The Tonal Structure of Organ Flutes
Home Up Other Publications Contact Me About the Author About this Website Prog Organ - a VPO Sitemap

 

THE TONAL STRUCTURE OF ORGAN FLUTE STOPS

by Colin Pykett   

Posted: 2003

Last revised: 19 December 2011

Copyright ©  C E Pykett 2003 - 2011

Abstract The variety of flute-toned stops on the organ is immense, judging by their names alone.  Most authors seem satisfied having addressed the matter in descriptive terms (e.g. the shapes of the associated pipes), and it is therefore more difficult to go further to discover a physical basis for the range of tones and why our ears perceive them as they do.  For example, what is it about the sound of a Stopped Diapason that makes it blend better with other fluework than a Harmonic Flute?  Or why must the Tibias of a theatre organ sound as they do to satisfy aficionadi of that style of instrument?   Or why is a Claribel Flute usually regarded as quieter than an Open Diapason when its measured sound level can be higher?

This article summarises the outcome of some 25 years research into these matters, and it covers aspects of the subject ranging from the physics of sound generation in organ pipes to the perceptual mechanisms involved in hearing.   By analysing the sounds of a series of actual flute pipes made in the 19th and 20th centuries, one can see that a pre-occupation of organ builders appeared to be suppressing the harmonic structure  in favour of the fundamental in the pursuit of loud solo stops.  Unfortunately the basis of loudness as a subjective phenomenon is not necessarily well served by this approach.   This incompatibility is the main reason why many flutes do not blend well, and nor are they necessarily as loud as might have been wished.

Contents

(Click on the titles as required to access particular sections of the article)

Introduction

The Acoustic Frequency Spectrum of Organ Flutes

The Stopped Diapason

The Claribel Flute

Some facts about Loudness

The Blending Properties of Flute Stops

The Hohlflöte

The Harmonic Flute

The Tibia

Concluding Remarks

References

 

Introduction

The variety of flute-toned stops on the organ is immense, judging by their names alone.  Some of these are fanciful to the point of being meaningless (e.g. Flûte d’Amour, though some might want a Love Flute on an organ nonetheless). Some are merely different names for stops which often sound much the same (e.g. Stopped Diapason and Chimney Flute), and still others are occasionally misused (e.g. Hohlflöte instead of Harmonic Flute).   Yet despite problems of nomenclature there is no doubting the wide range of tones which exists.  A summary addressing the matter in descriptive terms is at reference [1], complementing the similar treatments found in most books dealing with the organ.   It is more difficult, however, to go further to discover in the literature a physical basis for the range of tones and why our ears perceive them as they do.  For example, what is it about the sound of a Stopped Diapason that makes it blend better with other fluework than a Harmonic Flute?  Or why must the Tibias of a theatre organ sound as they do to satisfy aficionadi of that style of instrument?   Or why is a Claribel Flute usually regarded as quieter than an Open Diapason when its measured sound level can be higher? 

The answers to such questions are subtle, and they encompass a real problem which highlights a deficiency in the literature.  It can be illustrated in another way by looking at two well-known texts on the physics of music.  Benade’s Fundamentals of Musical Acoustics [2] was written primarily for the musician who desires a better understanding of the physical basis of the Art, yet it contains not a single chapter dealing with organ pipes.  The word “pipe” does not even appear in the index !  The Physics of Musical Instruments by Fletcher and Rossing [3] approaches matters from the opposite perspective:  it was written for those who have a considerable grasp of physics and mathematics besides an interest in musical instruments.  Here we find an entire chapter devoted to flutes and organ pipes, though again virtually nothing relating to questions such as those posed in the previous paragraph.  I must hasten to add that these are observations, not criticisms.  Both these excellent books are in my library and in almost daily use.  It would be unreasonable to demand or expect that every conceivable question which can be posed about the physics of music should be answered within their pages, particularly as we are verging on the psychology of perception.  But when such questions arise it is then all the more rational to try to answer them in other ways.   

This, then, forms the background for this article.  Much of it is based on the results of research carried out over some 30 years, and some of this is original in the sense it does not seem to have appeared elsewhere, at least in the public domain if at all.  Other material is better known and included for completeness.  Although the subject matter is approached from a physical basis,  there is nothing that should not be readily understood.  Mathematics has been avoided except in a few cases, and these are relegated to a smaller typeface to indicate material which can be skipped without significant loss of comprehension.  Sometimes we shall stray into other topics such as some detailed aspects of acoustics, and these also are identified by small print. 

It is recommended that this article is read in conjunction with another on this website dealing at a simple level with the way flue pipes speak [4], to which frequent reference will be made.

 

The Acoustic Frequency Spectrum of Organ Flutes

The concept of a frequency spectrum is discussed in [4].  Such a spectrum is a graph of the amplitudes (strengths) of the harmonics in the sound produced by the pipe when it is speaking in its steady-state phase (i.e. once the initial attack transient has died away).   

An illustration of a generic spectrum is in Figure 1, though this does not relate to a particular type of flute. We shall come to specific flute spectra later.   The diagram shows the amplitudes of 10 harmonics, starting with the fundamental followed by the second, third, fourth, etc harmonics.   In mathematical terms this is called a discrete monotonic decreasing spectrum: discrete because there is acoustic energy only at the discrete frequencies of the harmonics, and monotonic decreasing because the amplitudes decrease steadily rather than jumping up and down.

