Tremulants and Room Acoustics
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  The Interaction of Tremulants with Room Acoustics 

 

by Colin Pykett

 

"whether there be knowledge, it shall vanish away"

  (Holy Bible, St Paul's first letter to the Corinthians, xiii. 8)

 

Posted: 18 May 2011

Last revised: 23 December 2011

Copyright © C E Pykett 2011

 

Abstract.  This article shows that the subjective effect of a tremulant can be modified by the ambient acoustic of the room in which the organ resides.  The phenomena are demonstrated by sound clips which show that, at one extreme, the perception of certain types of tremulant can vanish in some circumstances.  It is explained in detail how this effect arises, and it is concluded that in less extreme cases it is nevertheless  likely that the subjective character of a tremulant will vary because of the different reverberation times of different rooms.  These effects seem not to be well known and it is thought to be the first time they have been reported and demonstrated. 

 

Although the effects might be of interest to pipe organ builders, they have particular implications for the digital simulation of pipe organs using tremulated sound samples. This is because, when the simulation is played subsequently in a different room with a different ambience, the subjective effect of the tremulant will likely be different also.  Therefore, unless the characteristics of the tremulant can be adjusted, it may not be possible to re-create its subjective character satisfactorily.  This will assume importance for the digital simulation of theatre organs whose tremulant characteristics are usually regarded as critical.

 

Contents

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

 

Introduction

 

First things first - definitions of ‘wet’ and ‘dry’

 

The mystery of the vanishing tremulant

 

What is this telling us?

 

Some controlled experiments 

Frequency modulation only

Amplitude modulation only

Discussion

How do we detect frequency shifts?

 

Conclusions

 

Notes and References

 

 

Introduction

 

An article elsewhere on this website deals with the simulation of pipe organ tremulants [1].  It reviewed the difficulties of achieving an accurate simulation regardless of the simulation technique used, and it concluded that only an approximation to the effects of real tremulants is achievable in practice using current digital synthesisers of any type.

 

Another article considered the effects of room ambience on the sounds of pipe organs [2], and in particular it reviewed the pros and cons of digitally simulating them ‘wet’ or ‘dry’ (i.e. with or without the inclusion of the ambient acoustic of the room containing the pipe organ).  The discussion referred essentially to the digital simulation of untremulated pipe sounds because tremulants were not considered explicitly.

 

The present article now pulls together these two previous ones by considering the effects of room ambience on tremulants.  It is shown that the subjective effect of a tremulant is strongly influenced by the acoustics of the room in which the organ resides, a conclusion which applies both to pipe and electronic organs.  The effects can be so dramatic that the perception of a tremulant can completely vanish under certain conditions, a fact which does not appear to be generally known and which has not been reported before as far as I am aware.  Therefore, although this article is aimed mainly at the digital organ community, particularly those with theatre organ interests, it contains material which might also be of interest to pipe organ builders in view of the sensitivity of subjective tremulant perception to the acoustic environment of the instrument.

 

 

First things first - definitions of ‘wet’ and ‘dry’

 

We first need to define what is meant by the terms ‘wet’ and ‘dry’ for the purposes of this article.  In common parlance a wet room is generally understood to be one which imposes a significant change on any sound emitted within it, and this usually means a room such as a cathedral which has a reverberation time of several seconds.  This is a rather vague definition, for example it does not emphasise other aspects of room ambience such as colouration, but we can use it here for the time being.  However a difficulty then arises when we speak equally loosely of a dry room, one which has little or no subjective reverberation.  Examples of such rooms would be the small, heavily carpeted ones found in domestic houses.  But such rooms are far from being totally dry because they all reflect sound from their walls and from the objects they contain.  Therefore they impose changes such as acoustic colouration on all emitted sounds even though their reverberation times are small. 

 

The only rooms which can properly be considered totally dry are those which have no acoustic reflections at all from their boundaries and contents, and these are called anechoic.  Only by entering an anechoic chamber of the type used for calibrating high quality loudspeakers and microphones can one appreciate the dramatic difference between an anechoic room and a dry but non-anechoic one, but not many people have had the opportunity to do this [3].  However it is easily possible to hear sounds anechoically in another way, at least those which are generated and reproduced electrically, by feeding the signals directly to headphones.  This is because headphones supply sound to the ears in a manner which is insulated from the acoustic environment of the room one happens to be in.  Nevertheless, in this case it is important that the sounds were not first radiated into any sort of room (other than an anechoic chamber) before being picked up by microphones and then fed to the phones.  If this was done the signals would no longer represent an anechoic environment.  The signals must be electrically generated and then reach the phones directly.  No intermediate acoustic transmission path must exist apart from that between the phones and the ear drums.

