The End Of The Pipe Organ?
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The End of the Pipe Organ?


by Colin Pykett


Posted: December 2005

Last revised: 9 April 2012

Copyright © C E Pykett 2005-2012


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Abstract  This article discusses whether we can foresee the end of the pipe organ, partly because of improvements in recent years to its digital competitor.  At present the digital organ remains far from perfect, but if it is assumed that improvements will continue it is legitimate to query whether the end is now in sight for its traditional and much more expensive forbear.  Currently, the two most audible and objectionable forms of distortion in digital organs, intermodulation and signal mixing distortion, occur mainly because of insufficient loudspeakers of indifferent quality.  These result in the well known defect of any digital organ in which its sound considerably degrades as the number of stops and notes build up.  It is shown that neither form of distortion can be overcome completely, and that there is no prospect that the problems will be solved in the foreseeable future.   Although significant improvements could be made, in practice they would require so many loudspeakers at so great a cost that it is unlikely organ manufacturers as a whole will venture routinely in that direction.  Moreover, there is no prospect that harmonic distortion will be improved at all.  These conclusions have resulted from the most detailed technical analysis of the problems ever published for the electronic organ application.  Therefore it is safe to say that digital organs will never be able to match the sound of the pipe organ in the foreseeable future, particularly regarding its major choruses and tonal build-ups, because pipe organs do not suffer from distorted sound at all.


However this does not mean that the future of the pipe organ is secure, because superior sound alone will not necessarily win in the hard world of business.  Many potential customers will continue to be seduced by the relative price differential of digital organs, and many either will not be able to perceive the tonal defects of digital organs highlighted in this article or they will decide they are not sufficiently important.  Another factor working against the survival of pipe organs is their highly variable quality, together with some appalling examples of complacency and disregard for the customer on the part of organ builders. These conclusions arose from the survey in this article of the strengths and weaknesses of both the pipe and electronic organ businesses, and they illustrate that the pipe organ business is experiencing problems purely of its own making.  Therefore, for champions of the pipe organ to exploit the digital organ as a scapegoat in this situation is both superficial and disingenuous.


It is concluded that the eventual fate of the pipe organ may be to attract little more than antiquarian interest well within the lifetime of many who read this article, though perhaps this could be averted if the anti-electronics lobby could be persuaded to moderate their stance.  Some suggestions are made for bringing this looming crisis to the notice of a wider public.




(click on the titles to access the corresponding sections)




The Pipe Organ Business


The Electronic Organ Business


Technical Matters


Harmonic Distortion


Intermodulation Distortion


Solutions to the distortion problem

Signal Mixing

Demonstration of the signal mixing problem


Solutions to the signal mixing problem 



Appendix 1 - Illustrating the generation of harmonic distortion and intermodulation distortion


Appendix 2 - Estimating the power of intermodulation distortion products


Appendix 3 - A practical demonstration of intermodulation distortion


Notes and References





It was the original intention that this article would be entitled will the pipe organ ever be ousted by electronics?  However this turned out to be rather unwieldy in an editorial sense so it was discarded.  Nevertheless the thrust of the article remains unchanged, which is to investigate whether the advances made in digital electronic organs will continue and eventually render them so good that nobody with their feet on the ground could ever justify buying a pipe organ.  But to do this I found it necessary to look more widely at the pipe and electronic organ businesses first, because technology alone is not the beginning and end of the matter.  Some of the most popular consumer items today are not always the best in a technical sense, a good example being the ubiquitous IBM PC.  Obviously, an analysis of why this is so could not not proceed if it was confined merely to technical issues, thus the same applies to organs.


This is one reason why the pipe versus electronic debate continues today with unabated vigour, even now that digital organs have shown themselves capable of reproducing the sounds of pipes to a high degree of realism.  But will this continue in perpetuity, illustrating at one extreme merely an addiction to interminable dispute by those with insufficient to fill their daily lives, or could it result in the eventual demise of one sort of instrument or the other?  Presumably the pipe organ is more at risk because it is so much more expensive, though it should be remembered that the market for both types is declining rapidly.  Over the last few decades the number of firms in the two industries and the numbers employed by them have experienced dramatic global attrition.  Therefore it is interesting to analyse the situation as it exists now and to speculate, as objectively as possible, what the outcome might be.  Among other matters, this article examines in detail some current technical shortcomings of all electronic organs.  If these cannot be overcome in the future it would mean that digital organs will never be able to match the sound quality of real pipes.  Whether this would in turn imply a long term future for the pipe organ would still require a business analysis for that industry’s products though.  Superior sound alone will not necessarily win in the hard world of business.


The Pipe Organ Business


“... as we all know, organ builders have always used their customers as guinea pigs ...”


Harrison and Harrison Ltd [5]


The current British pipe organ industry is exceedingly small when measured against any business metrics.  In 2004 it was estimated that there were only about 400 people employed both in organ building and in the related component and pipe making firms in the UK [1].  This compares with about 500 only two years earlier [2], indicating a rapid and startling decline on the face of it.  If this decline continues at the same rate year on year, there will be nobody left by 2012.  In 2007 the largest firm (Harrison & Harrison) employed less than fifty and most of the smaller ones, which still form the majority, numbered a workforce of less than five.  Some self-employed individuals eking a living from organ building have no dedicated premises, not even a garage doubling as a simple workshop.  In the last few years some well known and respected names have disappeared from membership of the Institute of British Organ Building (IBO), leaving an unseemly eddy of rumour and speculation in their wake.  Other great names from the past, including Hill, Norman & Beard and Rushworth & Dreaper, have vanished altogether.


Yet size alone cannot be used as a yardstick to measure the health of a craft as opposed to a commodity producer of cars or toothbrushes.  In Britain there is a number of small concerns which produce furniture, for example, to standards of meticulousness and beauty easily the equal of anything which graced earlier centuries.  It is these craft analogues which are a better and fairer guide when interpreting the bare statistics relating to pipe organ building.  And, just as with dining tables, it is therefore appropriate to examine the quality of organ building today before drawing conclusions about its future.


Although a subjective judgement carrying negligible weight, I find that most of today’s new pipe organs look stunningly beautiful.  The fact they regularly adorn the covers of the major organ magazines suggests that many people agree.  This contrasts starkly with the situation a century or more ago, when the casework of new organs often seemed to be at the bottom of the list of priorities.  Henry Willis was one of the worst perpetrators in this regard, and although it is an aural delight that a few of his finest organs still exist largely untouched, the sight of his work at Salisbury cathedral verges on the offensive.  So we have certainly regained our touch in this area.  Or have we?


The new casework for the Willis organ in Emmanuel Church, Wylde Green is the work of an eminent designer.  It boasts a number of materials ranging from oak to MDF, the latter because of “limited funds”.  But, oh joy, we are told by the organ adviser and the builder that it apparently doesn’t matter because the “MDF is completely invisible to even the most informed onlooker” [3].  Really?  Why bother with the oak then, if MDF will do?  One is accustomed to the uncritical and self-congratulatory approach of some in the cloistered world of British organ building when appraising their own work, but in this case it does rather emphasise the hypocrisy of their brethren who complain that “electronic instruments are often cheaply finished” [4].  A measure of hypocrisy might also be ascribed to that increasing number of organ builders who are willing to include electronic stops in their instruments, sometimes in cathedral organs, yet who presumably subscribe to the overall denigration of digital organs by their colleagues.  There are also well known organ advisers who now claim sufficient expertise to be able to advise in the very different and highly technical field of electronics [9], yet who routinely refer to such instruments rather loftily as “simulations” whereas pipe organs are “real” [10].  Whether this is hypocritical I could not say – perhaps like beauty, it depends on the beholder.  I do however feel that those in the pipe organ business cannot continue to have it both ways for too much longer.


In terms of key actions, customers are still expected to put up with products which are experimental or otherwise unproven.  Rather breathtakingly, Harrison & Harrison's works manager wrote recently that “as we all know, organ builders have always used their customers as guinea pigs” [5].  Well, well.  That would explain a lot, and it confirms what many have thought for a long time.  It also bears out the depressing conclusions of my critique of electric actions elsewhere on this website [11].