 

 

The vertical axis represents harmonic amplitude on a decibel (dB) scale.  A decibel in this case is a logarithmic quantity defined as 20 log10 (a1/a2), where log10 denotes the logarithm to base 10, and a1 and a2 are harmonic amplitudes.  The amplitudes will have been derived from some form of spectrum analyser connected to a microphone, or to a recording made from a microphone.  In this example a2 is always the amplitude of the fundamental and a1 that of the relevant harmonic.  The set of numbers which result are then normalised so that the amplitude of the fundamental becomes 60 dB.  

For example, consider first the fundamental itself.  In this case a1 = a2, therefore the ratio a1/a2 will always be 1.  Since the logarithm of 1 is 0, the dB level of the fundamental will always be zero.  But we have decided to normalise it to 60 dB so we merely add 60 to this and all other values. This avoids having to cope with negative values for the other harmonics.  Now suppose that a1 is 3 units for another harmonic, and a2 (for the fundamental) is 6 units (the units could be the voltage of each harmonic as measured by an electronic spectrum analyser).  Then a1/a2 equals 0.5, thus 20 log10 0.5 = - 6 approximately.  Adding 60 gives a value of 54 dB.  Exactly the same procedure is followed for all other harmonics.  Therefore a difference of - 6 dB indicates a halving of the sound level for a particular harmonic compared to the fundamental.  

It will also be noted that the horizontal axis in Figure 1 is plotted in an unusual manner.  Instead of spacing each harmonic equally along the frequency axis, the gaps between them are in a logarithmic proportion.  Therefore Figure 1 is plotted using logarithms for both axes, and a reasonable question is why this complication has been introduced.  The most important reason is that, for flutes, the harmonic amplitudes then often lie close to one or more  sloping lines as depicted in the diagram.  If non-logarithmic values were used this simple and important visual feature would be obscured.  The tonal qualities of flutes are strongly related to the slopes of these lines, as will be described later.   

In fact the matter is probably more profound, because the ear and brain process both amplitude (related to loudness) and harmonic (frequency) information in a logarithmic manner.  Thus units related to decibels are used to measure loudness in acoustics, and of course musical intervals are frequency ratios expressed logarithmically – an octave from lowest C to tenor C at 8 foot pitch encompasses a frequency difference of about 64 Hz, whereas between middle C and treble C the difference is about 256 Hz.  Yet the ear perceives both as an octave because the frequency ratio is 2 in each case.  Therefore this may indicate that our neural processing latches onto simple structure in sounds after they have been pre-processed logarithmically in both amplitude and frequency, implying that the choice of spectrum display above has some relation to the mechanisms of aural perception.  

The other main classes of organ tone – diapasons, strings and reeds – also exhibit relatively simple but quite distinct spectral structures when displayed in the doubly-logarithmic manner of Figure 1.  For example, a reed spectrum is more or less flat at first as far as the 9th harmonic or so, after which it suddenly falls off rapidly.  In fact all of these characteristic organ tones have spectra whose harmonic strengths can usually be approximated by simple but different combinations of straight line segments.  Of course, these are generalisations, but they offer clues as to why these tones sound characteristically different, and how the ear and brain might be processing the sounds.  

It is possible to synthesise electronically the sound corresponding to the spectrum in Figure 1 and it turns out to be rather coarse and uninteresting, midway between a somewhat characterless flute and a muffled diapason. This is not surprising because the spectrum is purely illustrative – it was drawn freehand and does not relate to any particular stop.  Nevertheless such a stop, if it was ever made, might have attracted a meaningless name such as Melodia or Dolce in early 20th century organs. 

If, however, a simple change is made to the spectrum things change dramatically.

 

 

Figure 2 is again an illustrative spectrum, but one in which the even-numbered harmonics have been partially suppressed.  Therefore the spectrum as a whole is no longer monotonic, because adjacent harmonics jump up and down in amplitude.  This allows the odd and even harmonics to belong to two separate “straight line” structures.  The ear is extremely sensitive to such differences; in this case the change imparts a hollow pipe-like quality to the sound which seems to be considerably more attractive to most people than the characterless tone of the earlier example.  Such a structure characterises many flute stops to some extent.  This can be true regardless of whether the pipes are open or closed. 

We shall now proceed to examine the acoustic structure of various types of flute pipes.

 

The Stopped Diapason

The Stopped Diapason is not really a diapason but a flute, and it is a peculiarly British stop name.  Stopped Diapasons are generally made of wood but with other characteristics not too dissimilar from those of metal diapasons, such as pipe scale and mouth dimensions.  However the main difference between the two, which results in an entirely different quality of tone, is the presence of a stopper in the wood pipe.  This has two effects: firstly the even-numbered harmonics are reduced in strength, and secondly the pipes are only about half the length of open pipes for the same pitch.  The action of the stopper in suppressing the even harmonics, and in making the pipe shorter than an open one of the same pitch, is explained in [4].  Thus the hollow-sounding effect of a spectrum of the generic form of Figure 2 is characteristic of  Stopped Diapasons also. 

