Additive Synthesis with Drawbars

The Hammond B3 is the classic drawbar organ. As with an air-driven pipe organ, the registers (drawbars, or “stops” on a pipe organ) can be pulled out, in order to engage them. In contrast to a pipe organ, however, the B3 allows seamless mixing of any drawbar registers. The closer toward you that the drawbars are dragged, the louder the corresponding tones.

Despite characteristics such as key clicks, variable intonation, distortions, and crosstalk (all of which the EVB3 emulates), playing a single note, with a single register, results in a pure sine tone. Mixing sine tones results in more complex harmonic spectra; this is known as additive synthesis. Organs—even pipe organs—can be regarded as additive synthesizers. There are, however, several limitations that need to be considered before viewing the instrument in this way. These limitations, on the other hand, constitute the charm and character of any real musical instrument.

The naming of the drawbars is derived from the length of organ pipes, measured in feet ('). This naming convention is still used with electronic musical instruments.

The lowest register—16' (far left, brown drawbar)—and the higher octave registers—8', 4', 2', and 1' (white drawbars)—can be freely mixed, in any combination. 16' is commonly described as the sub-octave. With the sub-octave regarded as the fundamental tone, or first harmonic, the octave above 8' is the second harmonic, 4' the fourth harmonic, 2' the eighth harmonic, and 1' the sixteenth harmonic.

With the 5 1/3' register—the second brown drawbar—you can add the third harmonic. This is the fifth above the 8'. Basically, the drawbars are arranged by pitch, with one exception. The second drawbar (5 1/3') sounds a fifth higher than the third drawbar. See The Residual Effect for an explanation.

The 2 2/3' register generates the sixth harmonic, 1 3/5' the tenth harmonic, and 1 1/3' the twelfth harmonic.

An electromechanical tonewheel organ offers the choice of the following registers/harmonics:  1 (16'), 2 (8'), 3 (5 1/3'), 4 (4'), 6 (2 2/3'), 8 (2'), 10 (1 3/5'), 12 (1 1/3'), and 16 (1'). As you can see, the harmonic spectrum is nowhere near complete. This is one of the main reasons for the common practice of using overdrive and distortion effects with electromechanical tonewheel organs—they enrich the harmonic spectra by generating more harmonics.

Note: 2 2/3' is the fifth over 4'. 1 3/5' is the major third over 2'. 1 1/3' is the fifth over 2'. In the bass range, this can lead to inharmonic tones, especially when playing bass lines in a minor key. This is because mixing 2', 1 3/5', and 1 1/3' results in a major chord.