Continuing this theme which questions the quality of some organ building today, it was the view of the Diocese of Rochester in 1991 that “most small firms produce poor work which rarely lasts for more than a few years” [6].  The British Institute of Organ Studies (BIOS), enthusiastically donning the uniform of the Thought Police, stoutly declared that it “along with other bodies associated with the Organ, will be pressing for this publication to be withdrawn from sale” [7].  That the publication was not, to my knowledge, withdrawn was a victory for free speech in a country which prides itself on maintaining it.  Nevertheless there was much with which one could have taken issue in the Rochester publication, in particular that evidence was not actually presented showing that most small firms do shoddy work.  However there is no doubt that some do, as my own experience as an organ adviser attests.  The situation is not helped by the frequency with which some organ advisers appear to recommend such firms, especially in rural areas.


When new pipe organs cost typically around £10,000 per stop, their highly variable quality as outlined above is scarcely likely to encourage reluctant customers to beat a path to the door of their nearest organ builder.  The industry needs to be constantly aware that if it falls below some critical mass level, any business model will show that it will collapse completely and suddenly.  Although serious in itself the greater potential cataclysm is that, like those of some other ancient crafts, its highly skilled practitioners will shortly thereafter cease to exist.  It is not a business that could easily be resurrected once lost, unlike the electronic organ industry which rides like a pimple on the back of mainstream digital technology developed for other purposes.


The Electronic Organ Business


"It is the vice of a vulgar mind to be thrilled by bigness, to think that a thousand square miles are a thousand times more wonderful than one square mile, and that a million square miles are almost the same as heaven. That is not imagination. No, it kills it."


Howard’s End, E M Forster

Although there are large pipe organs, the theme of ubiquitous and overtly vulgar bigness does not pervade that world to anything like the extent found with electronic ones.  I am speaking of the size of the bloated stop lists of course.  Perhaps this is merely because very large pipe organs are obviously too bulky and expensive to be ordered frequently, and perhaps that is also a mercy.  But these constraints affect electronic organs hardly at all, because large instruments may actually cost little more to make than small ones once the costs of things like the console and loudspeakers have been committed.  Thus, rarely does an electronic organ manufacturer tax himself within the discipline of designing an organ with a modest stop list, though there are exceptions.  This factor alone demonstrates the limited horizon of his artistic pretensions,  bearing in mind that it is difficult to see why more than about a dozen speaking stops per department should be necessary in most situations. This mine-is-bigger-than-yours attitude is also seen in the smallest and cheapest electronic organs which often offer multiple voicing options as well.  Thus each tab does duty for several stops, thereby turning playing into a confusing nightmare. 


Big stop lists aside, in many ways the market for electronic organs is little different to that for pipes.  The days when people rushed to buy them after realising they could have a home organ at a reasonable price have long gone, maybe because spouses eventually put their foot down about having a huge conventional console in their living space and the often unpleasant noises which emanated from it.  Also the availability of even cheaper plastic “keyboards” has long saturated much of the domestic market, and they are now making significant inroads into churches as well.


Therefore manufacturers now have to concentrate more exclusively on the residual and diminishing church market just as pipe organ builders do.  Generally they are better at selling into it, however.  This was diffidently acknowledged by the Royal School of Church Music (RSCM) which has said that "electronic organ firms place far more emphasis on sales and publicity skills than pipe organ builders in the UK" [8] I do not subscribe to the view that success in selling is in itself reason to be critical of a firm, because it sometimes reflects that peculiar and prevalent British disease which automatically belittles commercial acumen.  Provided sales and marketing functions are executed ethically and without undue pressure I cannot see why a firm should be criticised for being successful in this regard.  However the business culture of some firms is demonstrably questionable, and in these cases it is entirely legitimate to criticise them.  As an example, I was once contacted by someone seeking information about the products of a well known manufacturer of digital organs and I replied in good faith.  It turned out he was none other than the board chairman, would you believe, and he remained brazen even when "outed" in trying to set traps for me!  So the RSCM is probably right to hint that a touch of caveat emptor on the part of customers will not go amiss - firms which treat me like that presumably think nothing of treating others the same way.


In the interests of balance and fairness it is necessary to record that pipe organ builders also sometimes indulge in curious publicity practices.  The organ at St Peter's, Eaton Square in London was advertised in 1992 as "the largest mechanical-actioned organ in the United Kingdom", the advertisement also including the phrase "and yes, the Solo Tuba Mirabilis 8' (on 12" wind) ... also has tracker action" [13].  In fact the instrument depends on electrical assistance over more than half the manual compass, a fact not revealed in the public domain until seven years later [14].


Although prices vary considerably, a better-quality custom built four manual electronic organ with around 100 stops could cost around £100,000.  Therefore, at about £1000 per stop, this is compatible with the often-quoted statement that they are around one tenth the cost of an equivalent pipe organ.  This is a most compelling reason for any customer to consider them seriously.  The price differential of the cheapest ones might be a mere one fiftieth.  A church is often committing public money when purchasing an organ, in the sense that much if not all of it will have been gifted in some way.  Therefore, whatever the sentiments of those responsible for the purchase regarding electronic organs, it would generally be a dereliction of their duty not to consider all reasonable options.


The electronic organ business is not regulated by trade organisations comparable to the IBO, but even if it was I doubt it would expose itself with the commendable candour which has enabled me to write some earlier parts of this article dealing with pipe organs.  On the contrary, it embraces a culture of coyness, secrecy and even slyness as the anecdote above demonstrates.  Even when he is trying to get a customer on the hook, a manufacturer will not always reveal all the trade secrets the customer might want to know about the instruments on offer.  As just one example, it is actually quite important for customers to be given the answers to questions such as how many Musicom modules per department are used in organs using that form of digital technology (additive synthesis).  Why?  Because it would then reveal how much polyphony is available, and whether it is compatible with the number of speaking stops.  In turn this would enable the customer or his technical adviser to estimate the likelihood of the player experiencing missing notes with full combinations.  The issue also applies to instruments using other synthesis techniques (sampled sound and physical modelling, both of which are similarly modular in the sense of their technical architectures).  While some firms are more open than others, they form the minority.  Instead we are more often treated to a patronising and juvenile display of buzz words and factoids no doubt intended to throw the client off the scent, as anyone can see from the advertisements.  Actually, and to be fair, this is not a phenomenon characterising solely digital organs because almost any manufacturer of electronics today for some reason loves to endow his products with naff soubriquets.  This even affects the pipe organ scene where electronic (solid state) control systems are involved.


Also because of the cloak of secrecy it is more difficult to estimate the size of the digital organ business.  One indisputable fact is that, like pipe organ builders, the number of firms has undergone dramatic attrition over the last two decades or so and for much the same reasons.  But a feature of electronic organ manufacturers is the rapid and continual evolutions they undergo.  Partly this is a reflection of their better business savvy, enabling them to stay in business in some form even when times are tough, and nobody can blame them for that.  Indeed, it is in the interests of existing customers that this should be so.  But it evokes surprise when an individual who was the technical director of one firm suddenly becomes the managing director of another with a different name but still at the same address.  What this does to warranties and guarantees will only be discovered the hard way.


Thus electronic organ makers have, understandably, come in for a lot of stick over the last fifty years or so for many reasons including those above.  However this tends to mask some of their positive aspects, of which one is the effort made by some of them to keep their products going well beyond the point at which their technology has become obsolete.  For example, Copeman Hart installed one of the largest analogue instruments ever made in the Royal Concert Hall in Nottingham in 1983.  Recently the instrument has been converted to digital operation.  Statistics such as these are comparable to the pipe organ situation, where major interventions every quarter of a century or so are not uncommon nor unreasonable.  Allen organs have claimed in the recent past that any instrument they have ever made will be kept working, although when originally writing this (12 October 2005) I was unable to find it mentioned on their website.  Considering that their earliest analogue organs used valve (tube) technology well over fifty years ago, this must be a considerable comfort to their customers if it is still the case.