The actual spectrum is different in detail however, and an example is shown in Figure 3.  This shows the harmonic structure of a Stopped Diapason pipe in the middle of the compass on the little 1858 Walker organ in St Mary’s church, Ponsbourne in Hertfordshire.  An article relating to this instrument appeared in [5].  We can see that there are only 6 harmonics of appreciable strength, and that the odd ones (including the fundamental) are stronger than the evens, giving the hollow sound alluded to already.

 

 

An examination of the pipework revealed the presence of holes bored through the stopper handles of this stop, and this is one way in which the relative proportions of odd to even harmonics can be adjusted.  (The hole also affects the pitch of the pipe slightly, but this can be compensated when tuning the pipe by moving the stopper).  The hole at the top of the pipe allows even harmonics to develop in the sound which are stronger than would otherwise be the case, and it is one of the techniques available to the pipe maker and voicer to enable them to adjust the tone to their liking.  As we have noted already, the ratio of odds to evens is a critical tonal parameter.  However, the holes in some specimens are ineffective – as I write this I have in front of me a run-of-the-mill Stopped Diapason pipe sounding tenor F.  Its hole is about 6 mm in diameter, and it makes absolutely no difference to the tone whether you cover it or not when blowing the pipe!  This shows that the length and diameter of the hole have to be related to the pitch of the pipe – any old hole will not do. 

The effect of the pierced stopper can be obtained in another way by making the pipe of metal and adding a projecting  “chimney” to a canister covering the top.  Often, therefore, there is little or no difference in practice between a Stopped Diapason and a Chimney Flute in terms of the sound produced.  The fact they are made of different materials still leads some to disagree, though I know of no objective research which confirms this.  While the pipe material might produce minor changes in tone quality, the effect is very much a second order one.  If there are differences they are more likely due to the different natural frequencies of the pipes induced by the different cross-sectional shapes, a topic which is discussed more fully in [4].   (To my mind this matter of pipe materials was closed many years ago by a careful study which concluded “it is, moreover, particularly shocking to hear a good diapason tone from a pipe with its cylinder made of wrapping paper” ! [6]). 

Stopped Diapasons generally blend well with other fluework, and it is not unusual to find one which will support an entire diapason chorus.  Given the gentle nature of the stop when played alone, this might seem remarkable.  They also complement other stops of the same pitch such as an Open Diapason, and a combination of Stopped Diapason at 8 foot pitch with a 4 foot open Principal is likewise effective.  A chorus of Stopped Diapasons at several pitches, or even a single stop played with octave couplers, can delight the ear.  These issues will be amplified later when some other types of flute have been discussed.  For the present it is relevant to note that one reason why the stop blends well is because of its even-numbered harmonics of low amplitude. In all the cases just mentioned, the frequencies of these harmonics coincide with others provided by the other stops drawn at the same time.  For example, the weak second harmonic of an 8 foot Stopped Diapason is of the same frequency as the strong fundamental of a 4 foot Principal.  Therefore, in homely parlance, we can say that the Stopped Diapason has convenient gaps in its acoustic spectrum into which stronger harmonics from other stops can fit, rather like a hand in a glove.  Seen in this way the good blending properties of the stop are understandable at an intuitive level.  However there are also issues relating to the subjective loudness of the stop which are more complex, and these will be introduced later.

 

The Claribel Flute

The Claribel Flute is made of open pipes which are therefore twice as long as those of the Stopped Diapason.  For this reason the lowest octave, sometimes more, might consist of stopped pipes to conserve both space and expense.  Usually the pipes are of wood, and sometimes they are of harmonic construction above middle C or so (see later for a discussion of the Harmonic Flute). It was a stop much used by Henry Willis. The driving force behind the development of the Claribel Flute in the nineteenth century was the search for a more powerful flute which could be used as a solo stop, and for this reason it is made with a wide mouth and supplied with copious wind. 

A representative Claribel Flute spectrum is shown in Figure 4, taken from the large and beautiful Rushworth and Dreaper organ in Malvern Priory.

 

 

There are several differences between this spectrum and that of the Stopped Diapason (Figure 3): 

1.      There are a few more harmonics present.

2.      The even harmonics are of higher amplitudes relative to their neighbours.

3.      The difference in amplitude between the fundamental and the next strongest harmonic (the third harmonic in both cases) is about 25 dB, whereas for the Stopped Diapason this parameter was about 15 dB.  Therefore much more of the acoustic energy is concentrated in the fundamental for the Claribel Flute than for the Stopped Diapason. 

A feature common to both stops is that the even and the odd harmonics belong to identifiably different series, the evens being weaker than the odds.  For the Stopped Diapason this was explained above as due to the action of the stopper.  But the Claribel Flute has no stopper so it is all the more interesting that this feature persists, though it is less pronounced.  The principal reason for this characteristic, which is extremely important in determining the subjective flavour of the sound, lies in the hands of the pipe designer/maker and the voicer.  It is shown in [4] that the position of the upper lip relative to the air stream strongly influences the proportion of even to odd harmonics in an open pipe. 

While the Claribel Flute makes an attractive solo voice, its blending properties are inferior to the Stopped Diapason.  This is mainly because of the much stronger fundamental, though it is unclear at first why this should be so and it brings us to a necessary though somewhat extensive diversion – a discussion of loudness.

