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The Hammond Organ

The Hammond organ is an interesting and unique musical instrument. The table below shows the frequencies of its scale, along with those of some related instruments.

   Equal       Hammond          Telharmonium     Pari-E 

C  261.62557   261.54  85 104   261.62 320  80   261.607
   277.18263   277.07  71  82   277.19 356  84   277.179
D  293.66477   293.70  67  73   293.66 440  98   293.645
   311.12698   311.11 105 108   311.12 352  74   311.124
E  329.62756   329.60 103 100   329.70 494  98   329.606
F  349.22823   349.09  84  77   349.20 315  59   349.226
   369.99442   370     74  64   369.95 362  64   369.972
G  391.99544   392     98  80   391.89 725 121   391.994
   415.30470   415.14  96  74   415.32 508  80   415.281
A  440         440     88  64   440    444  66   440    
   466.16376   466.09  67  46   466.01 456  64   466.139
B  493.88330   493.71 108  70   493.85 672  89   493.885

On a conventional organ, if 8', 2 2/3', and 1 3/5' stops are pulled, when a note is played, three pipes will sound: one that produces a sound with the fundamental frequency of the note associated with that key, another one producing a sound whose fundamental frequency is exactly three times that frequency, and still another producing a sound whose fundamental frequency is exactly five times that frequency.

This will be true no matter what temperament the organ may have been tuned for, whether equal-tempered or meantone; the frequency relationships between ranks of pipes will be based on the exact just frequency ratios.

The Hammond organ drawbars for the upper and lower manuals corresponded to the following pipe lengths:

Brown 16'
Brown  5 1/3'                            3*(16')
White  8'                                2*(16')
White  4'                       2*(8')   4*(16')
Black  2 2/3'                   3*(8')   6*(16')
White  2'              2*(4')   4*(8')   8*(16')
Black  1 3/5'                   5*(8')  10*(16')
Black  1 1/3'          3*(4')   6*(8')  12*(16')
White  1'      2*(2')  4*(4')   8*(8')  16*(16')

This table also shows the nominal harmonic relationships between the tones produced by the pipe lengths. Note the color coding: drawbars associated with the 16' tone, and a harmonic related only to it, are brown; the nominal fundamental, and its power-of-two harmonics, all being on the same note, are white, and the harmonics from other notes are black. This was used in instructions for the organ to give some simple general advice on their use.

The pedal clavier on most Hammond drawbar organs only had 16' and 8' drawbars associated with it. A few models of Hammond organ, such as the RT-2, RT-3, D-100, and D-152 had a solo pedal unit; with that unit, the sound for that keyboard was not made with the tonewheels, but by a monophonic electrical circuit based on the same principle as their Solovox. This was in addition to the pedals functioning as a third manual and making use of the signals generated by the tonewheels.

The Hammond organ does not have multiple ranks of tonewheels. Therefore, when the drawbars for 8' and 2 2/3' are both pulled out, instead of the 2 2/3' drawbar causing an exact third harmonic to be added to the sound produced by the 8' drawbar, the note a twelth above, in that organ's approximation to equal temperament, is what is added.

There is one exception to this. The table above shows the two gears used to cause twelve shafts bearing tonewheels to rotate at speeds which allow equal temperament to be approximated. Thus, a C of about 261.54 Hz is produced by a gear with 85 teeth, rotating at 1200 RPM, or 20 times a second, driving a gear with 104 teeth. That gear turns a shaft, causing it to rotate about 16.346 times a second. A tonewheel on that shaft with 16 teeth will generate the note middle C with about 261.53846 Hz as its frequency.

The C shaft contains tonewheels with 2, 4, 8, 16, 32, 64, 128, and 192 teeth. Since the Hammond organ does not require eight full octaves of frequencies, instead of having the last tonewheel have 256 teeth, it has 192 teeth; thus, the highest C is taken from a 192-tooth wheel on the F shaft, and so on.

Thus, notes played on a Hammond organ, unless the 5 1/3', 2 2/3', 1 3/5', and 1 1/3' drawbars are not used, will have unnatural "harmonics" which are one element of its unique sound.

By the way, while the original patent for the Hammond organ did not show exactly the same gear ratios as were used in the production organ, almost all of the ones that were shown that were different were still exactly equivalent to the actual ones. How could this be?

