Hammond clarification

Let me clarify something, in case my oversimplistic reply to Kool Music was
the source of any confusion.

I thought those on the tuning list might be interested as well.

If you analyze the timbre of a Hammond organ will all the drawbars on zero
_except one_, say the double octave, you will indeed see a perfectly
harmonic timbre. Only one partial will be very strong, while the weak
overtones above that will be exact integer multiples of the frequency in
question. This is because the signal is produced by a spinning wheel, hence
a perfectly periodic vibration, and any perfectly periodic vibration has
exact integer overtones.

But, if you now engage another drawbar, say the double octave plus major
third, you will now have _two_ overtone series, both with a strong
fundamental and weak overtones, and they will be close to an equal-tempered
major third (rather than a just major third) apart. This can be seen by
examining the gear ratios on the Hammond. We can look at each pair of gears
a major third apart (yes, these are the gears engaged even by the drawbars).
Each individual gear has a two-digit gear ratio with the central 320Hz gear:

C#4 71/82
D4 67/73
D#4 35/36
E4 69/67
F4 12/11
F#4 37/32
G4 49/40
G#4 48/37
A4 11/8
A#4 67/46
B4 54/35
C5 85/52

Octave (2/1) gears are used to obtain higher and lower octaves.

Now let's calculate the ratios for the major thirds that result:

notes ratio cents
C#-F: 984/781 400.0029
D-F#: 611/485 399.8265
D#-G: 63/50 400.1085
E-G#: 1072/851 399.6886
F-A: 121/96 400.6809
F#-A#: 1072/851 399.6886
G-B: 432/343 399.3873
G#-C: 1604/1273 400.1305
A-C#: 568/451 399.3162
A#-D: 92/73 400.4849
B-D#: 1225/972 400.5042
C-E: 470/373 400.1809

By contrast, a pure JI major third is 386.3137 cents.

Anyhow, if you engage all the drawbars, the strongest frequencies will be
tuned virtually in equal temperament with respect to each other. It is true
that, since each drawbar's tone is not a perfect sine wave, you will also
have some weak frequencies corresponding to exact integer multiples of the
various ET tones.

Finally, this was the design of the original Hammond organ, and old Hammonds
were made this way. It may be that newer Hammonds use some other mechanism
for the drawbars, perhaps using true harmonic relationships, while the keys
would of course still engage the ET approximations. And that may be one
reason the old Hammonds are more desirable!

Can one tune the Hammond by changing the speed of the tonewheels or some
other way?

Hi Alexandros.

To tune the Hammond to a frequency other than A-440, one could use a
transformer to change the 60Hz AC current to another frequency.

If you were in Europe and plugged in a Hammond without a transformer, you'd
be in A-366.67!

To use a tuning other than equal temperament, you'd have to go in and start
replacing the gears. The gears have numbers of teeth corresponding to the
numerator and denominator of the ratios I posted.

-Paul

Hello Paul,
I am interested on the Hammond organ but I want all my instruments tunable.
The way you refer for tuning it in a way other than the equal temperament is
possible/practical ? Do you know if anyone tried it?

> The way you refer for tuning it in a way other than the equal >
temperament is
> possible/practical ?

It would be a lot of work to make a new set of gears and to take apart the
organ and put it back together with the new gears.

>Do you know if anyone tried it?

Maybe Terry Riley??

"Paul H. Erlich" wrote:
>
> > The way you refer for tuning it in a way other than the equal >
> temperament is
> > possible/practical ?
>
> It would be a lot of work to make a new set of gears and to take apart the
> organ and put it back together with the new gears.
>
> >Do you know if anyone tried it?
>
> Maybe Terry Riley??

He played Yamaha.

--
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