 

Therefore we can loosely define three types of acoustic environment for present purposes:

 

Anechoic - the sound is either radiated into and heard within an anechoic chamber, or generated from an electrical source and supplied direct to headphones with no intermediate acoustic transmission path .

 

Dry - an acoustic ambience characteristic of small rooms with short reverberation times.

 

Wet - an acoustic ambience characteristic of large rooms with long reverberation times.

 

 

The mystery of the vanishing tremulant

 

Having defined these terms it is now appropriate to demonstrate how different ambiences can sometimes affect dramatically one’s perception of the same tremulant.  After that I shall attempt to explain the observed phenomena.

 

The following short audio clips are of the same piece of music taken from the second movement (Pastorale) of Guilmant’s first organ sonata.  He called for a vox humana, stopped flute and tremulant on one manual, accompanying a clarinet solo without tremulant on another.  (There is also a quiet 32 foot flue combination on the pedals, and depending on the quality of your audio set-up you might not be able to hear the 32 foot stop, but this is unimportant here).  For the purposes of this demonstration, the piece was played on an electronic organ and recorded electrically direct onto a digital medium.  Thus no microphones were used, and no acoustic transmission path in the room containing the organ was involved.  Nor was any artificial reverberation added to the sound.  Therefore the recording was anechoic in the sense of the definition above in that no room ambience was impressed on the recording.  The setup is illustrated in Figure 1.

 

 

 

Figure 1.  Making an anechoic recording

 

 

Experiment 1 - anechoic recording auditioned through headphones

First of all, listen to the audio clip below through headphones - the use of phones is essential for this experiment.  Do not use 'headphone virtualisation', 'externaliser' or similar effects intended to simulate the effect of loudspeakers in a room.  Simply route each channel to its respective earpiece.

 

  Example of a tremulant recorded anechoically -1 MB/1m 7s

 

You will probably agree that it sounds very lifeless indeed, equivalent to what would be heard if the organ had been played through loudspeakers in an anechoic chamber.  Therefore, as mentioned above, this is an example of an anechoic environment.  The important point here is that I will be interested to know whether you can detect the tremulant, because I cannot.  Therefore, please do email me if you can hear it (see the Contact Me page for my email address), because it is likely that not everyone perceives sound in the same way and I would like to collect as many examples of people’s experiences as possible.

 

Experiment 2 - anechoic recording auditioned through loudspeakers

Now play the same clip again but this time through loudspeakers in any convenient listening room, either wet or dry.  Although it will still sound rather dead unless your room is very large and you are a long way from the speakers, in this case I shall be surprised if you cannot hear the tremulant!  Again, please let me know if you cannot detect it at all though.  You might find the tremulant ‘depth’ varies as you move around the room, or as you approach and move away from the loudspeakers.  Different rooms will probably affect the way you perceive the tremulant also.

 

Experiment 3 - non-anechoic recording auditioned either through headphones or speakers

Now play the second audio clip below using headphones and then loudspeakers.  It was produced using the same anechoic recording as the one above, but with some artificial reverberation added from an effects processor to make it ‘wetter’.  Therefore it now sounds more natural.  This modified setup is illustrated in Figure 2.

 

  Example of a tremulant recorded non-anechoically - 1 MB/1m 7s

 

 

 

Figure 2.  Anechoic recording with added reverberation

 

 

The important point this time is that you should be able to hear the tremulant both through loudspeakers in any room and through headphones in this case - please let me know if this is not so for you.

 

 

What is this telling us?

 

So what is all this telling us?  On the face of it, the way we perceive a tremulant does seem to be strongly affected by room ambience in that the effect seems to vanish altogether in some circumstances, albeit an extreme (anechoic) one in the experiments above.  During my organ research over several decades I have noticed the subjective variability of tremulants from time to time, but have only recently decided to look into it further.  Hence this article.  I hope that, like me, you find it intriguing enough to warrant a little more investigation.  So as a first step let us briefly review what effects a tremulant imposes on the sounds of real organ pipes.

 

I described several types of tremulant and their effects in detail in the earlier article already referred to [1] and will not repeat the material here.  To summarise, and at some risk of oversimplification, we can probably say that all tremulants affect both the frequency and the amplitude of the sound emitted by a pipe.  The variations are periodic (cyclically repeating) and they follow the beat of the tremulant.  Because tremulants affect cyclically the wind pressure applied to a pipe, it goes slightly sharp and gets slightly louder as the pressure increases, and it goes flat and gets quieter as the pressure falls (this is the case for flue pipes - reeds are less predictable).  Therefore we can say that, in general, a tremulant imposes simultaneous frequency and amplitude modulations (FM and AM) on the sound.