 

Some facts about Loudness

Loudness is a subjective phenomenon and a complex and elusive topic which has attracted a huge amount of research, and it is difficult to summarise.  However the most important factor to grasp is the difference between the amplitude of a sound and its perceived loudness.  The former is a physical quantity existing in the air which can be measured easily and accurately, whereas the latter is a property of our ears and brain.  It, too, can be measured, though not so easily and certainly not so accurately.  One of the more curious phenomena encountered is that our perception of loudness grows only slowly as the amplitude of certain types of sound is increased. 

To illustrate this, let us assume we have an organ pipe which emits a pure tone.  No organ pipe does actually emit only a pure tone – if it did, its spectrum would only contain one line at the fundamental frequency.  However, for the purposes of this discussion the sound of a Claribel Flute is not too different from a pure tone, as its spectrum in Figure 4 shows.  We have noted already that the amplitude difference between the strongest harmonic (the fundamental) and the next strongest (the third harmonic) is about 25 dB.  25 dB is the same as a ratio of about 18: therefore the amplitude of the fundamental is 18 times larger than that of the third harmonic.  This disparity is even greater for the other harmonics, which are all smaller.  Therefore it is not unreasonable to say that this particular pipe emits a sound not too far removed from a pure tone.  

It can be shown that the perceived loudness of such a pipe (assuming it emits only a pure tone) doubles when the amplitude of the sound is more than tripled. The loudness is only multiplied by four when the amplitude increases tenfold !   This assumes not only that the pipe emits a pure tone, but that its initial loudness is one unit.  Loudness is measured in sones, a logarithmic unit whose definition we shall skip.  (An alternative unit of loudness is also used, called the phon. Unfortunately the two units are not the same, and here we shall use only the sone). There is no simple relationship between the amplitude of an acoustic signal expressed in decibels and its loudness in sones.  This is partly because of the enormous disparity in the response of the ear at different frequencies.  We can hear sounds over a range of between nine and ten octaves, but the frequency within this range at which the ear is most sensitive is around 3 kHz. This corresponds roughly to the pitch of a tiny organ pipe sounding the top F# of a 4 foot stop. Beyond the extremes of the frequency range we are completely deaf to any sounds, even though some other animals are not.  This explains why we, like cats, can be disturbed by the slightest rustles of a foraging mouse (frequencies of a few kHz) in the still of the night, yet a 32 foot flue stop (frequencies around 20 Hz) has to be powerful enough to rattle the furniture and windows in a cathedral before we can hear it as a pulsating sound of very low frequency.  Therefore our perception of loudness is strongly related to the frequency of the sound and not just to its amplitude, as everyday experiences such as those mentioned demonstrate. 

When an attempt is made to measure the loudness of sounds which include many frequencies simultaneously, the complexity escalates further.   For example, who could say whether an insipid sound consisting only of a pure tone has the same loudness as the sound of the wind rushing through a tree?  Unfortunately, exactly this type of experiment needs to be done when trying to establish how our ears assign loudness to the sounds of the real world.  Difficulties such as these mean that our understanding of the loudness phenomenon, to say nothing of more subtle aspects of auditory perception, remains only approximate.  

Another curious result is obtained when we consider the situation where several pipes of the same pitch sound simultaneously.  Assume we have a very large hypothetical organ which consists only of 8 foot Claribel Flutes.  Each stop is identical to the others.  If we draw just one stop and play a single note, we shall of course perceive a sound with a certain loudness.  But it is an extraordinary fact that to double this loudness, we should have to draw another nine stops in addition.  To quadruple the loudness of the single stop we should need to draw another 100 !  These hypothetical experiments are subject to the same assumptions as before, that each stop is a pure tone and that each sounds with a loudness of one sone.  Nevertheless, the foregoing fulfils a useful purpose.  In reality it is indeed necessary to draw many real flute stops on an organ before a significant increase in loudness can be perceived, and that is the point.  

It is not difficult to prove this to yourself.  You can carry out the following experiment which I have often done.  Consider a typical three manual organ with, say, a Lieblich Gedackt on the swell, a Claribel Flute on the great and a Stopped Diapason on the choir.  It is best if all of them are of comparable subjective loudness, give or take a little.  On such an instrument if you draw the swell to great coupler and play middle C on the great, thereby causing both the Claribel and the Lieblich to sound, you will often find the effect to be scarcely louder than either stop on its own.  A similar result will frequently be obtained by drawing the choir to great and playing on the Claribel and the Stopped Diapason.  Using both couplers and thereby playing on all three stops at once, the further increase in loudness may again be slight. 

Yet if the notes played are different the result usually changes dramatically.  For example, now play the following three-note chord on a single stop:  middle C, treble C (the octave above) and treble G (the G above the second note).  The subjective loudness of the chord is many times larger than if the three notes had been identical in pitch. Every time I do this experiment the result surprises me – the chord is louder by an unexpected amount than playing the same note on the three flutes together. (The perceptive reader will have noticed that the notes chosen are in fact at the frequencies of the first three harmonics of the root note, middle C.  The significance of this will be discussed later.  However we do not need to choose these notes to demonstrate the effect just mentioned). 

