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When Laurens Hammond introduced the Hammond electric organ to the world in 1934, he gave us an instrument with more control over the nature of the sound produced than any other before it (and many since). The Hammond organ's drawbars let the player control the nature of the sound at the level of individual harmonics, much like a painter can control the nature of color by mixing a very few primary colors. This article is intended to clarify the function of the drawbars, and addresses such issues as combining drawbar settings (for example, how to combine 8' and 4' flutes with 8' strings), and how to create a drawbar setting that most closely matches a particular instrument sound. A Brief Introduction to the Nature of SoundAny steady tone has three main attributes: volume, pitch, and timbre (pronounced "tamber"). The first two are pretty much self-explanatory, and won't be discussed here. The third refers to the quality or character of the tone. Two tones can be of the same volume and pitch but still sound radically different (imagine the same note played on a trumpet and a xylophone). There are several aspects to timbre, one of which is the distribution of harmonics in a tone. Most tones consist of a fundamental, together with several harmonics present in varying degrees. The frequency of the fundamental is what we usually perceive as the tone's pitch. The purest tone consists of only a fundamental, and looks and sounds like this:
Harmonics are additional pure tones superimposed on the fundamental, each of which has a frequency that is an integer multiple of the fundamental. Instead of hearing the harmonics as distinct tones, our ears and brain hear a tone of the fundamental frequency, but with a different character than the pure tone. For example, here is a tone with the same pitch as the sample above, but consisting of the fundamental with a bit of the third harmonic (3x the fundamental frequency) and a bit less of the fifth harmonic (5x the fundamental frequency) thrown in:
Notice that the tone still has the same pitch, but that the character of the sound is very different. The Hammond drawbars give the player control over the combination of fundamental and harmonic frequencies. There are nine drawbars for setting the levels of the fundamental and various harmonics and sub-harmonics (lower in frequency than the fundamental). Each drawbar has nine positions labelled from 0 to 8. Zero means off; the harmonic controlled by that drawbar will not appear in the generated tones. The remaining positions will cause the specified harmonic to appear in varying amounts, with each increment producing about a 3dB increase. As a convenient shorthand, drawbar settings are usually written as a sequence of nine digits broken into groups of two, four, and three digits respectively. For example, a possible drawbar setting sounding like an 8' Tibia stop is 00 8040 000. Drawbar Settings as (Pipe Organ) StopsThe individual drawbars are believed by some to be the equivalent of stops on a pipe organ, but they should not be seen this way. When an organist selects a single stop on a pipe organ, the resulting tone will be a complex one with many harmonics. The complexity of the tone depends on the type and number of ranks of pipes that the stop controls. A stop controlling a single rank of flute pipe will produce almost pure tones, whereas one controlling two ranks of diapason pipes will produce tones rich in harmonics. Hammond drawbars on the other hand select individual harmonics. Usually several drawbars must be pulled varying amounts to achieve the effect of an individual stop. For any given stop found on a typical church or theatre pipe organ, there will be a drawbar setting that approximates the sound of that stop on a Hammond organ. Sometimes the imitation will be almost perfect (when all the harmonics produced by the pipe stop are also ones available via the drawbars), and sometimes less so (such as a stop that contains a significant amount of 7th harmonic). Here are some typical pipe organ stops, along with possible Hammond drawbar registrations to imitate those stops, and an audio clip of each:
