Additive synthesis with draw bars

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

Despite characteristics such as key clicks, variable intonation, distortions, and crosstalk (all of which Vintage B3 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. Several limitations should 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 draw bars is derived from the length of organ pipes, measured in feet ('). This naming convention is still used with electronic musical instruments.

Halving the length of a pipe doubles its frequency.
Doubling the frequency results in an upward transposition of one octave.

The lowest register—16’ (far left, brown draw bar)—and the higher octave registers—8’, 4’, 2’, and 1’ (white draw bars)—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 draw bar—you can add the third harmonic. This is the fifth above the 8’. Basically, the draw bars are arranged by pitch, with one exception. The second draw bar (5 1/3’) sounds a fifth higher than the third draw bar. 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.

Download the guides:

Logic Pro User Guide: Apple Books | PDF

Logic Pro Instruments: Apple Books | PDF

Logic Pro Effects: Apple Books | PDF

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