   Equal    Hammond          Original Patent                   42-89

F  349.23   349.09  84  77          54  99  /14 *9   /7 *9      84  77
   369.99   370     74  64          37  64  /2       --         74  64
G  392.00   392     98  80          49  80  /2       --         98  80
   415.30   415.14  96  74          48  74  /2       --         96  74
A  440      440     88  64          66  96  /4 *3    /2 *3      88  64
   466.16   466.09  67  46          67  92  --       *2         67  46
B  493.88   493.71 108  70          54  70  /2       --        108  70
C  523.25   523.08  85 104          85 104                      85  52  --   /2
   554.37   554.15  71  82          71  82                      71  41  --   /2
D  587.33   587.4   67  73          67  73                     134  73  *2   --
   622.25   622.22 105 108          70  72  /3 *2    /3 *2     105  54  --   /2
E  659.26   659.2  103 100   659.1  69  67  (different)        103  50  --   /2

The answer is that the number of teeth in a tonewheel, instead of remaining constant over an octave from C to B, and then doubling for the next octave, remained constant over an octave from F to E, and then doubled for the next octave. So the gears for the notes from C through E were changed, usually by cutting the number of teeth on the driving gear in half, and, when that was not possible, by doubling the number of teeth on the driven wheel. Occasionally, other changes took place.

Thus, despite several of the gears looking different, in only one case did the note generated have a different frequency.

In the upper half of the tone generator, however, the modern gear ratios were used for the first seven frequencies in each octave, and then the last five frequencies of each octave used gears modified so that only a 128 tooth tonewheel, instead of a 256 tooth tonewheel, would be needed for the highest frequencies. The same basic principle, but this time applied in the opposite direction, cutting the number of teeth on the driven wheel in half in preference to doubling the number of teeth on the driving wheel, was used.

According to the original patent for the Hammond organ (U.S. Patent 1,956,350), the drawbar settings for the Hammond organ engage the following number of turns on a transformer (to reduce the number of internal connections - and transformers - required, it is a transformer which accepts the generated frequencies in the organ to include them in the final output, rather than one that supplies a given frequency at different levels):

   0  1  2  3  4  5  6  7  8
   0  6  8 11 16 23 32 45 64

Note that the number of turns doubles exactly at each step as one advances through the settings 2, 4, 6, and 8. As power is proportional to the square of amplitude under certain conditions (such as driving a constant load, where a doubled voltage will also lead to a doubling in current), the statement that each drawbar increment from 1 to 8 represents a doubling of audio power for a given harmonic, or a 3db increase, is likely to be correct. Other ways to see this are by noting that if a loudspeaker's excursion doubles, the velocity of the cone doubles as well, or by noting that if there are multiple sources of a sound at the same loudness and frequency, because phase relationships are random, the net amplitude increases as the square root of the number of sources of sound.

On the web site of Stephan Vorkoetter, a method is noted for combining drawbar settings accurately on the basis of this premise. Most previous authorities simply advocated adding the numbers in drawbar settings linearly.


In the case of the Telharmonium, one patent describes the use of six switches, each one controlling twice as many windings of a transformer as the next, so values from 1 to 63 as well as 0, or off, are available for each partial, and these are linear in amplitude rather than exponential. This leads to the following table of conversion from Hammond drawbar registrations to settings for the partials on the Telharmonium:

      1  2  4  8 16 32 64
 8                      *
 7    *     *  *     *
 6                   *
 5    *  *  *     *
 4                *
 3    *  *     *
 2             *
 1       *  *

Note that the switch settings for the odd numbers are not always just shifted over a place each time, as they reflect the results of rounding.


The German manufacturer Wersi also produced drawbar organs. The original analog models, the Helios and Galaxis, produced the different frequencies through square waves which went through a frequency-divider network; in addition to the drawbars, they also had conventional stops, which did not merely activate drawbar settings, but which made use of specific filter circuits for each voice to be provided, as typically done with non-drawbar organs. As their sound can be very similar to that of a Hammond, it may well be that for the signal that went through the drawbars, the 3rd and higher harmonics were filtered out (only one filter per octave would be needed for that, since the third harmonic is a twelfth higher).

The selection of drawbars which their organs offered was:

 Upper       Lower       Pedal
 Manual      Manual      Clavier

* 16'                    * 16'
*  8'        * 8'        *  8'                                 2*(16')
*  5 1/3'                                                      3*(16')
*  4'        * 4'        *  4'                        2*(8')   4*(16')
*  2 2/3'    * 2 2/3'                                 3*(8')   6*(16')
*  2'          2'           2'               2*(4')   4*(8')   8*(16')
   1 3/5'      1 3/5'                                 5*(8')  10*(16')
   1 1/3'      1 1/3'                        3*(4')   6*(8')  12*(16')
  [1 1/7']                                            7*(8')  14*(16')
*  1'          1'           1'       2*(2')  4*(4')   8*(8')  16*(16')
    [8/9']                                            9*(8')  18*(16')
     4/5'                                    5*(4')  10*(8')  20*(16')
     2/3'                            3*(2')  6*(4')  12*(8')  24*(16')
                              1/2'   4*(2')  8*(4')  16*(8')  32*(16')
                             [1/4']  8*(2') 16*(4')  32*(8')  64*(16')

In the case of the pedal keyboard, the sources are not clear, but I have taken what seems to make sense as hinted at by one of them. I could imagine the pedal keyboard being given a 12' rank, but not a 1 1/2' rank.