Technical Matters  


" ... the prevalence of the loudspeaker in our daily lives has blunted the ears of many to the subtle beauties of really first-rate organ tone ..."


W L Sumner [15]


In another published article [12], also now on this website, I have discussed many technical issues relating to electronic organs so it is unnecessary to repeat it here.  However the area of loudspeakers will now be revisited in some detail because it is here where further improvement, although technically possible, is unlikely to be cost effective.  So difficult are the problems that one can predict with some confidence that this statement will remain true for a rather long time, if not in perpetuity.


Sumner's remark was written at a time (c. 1960) when many people were already not bothered by distortion, and most probably did not even know what it was or what to listen for.  They had already endured some 35 years of music broadcast with an audio bandwidth of 5 kHz over the "wireless", reproduced monaurally and with high background noise levels through the most rudimentary loudspeaker systems.  The contemporary "gramophone" was even worse.  The situation was compounded by the emergence at that time of additional sources of gross distortion introduced deliberately, such as the fuzz boxes used with electric guitars.  (When I was a schoolboy in that era I was sometimes implored by my pop-loving friends to make one for them).  These long and painful birth pangs of electronically reproduced music can only have assisted the ascendancy and encouraged the mediocrity of the electronic organ over the same time frame.  Today it remains unfortunate that the majority of those who listen to music through loudspeakers apparently believe that things have reached a summit of excellence, exemplified by the "digital sound perfection" claimed in certain quarters.


Yet surely nobody with any discernment could seriously argue that any digital organ today is indistinguishable from pipes, though if they did it could only be because they do not listen to live music frequently enough.  Such a claim is as patently absurd as saying that listening to a CD can be indistinguishable from listening to a live orchestra.  If on returning from a concert, not necessarily of organ music, such people cannot detect the difference between the sounds just heard and those which issue from their hi-fi system, then I am afraid they are suffering from Sumner's blunted ear disease.  Even the best loudspeakers suffer from shortcomings such as that rough, tearing type of sound introduced when massed violins are playing or when listening to a chorus of women’s or boys’ voices.  Comparable effects with electronic organs result in the well known phenomenon that, while individual stops or small combinations might be good or excellent, anything beyond this becomes progressively more excruciating.  I often find that it becomes physically impossible to continue playing many electronic organs after ten minutes or so because of the aural distress they cause, and this is largely because of the distortion generated by the poor quality loudspeakers used.  I have yet to experience this effect with any pipe organ, even indifferent ones, where of course the distortion of the signals entering the ears is zero.  I shall show later that the worst distortion products of loudspeakers occur at frequencies of a few kHz and above, which is where the ear is most sensitive.  These frequencies are also handled by tweeters, which generally have a performance far worse than that of lower frequency loudspeakers.  Often the distortion performance of tweeters is so bad that it will not be mentioned and definitely not quoted.  And because loudspeakers are unlikely to improve in the foreseeable future, it is therefore my contention that digital organs will never sound as good as pipes.


The reason why loudspeakers are unlikely to improve is because they have in fact deteriorated significantly in quality over the last few decades.  This is because of the evolution of the loudspeaker business from a state where technical excellence was a driver to its state today where innovation has been stultified and profit has become the dominant motive.  This effect, called commoditisation, is a well known business phenomenon and a fuller analysis of its unfortunate effect on the loudspeaker industry can be found elsewhere [e.g. 16].  To illustrate it I can refer to my KEF "Reference 104" hi-fi speakers purchased over 30 years ago.  The proprietary drive units they contain are unobtainable today, nor are the highly optimised crossover units which were constructed with special components, indeed they are now highly sought-after and so-called replacement items are far inferior.  Were these qualitative statements merely pure nostalgia on the part of one entering his dotage I would not have insulted the reader by including them here.  However I am able to back them up by quantitative measurements of the sort to be described presently.  There are few loudspeakers available today with the quality of these elderly KEF's or other quality makes of the same vintage.


Consequently, although digital organ manufacturers can exercise control over other aspects of their products, they are just as stuck with the limitations of today's loudspeakers as anybody else, and this is as true of an instrument costing £100K as it is of one selling for under £10K.  Loudspeakers really are the Achilles heel of any audio system today.  To illustrate this I shall now dwell on just two aspects of loudspeaker performance - distortion and signal mixing.  From this point on the material in this article becomes significantly more technical though I have tried to minimise its impact on comprehension.  Further details for specialist readers have been placed in Appendices.




The distortion of acoustic signals entering the ear from natural sources, such as real organ pipes, is always exactly zero (unless the organ is situated in one of that regrettably large number of auditoria using electronic sound reinforcement or adjustable ambience systems).  This is why pipe organs sound so fresh compared to even the best electronic ones.


Distortion is produced by a loudspeaker just as with any other component in the reproducing chain, such as the power amplifier which feeds it.  Any such component will introduce distortion if its output is not always the same multiple of its input.  For example an amplifier might have a gain of 10, which means that for any voltage applied to its input, exactly 10 times that voltage must in all circumstances appear at its output.  Such an amplifier is said to be linear.  Unfortunately such perfection is impossible to achieve and a small error has to be accepted.  In the case of good power amplifiers the error will be typically 0.01 %, which means the nominal gain figure of 10 will in practice vary between 10.0001 and 9.9999 over the working voltage range of the amplifier.  This small deviation is virtually imperceptible to the ear, though this does not prevent interminable discussion among hi-fi pundits.


For loudspeakers things are very much worse, and it is therefore very odd that the same pundits seldom seem to bother about it.  The reason is that speakers are basically mechanical, rather than purely electronic, devices.  Also, unlike electronic circuits, the principle of negative feedback has rarely been applied to them [18].  Negative feedback increases the linearity of a system and reduces its distortion.  A loudspeaker has a supposedly perfectly-formed coil of wire moving in a supposedly perfectly uniform magnetic field.  The coil is attached to a cone which moves and radiates sound waves, the motion being controlled by a spring suspension of supposedly perfect characteristics.  However it is impossible to attain a degree of mechanical perfection such that perfect linearity is achieved, in the sense that a given voltage applied to the coil will always result in exactly the same amount of movement of the cone.  As with amplifiers, there will be some distortion over the working voltage range of the loudspeaker, but in this case the figure is at least 50 times worse and often more. Thus distortion figures as "good" as 0.5% are rare, and for this embarrassing reason they are seldom quoted other than in vague terms.  For example, my KEF loudspeakers over which I was eulogising earlier have a distortion specification described hazily in the brochure as "< 1%".  If the figure was 0.5% or better I imagine they would have said so, therefore (being charitable) presumably it was somewhere between the two values.  Thus even the better manufacturers in the golden age of loudspeakers got rather coy and evasive when it came to distortion.  Today things are usually much worse, and a Toshiba Regza C3030 digital flat screen television retailing for nearly £1000 in 2007 has a quoted distortion figure of 10% at only 10 watts power output.  It is therefore quite incredible what the public will put up with [22].


Reasons for the poor distortion figure include inhomogeneities of the magnetic field, errors in the coil geometry and non-uniform wire diameter, nonlinear suspension characteristics of the cone/coil assembly, and enclosure effects.  The latter arise because the cone often has to compress and expand air inside a sealed enclosure, and in such cases the nonlinearities get worse as the frequency gets lower.  Other sources of nonlinearity can arise in the electrical crossover networks feeding power to the units of a multiple speaker system.  These are due to nonlinear inductances if ferrite-cored coils are used, or nonlinear electrolytic capacitors at high current levels.  To achieve an overall distortion figure less than 1% means that the separate contributions from all these sources must be much less than this, and this level of performance is only achieved in a few very expensive products today.  Seldom will a digital organ manufacturer use such loudspeakers as it would price him out of the market.


