Sunday 22 May 2011

Additive Fourier Synthesis


Regular readers (poor things!) might recall that I won a genuine set of Hammond Drawbars on eBay (originally salvaged from a Hammond L100 donor organ)...


I've already explained that "drawbars are gain controls for individual harmonic components" - allow me to be a little more precise...

The nine drawbars in a "set" give partial control over the elements of two harmonic series; one series built on the fundamental (which is associated with the "8 foot" drawbar - the "foot" dimension being a legacy of pipe organs) and the other built on the sub-harmonic an octave below that fundamental. Of course, the fundamental changes with each key that is depressed - but if you imagine we're depressing only "middle C", the following picture is worth several lines of my boring words...


Notice from my graphic that the sub-harmonic series' drawbars are coloured brown, those which sound the same note (in terms of tonic sol-fah) as the fundamental are white, and other elements of the series are black. You will also notice that the seventh harmonic is absent (as it is a de-tuned minor seventh which doesn't sound so good!). Anyway - enough music for the moment - let's get back to some electronics.

The drawbars are a series of multi-way switches, in which each drawbar has a contact able to touch some of seventeen commoned bus bars. The size of the contact is such that two busbars are contacted at any time, avoiding open-circuits during movement. In original use, the busbars were connected using a resistance network, making a series of stepped resistors.

The resistor network was implemented using resistance wire, and the lengths of these wires (proportional to the resistances) reveals that it is a non-linear ladder. The resistance wires were still in place in my unit from eBay...


My interface had been developed for use with a series of potentiometers...


... but this wouldn't work with the drawbars. I had to re-interpret to work with the "multi-way" switches. Fortunately, the change was minor - you can see one drawbar's worth of circuit here, with the common block inherited from the "potentiometer" scheme above...


Notice that, as in the original Hammond organ from which these drawbars were harvested, I needed a resistor ladder. I designed the taper of this ladder to generate a voltage output proportional to the drawbar setting - this one was much higher impedance than the original ladder (by a factor of ~10000).

Here's the genuine Hammond drawbars in place...


and here's a screen-shot of the resulting settings in OrganizedTrio - EUREKA!



Bubbling over with success I went on to try to connect up a pedal drawbar (the L100 had only one (16') pedal drawbar) but hit a problem. The Organized Trio VST plugin doesn't allow external control of the pedal drawbars despite the claims of its documentation -


Oh well - it does sound good and the price certainly was right - cheapskates can't be choosers!

The absence of pedal drawbars left me with lots of "free" analog interface lines, which could be used to connect either analog (i.e. proportional) or "Boolean" (i.e. On/Off) controls. I had planned to do the latter with a separate "switch matrix" scheme, but opted for as simpler approach, using the analog interface, in which the potentiometer used for proportional controls was replaced by a spdt switch, to give "full-on" or "full-off" control...

Here's a temporary control solution, in which switches in the percussion and vibrato / chorus control sections have been implemented using toggle switches...


This gives me pretty much all the controllability of a B3 (bar the pedal drawbars and the restricted lower manual drawbars of the L100). Anybody know where I can buy nice soft action rocker keys???

In the course of adding these "Boolean" controls, I noticed another "funny" about Organized Trio. The percussion "On/Off" isn't a two-state control at all - in fact it is another "level" control, with proportional action. I wonder if the others are like this too.

That's all for now

...-.- de m0xpd

2 comments:

  1. Great work, but how did you avoid that the open circuit with your resistor ladder ?
    Vy 73 OZ 1 dmv

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  2. Claus - thanks for your comments. I'm not sure which "open circuit" you refer to in your question... It is possible to get the drawbars to go "open circuit" under strange operating conditions (pressing down on the "tab", for example), but the drawbar is designed to avoid this. HOWEVER, this is now old news - I'm now two generations further on than this old post, and I've changed to a system in which I use standard Hammond Drawbars with their original resistor ladder, driven from 5 volts d.c. and a new home-brew analog multiplexer to read all (38) drawbars. I'll get round to writing it up one day!
    73 de m0xpd

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