 

The amounts of FM and AM vary between one tremulant and another and from one pipe to another, though usually both types of modulation co-exist simultaneously.  Although there are several other factors, it is probably true to say that the degree of subjective satisfaction afforded by a tremulant depends partly on getting the balance right between the frequency modulation and the amplitude modulation.  Either type of modulation alone will produce a tremulant effect of sorts, but most people seem to prefer frequency modulation if given the choice.  This quickly became apparent in the earliest days of electronic organs from about 1930 onwards, because it was easier in those days to engineer amplitude rather than frequency modulation by periodically varying the gain of a variable-mu valve (vacuum tube) in an audio amplifier.  Therefore amplitude modulation was used for tremulants in many early electronic organs at first.  Similar amplitude modulation vibrato was also commonly applied to other electrical musical instruments such as guitars.  However, when used with anything beyond modest modulation depths, a pure AM tremulant can sound uninteresting and unpleasantly synthetic to many ears.

 

For this reason, frequency modulation subsequently became more popular for electronic organs even though it was more difficult and expensive to engineer.  One of the best-known examples of an early and elaborate FM tremulant was the vibrato system developed for the Hammond organ, which employed a precision-made rotary capacitive scanner.  This repetitively tapped off phase shifted signals within a lumped-constant transmission line consisting of a huge number of discrete components, and the whole system acted as a frequency modulator.  This, the defining sound of the Hammond organ, has since become iconic and it has to be carefully modelled if a digital Hammond simulation is to be successful.  In view of its continuing popular appeal this example confirms that, unlike amplitude modulation, a tremulant using pure frequency modulation is more generally acceptable.  It sounds richer and more natural even at high modulation depths.

 

Nevertheless we have yet to explain why the subjective effect of a tremulant, be it AM or FM or both, depends so strongly on the acoustic environment of the organ in question, whether pipe or electronic.  To make progress requires that we now perform experiments with some controllable test signals of a simpler nature than the rather complex music examples considered above.

 

 

Some controlled experiments

 

A number of controlled experiments were carried out, though it is not practical to describe all of them here.  Only two results will be discussed, both obtained using a 440 Hz sine wave signal on which various frequency and amplitude modulations were impressed.  (440 Hz is the normal fundamental frequency of a note at 8 foot pitch sounding the A above middle C).

 

A tremulant frequency of 6 Hz was used for the experiments discussed below (this means the pulsation frequency of the tremulant was 6 times per second).  This lies within the frequency band of most tremulants found on pipe organs and on electronic organs which attempt to simulate them.

 

Frequency modulation only

When frequency modulation with a maximum deviation of ± 15 cents [4] from the untremulated frequency was applied to the sine wave with its amplitude remaining constant, the result was easily perceptible as a strong ‘wobble’ in a small room when the sound was heard through loudspeakers.  However it was not perceptible at all using headphones.  These results were independent of the volume of the sound over a wide range.  Therefore this confirms the previous demonstration using a recording of real organ music, in which the tremulant effect also vanished in anechoic conditions.

 

15 cents corresponds to a frequency deviation of about 0.9% away from the mean frequency of 440 Hz.

 

Amplitude modulation only

When amplitude modulation with a deviation of 1 dB [5] from the untremulated amplitude was applied to the sine wave with its frequency remaining constant, the result was comfortably perceptible as a ‘wobble’ on both loudspeakers and headphones.  This differed from the FM case above, as it showed that an AM tremulant with these particular characteristics can be heard in an anechoic environment whereas an FM one cannot.

 

1 dB corresponds to an amplitude increase of about 12%.

 

Discussion

The FM and AM deviations quoted above illustrate an important feature of our auditory systems.  To illustrate this, note first of all the large difference, in percentage terms, of the two deviations (0.9% for FM and 12% for AM).  These are typical of those in the tremulants applied to both pipe and electronic organs [6].

 

An amplitude change of 1 dB (12%) is about the minimum which can easily be perceived, and it is inconsequentially small for most practical purposes. (This is why a change of ± 3 dB is used universally in audio engineering to define the useful or ‘flat’ frequency bandwidth of an amplifier for example, and it corresponds to a significant gain variation over the band from - 30% to + 40% approximately.  This is actually far from flat of course, and therefore it illustrates how relatively insensitive is the ear to amplitude changes).