There are two types of distortion of interest here - harmonic distortion and intermodulation distortion, and both are produced by the nonlinearities in the reproducing chain.  The morsel of college-level mathematics in Appendix 1 shows why this is so.  Because loudspeakers are by far the most nonlinear items in the chain, it is here where our attention has to be targeted.  Harmonic distortion is the figure usually measured and quoted for good loudspeakers, whereas it is intermodulation distortion which causes the most objectionable effects in digital organs.  Both will now be discussed.


Harmonic Distortion


Harmonic distortion is the appearance of spurious acoustic power at harmonics of the input signal.  For example, if the input signal is a pure sine wave there should be no power at harmonics of that frequency in the radiated sound from a loudspeaker. But if there is harmonic distortion present, the output could well have a frequency spectrum of the sort shown in Figure 1. 




Figure 1.  Illustrating harmonic distortion


The fundamental frequency of the input sine wave shown is about 2.5 kHz, corresponding to the top D# on a 4 foot stop, and the largest spurious harmonic is about 45 dB less than the fundamental.   The harmonic distortion figure for this signal is -40 dB or 1%, a value typical of a reasonable quality loudspeaker in this frequency range.


The curious thing about harmonic distortion is that it is often difficult to detect unless one takes deliberate measures to render it noticeable.  For example a sine wave at this frequency with its harmonic distortion, as depicted above, still sounds pretty much like a pure sine wave to a casual listener.  It is only if you switch back and forth between the distorted signal and one of lower distortion that you can detect the difference easily.  This is because all natural sounds have harmonics and the ear is accustomed to them - the natural world never generates a pure sine wave - and organ pipes are no exception.  Therefore even the "purest" sounds on a digital organ such as flute stops possess a retinue of harmonics, and a slight distortion of their frequency spectra makes little subjective difference to the perceived tone colours.  For stops with more energy in the harmonics such as reeds and strings, a small amount of harmonic distortion is completely undetectable.  (These statements only apply to sounds under normal listening conditions; if you try to detect the distortion deliberately such as in A-B comparison tests of the sort mentioned above, then you can generally perceive it).  However things are very different with intermodulation distortion.


Intermodulation Distortion


We do not listen exclusively to single musical notes of the type just discussed.  For the most part music consists of several or many notes sounding simultaneously, and this results in intermodulation distortion in a loudspeaker.  Intermodulation distortion differs from harmonic distortion in that the distortion products are not confined to the harmonic frequencies only; the products are new frequencies not present in the input signal.  In particular intermodulation distortion is characterised by the appearance of the sum and difference frequencies of all frequencies present in the input signals, and it occurs if the input contains non-harmonically related frequency components.  For example, if  the input signal consists of two pure sine waves at 1 kHz and 1.2 kHz, frequencies of 2.2 kHz (the sum signal) and 200 Hz (the difference signal) will be measurable at the output if intermodulation distortion is present.  Note that these distortion products do not coincide with the harmonic frequencies of either input signal, and it is this feature which renders intermodulation distortion so noticeable and objectionable.  Its distortion products are not masked by any genuine harmonics of the input signals as with harmonic distortion, and because they are therefore so "exposed" the ear has little difficulty in detecting their presence.   As with harmonic distortion, it is the nonlinearities mainly in the loudspeaker which are responsible for intermodulation distortion, as shown in Appendix 1.  When such nonlinearities are present, and they always are, both harmonic and intermodulation distortion will always occur.  Because intermodulation distortion is so objectionable far less attention is devoted to it by loudspeaker manufacturers, and it is rare to see it even mentioned.  It is just too embarrassing a subject.  An excuse sometimes offered is that intermodulation distortion is more difficult to measure than harmonic distortion.  Although this was true when only analogue test gear was available, it is untrue today. It is shown in Appendix 3 how easy it is to demonstrate and measure the intermodulation distortion performance of a loudspeaker using an inexpensive PC-based digital test set-up.


The total distortion power at the spurious intermodulated frequencies can be surprisingly high.  It is shown in Appendix 2 that just two notes played on a reed stop having around 30 harmonics per note could generate a total intermodulation distortion power only 22 dB below the undistorted input power for a typical loudspeaker with 1% distortion.  Intermodulation distortion is a form of noise, and today we are used to an extremely high signal-to-noise performance in digital audio systems.  That of a CD player itself is up to 96 dB, and if you are familiar with decibel arithmetic it is easy to show that this laudable figure is over 25 million times better than the distorted sound power ratio which could actually emerge from the speakers in these circumstances.  This appalling result is mainly because of the very large number of intermodulation products which occur - each harmonic of each note will generate a sum and a difference frequency with every harmonic of the other note.  Therefore in this case with 30 harmonics for each note, there are 1800 sum and difference frequencies.  And this is just for two notes! When more than two notes with many harmonics are played it is easy to see that the total number of distortion products escalates extremely rapidly.  The fact that these products are scattered liberally across the entire audio spectrum is why this form of distortion does actually sound like noise,  and it is one reason why most digital organs sound so unconvincing and unpleasant when large numbers of stops are used.  In fact the better the frequency response of the organ, the worse it will sound in these situations.


The somewhat dramatic theoretical result quoted above might surprise many readers, therefore it was validated experimentally.  Two sine waves with -40 dB harmonic distortion (i.e. with a spectrum similar to Figure 1) were applied to a single loudspeaker and the sound picked up by a microphone. Note that each wave could be considered as a sort of flute-like tone with an exceptionally small amount of harmonic development.  The signal from the microphone had the spectrum shown in Figure 2.



Figure 2. A practical demonstration of intermodulation distortion.


The two largest peaks were at the fundamental frequencies of the two input signals.  But note particularly the large number of additional spectrum lines which were present, mainly at the various sum and difference frequencies of the upper harmonics (the sum and difference frequencies of the two fundamentals themselves are identified in the diagram).  Most of these lines were due to intermodulation distortion in the loudspeaker itself.  Note also that the largest distortion product is only about 25 dB below the amplitude of the two fundamentals, thereby confirming that the theoretical estimate of 22 dB derived in Appendix 2 was actually quite realistic.


This awful plot was for only two sine waves of relatively high purity using a reasonable quality loudspeaker.  Just think what it could look like for a full chord of reed tones having large numbers of high amplitude harmonics!  It would be even worse with a loudspeaker of inferior quality.


Complete details of the experimental technique used to derive this result are in Appendix 3.


Solutions to the distortion problem


Can the distortion problem be solved?  Yes it can to some extent, provided one is prepared to pay for an unusually elaborate and expensive loudspeaker set-up, and provided the hardware and software of the digital organ are sufficiently flexible in routing signals to those loudspeakers.  The solution relies on a fortuitous aspect of digital organs which does not apply to ordinary audio signals as in hi-fi systems etc.


With audio signals as recorded on a CD one has to take them as they come and accept the consequential distortion of the reproducing chain.  With a digital organ things are different, however.  If one has 12 independent loudspeaker channels (each comprising a power amplifier and the loudspeaker itself) one can route the semitones (note-names) to different channels - all the C's to one channel, all the C#'s to another, and so on.  (This also assumes the digital hardware and software of the organ would allow this to be done - many would not).  Such a speaker system would suffer from practically no intermodulation distortion because all of the signals applied to any one speaker channel are now harmonically related.  No improvement in harmonic distortion would result from this method, but it has been shown already that intermodulation distortion is the more noticeable and objectionable.


This number of audio channels would be expensive but not prohibitively so for the higher quality instruments.  Each channel, consisting of a good quality power amplifier and loudspeaker system, might cost around £500 when the costs of installing the system in the building are included, plus a profit element and VAT on the whole lot.  Therefore the minimum cost of the loudspeaker system would be typically £6000.  At least one additional audio channel would be needed for the 16 and 32 foot stops on the pedals, because it is assumed only the higher-pitched stops would be handled by the afore-mentioned loudspeaker array.  This is because the lowest frequency notes on the pedals need high power loudspeakers of special characteristics, but because only one note at a time is usually played, intermodulation between multiple notes does not often exist.  Therefore it would be unnecessary to provide more than a few channels to handle the lowest frequency stops.


