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Undulating stops in the pipe organ
Colin Pykett
Posted:
14 March 2024
Abstract. Undulating stops are often found, even in the smallest organs where it might be thought that an ordinary rank would have provided better value for money. To add insult to injury, they are then frequently neglected so that they receive scant attention when it comes to routine maintenance, tuning and correcting deficiencies of pipe speech. Consequently the perspective of this article is that they deserve as much thought and attention as all the other stops in an organ, if only to defend their initial cost.
Several matters are discussed concerning the detuned ranks used in undulating stops, in particular those relating to how they are tuned. A topic which is frequently aired concerns whether they should be tuned sharp or flat to the unison stops, and an objective basis to support the apparently widespread preference for sharp tuning is presented. Another tuning issue relates to whether the beat frequency should be constant over the key compass or whether it should be varied, and if so, how. This is illustrated by explaining the Terzschwebung (third-beating) tuning method, frequently mentioned but not always understood, and its pros and cons are considered.
The material draws on the physics of music, but only a few necessary results rather than the details are presented. Mathematics is avoided entirely.
Contents (click on the headings below to access the desired section)
Undulating stops are those in which ranks of pipes of nominally the same pitch are slightly mutually detuned so that they produce a slow beating effect when sounded together. The beat frequency typically will lie in the approximate range from 0.5 to 5 Hz. The subject is surprisingly many-facetted considering the simplicity of the idea, and this article explores some of the main aspects.
In organs with otherwise English stop names, beating registers are often referred to generically as 'celestes', anglicised from the French adjective meaning 'heavenly' or 'celestial'. Although countless stop names have been used, 'celeste' seems to occur in many if not most of them. Exceptions include the Unda Maris (literally 'wave of the sea' or 'ocean wave') and Vox Angelica. An example of how a celeste sounds is in the mp3 clip below, which consists of a hymn tune played firstly on a Viol d'Orchestre string-toned stop alone and then repeated with a celeste added:
Hymn tune 'Richmond' played on a Viol d'Orchestre alone then with a Celeste
Undulating stops are often found even in small and modest organs, where it might be thought that the money could have been better spent on a normally-tuned conventional rank rather than sinking it into something of a luxury. In these and many other cases the stop knob or stop key usually controls a single rank of detuned pipes which must be combined with others of the same nominal pitch to get the undulant effect. This arrangement enables a range of slightly different effects to be generated depending on the combination selected, and it gives some flexibility to accommodate the requests of some composers who call for specific stops. Percy Whitlock, for example, asked explicitly for the 'Open Diapason and Celeste' on the swell organ in the Andante Tranquillo movement from his collection of Five Short Pieces. However, in other organs the stop is a compound one which controls two ranks simultaneously, thereby resulting in undulation directly without needing to add another. Using his then-novel electric action, Robert Hope-Jones went one step further by providing three-rank celestes in some of his larger organs, as at Worcester cathedral in 1896. Here, there was one in-tune rank, one tuned slightly sharp to it and another tuned flat. The first two spoke when the stop tablet was pressed half way, as far as a perceptible mechanical detent, and the flat rank was added when the tablet was pushed fully home [1]. Hope-Jones also used a different double-touch method of control elsewhere, including in some small organs such as that at Pilton in Devon (1898), where a single detuned rank was added to the Phoneuma stop on the swell organ if the corresponding tablet was pressed twice in succession.
The detuned rank usually comprises pipes with a mild string or narrow-scaled open flute tone quality, often voiced deliberately to form effective undulating hybrids with other diapason, flute or string stops of the same notional pitch in the same division. Apart from those in large organs most celestes are of 8 foot pitch, though they are often used with octave and suboctave couplers. In ordinary organs an 8 foot celeste rank frequently terminates at tenor C to avoid the expense of the longest pipes, so the use of both couplers reduces the effective playing range to only two octaves in this case. In a few of the largest instruments separate 'string' divisions are found which comprise nothing but huge celeste choruses at a wide range of pitches, including mutation ranks.
Celestes using reed pipes in pipe organs are hardly ever encountered, though on reed organs their presence is more the rule than the exception.
The subject of how the detuned rank should be tuned can get rather complicated, perhaps surprisingly so, and several issues are examined here. It scarcely needs to be said that the discussion embraces only those celeste stops where due thought and care has been given to the matter, rather than the regrettably large number whose voicing and tuning was obviously haphazard from the outset using only the criterion of 'it sounds about right'. Yet even when initially tuned properly, many celeste ranks are virtually ignored subsequently by busy tuners who do not have the time or inclination to care for them thereafter. That might be understandable for a tiny church organ out in the boonies with half a dozen congregants on a good day, but certainly not for a large and monstrously expensive instrument having several undulating stops which were designed as integral parts of the sound canvas. Why should one not devote as much thought and attention to the detuned ranks as to all the others in any organ?