 

Yet a frequency deviation of the same amount as the amplitude deviation, 12%, would correspond approximately to a pitch change of a whole tone, which is certainly easily perceptible under any circumstances.  Anyone can detect a whole tone frequency shift, and it would be excessive for use in a realistic tremulant.  In any case, the frequency of a normal flue pipe could not possibly be persuaded to deviate by anything like this amount simply by varying its wind pressure in the way a tremulant does [6].    This is why tremulants are forced to use much smaller (relative) frequency shifts than amplitude shifts, and my experiments outlined above confirmed this.

 

Therefore our auditory systems seem to have evolved to take more notice of frequency changes than changes in amplitude, to put it rather crudely.  They are more sensitive to frequency than to amplitude.  Why this might be so is of little consequence here because we are not about to digress into evolutionary biology, and we just have to accept it as fact.  But we have now reached a critical point in the discussion, because this fact turns out to be the crux of the matter.

 

 

How do we detect frequency shifts?

 

Although we are indeed very sensitive to frequency, we do not have the ability to assign absolute values to it.  If we hear middle C played on the piano, we do not immediately say “aha, that note has a frequency of 261.63 Hz and therefore it is middle C”.  Most of us cannot be sure whether it is middle C at all, although the minority with absolute pitch claim that they can.  When one thinks about it, this is perhaps rather strange - what spectrum analyser worthy of the name (the ear incorporates a spectrum analyser) does not give you frequency values in some manner?  Put another way, why do we all not have absolute pitch?  No matter, it’s unimportant here.

 

What does matter is that all of us have the ability to detect minute frequency differences between two notes provided they sound simultaneously.  This is observable in a celeste stop on the organ, in which two pipes which are not quite in tune beat slowly.  Beats are highly noticeable and important in music and they underlie the whole business of concordant and discordant intervals, and therefore scale, key, temperament and the entire edifice of Western harmony.  This is a wonderful subject in itself, but we must again rein in our digressions.  Yet if one plays the two pipes of a celeste separately rather than together, it is more difficult to detect that they are out of tune because there is no beat.  It is solely the presence of beats in musical instruments which enables the ear to detect small frequency changes and thus to bring two pipes or strings exactly into tune.  A 2 Hz beat at middle C, typical of a celeste stop, means that the two fundamental frequencies differ by about 0.8%.  This tiny amount is almost the same as the figure of 0.9% which arose in my FM tremulant experiments on sine waves outlined above, and this is probably no coincidence.  Therefore, although these minute frequency differences are obviously important in auditory perception if only because they underpin the very basis of music, they can only be detected easily when the two notes in question sound simultaneously.

 

Although it might not yet be obvious, we have now solved the mystery of the vanishing tremulant.  In the Guilmant sound clips above, the tremulant in question was almost entirely an FM one.  The amount of AM was very small, and such tremulants are quite common in both pipe and electronic organs.  In anechoic conditions it is only possible to hear the instantaneous frequency of a tremulated note, thus we cannot detect more than one frequency at a time, and so we could not detect that the frequency was varying with the small deviation of less than 1%.  Therefore we could not detect that an FM tremulant was operating either (at least, I could not).  By contrast, in non-anechoic conditions the room reverberation provides the ‘acoustic memory’ necessary for the ear to hear multiple frequencies simultaneously.  These frequencies are the current instantaneous frequency and those which just preceded it within an interval related to the reverberation time, and they form a band whose width is also related to the reverberation time.  With longer reverberation times, more frequencies will be simultaneously available to the ear in this band as the tremulant operates, whereas with shorter ones the bandwidth will be narrower.  But regardless of reverberation time, it is the simultaneous presence of the different frequencies constituting this band which is the necessary condition enabling the ear to detect that the frequency is changing at all (at least, this is true for the small frequency changes involved in FM tremulants).

 

But because reverberation time influences the width of the decaying frequency band available to the ear at any instant, the same tremulant is likely to sound different in different rooms having different ambiences.  This has implications for the digital simulation of pipe organs using tremulated sound samples recorded in the room in which the organ resides, because when the simulation is played in a different room with a different ambience, the effect of the tremulant will likely be different also.  Therefore, unless the characteristics of the tremulant can be adjusted, it may not be possible to re-create its subjective character satisfactorily.  This is an aspect of the ‘ambience conflict’ which was discussed in an earlier article [2], and it will assume particular importance for the digital simulation of theatre organs whose tremulant characteristics are regarded as so critical.