While a 12 loudspeaker array would suffice for a small to moderate sized instrument of no more than two manuals, larger ones would benefit from a second array.  In fact the more the better, and an independent array of 12 speakers for each manual department would be a reasonable goal for instruments of the highest quality.  Not only would this approach keep intermodulation distortion to a low level but it would enable features such as the spatial separation of the departments to be convincingly simulated.  Simulating the C and C# sides of a pipe organ soundboard would also be easy with this number of speaker channels.


However it is possible to reduce the number of loudspeaker channels required by observing that seldom will all the semitones be played simultaneously.  This would only be the case when laying one's arm across the keys, and while this technique is occasionally called for (for example in various "Storm" or "Steam Train" music, or when playing Tiger Rag á la Reginald Dixon), the presence of intermodulation distortion in such cases would be undetectable amid the general cacophony.  Most organ music uses fairly simple harmony in which only four or so different note-names appear simultaneously.  Indeed, much of the time the harmony is based on only three simultaneous note-names using the tonic, subdominant and dominant triads and their inversions.  From time to time a fourth note is required, as when dominant or diminished sevenths occur or in modern music which makes use of the submediant.  Four audio channels would therefore be the absolute minimum needed to ensure that the various note-names could always be routed to different loudspeakers.  However, as some of these notes would be played on stop combinations which include mixtures and mutations, this has to be taken into account when estimating the likely number of audio channels required.  Therefore six channels would be more satisfactory, though not completely so, to cater for the additional fifths and thirds which would arise.  Provided the hardware and software of the organ system allows the note-names to be routed dynamically in real time to the different channels, an array of only six loudspeakers per department would represent a good solution to the intermodulation distortion problem.  Although rather luxurious when measured against much current practice, it is nevertheless not beyond the realms of possibility.


Therefore, has the loudspeaker problem been solved?  No it has not, because the next major problem, signal mixing, has not yet been addressed.  And remember that harmonic distortion has not been improved at all.


Signal mixing


All current digital organs require many different signals to be mixed down before feeding them to a relatively small number of loudspeakers.  The signals represent all the notes of all the stops which are currently being played.  For example, if a chord of four notes is played on a combination of eight stops, there are 32 separate signals being generated within the organ system.  Only the most expensive organs would have this number of loudspeaker channels, and then rarely, therefore the software inside the organ's computers has to decide which signals are fed to which loudspeakers.  When more than one signal is fed to one loudspeaker it is necessary to mix the various signals electronically first.


This invariably produces an artificial and objectionable result, because electronic mixing always introduces distortion of the timbres (tone qualities) of the various signals being mixed.  This is because of phase interference at similar frequencies in the various signals.  For example, consider the case where two unison diapasons are drawn.  These will have similar timbres, which is the same thing as saying that their frequency spectra will be similar with similar numbers of harmonics at identical frequencies.  Electronic mixing results in a composite signal at each harmonic frequency which depends on the amplitudes and phases of the original harmonics.  The result is a corresponding harmonic in the mixed signal which might bear little resemblance in amplitude to either of the original harmonics.  Therefore the composite sound of the two diapasons when mixed electronically into a single waveform will often bear little resemblance to either of the two original sounds.


Generally the result is even worse than this, because the fundamental frequencies (and therefore the harmonic frequencies) of the two signals in this example will usually be very slightly different.  On the face of it this is a good thing, because the frequencies of two real diapason pipes will never be exactly the same in a pipe organ either.  Such frequency offsets are introduced deliberately in digital organs to imitate this effect, and provided the two signals in this case are always fed to separate loudspeakers there is no problem. However if they are mixed electronically before being pushed through a single loudspeaker, their slight mutual de-tuning will become dreadfully apparent as the fundamentals and all the harmonics drift in and out of phase with each other.


Why does this effect not occur when mixing occurs acoustically, that is, when two sound signals from two or more loudspeakers are allowed to mix naturally in the listening room?  The reason is that there are myriad reflections in any room, and acoustic phase interference in the resultant complex sound field at any frequency is never as severe as the phase interference when electronic mixing is done.  Because a pipe organ always enjoys purely acoustic mixing, it never suffers from the effects just described for digital organs.


Demonstration of the signal mixing problem


For those who have had difficulty following this so far, and most people experience this at first when initially exposed to the problem, it might be helpful to demonstrate the situation with a real example which you can listen to if your computer is set up to download and play mp3 sound files in stereo.  Either loudspeakers or stereo headphones can be used.  I set up two 8 foot diapason tones in a digital organ both notionally sounding middle C.  However the frequencies of the two differed by one cent (one hundredth of a semitone).  This small amount of de-tuning is representative of what would be heard in a pipe organ, and it results in a very slow beat between the two sounds.


If you click on the "stereo" link below you should hear the two diapason sounds issuing from the two separate audio channels of your computer.  In this case the signal mixing is being done acoustically in your listening environment (or in your brain if using headphones), and although the slow beats between the two tones can be detected, it is not objectionable.  Indeed, it sounds quite natural and it assists the ear in determining that two sound sources are present. Note the file was recorded at a fairly high level, therefore do not have the volume of your audio system set too high. 


Two diapasons in  STEREO (mp3, 206 KB)


By modifying the software I then mixed the same two signals electronically, just as a digital organ does.  The resulting mono sound file will play monaurally into both channels of your audio system if you click on the "mono" link below:


Two diapasons in MONO (mp3, 211 KB)


Notice in this case how the beats are very much more pronounced, and how the timbre of the single composite tone varies over a beat cycle.  In particular notice how the fundamental vanishes completely owing to phase cancellation at one point in the cycle.  These effects are of course completely unnatural and highly objectionable, yet they occur to some extent in every electronic organ ever made no matter how expensive or how heavily promoted.  This is simply because there are never enough loudspeakers to cater for the number of signals which can be generated simultaneously.


Solutions to the mixing problem


Can the mixing problem be solved?  Although it could be in theory, it would be impossibly expensive to implement a complete solution in practice.  A complete solution would need as many loudspeaker channels as signal sources within the organ.  Digital organs have a finite though relatively large number of note generators which are assigned dynamically and in real time by the computer system as the organ is being played.  For example, the better organs will often have a polyphony of 128 per manual department, which means that up to 128 separate notes per department can sound simultaneously.  This number of note generators would be demanded under quite modest playing conditions if a chord of 8 notes, say, was played with 16 stops in use (noting that an n-rank mixture counts as n speaking stops if implemented properly).  Yet no organ under the sun would have 128 loudspeaker channels per department, and therefore electronic signal mixing will occur frequently inside the organ when playing any digital instrument.  The sounds emanating from the organ would suffer badly, indeed they always do suffer badly, from the mixing phenomenon just demonstrated.


Thus even the array of six loudspeaker channels per department which we have proposed already to reduce intermodulation distortion would not even begin to resolve the mixing problem.  And because the mixing problem gets progressively worse as more notes are demanded, i.e. as the number of stops drawn increases, the distortion due to mixing gets subjectively worse as full organ approaches.  This is the same as for the case of harmonic and intermodulation distortion, and it is a further reason why digital organs are less effective with full combinations.


Nevertheless, a considerable reduction in the required number of loudspeaker channels can be effected by noting that it is stops of the same pitch which suffer most from undesirable mixing phenomena.  An 8 foot diapason mixed electronically with a 4 foot one would still be undesirable, though the effects would be less noticeable than in the case of the example heard earlier.  There are several reasons for this, including the fact that phase interference only occurs for the even-numbered harmonics of the 8 foot stop in this case rather than for both the even and odd harmonics.  Therefore the software of a digital organ can be designed so that it routes notes to different audio channels only if their pitches are the same.  As an example it might be decided that more than four stops of the same pitch would seldom be drawn simultaneously on each department.  In this case a set of six loudspeakers would be required for each of those four situations, implying the need for 24 loudspeakers.  This number would be required for each department, otherwise an unacceptable degree of electronic mixing would still arise when departments were coupled.


