adjustments required to get them to speak properly, of which more later, means that it is practical to make only the longer ones of wood. The stops are found at several pitches on both manuals and pedals, examples at 16, 8, and 4 foot being widespread. But higher and lower pitches are not unusual, and even mutation ranks and string mixtures have been made. Strings play an indispensable role in the chorus work and sounds of the theatre organ. In all instruments, including the smallest, one is likely to find the undulating stops involving detuned string ranks (celestes) which are a near-ubiquitous feature.
No attempt will be made here to describe the morphology of string pipes in detail - their history and evolution, shapes, sizes and methods of construction - because illustrative material of this sort is widely available elsewhere. However the pipes are of smaller scale, that is they are narrower, than those of other flue stops. It would be unusual to find an 8 foot string stop of even the mildest tone with pipes larger than 50 mm in diameter (under 2 inches) at middle C, and for 'keen' imitative strings it will be much smaller. The 8 foot Viol d'Orchestre on the choir organ of the famous Hope-Jones instrument of 1896 at Worcester cathedral had pipes so slender that the longest ones (27 mm in diameter at CC, barely over an inch) had to be enclosed in wooden sleeves to protect them. Recently this stop has been touchingly retained in the solo division of Tickell's rebuilt Worcester organ of 2008. These narrow scales encourage the retention and acoustic radiation of the extensive harmonic series generated at the mouth. The pipes also have to be made somewhat longer than other flue pipes speaking the same note because their end corrections at the top are smaller than those of wider ones.
Some imitative stops with names suggestive of orchestral instruments (e.g. Viol d'Orchestre) tend to have keener tones than others, their mouths tend to be laterally narrow relative to pipe diameter, they have a low cut-up, languids are heavily nicked and fairly high wind pressures are used. The longest pipes of these stops, below tenor C on an 8 foot rank, also use 'beards' or bars across the mouths, not only to stabilise their speech but to enable them to speak at all. Many string stops have pipes equipped with a range of appurtenances such as bells or cones. Some pipes are closed at the top and speak through a hole or vertical slot, whereas still others are open but retain the slot. Some of these artefacts can be related to the physics governing pipe speech and they are touched on later, but others seem to be of doubtful value given the additional difficulties they throw onto the long-suffering pipemaker.
Early string stops such as those of Wender could only have had a mild tone quality, possibly little different to a geigen diapason. Even if his Viol di Gamba had aural similarities with those of the same name today [9], he could not have gone further to produce the extremes of keen string tone which we find in modern imitative stops such as the Viol d'Orchestre. These did not appear until the middle of the nineteenth century when William Thynne applied a beard to the mouths of exceptionally small-scaled (narrow) metal pipes to enable them to speak in the bass register. Not long afterwards the method was appropriated by Robert Hope-Jones who employed Thynne's disciple, John Whiteley, one of the several skilled voicers who enabled H-J to realise the extremes of tonality which became a hallmark of his organs. Similar voicing techniques were used by makers of fairground organs, notably Anselme Gavioli, whose instruments (containing 'violin' ranks) had to shriek as loudly as possible in the open air.
The narrowness of string toned pipes means they encourage the retention of more harmonics than would wider pipes for the reasons described in detail in reference [1] (see the section entitled 'The Influence of Pipe Width on Tone Quality'). The explanation is that the natural frequencies of a narrow pipe coincide closely with those of the harmonics generated at the mouth, and therefore the former tend to amplify the latter through a process akin to resonance. A range of more or less critical voicing adjustments also play an important part in generating more harmonics to start with as the air jet issuing from the flue interacts with the mouth. Thus the mouths are cut low, around 6 mm at middle C of an 8 foot stop, which is only about half the cut-up of a typical principal. (See 'The Influence of Voicing Adjustments on Tone Quality' in [1]). Another adjustment in the voicer's repertoire is the setting of the languid so that the air sheet hits the top lip at the correct angle. This is particularly critical for strings, because if the voicer does not get it right the pipe might well not speak at all. The physics of the mouth-languid interaction is so interesting that a fuller description will be deferred until later. For now it is only necessary to take away the fact that the sounds of string toned pipes have lots of harmonics.
Because organists are thoroughly familiar with string toned stops and have been so for centuries, it sometimes requires a conscious effort to remember that they produce their sounds by blowing air through pipes rather than by bowing a string. Since the two sound production mechanisms are entirely different, it is perhaps remarkable that the slightest vestige of subjective similarity can (sometimes) exist. Therefore it is convenient to continue the discussion of the tone quality or timbre of string toned stops by looking briefly at some characteristics of bowed-string instruments at a simple level. Well over a century ago the astonishingly gifted German polymath, Hermann von Helmholtz, was the first to observe directly (i.e. with his eyes) how a bowed string vibrates by means of some exceptionally elegant experiments [10]. He confirmed what intuition suggested, that the string executes a sort of stick-slip motion as the bow drags it to a point at which its increasing tension then causes it to return rapidly towards its original position. When this motion is repeated, the string therefore oscillates in a sawtooth-like fashion at a particular frequency. Although this is a simplified description of just one aspect of a complex range of behaviours, a bowed string nevertheless does demonstrate periodic (cyclically repeating) near-sawtooth displacement regimes in some circumstances [11]. Of course, the resulting vibrational energy from the string is then modified in diverse ways by body resonances and other factors before radiating into the surrounding air, these features accounting for much of the tonal subtlety of stringed instruments which we shall not go into here. However, because we can legitimately regard a bowed string as a mechanical generator of sawtooth waves under some conditions, we can proceed to understand the subjective similarity between the sounds of stringed instruments and string toned organ pipes. What links the two types of sound as far as the ear is concerned are the gross features of their respective harmonic structures, which turn out to have some aspects in common.