So, against this background, the first question to be explored concerns whether the celeste rank should be tuned sharp or flat to the in-tune ones. Opinion seems divided on the matter, though on the basis of anecdotal evidence it is perhaps true to say that most organists and tuners prefer it to be tuned sharp. More often than not, however, they can seldom articulate convincing reasons for their choice. This is not a criticism, since in music Art must transcend logic. On the other hand some express no preference, arguing that if the two ranks are so nearly in tune, as they are, then there cannot be any meaningful subjective difference. They argue that a beat is merely a beat, and it matters not which rank is sharp or flat relative to the other. On the face of it this argument might appear cogent.
However I must admit to some surprise on finding that after a little arithmetic (not included here), one can discover a possible objective basis to support a preference of sharp over flat tuning. The reasoning is as follows. Let the beat frequency across the compass of the stop (i.e. the combination of the in-tune and detuned ranks) be set to N beats per second (Hz). Thus N is the beat frequency between any pair of in-tune and out-of-tune pipes across the keyboard. It is assumed that N is made constant across the whole double rank by careful tuning of the detuned pipes. (But note that this matter, a uniform rather than a varying beat frequency across the compass, is also widely debated and it will be discussed later).
For both sharp and flat detuned ranks, it can then be shown that there will be a beat between adjacent octaves on the detuned rank of N Hz. Thus in plain parlance the rank will not be in tune with itself. It means that, if you play (say) middle C and treble C on the detuned rank alone, the two notes will beat at N Hz. This will occur for any octave across the whole detuned rank. Thus the octaves of the detuned rank are not pure (not in exact tune), which differs from normal ranks which are always tuned with pure octaves. However, here's the rub: the octaves are sharp (widened) by N Hz if the celeste is tuned flat to the in-tune rank, and they are flat (narrowed) by the same amount if the celeste is tuned sharp. This shows that there is a small difference between the two cases of a sharp and a flat celeste rank. The difference is calculable, measurable and therefore objective rather than being purely subjective. Therefore it is possible that some people might be perceiving these differences, perhaps unconsciously, when expressing a preference for one type of tuning over the other.
This is not at all extraordinary if one looks at the situation another way: the detuned rank has had an unusual 'temperament' imposed on it where the octaves are impure, and in all temperaments the small yet deliberate tuning differences between intervals give rise to the perceived flavour of the temperament. Here we are dealing with two different 'temperaments' where in one case the impure octaves are flattened away from pure and in the other they are sharpened. Many people are fastidious about which temperaments they prefer, on the basis of their flattened and sharpened intervals and the way they beat, and this case is not really any different when one looks at it this way.
From here one can now go further. The apparent preference for a sharp celeste might be related to the particular type of impure-octave 'temperament' imposed on the detuned rank as explained above. As mentioned, a sharp celeste rank has slightly narrower octaves than the exactly-tuned octaves of the in-tune rank. This also means that its major thirds will be slightly purer (narrower) than they would otherwise be, and it is the rapidly-beating thirds in many temperaments (and certainly in equal temperament) which are among the most objectionable intervals. On the other hand, a flat celeste rank has slightly wider octaves and therefore wider thirds also. These will beat even faster than they do in equal temperament and consequently they might be marginally more objectionable to someone whose ears can detect the difference. It is therefore possible that those who express a preference for a sharp celeste are indeed picking up on this disparity, suggesting that there could be an objective basis for their opinion.
However, the arguments above have assumed that beating thirds between two pipes can actually be heard, whereas in practice this is not always possible. A beat between two pipes speaking a major third will only appear if the fourth and fifth harmonics in their sounds are audible. This will be the case for string-toned pipes where these harmonics are strong, but for flute pipes they will be weak or absent. In these cases the beat will be weak or absent also. Flute pipes are used in some undulating stops, and it is interesting that in such cases the preference for a sharp detuned rank is sometimes replaced by one for flat tuning instead, or by no preference at all. This opinion is sometimes encountered in connection with the Unda Maris stop for example, which often uses flute rather than string pipes. It provides anecdotal support for the reasoning above which sought to explain the apparent preference for sharp tuning in string-toned celestes.
Uniform or variable beat frequency? A second major tuning issue to be discussed concerns whether the beat frequency should be held constant over the key compass or whether it should be varied, and if so, how?