Therefore, to simultaneously reduce both intermodulation distortion and phase interference due to mixing, around 48 loudspeaker channels would be appropriate for a small two manual digital organ, and for a large one many more would be necessary. Using the previous cost figure of £500 per channel, this means the loudspeakers could cost around £24,000 just for a small instrument.  Such figures do not necessarily put the digital organ beyond consideration, but they are obviously substantial and therefore it remains a fact that few either now or in the future would enjoy the benefits that such a system would confer.  It is true that a small number of instruments have used between 100 to 300 loudspeakers, but in view of the cost and size of such installations it is remarkable that the money was not better spent on a pipe organ.  The only example known to me of a commercial instrument fully utilising the principles outlined here was the Shaw Concept Organ of the 1970's made by the Canadian firm founded by Andrew Neil Shaw.  This typically employed 175 independent loudspeaker channels just for a small instrument.  Its cost was said by the makers to be about two thirds that of a comparable pipe organ and it occupied about one eighth of the space [24].


Remember that such a large number of loudspeakers is not a complete solution to the problem, because situations will still arise when insufficient are available to prevent intermodulation and signal mixing distortions under all circumstances.  Also it is impossible to do anything at all about harmonic distortion.  Therefore, even when spending this sort of money on loudspeakers the sound of digital organs will remain significantly inferior to the real thing for the foreseeable future.  At best they are likely to remain a just-acceptable imitation of the pipe organ.




This article has shown that the two most objectionable forms of distortion in digital organs, intermodulation and signal mixing distortion, occur mainly because of insufficient loudspeakers of indifferent quality.  Neither form of distortion can be overcome completely, and because the quality of loudspeakers today is probably at a thirty-year low, there is no prospect that the problems will be solved in the foreseeable future.  Although significant improvements could be made, in practice they would require so many loudspeakers and at so great a cost that it is unlikely organ manufacturers as a whole will venture routinely in that direction.  Moreover, even using these methods, no improvement at all could be made in the related area of harmonic distortion.  These conclusions have resulted from the most detailed technical analysis of the problems ever published in the public domain for the electronic organ application.  Therefore it is safe to say that digital organs will never be able to match the sound of the pipe organ in the foreseeable future for those with ears to hear, particularly regarding its major choruses and tonal build-ups.


However this does not mean that the future of the pipe organ is secure.  Many potential customers will continue to be seduced by the relative price differential of digital organs, which currently lies between one tenth and one fiftieth of the cost of a comparable pipe organ.  Moreover, many either will not be able to perceive the tonal defects highlighted in this article or they will decide they are not sufficiently important.  Therefore decisions will continue to be taken along the lines of "they are jolly good for the money, so let's buy an electronic".  Yet another factor working against the survival of pipe organs is their highly variable quality, together with some appalling examples of complacency and disregard for the customer on the part of organ builders. These conclusions arose from the survey in this article of the strengths and weaknesses of both the pipe and electronic organ businesses.  Quoting the British Institute of Organ Studies (BIOS), it is therefore easily possible to "postulate a scenario in which pipe organs are exceedingly rare ... along with the role of the organ in a long-defunct parish system" [17].


So will the pipe organ vanish within our lifetimes?  I suppose I ought to venture an opinion given the provocative title of this article.  Yes, like BIOS, I think there is considerable doubt that it can survive for much longer whether we like it or not.  We have seen that although it will retain the edge in terms of sound quality, the British pipe organ business today is to a large extent reaping the harvest of its shortcomings in other areas.  Therefore it is superficial and disingenuous for its protagonists to continue to project their indignation solely in the direction of the electronic organ.  Moreover, some if not many of those protagonists actually seem to like digital organs more than they care to admit.  A significant number of cathedrals now rely on them for many of their musical activities, perhaps partly because of the long-accepted fact that a single immoveable pipe organ simply cannot do the job in most cathedrals.  This was one reason why Robert Hope-Jones was called upon in the 1890's to enable the separate quire and nave organs at Worcester to be controlled from a single console (even though that was not quite how his endeavours turned out).  It is not without significance that this same cathedral installed an early Bradford digital organ (now gone) in the nave about a century later, and that little time was lost in issuing recordings made upon it.  One CD only mentioned that a digital organ had been used in the small print on the back sleeve [19], although only those with several layers of cloth over their ears would have had any doubt about the matter.  (Any electronic organ heard on a CD suffers from a double dose of distortion - that from the organ itself which is then distorted again by the speakers connected to the CD player).


An increasing number of other cathedrals and their organists are also well disposed towards electronic organs, as witness the enthusiastic reception of a CD of an Allen instrument by one of them [20].  As at Worcester, electronic organs are now found widely elsewhere, and even some cathedral pipe organs now include electronic stops (e.g. Southwell Minster).  These remarks do not imply disapproval, they merely acknowledge that the movers and shakers at the pinnacle of church music - the cathedrals - have by and large obviously accepted the electronic organ.  The same applies to the secular world, with many concert organists since the time of Virgil Fox identifying themselves with electronic organs.  Others of fabulous technique who have embraced the instrument, warts and all, include George Thalben-Ball and Carlo Curley.  The service such people have rendered over the last thirty years or so in maintaining the public profile of the organ and its music would have been far less effective had they confined their efforts solely to the pipe organ in cold and otherwise incommodious churches.  Despite its shortcomings, electronics has enabled them literally to take the organ to the people, which surely is what music is all about.


In view of all this it is singular that next to no mention of electronic organs occurred in The IAO Millennium Book compiled largely by people drawn from the church music establishment, particularly as both theatre organs and recorded music were accorded their proper place [21].  (The IAO is the UK-based Incorporated Association of Organists).  The rise of the electronic organ in the closing century of that millennium was the most significant event in the history of the organ, even if we adopt the IAO's presumed narrow definition of an organ only as an instrument with pipes.  The significance is, of course, because of the threat posed to its very survival by digital organs.  Therefore this milestone book made small attempt to look to the future and in that respect it mirrored the IAO's house journal, Organists' Review - when this article was first posted in 2005 this magazine was still apparently rejecting advertisements for electronic organs, although the situation now seems to have changed following a subsequent editorial and policy shake-up [23].  The situation was all the more extraordinary given the private acceptance of and involvement with electronic organs on the part of much of the IAO's governance and membership, an unseemly reflection of corporate double standards that did little to further the cause of the pipe organ nor of the IAO itself.  It is more likely to have done harm because the situation had persisted for many years, and it is probably inevitable that the pipe organ will eventually attract little more than antiquarian interest well within the lifetime of many who read this article.  Those of us who love the instrument can draw little comfort from the scenario.


Can anything be done to ensure the survival of the pipe organ?  In one sense the answer has to be affirmative, because most problems have solutions of one sort or another.  However whether it is already too late is for consideration in this case.  Assuming it is not too late, an obvious step is to bring the matter more assertively to the notice of the public, and I mean the public at large which likes music of all kinds, not just that cosy coterie which already belongs to sundry organ-related societies.  Preaching to the converted seldom achieves very much.  There is nothing intrinsically sinful about liking organ music one minute but then putting on a rap CD the next (personally I prefer Abba or the Beach Boys but that merely betrays my vintage).  There is still widespread affection for the Church and anything to do with it in Britain, judging by the outcome of some opinion polls in recent years.  That only a minority of those polled were actually churchgoers is perhaps of lesser importance here.  One of the most popular forms of organ concert today is of the "battle of the organs" type in which players perform on both electronic and pipe organs in a cathedral or concert hall, and there is no reason why this model should not percolate down more widely to local level.  Instead of giving a recital just on the pipe organ in his/her church, an organist might consider importing an electronic as well.  If necessary, some private owners of electronic organs might be willing to loan their instrument for the occasion, and indeed play it.  The opportunity could be taken to point out the strengths and weaknesses of both types of instrument, and in doing so it could be brought to the notice of the audience that the survival of the pipe organ is at risk and whether this matters to them.  It is so easy for us organ nuts to forget that this simple fact is probably almost unknown to most members of the public who in principle are well-disposed to the organ.