Figure 1. A sawtooth wave and its frequency spectrum showing its harmonics
Figure 1 shows both a sawtooth waveform and its frequency spectrum, that is, a graph of the harmonics contained in the wave. A sawtooth waveshape is that which approximately describes the periodic stick-slip displacement of a bowed string as discussed above. Its first harmonic is the fundamental frequency which has been assigned an arbitrary level or amplitude of 60 decibels (dB) in the frequency spectrum, because for the purposes of this discussion it does not matter what value is used. Thus we see that a logarithmic scale has been employed for both axes of the spectrum because decibels are defined using logarithms, and in the case of the horizontal axis it explains why the harmonics get progressively squeezed together towards the higher frequencies. Although you might think this complicates the situation, it has been done so that an important feature of a sawtooth waveform can be illustrated. This feature is that the harmonic amplitudes decrease at a uniform rate of 6 dB per octave, as shown by the sloping dotted line. This can easily be seen from the graph because the second harmonic of any sound is always at twice the frequency of the first (the fundamental), and therefore it is one octave above the fundamental. Their amplitudes differ by 6 dB, which means that the smaller one is half the amplitude of the larger. The same ratio applies to the amplitudes of the 2nd to the 4th harmonics, the 4th to the 8th, and so on because these pairs are all one octave apart in frequency.
Another important feature of the harmonic spectrum follows from the foregoing, and this is simply that there are a lot of harmonics in a sawtooth wave and hence in the sound of a bowed string. The gentle slope of -6 dB per octave means that the harmonic amplitudes decrease relatively slowly as frequency increases, and consequently there are many of them before they finally decay into insignificance. Armed with these observations we can now proceed to examine the sounds of real string toned organ pipes, which in this article incline towards the keener-toned class of stops. There would be no point delving too deeply into those with milder tones because these are little different in kind to small-scaled principals both in terms of their sounds and their physics, and for these reference [4] can be consulted.
Figure 2. Harmonic structure of a Viol d'Orchestre organ pipe (Malvern Priory, England)
The harmonic structure of a pipe forming part of a keen string toned organ stop is shown at Figure 2. This was derived from my own recordings of the large and beautiful organ by Rushworth and Dreaper at Malvern Priory, England and this example corresponds to the F# pipe above middle C of the 8 foot Viol d'Orchestre stop on the solo organ. The harmonic structure of the pipes making up any given stop varies randomly to some extent from note to note, and it also varies systematically across the compass as a result of the pipe scales and voicing techniques used. However these issues do not affect the following discussion because the example shown is representative of imitative string stops as a whole for present purposes. The first point to note is the large number of harmonics, as in the case of the sawtooth wave. About 30 can be seen in the figure, and many more actually existed at even higher frequencies within the dynamic range of 60 dB which was analysed (a factor of 1000:1 in amplitude). It is also of interest that in this case the harmonic amplitudes fall off at rate of close to -6 dB per octave over part of the spectrum (between the 5th and 10th harmonics), again as for the sawtooth. One must not press the analogy between sawtooth waves and string toned organ pipes too far because the spectrum in Figure 2 represents the sound emitted by an actual pipe, a complete 'musical instrument' if you will, whereas that in Figure 1 merely corresponds to a simplified model of a bowed string with no consideration of what the rest of the instrument does to the vibrational energy it generates before we hear the sound. Thus it is interesting that any correspondences exist at all given these major differences, and they offer at least a partial explanation of the subjective tonal similarities between string and pipe.
As well as the similarities, there are of course several obvious differences between the spectra of Figures 1 and 2 and these will be discussed presently. But returning to the number of harmonics in the spectrum for a moment, it is the case that organ strings often contain more harmonics than any other class of tone. This includes the reeds, which also exhibit extended harmonic structures. However it is possible to generalise by saying that reeds frequently present a spectrum in which the harmonic amplitudes fall relatively slowly between the fundamental and the 5th - 10th harmonic or so, but then they fall off more rapidly. This gives reed spectra a characteristically different shape from those of strings, which of course explains why they sound markedly different.