A common practice is to first tune the detuned rank sharp or flat (as desired) against an in-tune rank across the middle octave so that the result is subjectively acceptable. Then the remainder of the detuned rank is set simply by tuning it pure against itself by octaves. A practical advantage of this approach is that it is quick and easy to do, but it can result in the beat rate increasing towards the treble to an extent which can sound unpleasant. Conversely, the beats towards the bass can become too slow. These shortcomings can be avoided by maintaining a uniform beat rate across the keyboard, but this requires more careful tuning of the detuned rank on a note-by-note basis. To achieve a uniform beat rate, the degree of detuning in terms of cents (fractions of a semitone) must increase towards the bass and decrease towards the treble, but here again there can be disadvantages. If the rule is applied too slavishly, the effect can become just too out of tune in the bass this time rather than in the treble. For instance, if a uniform 2 Hz beat rate is desired the detuning required at tenor C on an 8 foot rank is 26 cents, just over a quarter of a semitone. Should the detuned rank be carried right down to bottom C, it has to be detuned by over half a semitone, making it grossly out of tune with the corresponding in-tune rank. Faster beats necessarily call for even greater amounts of detuning. To avoid this problem of two obviously out-of-tune pipes sounding simultaneously, the amount of detuning towards the bass can be shaded (reduced gradually) across the rank so that the beat rates between the two fundamental frequencies converge at the lowest note to about half of what they should be in theory (i.e. to about 1 Hz instead of 2 Hz in this example). Curiously, it is strange but fortuitous that this might not be readily apparent to the player or listener however. This arises because strong beats at the 'correct' frequencies still arise between the second harmonics of the pipe sounds, which generally become progressively stronger than the fundamentals towards the bass, at least in string-toned pipes.
The Terzschwebung (literally 'third-beating') method of tuning the detuned rank of a celeste is applied more frequently in continental Europe, particularly Germany, than in Britain. It exploits the frequency differences between tempered and pure major thirds to create a celeste rank which will always be repeatably tuned in exactly the same way each time, though some might regard it as awkward and tedious to achieve. The inescapable repeatability of beat rate, which cannot be varied to taste, might also be deemed too inflexible.
In this technique both the detuned and in-tune ranks are sounded together while a major third is played. If a 'sharp' celeste is desired, the upper pipe of the detuned rank and the lower of the in-tune one are first prevented from speaking using mops or other muting methods, as when mixture pipes are tuned. The two remaining pipes (the upper pipe of the in-tune rank and the lower of the detuned one) are then tuned to a pure (non-beating) major third by adjusting the detuned pipe. If a 'flat' celeste is sought then the alternate pair of pipes is silenced instead, and the upper pipe of the detuned rank is adjusted for zero beat against the lower of the in-tune one. In either case the procedure has to be repeated painstakingly, note by note, across the compass.
The method uses the significant frequency difference between tempered and pure thirds in equal temperament and some others, and it results in beat rates which increase towards the treble and decrease towards the bass. The beating frequencies which are obtained are always the same, thus there is no opportunity to adjust them to suit the preferences of particular organists or organ builders. For example, the beat frequency at F above middle C will always be 2.8 Hz (for a celeste at 8 foot pitch when the in-tune rank is tuned to equal temperament with middle A set to 440 Hz). But even if this constraint is deemed acceptable, the beat frequency doubles for each octave towards the treble and halves towards the bass, so it becomes very fast at the top of the keyboard and very slow at the bottom. For this reason the technique is sometimes applied only to a restricted region of the keyboard, beats outside this range then being set using other, possibly ad hoc, methods.
As mentioned above in connection with sharp versus flat tuning, the Terzschwebung method relies on being able to tune a pure major third, which in turn relies on there being an audible beat between the fourth and fifth harmonics of the pipes. These harmonics are strong in string-toned pipes but they are weak or absent in flutes, meaning that the beat will be weak or absent also. Therefore it is more difficult to tune a third pure, at least by ear, between a pair of flute pipes rather than strings. Consequently the method seems less applicable, in practice, to undulating stops using flute pipes rather than strings.
Undulating stops are often found, even in the smallest organs where it might be thought that an ordinary rank would have provided better value for money. To add insult to injury, they are then frequently neglected so that they receive scant attention when it comes to tuning and correcting deficiencies of pipe speech. Consequently the perspective of this article is that they deserve as much thought and attention as all other stops in an organ, if only to defend their initial cost.
Several matters concerning the detuned ranks used in undulating stops were discussed, in particular those relating to how they are tuned. One which is frequently aired concerns whether they should be tuned sharp or flat to the unison stops, and an objective basis to support the apparently widespread preference for sharp tuning was presented. Another tuning issue relates to whether the beat frequency should be constant over the key compass or whether it should be varied, and if so, how. This was illustrated by an explanation of the Terzschwebung tuning method, frequently discussed but not always understood, and its pros and cons were considered.
1. "The Organs of Worcester Cathedral", Colin Beswick, Worcester,
1967
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