Samuel Sebastian Wesley and keyboard temperaments in Victorian Britain
10 April 2022
Abstract. S S Wesley's eccentric views on temperament are nevertheless valuable because they show unequivocally that mean tone tuning was used in Britain before equal temperament became the norm around 1860. This follows from his frequent mention of Wolf intervals, and only the mean tone temperaments have Wolves. However the consequential question as to which of the several mean tone tunings he had in mind is not so easy to answer. Hence this article discusses the quarter, fifth and sixth comma temperaments as candidates without calling on physics or mathematics. It simplifies the situation by removing fifth comma mean tone from consideration since it is indistinguishable in practice from sixth comma tuning, thereby reducing the choice to only the quarter and sixth comma temperaments.
Elsewhere it is claimed that several early English organs were tuned in fifth comma, though since this was based on measurements whose accuracies could not have distinguished reliably between fifth and sixth comma data, we can reasonably say that these instruments could just as easily have been tuned to sixth comma. Practical reasons supporting this view include the fact that sixth comma tuning has the least objectionable Wolf (demonstrated here by audio recordings), and it can also be tuned very easily by one familiar with equal temperament (and vice versa). This is because the beat rates of the two temperaments are related by a factor of exactly two. This would have been important at a time when mean tone tuning was being displaced by equal temperament - tuners could not have been oblivious to the fact that their lives would be simpler if they only had to learn a single tuning method which would suit two very different temperaments in common use.
Finally, since Wesley approved of Gottfried Silbermann's work and mentions his (sixth comma) temperament frequently in his writings, it is concluded that the 'unequal temperament' he referred to was most likely sixth comma rather than fifth or quarter comma mean tone. Thus the balance of probabilities suggests that unequally tempered organs were tuned to this temperament in the first half of the 19th century before equal temperament became near-universal in Britain.
Samuel Sebastian Wesley (1810-1876) is well known for his vigorous opposition to equal temperament, which progressively displaced earlier methods of tuning keyboard instruments in Britain during the nineteenth century. Yet some of his finest compositions called on keys which today would be, and were then, considered intolerable (including by himself!) if performed using the types of unequal temperaments inherited from former times. This unresolved conundrum has posed a challenge ever since, and it is explored in this essay.
Wesley's position on the matter of temperament is unequivocal and well documented. Especially notable is that in 1863 he berated the readership and other correspondents of The Musical Standard in a series of diatribes ( - ) which illustrate his views . At this time he was still at Winchester cathedral though he would soon be moving to Gloucester. From this material we see how he failed to marshal his arguments convincingly, and it also illustrates how conservative and resistant to change he was. A few examples of how he allowed opinion to triumph over fact and even basic common sense in these writings are given below:
Most organists I have found decidedly hostile [to equal temperament]
In the 1860s this would have been unlikely, given the near-universal acceptance of equal temperament by that date ( p. 371 et seq).
the public must incur considerable expense in restoring an organ to its original state wherever the equal temperament has been introduced
With few exceptions, the reverse was the case.
Surprisingly for a musician of his calibre, he also claimed that:
Bach did not favour equal temperament ... his organ music being composed invariably in the good keys [of an unequal temperament]
This statement ignored the obvious reality that, despite key signature, the extensive modulation employed by Bach nevertheless results in the poorer intervals being encountered frequently.
Yet he also acknowledged that the gross shortcomings of the unequal temperaments he championed could not be swept aside lightly:
from the painful inequality termed "the wolf", I consider the liberty [of being able to play in all keys in equal tuning] to be far too dearly purchased at a sacrifice of the good keys
such defects being, as is admitted, painfully discordant to the ear
In cases where an organ was to be used with an orchestra, Wesley continued to insist that it could nevertheless be tuned unequally by making the following preposterous suggestion:
I conceive that the right course is for the Organist to cease playing where the wolves become unbearable
These are just a few extracts from this extensive published correspondence. His letters also demonstrate the combative and contradictory personality which damaged relationships with just about everybody he came across, including the clergy in his several cathedral and church appointments. But perhaps the most poignant aspect is illustrated by the perplexity expressed by some of those who knew and revered him as a musician. Wesley's pupil, Dr Francis Gladstone (1845-1928), wrote in 1900 :
There is one thing which I have never been able to understand, and that is how Wesley could endure the sound of his 'Wilderness', or of the beautiful service in E, when the organ was tuned to unequal temperament.
