The Hammond Organ
This page is intended to be a look at some of the key technical aspects of the B3 Hammond organ that contribute to the “Hammond sound”. My personal slant is towards copying this sound using other technology. Perhaps one day I'll build a “clonewheel” organ, but then again, Clavia might have nailed it! Still, building an organ would be a nice project.
- Key Click
- Harmonic Leakage
- Chorus/Vibrato scanner
- The problems with copying the B3
- The easy parts of the B3
- Working out the frequencies of the tones used
- What frequencies are used?
The harmonics, footages, and notes used on the Hammond drawbars are shown below:
As can be seen, for each note, the harmonics go three octaves above it, and one octave below.
The basic pitch of the instrument runs from tone 13 to tone 73. This pitch is provided by the 3rd drawbar, the fundamental.
The 5⅓' footage is oddly placed as the second drawbar, rather than in its logical position between the fundamental and 2nd harmonic, presumably because it is labelled as the ‘sub-3rd harmonic’.
Harmonic foldback is used to reduce the required number of pitches at both ends of the keyboard. It affects the 3rd and subsequent harmonics at the top, and the sub-fundamental harmonic at the bottom. This is shown in the following table, which shows the tonewheels (1-91) used for each harmonic
|Lower Foldback||Top Foldback|
The 3rd harmonic repeats the highest C. The 4th harmonic repeats from tone 56, G of the top octave. The 5th harmonic repeats from tone 52, D# of the top octave. The 7th harmonic repeats from tone 49, the lower C of the top octave. The 8th harmonic is repeated from tone 44, G in the fourth octave. Note that the 6th and 8th harmonics actually repeat some tones twice.
Since the lower tones that are folded back are actually present in the instrument for the pedals, it is possible to rewire a Hammond for true bass, with no lower foldback. The quirk is that the lowest octave of tonewheels are cut with a more complex shape and provide a waveform that is closer to a squarewave, with some 3rd and 5th harmonics present.
The diagram below shows the effect of the harmonic foldback on the top and bottom notes of the keyboard. The lowest note has its sub-fundamental folded back, even though the tone generator goes low enough, represented by the width of the grey bars. At the top, there are five tones which ‘go off the top’ of the generator and are folded back onto the top octave provided. Notice that this means that if you play the top C, it actually includes two of the same tones (tones 80 and 85) three times over!
In theory the full 5 octaves of the B3 keyboard would require 61 basic tones, plus 3 octaves above for harmonics and one octave below for the sub-fundamental harmonic. This gives a total of nine octaves, or 61+36+12 = 109 tones. Since there are only 91 tones available, the need for foldback is clear.
The mechanical key contacts on the B3 have audio level signals present on them. Switching these directly through to the output caused audible clicks. These clicks have become a signature part of the Hammond sound. The clicking is caused by a combination of the nine key contacts not shutting simultaneously, and contact bounce exacerbated by dirty contacts. This causes a random rapid switching of the signal in the initial portion of the note. Since this switching introduces transients, we hear this as a sound with much random high frequency content - a click. This could be simulated either by adding in transient noise, or by electronically simulating contact bounce.
The Hammond tonewheel generator contains a series of metal dividers, which break the generator up into “bins”. Each bin contains 2 tonewheels which are connected to the same driven gear. There is a certain amount of magnetic leakage between tones that are in the same bin, so it is possible to hear harmonic leakage either four octaves above or below the required tone. Good copies of the Hammond include this leakage.
The Hammond chorus/vibrato circuit has become famous in its own right, with organs that have a “real” scanner-based vibrato being more valuable than those without. So what is this circuit and how does it work?
In short, it is a 9 stage delay line. The delay is produced using LC phase shift circuits. It can produce only a very short delay of around 1mS . A variable delay is required for vibrato or chorus, and this is generated by the rotating scanner arm picking up signals from each stage of the delay in turn. Because of the way this is done (air-gap capacitor, essentially) the effect is a fade between one stage and the next. The scanner is set to scan each tap from 1 through to 9 and then back again 9 to 1. This is equivalent to a triangle wave modulation of the delay time. The complete cycle, from 1 to 9 and back, is 16 steps. Although three depth settings are available for each of the two effects (VIB1, VIB2, VIB3, CHORUS1, CHORUS2, CHORUS3) on the B3, there is no control of rate, which is set at a constant 7Hz. Any good copy has to be able to provide this speed.
Juergen Haible has spent some time copying the original Hammond scanner circuit and producing a modern copy. This uses a real LC phase-shift delay line, coupled to a pair of VCAs and other circuitry to do the fading from one stage to the next. This apparently produces an extremely close copy of the original sound, without any moving parts.
