Harmonics and 'cheats'

This essay first appeared on the electronic mailing list Piporg-l

There has been quite a lot of discussion recently about the various dodges sometimes used to make up for missing bass pipes - omitted through general lack of space, or (specifically) lack of height, or even lack of money. I thought that it might be useful to draw the threads together in one posting (even though most of the individual ideas have been explained in separate postings).

An open organ pipe sounds harmonics or overtones in addition to its fundamental. For an 8ft C pipe these are as follows

8' (8/1) 1st partial (funadmental)
4' (8/2) 2nd partial (octave)
2 2/3' (8/3) 3rd partial (quint)
2' (8/4) 4th partial (octave)
1 3/5' (8/5) 5th partial (tierce)
1 1/3' (8/6) 6th partial (quint)
1 1/7' (8/7) 7th partial (septième)
1' (8/8) 8th partial (octave)
8/9' 8/9) 9th partial (none)
4/5' 8/10) 10th partial (tierce)
8/11' (8/11) 11th partial (quart)
2/3' (8/12) 12th partial (quint)
8/13' (8/13)
4/7' (8/14)
8/15' (8/15)
1/2' (8/16)

(Note that the nominal lengths in feet for the 16' and 32' series can be worked out easily like this - the seventh partial of 32'C is 32/7' = 4 4/7')

These facts (as they appear in the observation of a vibrating string) were known in principle to the ancient Greeks (Pythagoras may not have been the only soul to have realised their importance). Note also that the connection between the sound of pipes and the understanding of this mathematical model made many ancient organ builders (and other artists) believe that this was an example of the glory of God's creation - this is why simple mathematics play such a large role in the history of pipe-scaling and case design - the craftsman whished to emulate the mathematical proportion found in nature in order to bring his work closer to God.

The 'difference tones' audible between two notes were first noted by the 18th century violinist Tartini, and by the end of the century the organist and theorist Vögler was suggesting that the organ chorus could be developed with the use of low-pitched mutations and that the old quint-and-unison mixtures were in some way 'unscientific'.

With Helmholz's new understanding of wave form in the nineteenth century came the knowledge that the timbre of a note depends on its harmonic structure - i.e. how much, relatively, of each partial is heard in addition to the fundamental. This is the principle that gives us the drawbar controls in a Hammond.

As has been explained by others, the phenomenon of difference tones can be used to create the illusion, to the listener, that another lower (or higher) note is being played. For example, if we play the notes 4' C (126 cycles per second approx) and 2 2/3' G (190 cycles per second approx) at once then we will get a difference tone between them of 190-126=64 cycles per second - which is 8ft C.

Organ builders discovered long before Tartini that stopped pipes give a less solid bass than open pipes and have always judged the scale of an instrument by noting what is the longest open pipe in the instrument (Ah! - say the French - un grand orgue de 16 pieds en montre, un petit de 4 pieds ....).

The explanation is that stopped pipes only sound the odd-numbered partials - the even-numbered ones are completely absent. Since, in an open pipe, the fundamental is REINFORCED by the difference tones between the partials, in a stopped pipe the fundamental will appear relatively weak.

So, various techniques have been used at different times to simulate missing low pipes.

Note first that a classical organ with a bold chorus of different pitches will do this anyway - there are so many difference tones being produced (not to mention the additional and very complex colour produced by difference tones between the various partials) that many pitches are emphasised for which there are NO pipes in the organ!

By the eighteenth century, at least in England, the use of an octave 'helper' pipe to produce a solid low note was well known. In English chamber organs, where there is no room for an open diapason bass (certainly not running down to the low GG often provided, which would have meant a pipe 10 2/3 foot long) one often finds low notes being simulated by a stopped pipe (usually borrowed from the stopped diapason) with an open 'helper' sounding the note an octave higher. The open octave pipe conviently sounds exactly those harmonics that are missing from the stopped bass...

The best English examples of helper basses are uncanny. Why do they work so well?

I think the reason is this: these low notes approach the bottom end of the range of human hearing. We can perceive the fundamental, but our brain understands it partly in reference to the harmonic structure and thus to the timbre of the note being played. A pipe with little or no hamonic content may sound very pure and subjectively very low, but we may have difficulty identifying the actual pitch. (Hence John Compton, in polyphonic mood, would occaionally provide only one pipe for the lowest 5 notes of a 32' open wood - it would play the same pitch whatever key was pressed but the ear heard a satisfying and convincing rumble). It is much easier to hear what note is being played if the pipes have a high harmonic content - like a Violone or a Bombarde. Eighteenth century English voicing is harmonically rich in the bass - the stopped basses are virtually large-scale wooden quintadenas and the open pipes are cut up low and voiced bright. It is the interaction between all these partials that is really doing the most convincing part of the work - the 'imaginary' bass seems to have real tone to it and the ear is satisfied.

Mander is one of several builders to revive the simple octave helper.