Figure 3. Harmonic structure of a typical Cornopean organ pipe
An example of this effect in a reed spectrum is shown at Figure 3 which is of a Cornopean pipe. This confirms the statement just made in that there is a pronounced 'knee' in the spectrum, in this case beginning at the 5th harmonic. Beyond the knee, the rapid loss in amplitude with increasing frequency for reeds (much greater than -6 dB per octave) means that they frequently contain fewer harmonics than strings, at least those which have a keen imitative tone such as the Viol d'Orchestre discussed already.
Other types of flue pipe have far fewer harmonics than strings, as shown in Figure 4 where the harmonic spectrum of a Claribel Flute and a Diapason can be seen. Like the Viol above, the latter were also derived from recordings of the Malvern Priory organ.
Figure 4. The harmonic structures of flute and principal organ pipes (Malvern Priory, England)
We have seen that the spectrum of an imitative string pipe contains many harmonics, and this together with other similarities explains its (sometimes remote) subjective resemblance to the sound of bowed string instruments. However if we look again at its spectrum (Figure 2) there is a feature virtually unique to string toned pipes. This concerns the first four harmonics which increase in amplitude, whereas in other flue pipes the fundamental is almost always the strongest (Figure 4). The reason for this is the narrowness of the pipe in the case of strings. The open top of an organ pipe is subject to much the same rules of acoustics as a loudspeaker, and it is well known that loudspeakers have to be physically large when they are called upon to handle low audio frequencies (woofers and sub-woofers) whereas they need only be small for the high ones (tweeters). A loudspeaker designer uses the term “radiation resistance” to denote the equivalent electrical load which a loudspeaker throws onto an amplifier, and this means that the amplifier has to supply power to move the speaker cone against the air for it to radiate sound. This power is dissipated in the radiation resistance. Importantly, the radiation resistance varies with frequency for a given loudspeaker. However an organ pipe is not driven electrically, and therefore it is better to use the more general term “radiation efficiency” in this article to avoid confusion. Nevertheless the issues involved are much the same in the two cases. Here we use the term to denote how efficiently the power of the vibrating air column of an organ pipe is transferred into sound propagating in the atmosphere beyond it. Like a loudspeaker, the efficiency varies with frequency and hence it is a function of harmonic number. Let us imagine what happens to a sound pressure impulse travelling up the pipe towards the open aperture at the top. When it reaches the top it first compresses a column of the surrounding air in front of itself (which, incidentally, is the first step in the formation of the end-correction which increases the effective speaking length of the pipe). Immediately, the local pressure enhancement within the column begins to dissipate by air movement at the speed of sound from inside to outside the column, leading to outward propagation of a wave-like disturbance beyond the column itself into the auditorium. Rather like ripples on a pond, it is this which causes the sensation of sound which we hear at a distance from the pipe. Intuitively we may see that the wider the column (i.e. the larger the cross-section of the pipe) then the longer the pressure equalisation process will take, because a high pressure area in the middle of a fat column has further to move before it dissipates within the atmosphere at large than if it was in the middle of a thin column. This dissipation time governs the time for which outward sound propagation from the pipe will occur in response to an emerging sound pressure impulse, and hence the amplitude of the disturbance at a given distance from the pipe. Thinking further, it is possible to deduce that for maximally efficient radiation of a particular frequency, the diameter of the pipe should be some appreciable fraction of a wavelength. If it is not then pressure dissipation, at the speed of sound, will take place in too short a time for the frequency being radiated and the disturbance will die out quicker. This is a fundamental size requirement for all structures, whether acoustic or electromagnetic, which have to launch a disturbance into the environment efficiently. Therefore it also applies to loudspeakers as we have already noted, and to Yagi television aerials (antennas) whose rod elements have to be around half a wavelength long. It also applies to the cross-sectional area of organ pipes. Fortunately it is unnecessary for the aperture of a pipe to be as large as half a wavelength in diameter, otherwise it would be of ludicrously impractical dimensions for most pipes. However it remains a fact that all pipes emit sound more efficiently at the higher harmonics than at the lower ones, just as with loudspeakers and for the same reasons. Consequently, if a pipe gets too narrow, its loss of radiation efficiency becomes noticeable in that it is no longer able to radiate the fundamental frequency with an efficiency comparable to that of the higher harmonics. At least some string pipes go below this limit of narrowness, and it results in the feature seen in the spectrum for the first few harmonics which progressively rise in amplitude.
So why do harmonics beyond the fourth start to fall off again? Why do they not carry on increasing in strength as the radiation efficiency continues to improve with increasing frequency (i.e. harmonic number)? This brings us back to how well each harmonic generated at the mouth of the pipe corresponds in frequency with its analogue in the series of natural resonances of the pipe itself. As already mentioned, this is discussed in detail in reference [1] (see the section entitled 'The Influence of Pipe Width on Tone Quality'). Beyond the fourth harmonic of this particular pipe, the frequencies of the generated harmonics and of the natural frequencies of the pipe begin to diverge to an extent that the latter cease to enhance the former so readily. We therefore have a sort of tussle between two opposing combatants - continually increasing radiation efficiency with harmonic number, but at the same time continually decreasing amplification via the pipe's natural resonances. For harmonics beyond the fourth, decreasing amplification wins and thus the harmonic amplitudes begin to reduce. There is also a third effect in that the harmonic amplitudes generated at the mouth decrease with increasing frequency in any case. We have seen this for a sawtooth wave above, and it applies to other harmonic generation mechanisms also as will be seen later.