Other, less stringent, copies would be possible using BBD devices. The problem with these would be getting the extremely short delay times required. Most chips would have too many stages and too slow a clock to get the times required. These also provide the same delay to all frequencies, not something which is a feature of Hammond's LC phase-shift delay.
Perhaps a more promising route would be to use 9 op-amp based phase shifters and then scan between the outputs of these using a circuit much like Juergen's.
There are various problems with copying the B3. They are:
This is not so easy to do, and even harder at reasonable cost. Ideally, the waves should not have fixed phase relationships between related notes, although they do have a reasonably fixed relationship in the original organ. The spring couplings between stages in the tone generator give this some fluidity though. This fixed-but-not-fixed phase relationship is another interesting aspect of the technology, but one with an unknown influence on the sound.
The original organs have nine contacts under each key. Even this is insufficient, since they rob one contact from a harmonic when the percussion is switched on. For every key that is pressed down, (at least) nine individual frequencies must be passed to nine separate output mixers, and a signal must be passed to a percussion circuit. This makes a total of 61x10 contacts required for each of two manuals (ignoring the pedals!) for a grand total of 1220 switch contacts, although as mentioned Hammond reduced this a little.
If there is a way to to wire this up without it looking “like the web of a spider suffering obsessive-compulsive disorder”, I haven't seen it. Even multiplexing doesn't seem to help, since it simply moves the problem back to become a question of getting the correct tones to the multiplexers.
This is the fundamental problem with any fully polyphonic organ - and all the best ones are.
The output circuits are pretty straightforward. The busbars are simple mixer circuits that sum all the notes pressed down, and the drawbars control the output volume from each harmonic's mixer. These harmonics are then mixed in the final output mixer before being amplified.
Getting this to sound like a B3 is a question of tone and technology - using tubes not transistors and so forth. If everything else is ok in your clonewheel organ, and you plug it into a valve amp Leslie speaker, it'll sound like a Hammond.
The frequency of a particular tone depends on a number of things:
- M - The main motor speed, 20 revs/second (1200 rpm)
- T - The number of teeth on the tonewheel
- R - The gear ratio. This is equal to the number of teeth on the driving gear / number of teeth on driven gear.
The ratios in the Hammond are as follows:
|Note||Driving (A)||Driven (B)||Ratio (A/B)|
The formula for the exact frequency of a tone is:
Frequency F (Hz) = M * T * R
Thus for Middle A:
20 * 16 * (88 / 64) = 440Hz
The As are the only notes on the Hammond which agree exactly with the equal tempered scale. The notes which are the farthest off pitch in the first seven octaves are the G#s. They are 0.69 cents flat from the correct pitch.
For C# = 4434Hz: 20 * 192 * (74/64) = 4440Hz
Essentially, the gear ratios determine the note, whilst the number of teeth on the tone wheel determines the octave. Hence all the tones in a single octave use wheels with the same number of teeth. The 91 frequency tone generator uses:
- 12 tonewheels of 2 teeth
- 12 tonewheels of 4 teeth
- 12 tonewheels of 8 teeth
- 12 tonewheels of 16 teeth
- 12 tonewheels of 32 teeth
- 12 tonewheels of 64 teeth
- 12 tonewheels of 128 teeth
- 7 tonewheels of 192 teeth
The last (top) octave is unusual, since Hammond could not cut wheels with 256 teeth. Instead they used wheels with 192 teeth and used the gear ratios from the F below upwards. This means the top half octave is farther off pitch due to the number of teeth on the tonewheel not equaling 256. In the top half octave, the C# is the farthest off pitch, about 1.93 cents sharp. This is still less than the 6 cents that supposed to be the minimum discernible pitch difference.
Equal temprament tuning means that it is impossible to find exact harmonics on the keyboard - each tone is a “best fit” rather than the exact value. However, the Hammond doesn't use a true equal temperament tuning, but rather its own approximation. In the case of the 6th, 3rd and sub-3rd harmonics, this leads to them being slightly closer to the true value than equal temperament, and in the case of the 5th, slightly worse. The differences are present, but very slight and probably not significant. Ignoring the top half-octave which is rather different, the results are summarized in the table below:
|Harmonic||True harmonic ratio||Equal temperament ratio||Hammond ratio|
The bottom octave runs from 32.69Hz to 65.38Hz. These tones are the complex tonewheels and are only available on the pedals.
The tones for the manuals run from 65.38Hz (the lowest C) to 2092.31Hz (the highest C). The tone generator also generates harmonics another octave and a bit above this, to the C above (4184.62Hz) and finally to the F# above that (5924.62Hz). This is the highest pitch in the organ.