Different selections of drawbars were offered on different models; the asterisks indicate the more limited selection of drawbars on the Comet or W10 organ, as against the larger W2 organ. The Galaxis organ, with three manuals, had 13 drawbars for each of those three manuals; the additional ones for the three manuals of the Galaxis are shown in the chart above in square brackets in the upper manual column. As well, it had an additional drawbar for the pedal clavier, also shown in square brackets.

Note that because the Wersi organs did not depend on tonewheels, in the Galaxis stops were provided not only for the 9th harmonic, which is acknowledged in Western music as resulting from two successive fifths (and two octaves), but even for the 7th harmonic, so as to make a more natural sound (since, after all, even if the Western musical scale does not attempt to provide notes which use the 7th harmonic to harmonize with other notes, this harmonic is still produced within the sounds Western musical instruments make), at least for the notes in the 8' range, while retaining the flexibility of additive synthesis.

The Classica organ apparently used an even more unusual rank of frequencies internally, not available on the drawbars, to create some of the voices on the individual stops.

At first, I thought that, since unlike the third and fifth harmonics, the seventh harmonic is not acknowledged in the construction of the Western musical scale, including a drawbar for the seventh harmonic would require a special rank of generators. However, I had forgotten that simply because a thing is not acknowledged, it does not mean that it does not exist. After all, in the equal-tempered scale, the tritone corresponds to the square root of two, which can be approximated by a 10:7 ratio or a 7:5 ratio. Thus, a tritone, a major third, and two octaves obtains a seventh harmonic within the musical scale.

However, as this table shows,

                     Ratio               Cents

Augmented Fourth     25/18     1.38889   568.7
                     7/5       1.4       582.5
Augmented Fourth     45/32     1.40625   590.2
Tritone              sqrt(2)   1.41421   600
Diminished Fifth     64/45     1.42222   609.8
                     10/7      1.42857   617.5
Diminished Fifth     36/25     1.44      631.3

the seventh harmonic doesn't lead to a better approximation to the equal-tempered tritone than those deriving from the third and fifth harmonics. As one can, however, view the difference between 7/5 and 45/32, for example, as being on the order of the schisma, this does tell us that the 53-note equal-tempered scale can be considered to be capable of embracing the seventh harmonic as well as the third and fifth harmonics.

Thus, the 1 1/7' drawbar could be what would be more conventionally thought of as a 1 1/8' drawbar.


Some later models of the Hammond organ, such as the H-100, the X-66, and the X-77 did include the seventh harmonic. That model had two extra drawbars, labelled I and II, after the conventional series from the original Hammond organ. The first is a 1 1/7' drawbar for the seventh harmonic and an 8/9' drawbar for the ninth harmonic; the second is a 4/5' drawbar for the tenth harmonic and a 2/3' drawbar for the twelfth harmonic; the two harmonics selected are both added to the degree that the drawbar controlling them indicates.

That later model produced 96 frequencies rather than only 91 frequencies with its tonewheel generator, as well; this was a characteristic of many later-model Hammond organs. Note that this didn't require expanding the tone generator, but merely replacing the five dummy tonewheels by real ones.

However, there would have been one wrinkle. Instead of seven tonewheels with 192 teeth, and five tonewheels with 384 teeth, twelve tonewheels with 256 teeth would have seemed more sensible, even though that would mean a slight change to some existing frequencies; but in either case, presumably that would have involved tonewheels with too many teeth to be practical. But the solution is obvious; since there were 24 driveshafts in the Hammond tone generator, all that was needed was to arrange for twelve of them to rotate at twice the speed of the other twelve; then, the tonewheels for the highest twelve frequencies, placed on those driveshafts, would only need 128 teeth.