To my mind this says it all. If gracious and well disposed contemporaries such as Gladstone could not comprehend Wesley's position at the time, what hope is there for us to understand it today? However, writing closer to events (1857) in The Musical Gazette, another critic was less generous (quoted in  p. 372):
I think Dr Wesley's accuracy of ear may not only be doubted but denied, after writing such passages as constantly occur in his service and anthems, knowing and advocating the ordinary mode of tuning organs in England; for the sake of rendering his own compositions endurable, one would have supposed the Doctor would have been the first to advocate the equal temperament
Moving on from Wesley's opinions, the more interesting questions now centre around the unequal temperaments that he favoured and about which we know little. Until equal temperament had more or less become established as the norm in Britain around 1860, it remains uncertain exactly what unequal temperament(s) it replaced. Consequently his eccentric writings are nonetheless helpful when searching for clues as to what these temperaments might have been. However it is clear from what some contemporary authors wrote, including Wesley himself as we have just seen, that these predecessor temperaments were grossly unequal in that they contained a Wolf fifth. In this article 'grossly unequal' simply means that not all keys were usable, therefore they were not so-called 'well' temperaments in which all keys could be used with little or no downside. The unequal temperaments espoused by Wesley were members of the class of mean tone temperaments which are characterised by a Wolf interval - only the mean tone temperaments have a Wolf. They also have nine very 'good' keys. The one follows from the other because the Wolf soaks up the out-of-tuneness which would otherwise corrupt the good keys. The Wolf interval is tuned intolerably sharp from pure, and it is conventionally placed between A flat and E flat. The purity of the good keys arises because many major thirds are tuned much closer to pure than in equal temperament. In the latter all thirds are considerably sharp from pure, resulting in its anodyne coarseness which has always attracted critics, including Wesley and Gottfried Silbermann. The good major keys in the mean tone temperaments are C, D, F, G, A and B flat, and the minors are D minor, G minor and A minor, making nine good keys in all. The remaining fifteen keys are inferior because they cannot avoid calling on notes which are significantly out of tune. The characters of these less attractive keys vary considerably from just about tolerable to virtually unusable, but A flat major is the worst. Another point worth bearing in mind is that there is no variation in key colour or key flavour among the nine good keys in mean tone tuning, a feature similar to equal temperament in which all twenty-four keys have the same flavour. This disadvantage seems not to be well known, and it results in rather jerky changes in key flavour as one crosses the boundaries between the good and not so good keys when modulating in a mean tone temperament. Therefore one pays a heavy price, both in terms of the many unusable keys and the erratic variations in key flavour, for the benefit of having only nine out of twenty-four keys well in tune in the mean tone temperaments. Yet such temperaments are those which Wesley obviously favoured in advocating his apparently minority view. With hindsight it is astonishing that a wide range of 'well' temperaments, such as Werckmeister III (1691), had already been in use across continental Europe for very many years when Wesley was active. It is just one feature of the insularity of the British organ scene which was only finally swept away when the 'German system' of organ building became established by the mid-19th century.
Although a temperament described in the Victorian literature as having a Wolf fifth points directly towards a mean tone temperament, this still begs the question as to what type of mean tone it was - and, of course, there might have been more than one type in use in Wesley's day. While the mathematics allows many theoretical possibilities, we can reasonably reduce them to only three candidates on the basis of historical evidence and aspects such as tuning practices at the time. These are the quarter, fifth and sixth comma mean tone temperaments, which will now be considered in turn.
Quarter comma mean tone temperament arose well over four centuries ago at a time when composers were freeing themselves from the restrictions imposed by the old modes by exploring the possibilities for greater modulation. This required additional usable thirds, together with the extra ('black') notes on the keyboard on which to play them. However it is perplexing that this ancient, medieval, tuning system with its shocking Wolf and so few well tuned keys persisted for so long, though one possible reason is seldom mentioned and this concerns ease of tuning. In today's world with its electronic tuning devices it is easy to forget that setting a temperament by ear was, and remains, a difficult operation requiring much experience. (Try it if you are unconvinced). In earlier times the difficulties were writ large because not only was it tricky to time beats accurately in an organ loft away from a clock when portable timepieces did not exist, but an understanding of the arcane theory behind the process was not widespread either. Indeed, we might ask how many tuners today really understand it? But quarter comma mean tone with its several perfectly tuned thirds allowed tuners to check their progress through the tuning sequence by listening for these pure intervals which exhibit no beats. No clock is needed to decide that a pure interval, with no beats, is exactly in tune. If tuners had mistuned previous intervals these thirds would not turn out pure as required, indicating that they should backtrack to make suitable adjustments. In this important practical respect quarter comma mean tone is unique among the mean tone temperaments discussed in this article - other types of mean tone tuning do not have these convenient pure 'check' or 'proof' intervals.