In this discussion we only considered sound radiation from the top of an open pipe. However much the same physics governs acoustic radiation from all other apertures in a pipe, including the mouth and any holes or slots in the pipe body itself.
So far we have considered the tone quality of string toned organ pipes by relating it to the harmonics observed in the frequency spectrum of the sound they emit, but we have said little about where these harmonics come from in the first instance. In reality there cannot be any direct analogue of the sawtooth generator discussed above because that related to a vibrating string rather than to a pipe blown by wind, so we have to look elsewhere for an alternative wind-driven mechanism capable of producing lots of harmonics. Details of this, the jet-drive mechanism of the flue pipe, are given in reference [1]. To summarise, wind issues as a jet from the flue slit at the base of the pipe mouth in the form of a thin sheet. It travels upwards towards the lip with a wriggling sinuous motion, and when it hits the lip it oscillates back and forth across it, into and out of the pipe body. This oscillation takes place at the fundamental frequency (pitch frequency) of the pipe. The oscillation frequency is defined by the time taken for impulses travelling up and down the air column above the lip, which periodically pull or push on the wind sheet at the mouth to stabilise its frequency and maintain its motion. In turn the energy of the sheet gives rise to those impulses in the first place.
Because the wind sheet flips into and out of the pipe body, we can liken it quite well to an air pressure pulse generator. In general the pulse shape will be asymmetrical in that the proportion of time the sheet spends outside the pipe will be different to the time it spends inside (although these times can be approximately equalised by the voicer for certain classes of tone, notably flutes). This general case is illustrated in Figure 5, which shows a pulse waveform whose wide portions are seven times as long as its narrow portions, this ratio being chosen at random for purposes of illustration. This waveform is said to have a 1:7 mark-space ratio, a usefully descriptive name though one deriving from the early days of telegraphy in the 19th century rather than organ pipe physics.
Figure 5. A 1:7 mark-space ratio pulse waveform and its frequency spectrum
The frequency spectrum corresponding to this pulse waveform is also shown in Figure 5 and it has a number of interesting features. Firstly it contains a very large number of harmonics, of which only the first 30 are depicted. Therefore it is an immediately attractive candidate for a theoretical harmonic generation model which has to explain the gross features seen in the actual frequency spectra of organ strings (Figure 2). But secondly, the amplitudes of those harmonics no longer lie on a simple sloping line as did those of the sawtooth wave (Figure 1). Instead they jump up and down in the form of successive bunches, each bunch containing 7 harmonics. Thirdly, each bunch is separated from its neighbours by missing harmonics, which in this example lie at the positions of the 8th, 16th, 24th harmonics and so on. It must be emphasised straight away that, apart from the qualitative richness of the harmonic retinue, one cannot assume that these features apply in every last detail to the harmonic generating mechanism in real organ pipes. Apart from anything else, the actual pulse shape of a real pressure waveform at the mouth of a flue pipe will not have the sharp edges nor the vertical rise and fall times of the idealised waveform sketched above. Therefore its actual spectrum will also differ in detail from the idealised one, and in particular it is unlikely that there will be a systematic sequence of harmonics which are completely absent (but see note [12]). Nevertheless, flue pipe spectra in which this sequence is attenuated rather than being absent are commonplace, and indeed encouraged by the voicer (see note [13]). But returning to string pipes, it is arguably possible to discern that the harmonics in the Viol spectrum of Figure 2 do fall into a number of distinct regions or bunches, at least if one exercises a little imagination. However this spectrum does not characterise the generating waveform at the mouth of the pipe but the sound which is perceived at a distance from the pipe as a whole. The latter has been considerably modified by the action of the tube itself as described in [1], so one could not expect the two to bear other than a passing resemblance to each other.
The number of harmonics generated at the mouth of the pipe by the process described above (or any other which involves the jet-drive mechanism of the flue pipe [1], as it must) depends on several factors, including the cut-up, the sharpness of the upper lip, and lip offset relative to the flue or to the air jet. All of these are adjustable by the voicer, at least in metal pipes. Other adjustments include the flue slit width, nicking of the languid, the foot hole diameter and adding a beard. Most voicing adjustments interact with each other to some extent so it is not possible to focus too strongly on one at the expense of the others. Nor should one be too dogmatic, because we are discussing here not merely a craft but an art in which good results stem from skill, experience and an unusually sensitive 'ear' rather than a mandatory knowledge of physics. However it is necessary to introduce a degree of simplification so that the subject can be treated at a relatively elementary level here. There is a vast descriptive and qualitative literature, much of it mutually contradictory, dealing with organ pipe voicing in terms of the operations carried out, and a representative selection appears in the 'references' sections of [1] through [5]. No attempt will be made to summarise the material here because only the physics underlying the various adjustments is of interest.