This is all pretty confusing, so let us summarise where we have got to.  I did say that loudness was an elusive subject!  There are three main facts to remember, all based on the difference between actual sound level and subjective loudness.  They are 

1.      The loudness of a single note played on an organ flute increases only marginally for quite large increases in its actual sound level. 

This is relevant to the pursuit of a powerful flute tone.  It takes a wide-mouthed flute pipe blown with lots of wind to make it sound anything like powerful.  Then one usually finds that such a pipe has a measured sound level (not the same thing as loudness, remember) higher than many a stop which actually sounds louder!  On most organs the great flute, although often capable of sustaining a solo role, would be regarded as softer than the Open Diapason.  Yet measuring the sound levels of these stops can be instructive :  I measured the sound level of a chord of four notes played on a Claribel Flute and then on an Open Diapason.  The flute had a sound level 10% higher than the diapason, yet subjectively it was quieter ! 

2.      If we play several notes of the same pitch on different flute stops, the apparent loudness increases but little. 

This explains the general dislike for “octopods”, organs with too many stops at unison pitch.  Such instruments are at a disadvantage when power and presence are required.  It was a lesson learnt slowly and painfully in the 19th century when the first large concert organs were built.  It was thought that by duplicating unison flute and diapason ranks of large scale, loudness would be achieved automatically.  It was an expensive way to discover the mistake. 

3.      If on the other hand we spread the acoustic energy over a wider frequency range, the apparent loudness increases dramatically. 

We proved this a moment ago when we did the experiment of playing a chord of several widely spread notes on a single stop.  The notes chosen were at the harmonic frequencies of the root note.  Therefore it is not surprising that if we have a stop whose harmonics are strong, it will often sound louder than one which has weaker harmonics.  This will often remain true even if the louder stop has a lower actual sound level.  Thus the sound of a Stopped Diapason will often be able to penetrate a chorus of other stops, whereas a duller-toned flute will not (it merely adds mud to the sound). 

This fact also explains why gentle mixture work on low pressure wind  is so important in enabling an organ to sound pervasive yet attractive.  The organ builders of the Baroque era understood this empirically.  We did not rediscover it until the 20th century, after the excesses of the Romantic period had exhausted themselves. 

There are many other factors involved in the perception of loudness but for the present we shall proceed with these alone. 

 

The Blending Properties of Flute Stops

Having discussed harmonic structure and loudness we are now in a position to throw further light on why certain flute stops, such as Stopped Diapasons, blend better than solo stops such as Claribel Flutes.  The Stopped Diapason has harmonics whose amplitudes are larger in relation to the fundamental than the Claribel Flute, therefore the acoustic energy is spread over a frequency range of several octaves.  This causes our ears to assign a relatively high degree of subjective loudness to the stop, even though its actual sound level is relatively small.  This is also true of stops such as many open diapasons and principals of moderate scale and operating on relatively low wind pressures – their acoustic power is also contained in a number of harmonics of significant amplitude.  Therefore all these stops represent similar “sound objects” in these respects, and they blend together subjectively quite well. 

A Claribel Flute (or similar loud solo flute) on the other hand differs in two ways.  Its sound level in the air is higher, and moreover that increased energy is concentrated in the fundamental frequency to a greater extent than for the Stopped Diapason.  This is because the other harmonics are weaker in relation to the fundamental.  Such a stop is therefore different in kind to others which might be sounding simultaneously – it is now a dissimilar “sound object”, and this affects its blending properties adversely.  Sometimes the concentration of the acoustic energy of a solo flute into the fundamental can be almost painful to listen to if you are close to it, as sometimes happens when you are playing the organ: the tone can seem to assault the ear when chords are played.   

 

The Hohlflöte

We have discussed two different types of flute so far, and explained their tonal differences in terms of their harmonic structure and their loudness.  We can now move on to consider further sorts of flute, examining them in similar ways. 

The Hohl Flute or Hohlflöte is a stop whose name is of considerable antiquity as it appeared frequently in northern European organs from about the 16th century onwards.  However several types of pipe have been used over this period, both open and stopped, with correspondingly wide variations in tone quality.  For the purposes of this article it is interesting because it illustrates another example of the 19th century progression which spawned a range of new flute tones.  Some remarks concerning nomenclature are also relevant, because occasionally one finds the name applied to a stop whose pipes are pierced with a hole half way up.  Such stops are more properly labelled Harmonic Flute and we shall visit them later.  The confusion probably arises because people might think the German hohl means hole, whereas it actually means hollow (though not as in hollow sound).  It’s all very confusing for non-linguists and might explain the uncertainty.  To be clear, the Hohlflöte we are discussing here is the version which appeared in the 19th century, made of open pipes, has no holes, but it will usually have a rather hollow sound. 

Such a flute is on the Hill, Norman and Beard organ at St George’s church in Dunster (or it was when I visited about 1980).  The spectrum of its middle C pipe is in Figure 5.