Cavaillé-Coll knew this trick, and used it in a variety of ways. For example, his pedal organs often seem very deficient in 16' flue basses. In the large organ at St. Etienne Caen, for example, there is only a Soubasse 16' and a narrow Contrebasse 16' on the pedal division. However, there are three 8' flues, one of which is a very large scale open wooden flute, rather soft. It is this last stop which provides the weight in the Pedal division, convincingly interacting with the 16s to provide a solid underpinning - and, of course, with admirable clarity. In smaller Cavaillé-Colls the Grand-Orgue Flûte harmonique 8' (usually with an open bass) does much the same work coupled through to the pedals.

Barbara Owen once pointed out to me the same system at work in an American organ of the 1860s (I think it must have been a Hook in or near Newburyport) - the excellent pedal division on a modest two manual consisted of Bourdon 16' and a big open flute 8' labelled (I think) Cello. Together they sounded like an Open Wood 16' to me - and at a fraction of the space and cost.

(Message to builders of really small new organs - don't waste your clients money by providing both 8' principal and 8' flute on the pedal - a single open wood 8', voiced soft but of very big scale, will do the work of both only better. And, while I am on about it, if you must use a fagotty (i.e. bassoon-like) half-length 16' pedal reed then have a Trumpet 8' too when you can - the two together will sound like a Bombarde 16')

Vögler in the eighteenth century realised about the possibility of generating low difference tones; his schemes (somewhat crankier even than Hope-Jones) contain many low-pitched quint ranks - 10 2/3', 5 1/3' etc. The French had a taste for difference tones - even if they didn't know how the effect was obtained - surely this is why the basse de tierce 16', 8', 5 1/3', 4', 3 1/5' (available on a handful of the biggest eighteenth century organs) is an effect of such solemn grandeur.

Moving back to the nineteenth century: thanks partly to the writings of Hemholz it was spotted that a low note could be 'generated' from two pipes a fifth apart, sounding the first and second partials of the note required. Thus a 32' can be simulated by drawing a 16' and a 10 2/3' at once - or providing both on one stop knob: the 'acoustic bass'.

From what has been said already it will be realised that an acoustic bass consisting entirely of stopped pipes will be pretty half-hearted. If, as sometimes happens, the two ranks are not next to each other, then the result will be even less convincing. The best acoustic basses are those with an open octave rank and a very soft (therefore likely to be stopped) quint rank - but such a method will not give a well-disguised break with stopped pipes - the tone is actually too rich. In any case, if the ranks are strong the quint is all too crude and obvious and it offends the ear. Thus quinted basses are always a bit problematic and give an unmistakable impression of cheapness (as do half-length reed tubes - but that's a slightly different story).

William Drake's house organ for John Wellingham has a 16' pedal bass conjured up from a stopped 8' and an independent stoppped 5 1/3'. This works much better than most quinted basses, probably because the 5 1/3' is independent and can thus be tuned pure (a quint stop derived from a unison rank will be out of tune thanks to the vagaries of temperament). Also he uses 'old English' voicing, and the harmonic content is that much richer than in nineteenth and twentieth century acoustic basses.

A potentially excellent alternative is found in the Haskell bass - an open pipe with a stopped tube suspended inside it. Like the stopped pipe, it sounds an octave lower than a simple open pipe of the same length, but with the harmonic structure intact. However, Haskell basses are rather gruff and unfriendly in tone. They are really too coarse to be used in the 8ft octave (where a helper is actually more musical, if weaker). The most effective use of the Haskell technique I know of is in turning an old 16' open wood into a very successful 32' rank (J. W. Walker, 1950s).

Also in the wake of Helmholz came the German development of the Bass Cornet. Low mutations appeared on the pedal divisions of large German organs in the 1820s and 30s (Walcker). The ex-Boston Walcker of 1862 contains such ranks, grouped together on one stop and labelled Grand Bourdon. The famous Pedal mutations provided by Cavaillé-Coll at Notre Dame (and by Mutin at Sacré-Coeur) have a similar intent and effect.

If correctly made then the effect is much like the old basse de tierce. No-one could really say that they can hear the note being simulated by a collection of higher unisons, quints, tierces, septiemes and whatever else; however the 'solemn grandeur' effect is there by the bucketfull, sometimes with a very satisfactory growling noise which gives the illusion of a string stop or even a very soft reed (only quicker in speech than either). They only work in combination - if you push in the rest of the chorus then there are exposed for what they are - discord machines.

Still more recently some organ builders have tried to push the idea even further, providing new and unusual off-unison ranks in order to offer the player new and unusual timbres. As these effects have been explored mostly by builders whose tonal ideal is concentrated at the bat level of the spectrum. The 'new and unusal timbres' turn out mostly to imitate small angry birds and alarm clocks. Germany in the 1960s was awash with Aliquots, Obertons, Nonenkornetts, Schreipfiefen and other insects.

Some of the above may give you the clue to why the Anglo-American tonal style of the period round 1900, with very, very little harmonic development in the chorus can sound so ... well, frankly, dull. Aural interest is not provided by the organ tone itself - which is terribly lacking in content - but in rapid changes of registration (it doesn't matter two hoots whether the other colours are harmonic flutes, violes d'orchestre, french horns or chrysolglots - they just have to be very different from each other). The old masters did not change stops often, not because they were either primitive or stupid, but because their tonal recipe satisfied the ear for long periods at a time.