Drawbar Settings as RegistrationsMore often than not when playing a church or theatre pipe organ, several stops will be selected at once, causing pipes from multiple ranks to sound when a key is pressed. Some stops are quite boring when played in isolation, so other stops are added to change the character of the resulting sound. Such a collection of stops to produce a desired sound is called a registration. Registrations can be set up manually by pulling the desired stops, or by means of pre-programmed combination pistons which can activate a handful of stops at once. If a drawbar setting can be considered equivalent to a stop, how does one create an entire registration? The answer lies in combining two or more drawbar settings into a new drawbar setting that combines the characteristics of all the desired stops. So like a simple stop, an entire registration is also a drawbar setting. The best way to combine the settings for multiple stops into a single setting for a registration is the subject of the next section. First, here are some registrations consisting of combinations of some of the stops from the previous section, with drawbar settings and audio clips:
Combining Drawbar SettingsThere are several schools of thought on how drawbar settings for stops should be combined to produce a registration. Mathematical analysis based on the physics of sound and the workings of the Hammond organ show them to be misconceived. The first is from the Dictionary of Hammond Organ Stops, in which Stevens Irwin suggests: The method is to add the drawbar-indications for each drawbar pitch, using the figure 8 if the sum comes to above 8. I find two serious flaws with this method:
Irwin then writes: Porter Heaps suggests taking the largest figure for each harmonic drawbar in the group of stops to be combined as the proper intensity for the final ensemble. In Hammond Organ Additive Synthesis - A New Method, Paul Schnellbecher responds, I couldn't accept the idea that combining two powerful stops and a medium string could be simulated by using the most powerful stop with only a tiny contribution from the string. Schnellbecher then proposes that a more sensible way is to just add the stops together, and then if at the end of this process any drawbar setting is higher than 8, divide each drawbar setting by 2 as many times as necessary until this is no longer the case. Although I agree with Schnellbecher's sentiments above, this suffers from the same flaw (not considering the logarithmic nature of the drawbar settings) as Irwin's suggestion. Furthermore, why divide by 2? Why not 1½ or π? It would make more sense to divide by the highest setting and then multiply by 8, thus giving the loudest drawbar a setting of 8. A Mathematically Sound ApproachThe method I'm about to propose adheres to the following principle: A combination of two drawbar settings should sound as much as possible as if the two settings were played at the same time on separate Hammond organs (or recorded separately and then mixed). Let's first look at combining the settings for a single drawbar, say the first white drawbar (8'). For example, suppose that both stops we're interested in combining have that drawbar set to 5. It stands to reason that in the resulting registration, the contribution of the 8' drawbar should have twice the volume that it has in either stop alone (after all, playing the same thing on two organs will be twice as loud as playing it on one). Recall that each drawbar increment corresponds to 3dB. That means that two increments correspond to 6dB, and that is equivalent to doubling the volume. Therefore, the resulting setting for the 8' drawbar should be 7. In drawbar setting numbers, 5 + 5 = 7. Similarly, 1 + 1 = 3, 2 + 2 = 4, 3 + 3 = 5, 4 + 4 = 6, 6 + 6 = 8, 7 + 7 = 9, and 8 + 8 = 10. In other words, whenever combining two equal settings, the result is 2 increments higher than that setting. What about unequal values? The trick is to convert from drawbar setting numbers to linear volume figures, add those together, and convert the sum back to a drawbar number. The following table gives the correspondence:
For example, to add drawbar settings of 4 and 7, add the corresponding linear volumes, giving 4.000 + 11.31 = 15.31. The result is within the range of the linear volume range of setting number 8, so the resulting setting should be 8. Let's try combining 3 and 6. Adding the linear volumes gives 10.83, which is within the range of setting 7. What happens if we add 8 and 7? The resulting linear volume is 27.31, which is above the highest available. In cases where the linear volume is greater than 19.02 (which corresponds to a drawbar setting of just under 8.5) we first have to finish adding the linear volumes of the other drawbars, then divide all the sums by the largest and multiply by 19.02. The resulting set of linear volumes can then be converted back to drawbar settings.
This procedure can be expanded to as many separate settings as you wish to
combine into one. Convert all the settings to linear volumes, add up the
corresponding volumes, divide by the largest and multiply by 19.02 if
necessary, and convert the results back to drawbar settings.