 

If you place a ruler so it lies across the tops of the bars representing the fundamental and the third harmonic, you will see that the second harmonic falls short of the sloping line thus defined.  Therefore, yet again, we find an open flute in which the amplitudes of some even harmonics are less than they would be if the spectrum was of the form of Figure 1, whose harmonics all lie on the same sloping line.  It is this feature which gives rise to the hollowness of the sound, just as with the other flutes.  However, by comparing Figures 3, 4 and 5 you will see that the separation of the even and odd harmonics into separate structures is not so obvious visually in the case of the Hohl Flute, which is why we needed a ruler to spot it.  Nevertheless the ear detects it, and it imparts a subjective degree of hollowness to the sound.  Not surprisingly, the amount of hollowness in these three tones varies though:  the Stopped Diapason sounds hollowest, the Claribel Flute is less so, and the Hohl Flute less hollow still.  These impressions accord qualitatively with the difference between the amplitude of the fundamental and the second harmonic in each spectrum. 

Other characteristics of the spectrum are more akin to the Claribel Flute rather than the Stopped Diapason.  In particular, the difference between the amplitude of the fundamental and the next strongest harmonic is nearly 30 dB (for the Claribel it was 25 dB and for the Stopped Diapason 15 dB).  Therefore this stop, too, has most of its acoustic energy compressed solely into the fundamental.  This gives the tone of individual pipes a rounded “bloom”, making the stop useful and beautiful for solo work just as for the Claribel.  However it blends less well with other fluework than the Stopped Diapason does, for the reasons discussed at length earlier.  Because of the relatively powerful fundamental, this stop can be viewed as yet another step along the road towards the development of smooth, powerful, pervading flute tone in the organ of the Victorian era.

 

The Harmonic Flute

Harmonic Flutes are double length pipes, usually open and of metal, with a small hole bored half way up.  They are associated particularly with the organs of Aristide Cavaillé-Coll.  The hole suppresses the formation of the odd harmonics, including the fundamental, because these all have a standing wave pressure maximum – a pressure antinode - at this point.  (The even harmonics have minimum pressure, a node, at the same position).  The hole allows these points of high pressure to leak away before the corresponding harmonics can build up.  The first few standing wave patterns of an open pipe without a hole are sketched in Figure 6.  In this diagram the horizontal distance between the curvy lines indicates the pressure excursions of the vibration of the air.  Thus where the lines cross the pressure is at a minimum, and where they are furthest apart the pressure is at a maximum.

 

 

Therefore the pipe speaks the octave above its normal pitch.  It is reasonable to enquire why this is done.  Why go to the considerable trouble and expense of making double-length pipes?  What features of the tone make it worthwhile?  The answer illustrates yet another move towards the power, roundness, gravitas and profundity of tone so beloved in the 19th century.  This is not to deny the beauty of these stops for solo purposes, but they blend even less well than the other flutes mentioned already. 

A typical Harmonic Flute spectrum is in Figure 7, representing a pipe from the solo organ at Malvern Priory.

 

Again we see the same sort of structure as before in that all harmonics are low in amplitude compared to the fundamental, the fourth harmonic being so low that it does not appear at all within the 60 dB (1000 : 1) dynamic range of the diagram. This is a feature which is sometimes found in harmonic flutes, though not necessarily always at the fourth harmonic position.  Clearly the missing harmonic affects the tone, and another factor is the second harmonic which is weaker than the third as in some of the other cases.  Also, no flute discussed so far has had as few as four discernible harmonics.  The combination of a strong fundamental and weak even harmonics occurred for some of the other flutes discussed already, and by now you should begin to expect it.  So, yet again, the tone of this flute is rounded and hollow-ish, nor does it blend well with other stops. 

The missing fourth harmonic is an interesting feature as it illustrates a property of stops which use the harmonic principle.  To understand this, it is necessary to appreciate that the spectrum lines in Figure 7 actually lie at the even harmonic positions of the pipe were it not for its hole.  To clarify, the fundamental in Figure 7 is at twice the frequency that the pipe would emit if you put your finger over the hole.  This is the same as the second harmonic of the pipe without the hole.  The second harmonic in Figure 7 is of the same frequency as the fourth harmonic of the pipe without the hole, and so on.  Now, the successive harmonics in any flue pipe lie successively further away from the corresponding natural frequencies of the pipe, and it is this factor which gives overall “shape” to the spectrum. (An expanded discussion of the difference between the radiated and natural frequencies of pipes is given in [4]). 

Because the hole forces the pitch of the pipe to lie at the second harmonic corresponding to its length, this means it is inefficient in the sense that the pipe does not resonate as easily as it would without the hole.  Moreover, the natural frequencies of a pierced pipe diverge extremely rapidly from the frequencies of the higher harmonics, more rapidly than for one which has no hole.  This makes the pipe resonate progressively badly at harmonics above the fundamental.  The upshot is that the harmonics can only form with difficulty for the Harmonic Flute, and it explains why some of them are so low in amplitude, even missing, and why there are so few.

 

The Tibia

The name means pipe in Latin, and because it also denotes the bone which takes the weight of the body it is a logical name for a stop which forms the foundation tone of the theatre organ.  The Tibia was invented by Hope-Jones, one of whose preoccupations appeared to be pushing existing organ tonalities to their practical if not logical extremes.  Given the path traced above, in which the succession of flute stops we have discussed shows a progression towards ever-increasing power and ever-decreasing blend, the Tibia is the end point.  No flute is more powerful, has fewer harmonics and blends so badly with other fluework as the Tibia.  Yet, as with other Hope-Jones’ inventions whose novelty was the principal characteristic, therein lay its future. 