The cut-up of a pipe mouth is its height expressed as a proportion of its width. High mouths attenuate the higher harmonics whereas low ones encourage their formation, thus the latter are used for keen string tones. The reason why this happens is simply that the thickness of the oscillating air sheet (measured along a pipe diameter orthogonal to the flue slit) increases as it propagates upwards from the flue. In other words, the sheet becomes fatter and less well defined in this dimension as it moves towards the upper lip, partly because of turbulence. As the sheet flips back and forth across the lip it is intuitively straightforward to see that fewer harmonics will be generated by a vaguely defined thick sheet than by a tightly constrained thin one. Referring back to Figure 5, the pulses in the waveform will be narrower and with faster rise times in the latter case, and these give rise to more harmonics in the spectrum because they do not fall off so rapidly in amplitude with harmonic number.
Sharpening the upper lip to a knife point by bevelling its front surface results in more harmonics being generated than if it had been left blunt. The reason is much the same as above because it means the air sheet flips more rapidly from inside to outside the pipe, and vice versa, when the lip is sharp. Thus the pulses in Figure 5 become narrower and better defined, leading to more harmonics being generated.
Assume we have a pipe whose upper lip lies directly above the flue slit. Further assume that the position of the languid relative to the flue results in an air sheet propagating vertically upwards rather than at an angle. In these circumstances the oscillating sheet will flip back and forth across the lip with a mark-space ratio of around 1:1. This is fine, indeed it is a sought-after situation, for flutes as explained at note [13], but it is decidedly unattractive for strings because the even-numbered harmonics will be attenuated. The desirable narrow-pulse waveform sketched in Figure 5 will have become an approximate square wave which in theory contains only the odd harmonics. This occurs because the nulls in the spectrum coincide with the positions of all the even-numbered harmonics for a square wave. In practice the even ones will still exist but they will be too weak and they will therefore degrade the desired string tone quality.
To remedy this state of affairs, the upper lip can simply be offset from the flue by pushing it slightly into the pipe or pulling it out, provided of course that the pipe is of metal rather than wood. Pulling the lip out appears to be the more usual procedure adopted in practice. Then the oscillating air sheet spends more time inside the pipe than outside, changing the excitatory waveform from square(ish) into the train of narrower pulses which we have seen is desirable for string pipes.
The languid of a metal pipe can be raised or lowered slightly relative to the lower lip by levering it upwards or tapping it downwards using suitable tools. This has the effect of altering the angle at which the air sheet travels towards the upper lip. It therefore changes the mark-space ratio of the pulse train delivered to the interior of the pipe and in this respect the results are similar to those described above by altering the offset of the upper lip.
The adjustment also has another effect in that it makes the pipe speak 'quicker' or 'slower'. These adjectives refer to the time taken for the pipe to reach its stable speaking regime. Flutes tend to be 'quick' whereas strings are 'slow' to come onto speech. In the latter case the air sheet is thrown so far outside the mouth at the position of the upper lip that it takes more time (i.e. more cycles of the fundamental frequency) to fully engage with the travelling air impulses inside the pipe when the pallet is opened. All organists will be familiar with this effect in which some pipes in a string rank seem to struggle to reach stable speech at all, and during this process they can emit the most peculiar sounds. Longer pipes are more prone to the problem than short ones because their mouths are higher, thus a given adjustment of the languid produces a correspondingly greater deflection of the air sheet at the upper lip than in a smaller pipe. Beyond about tenor C on an 8 foot keen-toned stop the adjustment becomes so critical that it is virtually impossible to get the pipes to speak stably or at all. This behaviour can be remedied by fitting a beard to the pipe mouth (see below.).
Many flue pipes are fitted with vertical ears at each side of the mouth. In the case of string pipes they increase the range of mouth heights and languid heights which will still result in stable speech. This is of considerable benefit in view of the small mouths which have to be used for strings, and in view of the reduction in the criticality of the adjustments which ears provide. In particular, it is possible to use even smaller cut-ups when ears are used than would otherwise be the case, and this further augments the high frequency end of the harmonic spectrum. It is reasonably obvious that ears constrain the lateral propagation of the oscillating air sheet, which would dissipate into the atmosphere beyond the pipe wall without them. In physical terms this increases the mass of the vibrating air at the mouth, and this results in the advantages mentioned. The fundamental frequency (pitch) of the pipe is reduced somewhat as a result of the increased mass, though this is not an issue because the pipe can of course be re-tuned subsequently.
Fitting a beard or bar between the ears at the pipe mouth controls and stabilises the position of a wind sheet which has been deliberately offset from the upper lip by deflecting it outside the pipe. Although stabilisation can be achieved to some extent by adjusting the languid position as described above, the adjustments become unfeasibly critical for the longer pipes. The beard physically prevents the sheet from straying too far away from the upper lip when the pallet opens, and while the pipe is speaking it helps the sheet to 'bounce' back into the mouth as it oscillates across the upper lip.
