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Producing
an accurate series of fifty harmonics for all of the notes on two 61 note
key-boards and either a 25– or 32 note set of bass pedals would make
a tone wheel instrument enormously complex, prohibitively cumbersome and heavy,
and extremely expensive. Therefore, Hammond and his people had to resort to
many, many compromises. As it is, the average Hammond contains thousands of
individual parts, so it is still a very complicated machine.
Laurens Hammond and his engineers studied real pipe
organs and other instruments until they finally determined that having control
over the first eight harmonics would give the Hammond sufficient tonal resources
to develop suggestive imitative accuracy and ver-satility for general musical
usage. Hammond also realized that since most of the lower har-monics either
are exactly the same, or very close† in frequency to pitches of the
normal equally tempered musical scale, he could use the same frequencies both
as fundamentals for some notes and as harmonics of others, thus eliminating
the need for a huge number of separate tone wheels and their associated parts.
Hammond also left out the seventh harmonic†,
however he provided two “sub har-monics” related to a tone
one octave lower than the fundamental for extra versatility for the musician.
Therefore, each key of a Hammond is capable of sounding nine harmonically
related sine wave frequencies. Furthermore, Hammond provided an ingenious
system whereby the musician can regulate the relative volume of each harmonic
from zero to full strength with eight degrees of loudness for each. Now
let’s calculate what this means. If there are nine harmonically
related frequencies available on each key, and each can be either fully
off or at any one of eight different volume levels, then this becomes
9 to the ninth power or the amazing total of 387,420,489 possible different
tonal combinations available on each playing key. Now that’s tonal
versatility! However, many of the available tonal combinations sound very
much like each other, and many others are octave duplications of the same
thing. Some are also musically useless. In actuality, there are perhaps
500 truly distinct usable tonalities. Each of these, however, is capable
of hundreds of subtle minor adjustments.
To make all of this possible, each playing
key on the instrument operates a set of nine switching contacts under
the key. Each contact carries one particular pitch or frequency. In schematic
form, it looks like figure thirteen. The correct nine frequencies from
the tone generator for each playing key are fed through isolation resistors
to the nine key contacts. When you push a key, a bakelite actuator simultaneously
pushes the nine contacts down and they contact the horizontal busbars
that run the entire length of the keyboard.
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Figure 13, left. This partially
diagrammatic drawing shows the arrangement under a typical key on a tonewheel
Hammond. When you push down on a key, it moves the bakelite contact actuator
down slightly which pushes the nine bronze contact springs down so that
they contact the nine corresponding busbars which run lengthwise through
the key-boards. Notice that each con-tact spring as well as the top of
each busbar has a palladium wire attached which insures a good electrical
contact.
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The busbars
convey the signals to the so-called Hammond harmonic drawbars, a series
of controllers which can connect each busbar selectively to either ground
or to one of eight taps on the primary of a transformer. The secondary
of this transformer feeds the resulting signal to the input stage of a
preamplifier for amplification and further processing. Let’s return
for a moment to the key contacts. A typical Hammond keyboard is a standard,
61 note organ keyboard. Each key has nine contacts. Therefore, the entire
keyboard has 61 × 9 contacts or 549 contacts in all, each carrying
one frequency.
Because there are only 91 available frequencies
from the tone generator, it is evident that the same frequencies must
appear on a number of different key contacts, which is indeed the case.
(Remember the compromises Laurens Hammond needed to make his invention
commercially practical?) Since the same frequencies appear on a number
of contacts, and since several of these may be closed at one time (depending
on the musician’s settings and playing requirements at any moment)
and also because the tapped primary winding of the transformer mentioned
above has extremely low impedance, it is necessary to put a small isolation
resistor in series with each contact.
In the Hammond, these resistors are actually
lengths of resistance wire which are connected between the tone generator
input terminals of a keyboard and the appropriate key contacts. Without
the resistors, if any keyboard busbar’s signal selector (drawbar)
was “off” or grounded, the entire output of one or more tone
wheels could be shorted to ground and would not be available on any of
the other contacts where it might be simultaneously needed. Thus Laurens
Hammond found right from the start that resistors were absolutely necessary
in his key contact assemblies.
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† With the exception of octave-related
harmonics such as 1, 2, 4, 8, etc. all of the other harmonics (such
as 3,5,6,7, etc.) do not correspond exactly to the notes of the scale.
The 3rd, 6th, and 9th harmonics are very close, however, and tempered
scale pitches can be used with essentially no noticeable discrepancy.
In the case of the 5th harmonic, the closest tone available on the tempered
scale is 14% sharper in pitch than the true fifth harmonic for any particular
tone, however, in an instrument like the Hammond, it is close enough
to be acceptable. When we look at the seventh harmonic, however, we
find that the true seventh harmonic is just about 30% flatter than the
closest equivalent pitch from the tempered scale. Laurens Hammond felt
that this was too much of an error, which is why he left the seventh
harmonic out entirely. Some models of the Hammond, such as the H series
and the X66 included a seventh harmonic, the feeling being that, because
these instruments would probably be used with the vibrato ON most of
the time, it would work. In my personal opinion, the seventh harmonic
when derived from the regular scale, in spite of its nearly 30% error,
does indeed work and adds much to some of the effects which are available
on these newer Hammond models. For a more detailed look, do a Google
search for "musical temperaments" and "harmonic series."
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