Tibias come in two varieties, open (Tibia Plena) and closed (Tibia Clausa).  (Occasionally the adjective Dura is also found).  The latter are more common than the former, and even large theatre organs such as the four manual Wurlitzer in the Granada, Tooting, will often only have the closed type (two ranks in that case).  Obviously closed pipes are cheaper and take up less space.  Therefore we shall only discuss the Tibia Clausa here. 

Besides their stopped construction, the pipes are of wide scale with high cut-up leathered mouths.  The area of the flue plus the fact they are blown at high wind pressures means they need vast quantities of wind.  Actually the construction of some Tibias varies across the rank, which of course contains many more than 61 pipes to enable the multi-pitch extension of the theatre organ.  Sometimes a combination of stopped and open pipes, of both wood and metal, was used across a typical Tibia Clausa rank. 

An example of a Tibia spectrum is shown in Figure 8, representing a pipe sounding tenor D sharp on an 8 foot stop.

 

 

Apart from sheer power, the feature which distinguishes it from the other flutes considered is the almost complete suppression of the even harmonics.  This endows the sound with an extremely hollow, almost eerie flavour.  It is without doubt quite unlike any other flute, though it has its own peculiar beauty which is perhaps why examples are occasionally found in straight organs also. 

Relatively few organists today seem to have experienced a Tibia themselves because the historical condemnation of Hope-Jones has deprived us of much of his legacy.  Therefore it is perhaps something worth trying when the chance to play a theatre pipe organ arises.  Not only are the sounds of the individual stops interesting, but the way they combine with some other extreme tonalities of the theatre organ are fascinating.  For example, many of the thin colour reeds such as the Vox Humana have weak even harmonics like the Tibia itself.  Combining such a reed at 8 foot pitch with a 4 foot Tibia fills in those gaps, so to speak, and produces an entirely different composite tone which is instantly recognisable as a popular theatre organ sound.  Many other registrational possibilities were described in a recent article [7].   

Of course, theatre organists maintain that the Tibia is nothing without its tremulant.  And it does need its own, a fact plainly unknown to or ignored by some makers of electronic substitutes.  This is one reason why theatre pipe organs have several tremulant tabs.  There are at least two reasons for the multiplicity of tremulants.  One is because of the Tibia’s almost insatiable demand for high pressure wind, which means that often it will have its own wind supply. Imagine the problems for the theatre organ builder who had to cater for a heavy chord played on a Tibia chorus from 16 to 2 foot pitches or beyond!  To tremulate a Tibia means it needs a separate tremulant motor because of the separately derived wind.  (Inadequate theatre organ tremulants sometimes gave up when the going got tough.  A scholarly investigation into the design of tremulants appeared in [8]). 

Another reason for the separate tremulant invokes the sciences of physics and perception.  A cyclical variation of wind pressure to a flue pipe, such as that imposed by a tremulant, makes its frequency and amplitude change.  For flute stops the frequency change is more important subjectively.  When the pressure rises the pipe goes sharp, and conversely it goes flat when it falls.  I plotted a graph of this effect for a stopped pipe which appears in Figure 2 of [9].  Therefore the pitch of the pipe has an impressed vibrato, similar to that of the violin, oboe or opera singer to name but a few. 

Because of this link to “proper” musicians, the heavy-handed criticism of theatre organists for their use of the tremulant might seem a little unfair.  All these executants are using vibrato partly to enhance the subjective loudness of their performances.  The reason why this occurs is beyond the scope of this article but it is explained, for example, in [2].  It is related to a fact already mentioned, that subjective loudness increases dramatically when the frequency of the sound is spread over a greater range.  For the Tibia, whose loudness has already been pushed to the absolute limit by the organ builder, the use of the tremulant makes it seem even more so. 

But why does this mean that a separate tremulant is needed for the Tibia?  The reason is that to evoke a perception of vibrato in a stop with such limited harmonic development, it is necessary to “swing” its fundamental frequency by a relatively large amount.  If a tremulant of such violence was applied to stops with many more harmonics such as strings, their upper harmonics (and amplitudes) would wobble around to such an extent that the effect would be ludicrous, assuming the pipes continued to speak at all.

 

Concluding Remarks

We have traced the development of a number of flute stops, starting with the Stopped Diapason which arose a few centuries ago and ending with the Tibia.  Those in between were treated in an approximate chronological order in the narrative, and they show some distinct trends towards the same ends.  They all demonstrate a progressive reduction in the number of harmonics, thus a concentration of the acoustic energy into the fundamental, and much other effort devoted to an increase in power. 

A necessary remark is that the acoustic spectra in this article were all associated with pipes near the middle of the compass, within an octave or so centred on middle C.  If the spectrum of any stop is examined at different points across the compass it will be found to vary considerably.  This remains true even when the random variations occurring from note to note are considered, and taking account of factors such as changes in pipe construction in the bass or treble for example.  All stops exhibit a characteristic variation across the keyboard due to the scaling of the rank and the variations introduced by voicing and regulation.  One can often discern the amount of care taken with the design and voicing of a stop by examining the changes in its spectra. A sloppily voiced stop will exhibit spectra which vary dramatically from note to note, largely obscuring the systematic variations that occur across the compass. 