But, and it is a big but, it will first be necessary for the pipes-versus-electronics brigade to bury the hatchet.  Now, not later!  Although the recent anti-electronics stance of the IAO itself now seems to be changing to reflect the real interests of its membership, that of organisations such as BIOS has remained fixed.  While one would not expect an overtly pipes-only body to embrace digital organs, the shocking degree of venom directed towards the latter by some of its members has long been conspicuously damaging, and completely irrelevant, to its cause.  History shows that nations only prosper once they have overcome their revolutions and civil wars, and I cannot see why that example should not be followed here.




Appendix 1 - Illustrating the generation of harmonic distortion and intermodulation distortion


The formation of both harmonic and intermodulation distortion can be demonstrated by considering a non-linear processor such as a square law circuit.  Let two pure sine wave signals having frequencies  f 1 and  f 2 be denoted by sin A and sin B, where


A = 2π f 1 t and B = 2π f 2 t   (t is time)


This composite signal having passed through a square law circuit is


(sin A + sin B)2 = sin 2 A + sin 2 B + 2 sin A sin B


Using standard trigonometrical identity formulas, this can be written as


½ (1 – cos 2A) + ½ (1 – cos 2B) + cos (A – B) – cos (A + B)


The first and second terms show the presence of frequency components (2A and 2B) at twice the original frequencies, i.e. at the second harmonics of the input frequencies.  This constitutes harmonic distortion.  The third and fourth terms show the presence of the difference and sum frequencies respectively, which constitute intermodulation distortion.


This equation also shows that harmonic distortion and intermodulation distortion are actually the same thing in terms of physics, the only difference being the frequencies at which the distortion products lie.  If the products lie at harmonics of the input signals they are termed harmonic distortion products, whereas if they lie elsewhere they are termed intermodulation products.  This can be seen if we let the two input frequencies  f 1 and  f 2 be the same.  Then the difference term A – B vanishes and the sum term becomes 2A (or 2B), the same as the harmonic distortion terms.  The intermodulation distortion has become identical to harmonic distortion in this case.


Note that the original signal frequencies are no longer present at the output, a feature of a perfect square law circuit.  In practice the non-linearity is not (fortunately!) of this form, being instead a relatively small perturbation of a linear transfer characteristic.  In this case the original signals would still be present and they would contribute most of the power to the output.  A square law was used merely to demonstrate the formation of these modulation products by a non-linear processor using only simple mathematics.


Appendix 2 - Estimating the power of intermodulation distortion products


A full mathematical treatment of intermodulation distortion is intractable and approximations have to be used.  The following is probably the simplest form of analysis possible but nevertheless it demonstrates the seriousness of the problem.


Let there be two input signals having different fundamental frequencies each with N harmonics (counting the fundamental as the first harmonic).  Every harmonic of one signal will generate a difference frequency with every harmonic of the other, therefore there will be N2 difference frequencies.  There will also be the same number of sum frequencies, therefore the total number of intermodulation products will be 2N2.


Let each frequency component (harmonic) in the input signal have equal power P.  Because power at different frequencies simply adds, the undistorted power of the two signals which create each product is 2P.  Therefore the distortion power for each intermodulation product will be 2Pk2, where k is the distortion amplitude ratio (k < 1).  (As k is conventionally expressed as a ratio of amplitudes, it has to be squared to get the corresponding power ratio).  Thus the total distortion power in the  2N2 distortion products will be D, where


D = 4N 2Pk2  


Let P = 1 watt and N = 30 (corresponding to 2 signal sources each with 30 harmonics with a power of 1 watt).  Also let k = 1%, a reasonable figure for a good quality loudspeaker.  Poor ones would be much worse.  Then D = 0.36 watts.  Since the total input power is 60 watts, this is 0.006 of the input power.  Therefore, expressed in decibels, the intermodulation distortion power is only about 22 dB down on the input signal power.


The large number of intermodulation products (1800 in this case) which are liberally sprinkled across the entire audio frequency spectrum can be legitimately regarded as a form of noise.  A signal to noise ratio of 22 dB is easily detectable by the ear, and in fact it is appallingly bad.  It is 26 dB worse than the quantisation noise of a telephone-quality 8 bit digital system, and 74 dB worse than that of the16 bit system as used in CD's and Minidiscs.  What this means is that the 96 dB SNR of a CD player can be transiently degraded to values of the order of 22 dB with certain types of programme material, purely because of the loudspeakers.  It results in effects such as that excruciating rough, tearing type of sound when massed violins are playing, or when listening to a chorus of women’s or boys’ voices.  Subjectively, the worst distortion products of these types of programme occur at frequencies of a few kHz and above, which is where the ear is most sensitive.  These frequencies are also handled by tweeters, which generally have a distortion performance far worse than that of lower frequency loudspeakers.  Often it is so bad that it will not be mentioned and definitely not quoted.


The assumption that all harmonics of the input signals have comparable power is not unreasonable for some reed stops and strings, and this explains why chords played using combinations of these stops constitute some of the least satisfactory effects with electronic organs.  The point of this analysis was merely to demonstrate the approximate level of intermodulation distortion to be expected with a loudspeaker of reasonable quality (i.e. with a distortion figure, k, around 1%).


Appendix 3 - A practical demonstration of intermodulation distortion


To verify that the theoretical analysis in Appendix 2 produced results of the correct order, the intermodulation (IMD) performance of an actual loudspeaker was demonstrated experimentally as follows.


The set-up in Figure 3-1 was used.



Figure 3-1. The two experimental measurement configurations. 


As shown in Figure 3-1, two sine wave signals were generated by a digital synthesiser (labelled SYNTH)  and an analogue function generator (labelled VFO – variable frequency oscillator).  They were applied to the left (L) and right (R) channels of a stereo power amplifier and then to loudspeakers.  Sounds were picked up by a Calrec studio quality capacitor microphone feeding a real time digital spectrum analyser with a dynamic range of 100 dB, which was therefore capable of analysing the full dynamic range of a 16 bit digital signal (96 dB).  The analyser was actually an ordinary PC fitted with an Audigy sound card running my own real time spectrum analysis and display program, which just goes to show how cheap and easy it is today to lay one’s hands on test gear of the highest performance.


Two loudspeaker configurations were used.  In (a) separate speakers were connected to the two amplifiers, therefore in this configuration the only place IMD could occur was in the microphone itself and any subsequent processing.  In (b) a single speaker was bridged across the two amplifiers to radiate both signals.  In this configuration IMD could also take place within the loudspeaker itself and possibly, though at a much lower level, in the output stages of the PA’s.  This was because the bridged configuration required the output stages to do the signal mixing.


Each speaker was of reasonable quality, using a KEF B200 bass unit, a Sony tweeter and a 3 kHz two way crossover unit. 


The spectrum of the VFO signal as generated, i.e. with the generator connected directly to the analyser, is shown in Figure 3-2. It was adjusted to have some residual harmonic structure rather than operate on a sine wave of  unrealistic purity, although note that the largest harmonic is about 45 dB down on the fundamental. Therefore the amplitudes of the harmonics were much lower than those which would occur in an organ pipe, and in fact they corresponded to a sine wave with -40 dB harmonic distortion in this frequency range.  The frequency shown is about 2.5 kHz, corresponding to the top D# on a 4 foot stop.    The other (SYNTH) signal was synthesised with a similar amount of intrinsic harmonic content.  (The lines at low frequency were due to a small amount of breakthrough at mains frequency and its harmonics due to hum loops).  Note the use of an audio frequency measurement range of 15 kHz, which most if not all electronic organs will not exceed.  Most people beyond middle age will not be able to hear the highest frequencies in this range anyway.  They will, however, often be able to hear IMD products at the difference frequencies.


Figure 3-2. Spectrum of the VFO signal as generated. 


With the set up of Figure 3-1 (a), i.e. with both signals playing through separate speakers, the spectrum picked up by the microphone is shown in Figure 3-3.


Figure 3-3. Microphone spectrum - signals radiated through separate speakers.