It can be instructive to listen to an organ tuned in quarter comma since I sometimes wonder how many of those who argue in favour of its virtues, while paying less attention to its limitations, can actually have heard it. Consequently the sound file below is a recording of Stainer's hymn tune 'Charity' played first in equal temperament and then in quarter comma mean tone. The tune is played on a digitally simulated Open Diapason stop in A flat , the worst key, to expose the effects of the Wolf interval which is sharp by more than one third of a semitone.
To be even handed I should also have included examples played in more favourable keys but one has to stop somewhere. So those who wish to explore the matter further can easily do so for themselves on a digital instrument having selectable temperaments.
In fifth comma mean tone the Wolf fifth is brought nearer into tune, though it still remains grossly sharp by nearly a quarter-semitone. Unfortunately there is a consequential downside in that this minor improvement sweeps away all of the pure thirds of quarter comma mean tone, though they still remain much better tuned than in equal temperament. The good and not so good keys are the same as in quarter comma mean tone, though none of the good ones now enjoy the pure thirds of the latter temperament. Fifth comma mean tone is thought to have been used in England in the 17th and 18th centuries ( p. 58), so it is a candidate for the unequal temperaments that Wesley would have known in the 19th. However it is more difficult to tune by ear than quarter comma mean tone because it requires the beat rates of eleven fifths to be set accurately. As noted already, there are no longer any pure 'check' intervals which assist the tuner when setting quarter comma mean tone.
Sixth comma mean tone goes a step further along the same road - the Wolf is brought still closer into tune than in its two cousins examined above. But although it might not howl quite as strongly, it nevertheless remains a Wolf in that it is sharp by nearly one fifth of a semitone. The pure thirds in quarter comma mean tone and the nearly pure ones in fifth comma are unavoidably degraded (sharpened) further in the direction of equal temperament in this attempt to soften the effect of the Wolf. Because Gottfried Silbermann used this temperament, it bears his name today.
The sound file below is again of the tune 'Charity', played first in equal temperament and then in sixth comma mean tone. The Wolf is noticeably less offensive this time than in the case of quarter comma mean tone, though remember that the thirds in the good keys are no longer as pure.
The mathematical differences between the fifth and sixth comma mean tone tunings are so slight that the two are indistinguishable in the real world inhabited by the practical musician . However there is an important distinction between them which concerns ease of tuning. When tuning an organ by ear the tuner first lays the bearings by setting the beat rates of all the fifths and fourths in a chosen octave as closely as possible to the mathematical recipe of the desired temperament. In sixth comma mean tone the beat rates of the fifths (excluding the Wolf) are exactly double those of equal temperament . Therefore a tuner accustomed to tuning in sixth comma could tune just as accurately to equal temperament by setting the bearings in an octave higher than usual. Conversely, one who was familiar with equal temperament could tune in sixth comma by working an octave lower. This convenient happenstance must have been known to Silbermann, who was sometimes prevailed upon to tune in equal temperament (which he called the 'sharp tuning' on account of its rather sharp thirds) even though his preference was for sixth comma mean tone. It is inconceivable that this trick was not known and used widely over the period we are discussing here (the 18th and 19th centuries) when the only way to tune was by ear. Thus both quarter and sixth comma mean tone temperaments offer practical advantages to the tuner, the former because of its convenient pure 'check' intervals and the latter because of its fortunate beat rate relation to equal temperament.
Which unequal temperaments was Wesley familiar with? Since he mentions Wolf intervals frequently in the published correspondence discussed earlier, they must have been mean tone temperaments since only these have Wolves. We can therefore ask which of the three varieties of mean tone examined above was he speaking of when using the term 'unequal temperament' in his writings.
He mentions Silbermann frequently and clearly approved of his work, and Silbermann preferred to tune in sixth comma mean tone. However it would be stretching a point to assume, solely on this basis, that Wesley's unequally tempered organs were therefore tuned to sixth comma. Nevertheless the discussion above highlighted other advantages of this temperament - of the three types of mean tone considered, sixth comma has the least objectionable Wolf, and it can also be tuned very easily by someone familiar with equal temperament (and vice versa). This practical point is potentially important as it might have influenced Victorian tuners at the time when mean tone tunings were being displaced by equal temperament in Britain.