 

 

Conclusions

 

The subjective effect of a tremulant can be modified by the ambient acoustic of the room in which the organ resides, demonstrated in this article by the extreme case of an anechoic room in which the perception of a tremulant can vanish altogether.  The phenomenon depends to some extent on the relative proportions of amplitude and frequency modulation induced by the tremulant.  When frequency modulation subjectively predominates, as it often does with real tremulants, the finite reverberation time of a real room is necessary for a sound field containing multiple simultaneous frequencies to be set up as the tremulant beats.  These frequencies are the current instantaneous frequency and those which just preceded it within an interval related to the reverberation time.  It is necessary for multiple frequencies to exist if the ear is to detect that the frequency is changing.

 

This is best understood for a tremulated sine wave, which (to a first approximation) consists only of a single instantaneous frequency component in an anechoic room with zero reverberation.  Because of the small frequency deviation of an FM tremulant (typically around 1%), the ear cannot determine that the frequency is changing in this situation.  Such small frequency changes can only be perceived when the ear is able to compare them with other, different, frequencies sounding simultaneously.  However when reverberation is present as it is in all real rooms, even acoustically dry ones, the ear can determine that the frequency is shifting by comparing it with previous frequencies which continue to decay over the reverberation time.  These frequencies form a band whose width is related to the reverberation time of the room.  Therefore, because of the different reverberation times of different rooms, the width of this decaying frequency band will also vary.  Consequently it is to be expected that the subjective effect of the same tremulant might be different in different rooms.

 

This has implications for the digital simulation of pipe organs using tremulated sound samples recorded in the room in which the organ resides, because when the simulation is played in a different room with a different ambience, the effect of the tremulant will likely be different also.  Therefore, unless the characteristics of the tremulant can be adjusted, it may not be possible to re-create its subjective character satisfactorily.  This is an aspect of ‘ambience conflict’ between one room and another, and it will assume particular importance for the digital simulation of theatre organs whose tremulant characteristics are regarded as so critical.

 

 

Notes and References

 

 

1.  “Tremulant Simulation in Digital Organs”, C E Pykett, 2009.

Available on this website (read).

 

2.  “Wet or Dry Sampling for Digital Organs?”, C E Pykett, 2010. 

Available on this website (read).

 

3.  It is a salutary and unforgettable experience to enter an anechoic chamber.  One well known acoustician, the late Arthur Benade, described his experiences thus on entering one such chamber while accompanied by a colleague:

 

“While I followed my friend toward the center of the room, the normal and oppressive feeling one gets in such rooms developed at first, and then something else called itself to the attention of my ears.  On a hunch, I asked my guide to stop and turn around so he faced me.  I then held out my hands about a foot (30 cm) apart and said, “I get the strong impression that there is some object about this big on the wall behind me.”  My friend looked up beyond my shoulders toward the wall in some astonishment.  There was indeed a small loudspeaker box hanging there, out of my sight, but whose size was about as I had indicated.  Nothing else was in the room.  How did this object make its presence and its size known so quickly?”  (Benade then went on to explain how this effect could have arisen in terms of acoustics).

 

(from “Fundamentals of Musical Acoustics”, A H Benade, Dover Publications Inc, New York, 1990)

 

4.  A cent is 100th part of an equally tempered semitone expressed as a frequency ratio.  In equal temperament all semitones have a frequency ratio equal to the twelfth root of 2, which is 2 to the power 1/12.  Therefore one cent is a frequency ratio of 2 to the power 1/1200. 

 

5.  A decibel (dB) is a way of expressing amplitude ratios such as two voltages.  If the two voltages are v1 and v2, then their ratio in decibels is 20log(v1/v2).  One decibel therefore corresponds to a ratio of 10 to the power 1/20 or 1.12, which is an increase of 12%.

 

6.  It would be physically impossible for the frequency of a typical tremulated flue pipe to vary much more than the figure of around ± 1% used in the discussion above.  This is simply because many pipes would then be thrown off speech at the extrema of the tremulant cycle.  To illustrate this, I made measurements of how the fundamental frequency of a flue pipe varied with wind pressure, and found that when it began to overblow (at the high pressure extreme) its frequency was 179 Hz.  When it ceased to speak at the other (low pressure) extreme its frequency was 174 Hz.  This represented a total frequency deviation of only 2.8% about the mean (± 1.4%).

 

More details of this experiment are in an article elsewhere on this website.  See Figure 7 in "How the Flue Pipe Speaks".