The flue is the narrow rectangle which gives an initial shape to the air sheet as it passes between the lower lip and the languid. Increasing the width (the smaller dimension of the rectangle) increases the area of the flue and hence allows a greater air flow, which increases the acoustic power generated by the pipe. However the increased width and diffuseness of the air sheet at the upper lip also means that the number of harmonics generated can be affected undesirably.
The effects of foot hole size cannot be divorced from those related to flue width because both control the air flow rate into the pipe. However differences arise in terms of voicing, because the foot hole is 'insulated' from the oscillating air sheet above the flue by virtue of the mass of air contained within the volume of the pipe foot, whereas adjustments to the flue affect the air sheet directly. The foot hole controls the overall power of the pipe, and its diameter is usually varied solely for this purpose rather than for niceties of voicing, at least when an organ is working on medium to high wind pressures in the chest below the pipe. This will usually be the case for keen string stops.
As its name implies, nicking is the process of cutting a series of small notches in the languid and sometimes in the lower lip as well. Their number, spacing and depth vary widely but for keen high-pressure strings the nicking is generally about as dense as it gets. While an Open Diapason might have 5 or 6 nicks per centimetre, a Salicional will typically have about 12 and a Viol d'Orchestre about 15.
Of all voicing techniques, nicking is probably the most mysterious. There is no doubt what it achieves regarding the tone and behaviour of the pipes so treated, but scarcely the vaguest qualitative description of how it works appears anywhere, not even in the most rigorous and specialist literature, and one searches in vain for a more satisfying and quantitative treatment. Therefore some space is devoted to it here with the intention of illuminating the matter to some extent.
Firstly let us recall how nicking modifies the sound of a pipe. It might speak less promptly when nicked but it will do so with less of a tendency to emit a pronounced attack transient. Nicking also reduces some of the rather objectionable 'buzz' or 'fizz' noises which string pipes can emit, effects which are more noticeable at close quarters. They occur because of edge tones [17] generated at the upper lip, often in the form of short bursts of noise or high frequency oscillations unrelated in frequency to the pitch of the pipe. These parasitic bursts appear one or more times during each cycle of the fundamental frequency as the air sheet moves back and forth across the lip. Another advantage of nicking reduces the tendency of a pipe to speak in two different modes of oscillation at once, an effect which is occasionally heard as the pipe switches randomly from one to the other.
From the above it seems reasonable to summarise the effect of nicking as a tendency to stabilise the speech of a pipe, but going further requires a digression into laminar and turbulent air flow. Laminar flow in the air sheet at the pipe mouth exists when it moves in an orderly fashion thoughout its volume, like ranks of soldiers marching in step. There is no lateral mixing, nor eddies or swirls. The sheet is just that - a homogeneous thin jet of air flowing uniformly upwards from the flue. This kind of flow can and often does exist in a pipe working at low pressure with no nicking. However if, for example, one wants to increase the pressure to get a louder sound, one encounters a point at which instability becomes a problem. For example a pipe might work perfectly well on the voicing machine yet require major attention to make it work in an organ for reasons which are sometimes unclear. Or its pitch and other aspects of its speech might be seriously affected by another pipe speaking nearby. Other forms of instability include mode switching as mentioned above. All these, and more, can happen when the desirable state of laminar flow is disrupted by the onset of turbulence. So what is the solution? Perhaps surprisingly, it is to encourage turbulent flow from the outset by nicking rather than striving to retain laminar flow. Once the air sheet exhibits turbulence none of the former attributes characterising laminar flow exist. The flow becomes highly irregular, and the instantaneous speed of the air sheet at any point ceases to have a fixed and unvarying value. Rather, it assumes a mean value at any given height above the flue but with considerable positive and negative excursions which occur randomly across the sheet. The onset of turbulence is illustrated in the photograph below of a smoking cigarette (Figure 6).
Figure 6. A smoker unwittingly demonstrating the onset of turbulence in previously laminar flow
How does nicking result in turbulence? The answer might seem obvious, and it is, but it is worth explaining nevertheless. One can imagine the air issuing from a nicked flue to consist of an array of vertical narrow ribbons, each one arising either from a nick or from the space between adjacent ones. A ribbon flowing from a nick moves at a different speed to its neighbours which do not issue from a nick because flow rate depends on nozzle size, as with a garden hose. Therefore, as the several adjacent ribbons move upwards, they rub and nudge against each other because of their speed differences. This results in lateral mixing of the air in the ribbons with the result that the flow swiftly becomes turbulent.