Fifth comma temperament was shown above to be so close to sixth comma that the differences would not have amounted to anything for a practical musician as opposed to an ivory-towered theoretician. Nevertheless one cannot dismiss fifth comma purely on the basis of arithmetic because some early English organs are said to have been tuned to it ( p. 58). But again, given the miniscule theoretical difference between fifth and sixth comma tunings, I am unconvinced that measurements could possibly have been made on the pipes of these ancient instruments to the accuracy necessary to favour one over the other. Nor does ease of tuning favour fifth comma over sixth since both are rather difficult to tune (many fifths need to be tuned accurately), though the convenient relationship to equal temperament (the factor of two in beat rates) enjoyed by sixth comma sways the argument in its favour.
Quarter comma mean tone has the most prominent Wolf but the purest thirds of all the unequal temperaments considered here. Wesley made much of the purity of the good keys, but since all three temperaments are much better in this respect than equal temperament it would be difficult to argue that he was comparing it solely with quarter comma. Ease of tuning was discussed above in terms of the pure 'check' intervals which only occur in quarter comma, and this might have made it popular with tuners when unequal tunings prevailed. But when equal temperament became increasingly fashionable in the 19th century, perhaps the ease of tuning sixth comma mean tone for tuners accustomed to equal meant that they shifted their allegiance in that direction and away from quarter comma.
Wesley's writings on temperament, though curious and highly opinionated, are valuable historically in that they show unequivocally that his use of the term 'unequal temperament' implied one of the mean tone tunings. This follows from his frequent discussions of Wolf intervals, and only the mean tone temperaments have Wolves. However the consequential question as to which of the several mean tone tunings were implied is not so easy to answer. In the absence of evidence beyond that discussed already it is not easy to argue unambiguously in favour of one to the exclusion of the others. But the situation can be simplified if we remove fifth comma mean tone from further consideration since the article has shown it to be indistinguishable in practice from sixth comma tuning. So the choice now reduces to that between the quarter and sixth comma temperaments.
We have noted already the claims that several early English organs were tuned in fifth comma, though since this conclusion was based on measurements whose accuracies could not have distinguished reliably between fifth and sixth comma data, we can reasonably conclude that these instruments could just as easily have been tuned to sixth comma. Practical reasons supporting this view include the fact that sixth comma tuning has the least objectionable Wolf (demonstrated here by audio recordings), and it can also be tuned very easily by one familiar with equal temperament (and vice versa). This would have been important at a time when mean tone tuning was being displaced by equal temperament - tuners could not have been oblivious to the fact that their lives would be simpler if they only had to learn a single tuning method which would suit two very different temperaments in common use.
Finally, since Wesley was well disposed towards Gottfried Silbermann and mentioned his (sixth comma) temperament frequently in his writings, it is concluded that the 'unequal temperament' he referred to was most likely sixth comma rather than fifth or quarter comma mean tone. All this implies that unequally tempered organs were probably tuned to this temperament in the first half of the 19th century before equal temperament became near-universal.
With hindsight it is astonishing that a wide range of far more subtle 'well' temperaments, such as Werckmeister III (1691), had been in use across continental Europe for well over 150 years when Wesley was penning his diatribes, yet they had made little or no headway in Britain where the crudeness of medieval mean tone tuning still held the field. It is just one feature of the insularity of the British organ scene which was only swept away when the 'German system' of organ building became established by the mid-19th century.
The Musical Standard, 1 April 1863, p. 242
7. In fifth comma mean tone temperament all fifths except the Wolf are flattened (narrowed) from pure by one fifth of the syntonic comma. This quantity equals 4.30 cents, where 100 cents is the frequency ratio of an equally tempered semitone. In sixth comma mean tone they are flattened by one sixth of the Pythagorean comma, 3.92 cents. The difference between these two quantities would scarcely have been noticeable at a time when wind pressures were ill-controlled owing to the fluctuations caused by manual blowing, together with winding systems which were often badly designed and engineered, and tuning techniques which only delivered approximate results at best. On top of all this would have been uncertainties due to the bewildering variety of pitch standards which affected the beat rates that tuners listened for, plus the usual problem of unpredictable tuning drift over time once an organ had been tuned. Hence the fifth and sixth comma tunings are indistinguishable for practical purposes.