In the cases discussed here all the stops demonstrated considerable skill applied to these matters, with the Harmonic Flute at Malvern Priory being the most consistent.  Over the middle two or three octaves of this stop the voicer must have devoted great care to the tonal finishing to get the sound consistent from note to note.  Outside this range the variation from pipe to pipe was somewhat greater.  Considering that none of today’s electronic instrumentation such as real time spectrum analysers was available to the builders of any of these instruments to assist them in voicing, such evidence is a remarkable testament to their skill and the acuity of their “ear” for the job. 

With today’s hindsight one can perhaps see the hint of a 19th century desire to make a pipe which generated only a pure tone – a sine wave in technical parlance.  After all, this would have been a logical end-point, though a reductio ad absurdam, of the struggle to reduce the harmonic content as far as possible, and therefore to compress the acoustic energy solely into the fundamental.  It is difficult for us to imagine a time when nobody had actually heard a pure tone from a musical instrument (because they can only be generated electrically), yet that is the situation when the succession of flutes described above was being pursued.  Moreover those who worked on the theory of sound after the time of Fourier, culminating with Helmholtz and Rayleigh, had demonstrated the importance of these curious artefacts as the building blocks of all periodic sounds.  So perhaps it is not surprising that people who earned their livings from making musical instruments might have been in the forefront of those who wanted to actually hear them in isolation. 

Hope-Jones was probably the first organ builder who was enabled to hear pure tones because of his credentials as an electrical engineer, and there is strong evidence that he did [11].  Having done so, it would not be surprising if he was disappointed by their stupefying dullness as musical sounds.  The vestigial harmonic structure in any of the flute tones discussed earlier is responsible for their beauty, and listening to pure tones would quickly demonstrate the importance of such structure.  So perhaps he was one of the first to go in a different direction, using pure tones as the basis of a real time additive synthesis machine.  He could not have built one because of the technological limitations of the day (curiosities such as the "Telharmonium" notwithstanding [10]), and they first arose in the guise of “organs” in the 1930’s, more than 15 years after his death, as the Compton Electrone and the Hammond organ.  Some of today’s digital electronic organs still use additive synthesis.

 

Notes and References

1. “Soundboard”,  John Norman, Organists’ Review, May 2002, p. 136. 

2. “Fundamentals of Musical Acoustics”, A H Benade, Dover 1990.  ISBN 0 486 26484 X 

3. “The Physics of Musical Instruments”, N H Fletcher and T D Rossing, Springer 1999.  ISBN 0 387 98374 0 

4. “How the Flue Pipe Speaks”, C E Pykett 2001, currently on this website.  (read)

5.  “Gleanings from the Cash Book: St Mary’s Hatfield: Church Expenses”, P Minchinton, Organists’ Review, May 1999, p 108 

6.  “The Effect of Wall Materials on the Steady-State Acoustic Spectrum of Flue Pipes”, C P Boner and R B Newman, Journal of the Acoustical Society of America, volume 11 p. 83, July 1940. 

7.  “Theatre Organ Playing”, R Bingham, in The IAO Millennium Book, ed P Hale, IAO 2000.  ISBN 0 9538711 0 X 

8.  “The Physics of Tremolo”, D Hedberg, Theatre Organ, vol. 29 no. 6, Nov/Dec 1987.  (Theatre Organ is the journal of the American Theatre Organ Society). 

9.  “Calculating Pallet Size”, C E Pykett 2001, currently on this website.  (read)

10.  Cahill's Telharmonium of about 1906 would have been known to Hope-Jones but it was not practical as a musical instrument.  One reason for its brief lifespan was the popularity of the Hope-Jones/Wurlitzer style of pipe organ which eclipsed it, together with the brutal rumour that its interference with telephone traffic so annoyed local businessmen that they sabotaged it.

11. Evidence that Hope-Jones foresaw the power of additive synthesis as a means of generating musical tones electrically is abundant.  His enthusiasm for the subject surfaced in a lecture he gave to the College of Organists in London (the forerunner of the RCO) as early as 1891, years before a vestige of the necessary technology was available, and this is remarkable in itself.  More detail can be found in the article on this website Hope-Jones at the College of Organists (read).  By then he had almost certainly used Helmholtz resonators to reveal the approximate harmonic structure of the tones emitted by organ pipes, and he had already designed a system on paper for re-creating them electrically from a large number of sine wave generators.  His electro-mechanical telephone amplifier, revealed in British Patent 15245 in 1890, looks virtually identical at first glance to the rotating wheels used in the Hammond organ of the 1930's, and it is more than probable that Hope-Jones discovered that it could generate sounds electrically as well as amplify them.  He could not have made a practical musical instrument at this time because electronic amplifiers and loudspeakers were things of the future, but he would have been able to hear the outputs from such generators using telephone earpieces.  It would not have been difficult for him to have gone further by combining the outputs of several harmonically-related generators to reconstitute complex musical tones and to hear them.  Given the background summarised here, it would have been surprising if he had not done this, and there is firm evidence that he did so later in his career in America.  All of this work was far in advance, both in theory and practice, of what any other organ builder of the day could have conceived of.  It supports the thesis of this article in suggesting that he saw the Tibia as a practical generator of approximately pure tones at a time when no other means of producing them was possible.