In this case the two signals were from the SYNTH oscillator at 7902 Hz, corresponding to top B on a 2 foot stop, and the VFO at 5588 Hz, corresponding to top F on a 2 foot stop.  These relatively high frequencies were chosen because it is in the higher frequency range where IMD is most objectionable, and where loudspeakers are least satisfactory in their IMD performance.  Most notes lower in the keyboard using reed and string stops will still have high amplitude harmonics in this frequency region (e.g. the 15th harmonic of treble C at 8 foot pitch is at 7849 Hz).  The fundamentals at the chosen oscillator frequencies are clearly visible as the two largest peaks on the display.


The small, highest frequency, peak is the 2nd harmonic of the 5588 Hz signal.  The low frequency “clutter” was due to room noise picked up by the microphone, including the computer fans, plus some low level mains hum and its harmonics.  Standing clear of this (to the right) is the only IMD product visible.  This was the difference frequency of the two fundamental frequencies at 2314 Hz, though it could not be heard in the room even when the VFO frequency was swept manually. This was because the difference signal was generated in the microphone, not the two loudspeakers which were radiating the separate frequencies into the room.  Note, though, that the microphone did not apparently generate a sum signal at 13,490 Hz.


Because the only opportunity for IMD to occur was in the microphone itself or in the subsequent electronics, this illustrated the relatively clean IMD performance of the particular microphone used for the tests.  Although IMD was not (of course!) quoted in the microphone data sheet, as with loudspeakers, a THD (total harmonic distortion) figure of 0.5% was claimed and the IMD performance would not be better than this because both THD and IMD are produced by the same nonlinearities.  0.5% is equivalent to an amplitude ratio of 46 dB, which is broadly compatible with the difference between the levels of the fundamentals and the difference frequency seen in the spectrum.


Keeping everything the same except for the loudspeaker connections, the configuration was then changed to that of Figure 3-1 (b).  Here the two signals were mixed electronically and then radiated from a single speaker instead of from two, and the resulting spectrum as picked up by the microphone is shown in Figure 3-4.


Figure 3-4. Microphone spectrum - signals radiated through the same speaker.


The amplitudes of the two fundamentals have changed somewhat owing to the different sensitivities of the two loudspeakers and the different loudspeaker-room geometry for one of the signals in this case.  The latter always leads to a different acoustic mode configuration in any room.  However the difference signal and the 2nd harmonic of the 5588 Hz signal are still there at almost identical levels as before.  The main difference between the two plots is the large number of additional spurious peaks, including the sum signal of the two fundamentals at 13,490 Hz.  The sum and difference signals of the two fundamental frequencies have been identified in Figure 3-4 for clarity.


The distortion products could be rendered more noticeable in the room by sweeping the VFO frequency by hand, whereupon multiple tones moving up and down in frequency could be heard clearly.  All of the additional spectrum lines were due to IMD in the loudspeaker itself, because there was no other source whence they could have originated except possibly for a much smaller proportion in the output stages of the PA’s.  Because all of the lines except the difference frequency are above the crossover frequency (3 kHz), it is clear that the tweeter and maybe the crossover network were responsible for generating them (recall that the difference frequency below 3 kHz was generated by the microphone).  Note that the largest IMD product is only about 25 dB below the amplitude of the two fundamentals, thereby confirming that the theoretical estimate of 22 dB derived in Appendix 2 was actually quite realistic.


This awful result was for only two sine waves of relatively high purity using reasonable quality loudspeakers.  Just think what it could look like for a full chord of reed tones having large numbers of high amplitude harmonics and with lower quality speakers!


Notes and References


1. “Review of the Year”, Ian Bell, Organ Building 2005, The Institute of British Organ Building. ISBN 0-9545361-2-6.


2. “Review of the Year”, Ian Bell, Organ Building 2003, The Institute of British Organ Building. ISBN 0-9545361-0-X.


3.  “Emmanuel Church, Wylde Green”, John Norman & David Wyld, Organ Building 2003, The Institute of British Organ Building. ISBN 0-9545361-0-X.


4.  See paragraph 3 at

     (Accessed 20 December 2009)


5.  “Key actions – some thoughts on their restoration and conversion”, Duncan Mathews, Harrison & Harrison Ltd, Organ Building 2005, The Institute of British Organ Building. ISBN 0-9545361-2-6.


6.  Reframing the Questions - A guide to the reordering of existing churches and the building of new”, Derek L.S.Phillips, The Bishop's Council of the Diocese of Rochester, 1991.  The passages relating to organs were available on the Internet on 11 October 2005 at


7.  Editorial, BIOS Reporter, January 1992, Volume XVI, No.1


8.  See:


            (Accessed 15 December 2009)


9.  Letter by John Norman, Organists’ Review, p. 175, May 2003.


10. “New Organs in 2001”, John Norman, Organ Building 2002, The Institute of British Organ Building.

      ISSN 1472-9040.


11.  “The Evolution of Electric Actions”, C E Pykett 2005.  Currently on this website (read).


12.  “Electronic Organs”, C E Pykett 1998.  Currently on this website (read).


13.  Advertisement in Organists' Review, Kenneth Jones, December 1992, p. 286.


14.  "Manual coupling in larger organs", Kenneth Jones, Organists' Review, November 1999, p. 322.


15.  "The Organ", W L Sumner, 3rd edition, Macdonald, London, 1962, p.255.


16. "Baffling the speaker buyer", John Watkinson,  Electronics World, October 2000, p. 753. ISSN 0959-8332.


17.  Editorial, BIOS Reporter, October 2005. (anonymous). ISSN 0309-8052.


18. A few efforts have been made over the last 40 years or so to introduce negative feedback into loudspeakers.  Notably, Philips produced a range of Motional Feedback Loudspeakers in the 1970's and 80's which measured cone excursion directly by means of an accelerometer and derived a feedback signal from it, though Philips themselves seem to have washed their hands of it long ago.  More recently Meyer have tried again with a unit in which the feedback signal is derived acoustically from a microphone.  Negative feedback enables differences between the drive and feedback signals to be reduced, thereby considerably reducing distortion.  Probably the main reason why these systems have not become widely used is because the market comprising those prepared to pay the price was, and remains, too small.  Moreover, no attempt has been made to apply the principle to other than the bass drivers, therefore distortion at high frequencies still depends critically on the degree of mechanical excellence of the tweeters.  Given that today's ordinary loudspeakers have in fact regressed in quality, this demonstrates the lack of sophistication of the mass market and its low expectations.  Sumner's "blunted ear" is still alive and well.


19. "English Organ Music 2" played on the Bradford Computing Organ in Worcester Cathedral by Donald Hunt.  NAXOS 8.550773, 1993.  The mediocrity of the instrument was well matched to the choice of music, which among other things explains why arguments still continue as to whether Elgar was "great" or not, and why many mainstream musicians find the organ laughable.  How our finest executants can immerse themselves in this sort of thing saddens me.  A completely awful CD.  Still, it might help to ensure the survival of the pipe organ!  (And, yes, I did hear this instrument in the flesh as well).


20. Review of D'Arcy Trinkwon's CD PD 0001 by Paul Hale, Organists' Review, May 1996 p. 130.


21. The IAO Millennium Book, ed. Paul Hale, Incorporated Association of Organists 2000.  ISBN 0 9538711 0 X.


22.  About the only way today to get significantly improved distortion performance is to use headphones of the highest quality.  For example, Sennheiser HD650 phones have a quoted distortion figure around 0.05%, 20 times better than my KEF Reference 104 loudspeakers, which themselves are seldom beaten.  Listening to music at realistic listening levels through these phones exposes the difference, and simultaneously educates one's ear as to what distortion (particularly intermodulation distortion) actually sounds like.  However headphones are scarcely a practical option for electronic organs when more than one listener is involved.


23.  The statement that Organists' Review refused advertisements for electronic organs was correct at the time this article was first posted (2005), at least on the basis of the simple fact that none had so far appeared in that journal.  However it seems that this policy has changed subsequently.


24.  The Shaw Concept Organ is widely described on the Internet.  For example, see (available on 16 March 2011).