We now only have to understand why a turbulent air sheet results in stable pipe speech. The reason is so obvious that it is easy to overlook, and it is that once turbulence has set in it is there for good. Unlike the fragile state of laminar flow which is easily disturbed, nothing will disrupt it to stop it being turbulent while the pipe continues to speak. The cigarette demonstrates this eloquently because it is inconceivable that the turbulent swirls of smoke could ever re-form themselves into laminar flow again. Turbulence is a physically degenerate state in the same way that heat is the most degenerate form of energy into which all other forms eventually descend. Both are consequences of the second law of thermodynamics which shows that randomness and disorder (high entropy) are the ultimate and preferred state of the universe. Turbulence is therefore an extremely stable state, though one which is far more difficult to characterise and understand than laminar flow. But because of the fortunate fact that it is obviously possible to make organ pipes work satisfactorily under a turbulent flow regime, they will by definition speak with more stability. The only issues remaining are those relating to speech differences between laminar and turbulent flow, such as the type of attack transient, and voicers have long learned how to cope with these [14]. Parasitic noises such as 'buzz' are less of a problem because the speed at each point of the air sheet oscillating across the upper lip no longer has a well defined value. The air at all points across the lip will move at the same average speed over time, but each one will depart randomly from this mean at any instant. Consequently artefacts such as parasitic edge tones are less likely to arise across the lip as a whole in this situation. As for transients, they are sometimes reduced by nicking because a turbulent air sheet itself requires a certain amount of time to become stable after the pallet opens. Therefore the initial impulse applied to the body of the pipe is less well defined for a turbulent air sheet than a laminar one and so it excites fewer natural resonances of the pipe, or it only excites them with lower amplitudes. It is more like a cloud than a sharp impulse when it first reaches the upper lip. However there is a lot more to transients than this and they are discussed further below.
String toned pipes can emit pronounced attack transients as they come onto speech. One reason is that the air jet is often thrown considerably outside the mouth when the pallet first opens because of the usual and necessary voicing adjustments appropriate to string pipes, and it can take many cycles of oscillation before the jet takes up its stable operating position. This period will typically occupy 50 cycles at the fundamental frequency, and during this interval an attack transient is heard.
We need not consider transients in more detail here because an entire article is devoted to the transients of string pipes elsewhere on this website [15]. It deals with the particular case of a large string toned pedal Violone pipe but this does not affect the issues discussed, which are generic to strings as a whole. They include the initial anharmonicity of the partials in the transient and how they are pulled progressively into phase-lock to become the exact harmonics of the steady state tone, the importance of choosing an appropriate operating point for the pipe on the frequency-pressure curve, and the type of action employed to open the pallet.
Celeste stops are those employing two or more ranks of deliberately detuned string pipes so that a slow wavering or beating effect is produced. Hope-Jones incorporated three ranks in the Violes Celestes stop in his Worcester cathedral organ of 1896. They were tuned sharp, unison and flat but only the first two spoke when the stop tablet was first pressed, the third rank coming on as well if it was pressed again. He used a similar method of control in his smallest organs which often contained a Phoneuma string stop - that at Pilton in Devon only had the usual two ranks but it was necessary to press the stop tablet twice to get them both to speak. Willis's beautiful organ at Salisbury Cathedral has two celeste stops, one in the swell organ (a Vox Angelica) and the other on the solo (Cello Celestes).
In passing we might note an interesting feature of the detuned rank of a celeste. If a uniform beat rate is desired across the compass, the detuned rank cannot be tuned in the usual manner with pure octaves. For example, if a uniform beat frequency of 2 Hz is desired, then the frequency of the detuned rank at middle C will be 263.63 Hz if it is tuned sharp to the unison one. (This assumes that the unison rank is tuned to equal temperament with A at 440 Hz, when its frequency will then be 261.63 Hz). To get the same beat frequency of 2 Hz at treble C, the detuned rank must then have a frequency of 525.25 Hz. This is slightly flat from its pure octave with middle C which would otherwise place it at 527.26 Hz. Therefore if we play on the detuned rank alone when tuned carefully in this way, we would hear the music in an unusual temperament using flattened (shrunk) octaves! For information, I have investigated temperaments using impure octaves extensively and reported them elsewhere on this website [16], though of course this has nothing to do with string pipes per se. Nevertheless, a suitably detuned celeste rank can afford an easy and quick way of assessing what a temperament using impure octaves can sound like for those who are interested.
The physics of string toned organ pipes has been surveyed at a non-mathematical level but without omitting the important features. On the contrary, some original material has been presented for the first time, including a description of the physics underlying the range of adjustments available to the pipe voicer rather than merely describing their effects on the pipe sounds. The effect of nicking has been discussed in particular detail because its mechanism at a physical level is not treated elsewhere in the literature. Among other things it was shown how nicking induces turbulence in the air jet issuing from the flue, and the effects this has on pipe speech was also covered.
The tenuous subjective correspondence between the sounds of bowed string instruments and string toned organ pipes was examined, and it was shown that both have a large number of harmonics. In the case of the organ this can sometimes exceed the number exhibited by reeds in the case of a 'keen' imitative string pipe. Nevertheless the harmonic generation mechanisms are entirely different in the two cases, and it was shown that the oscillating air jet at the mouth of a string pipe can be treated as a pulse generator whose mark-space ratio can be adjusted by the voicer. This enables the number and distribution of harmonic amplitudes in the frequency spectrum of the driving waveform to the resonator to be varied.