To make it easy to use the method described above, I've created an on-line drawbar calculator. Enter as many drawbar settings as you'd like to combine, one per line into the input area below, and click the Combine button:
Comparing the MethodsConsider combining the drawbar settings 00 7676 010 (an 8' Open Diapason) and 00 0402 010 (4' Octave) using each of the four methods:
The four methods produce very different results. In Irwin's method, the fourth and sixth drawbars (2nd and 4th harmonics) are too loud. In Heaps' method, the combined setting is the same as the first setting, as if the second had been ignored. Schnellbecher's method results in a combination that is quieter than either of its parts. Using my method, the highest setting is only 7 because none of the sums result in a volume louder than a setting of 7 would. Also notice the eighth drawbar (the 6th harmonic), where my method correctly accounts for the doubling of volume resulting from adding two settings of 1. Reducing the Volume of a Drawbar SettingIn order to achieve a desired balance between the upper and lower manuals when playing a piece of music, it is often necessary to reduce the volume of a drawbar setting (for instance, to make the accompaniment quiet enough that the melody can be clearly heard). The technique to reduce the volume is trivial: push each drawbar in by the same amount. For example, the following settings all produce the same sound but at increasingly lower levels:
Once the setting contains a "1" somewhere within it, any further reductions
will affect the character of the sound. Moving a drawbar from a setting of 8 to
7 or from 2 to 1 reduces the contribution of that drawbar by 3dB, but moving it
from 1 to 0 turns it off completely (i.e. reduces it by an infinite number of
decibels).
So far we've looked at how to combine drawbar settings representing one or more stops to create a setting for a registration. The other part of the puzzle is how to find a drawbar setting to match a particular pipe organ stop or other musical instrument in the first place. The traditional method is of course by ear. With experience, a Hammond organist learns how the relative settings of the drawbars affect the character of the sound produced. However, it takes a while to gain that experience, and in this era of instant gratification, there is an easier way! As we've discussed, the drawbars control the relative volume of the harmonics of the sounds produced. This distribution of harmonics is visible when one plots the frequency spectrum of the sound. For example, here is the spectrum of a 440Hz tone played with registration 00 8767 054:
The peaks and their amplitudes are:
If we now arbitrarily equate 0dB to a drawbar setting of 8, then every 3dB down from that corresponds to one drawbar increment down (anything -24dB or below becomes zero). One can see that the frequency spectrum of the tone corresponds exactly to the drawbar setting that produced it. One can take advantage of this to derive a drawbar setting for an arbitrary tone. Starting with a recorded sample of the tone, use a tool like Audacity to generate a spectrum analysis, and write down the intensity of each peak. Equate the highest intensity to a setting of 8 and determine the settings of the remaining drawbars relative to that, so that each 3dB down from the highest corresponds to one drawbar increment down. This technique works for almost any steady tone that one can get a recording of. For example, I found this short clip on www.freesound.org of a female vocalist singing melisma style. Here is the frequency spectrum from the second G# note in the performance:
The peaks and their amplitudes, and the corresponding drawbar settings, are:
The drawbar setting to match this singer's voice as closely as possible is thus 00 7843 000. Here is a clip of the aforementioned G# as sung by the vocalist, followed by the same note played with this drawbar setting:
The graphic above shows both the singer's waveform (blue), and the Hammond's (red). The shapes aren't exactly the same because the phase relationship between the harmonics isn't the same, but research has shown that our hearing is insensitive to phase relationship. Also notice that in the singer's waveform, there are additional small "jaggies". These are from the higher harmonics that the Hammond cannot produce. Here is another spectrum plot, comparing the spectra of the vocalist with that of the Hammond imitation. The purple areas are where the spectra coincide. Notice that all the higher harmonics are missing from the Hammond tone, as is all the non-harmonic content of the actual singer's voice:
Hammond ShortcomingsAlthough a Hammond organ can reproduce many pipe organ stops, pipe organ registrations, and arbitrary sounds quite well, it falls short in some respects. Some of the shortcomings are:
ReferencesDictionary of Hammond Organ Stops - A Translation of Pipe Organ Stops Into Hammond-Organ Number Arrangements, by Stevens Irwin, 1939, 1952, 1961, and 1971. A Primer of Organ Registration, by Gordon Balch Nevin, 1920. A copy of this book is available on-line at Scribd.com. Other Articles of InterestIf you found this article useful, you may also be interested in my other Hammond organ technical articles:
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