The sound radiated by a keen-toned string pipe has a uniquely interesting frequency spectrum as far as the family of flue pipes is concerned, in that the first few harmonics almost always increase in amplitude before falling away thereafter. This was attributed to the relatively poor radiating efficiency of a small-scaled (narrow) pipe which attenuates the radiated power at lower frequencies.
Thanks to Stefan Vorkoetter for having redrawn the diagrams used in this article from my inferior originals.
1. "How the Flue Pipe Speaks", an article on this website, C E Pykett, 2001.
2. "How the Reed Pipe Speaks", an article on this website, C E Pykett, 2009.
3. "The Tonal Structure of Organ Flute Stops", an article on this website, C E Pykett, 2003.
4. "The Tonal Structure of Organ Principal Stops", an article on this website, C E Pykett, 2006.
5. "The Tonal Structure of Organ Reed Stops", an article on this website, C E Pykett, 2011.
6. See www.preller-gottfried.de/html/bachkirche.htm (accessed 29 August 2012)
7. The firm formerly known as Orgelbau Hoffmann rebuilt the 'Bach' organ at Arnstadt in 1999. It is now called Hoffmann & Schindler, not to be confused with Heinz Hoffmann Orgelbau.
8. "Die 'Bach-Orgel' zu Arnstadt/Thüringen", Orgelbau Hoffmann, Ostheim vor der Rhön, 2000.
9. Virtually the entire rank formed from the original Viol di Gamba pipes of the Arnstadt organ has survived, and they were incorporated in Hoffmann's 1999 rebuild. However this does not imply that they necessarily sound today as they did originally, because they have been subjected to much interference in the intervening several hundred years. Notably, they were incorporated into a large Romantic instrument by Steinmeyer with tubular pneumatic action in the early twentieth century, so what might have happened to them then and since is anybody's guess. Thus, if we keep an open mind, it is not easy to judge whether they would have sounded similar to today's often mild string-toned stops with the same name when Wender first made this stop for his Arnstadt organ.
10. "On the Sensations of Tone", H L F von Helmholtz, 4th edition, 1877. (Translated by A J Ellis, Dover, New York, 1954)
11. "The Physics of Musical Instruments", N H Fletcher and T D Rossing, Springer, 2nd edition, 1999.
12. Occasionally one does come across flue pipe spectra in which certain harmonics are completely absent, an effect which is difficult to explain unless one invokes a pulse-generator type of mechanism. An example occurs in the Harmonic Flute spectrum shown at Figure 7 of reference [3].
13. For virtually all flute pipes the voicer, by accident or design, adjusts the mark-space ratio of the oscillating wind sheet to be approximately 1:1. This occurs automatically for many wood pipes because the flue slit often lies directly below the upper lip, and the positions of neither (nor that of the languid) can readily be adjusted. With metal pipes the voicer can vary the direction of the air jet relative to the lip either by adjusting the height of the languid or by slightly pulling/pushing the lip out of or into the pipe, or both. With a 1:1 mark-space ratio we have a 'square wave' rather than a waveform containing narrow pulses, and its harmonic nulls lie at the positions of all the even-numbered harmonics. Although they are not completely absent in practice, the power of the even-numbered harmonics is attenuated below that which principals and strings would normally exhibit and this gives rise to the somewhat 'hollow' sound of flute pipes, even those which do not have a stopper. This effect can be seen in the Claribel Flute spectrum in Figure 4.
14. It is no coincidence that the 'modern' voicing techniques which surfaced in the 19th century arose because of the contemporaneous appearance of blowing plant powered successively by water, town gas and finally mains electricity. Before that, pressures were perforce low when the only available source of power was from human muscle. In those days organ pipes would have worked mainly in a laminar flow regime, especially as open foot voicing was common and nicking was not used routinely. But when pressures began to rise to create the power and profundity so beloved in Victorian organs, together with the plethora of imitative stops such as keen string tones, the voicer had to invent and embrace a new repertoire of techniques to cope with the turbulent air flow in the pipes he then routinely had to handle. That he succeeded so well is a tribute to the craft, especially as physics has taken over a century to catch up.
15. "A Second in the Life of a Violone", an article on this website, C E Pykett, 2005.
16. "Keyboard Temperaments with Impure Octaves", an article on this website, C E Pykett, 2008.
17. Edge tones can arise at the upper lip of an organ pipe quite independently of the resonating tube above it. In fact experiments have been done to show that the tube can be removed yet edge tones will still remain at the mouth. They also occur when the wind howls through sundry sharp apertures in door and window frames, and they are caused by a succession of eddies arising alternately on either side of an air sheet. These flip the sheet across the edge at relatively high frequencies and thereby generate tones. Because they have no connection with the way in which an organ pipe actually speaks, edge tones are referred to as parasitic oscillations here.
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