Other possibilities exist. The higher driveshafts could have rotated four times as fast as the lower ones, to allow for seven tonewheels with 48 teeth and five tonewheels with 96 teeth, so as to preserve the exact pitches of frequencies 85 to 91. Or, instead of just starting from a speed that calls for tonewheels with 2, 4, 8, 16, 32, 64, 128, and 256 teeth, and changing it slightly on one set of driveshafts, so as to have one group of tonewheels with 2, 4, 8, and 16 teeth rotating at the original speed, and another set of tonewheels with 16, 32, 64, and 128 teeth rotating twice as fast, why not increase parts commonality by rotating the slow driveshafts at one-fourth of the original speed, placing tonewheels with 8, 16, 32, and 64 teeth on them, and the fast driveshafts at four times the original speed, also placing tonewheels with 8, 16, 32, and 64 teeth on them?

Of course, if preserving the exact previous values of frequencies 85 to 91 is vital, the group of tonewheels with 64 teeth on the fast driveshafts could be replaced with seven having 48 teeth, and five having 96 teeth.


In connection with this discussion, a note on the Telharmonium of Thaddeus Cahill may be in order.

This device, dating from the early years of the twentieth century, used tonewheels to produce sound, controlled by a keyboard similar to that of an organ. Thus, it might be imagined to have been very similar to the Hammond organ. However, there were significant differences in its design, which would have affected its sound.

The principal difference was that the gears of the drive shaft were not directly used as the tonewheels, which would have made the device similar to the Hammond organ, in the form described in the original patent (U.S. Patent 580,035). Instead, in this larger and more complicated device, they were geared to the actual tonewheels, on what were called "rheotone cylinders", which with conductive and insulating parts, produced square waves for the basic frequency, and its second through sixth multiples.

Thus, the mutation stops - 2 2/3 for the third harmonic, 1 3/5 for the fifth harmonic, and 1 1/5 for the sixth harmonic - were not borrowed stops, but produced exact harmonic multiples of the base frequency, rather than an equal-tempered approximation.

Mutation Stop
A stop on an organ which calls for a different note to be sounded, rather than the same note possibly shifted by one or more octaves, than the note normally associated with any given key on the organ keyboard, when it is played. Such a stop will have a length associated with it that is not a power-of-two multiple of the basic 8-foot length.
Borrowed Stop
A stop on an organ which, instead of simply selecting a pipe of a particular rank associated with the keys on the organ keyboard that will be played, causes pipes associated with different keys to sound instead (thus avoiding the need to build an additional rank of pipes to provide a mutation stop, for example).

A later patent (U. S. Patent 1,213,804), however, noted an improvement on the device which reduced the amount of apparatus required. Instead of using commutators in contact with the rheotone cylinders, inductive coupling with toothed wheels on the twelve main shafts was used. It was still the case, however, that wheels with numbers of teeth that were multiples of 3 or of 5 were present, thus permitting true overtones to be used. In this improved form of the device, the 2nd, 3rd, 4th, 5th, 6th, 8th, 10th, 12th, and 16th harmonics were all available for some notes, but, as with the Hammond organ, the higher harmonics were left out for the highest notes. (The book by Weidenaar, referenced below, notes that one Telharmonium had to be retrofitted to include the seventh harmonic, because that was necessary to produce a satisfying simulation of the timbre of brass instruments. This could be the explanation of why the Wersi Galaxis drawbar organ included the apparently unusual 1 1/7' stop as well.)

Another difference is that the twelve main drive shafts, which had gears on them with 4, 8, 16, 32, 64, and 128 teeth, were driven from a pulley, so their motion could be in the precise ratios called for by the equal-tempered scale. This in itself is a small difference, as the gearing in the Hammond organ makes such a close approximation to that as to be indistinguishable to the ear. And, in fact, while this was depicted in the original patent, gears were used in the actual versions of the Telharmonium that were built, but these gears did have a significantly larger number of teeth than those used for this purpose in the Hammond organ, likely following the design noted in a later patent (U.S. Patent 1,295,691).

In fact, as noted in the book Magic Music from the Telharmonium by Reynold Weidenaar, due to financial problems, only eight of the twelve driveshafts were present in the Telharmonium as actually built; thus, it made the opposite compromise to the one in the Hammond organ; the frequencies for B, and the three black keys in the octave other than E flat and B flat, were derived from harmonics of other notes, thus using an exact simple integer ratio where an equal-tempered one was appropriate, instead of the other way around.


The tone generators in Hammond spinet organs (real tonewheel organs, often available at much lower prices than the full-sized models) followed the same basic principles, but are arranged slightly differently:

                      Tone Generator                                            Spinet Tone Generator

       ---------------------------------------------                ---------------------------------------------
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  61--|--->(______64_____)  | |  (_______2_____)<---|--  1     61--|--->(______64_____)  | |  (_______2_____)<---|--  1
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [___104___][____85___][___104___]      |              |      [___104___][____85___][___104___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  13--|--->(_______4_____)  | |  (______32_____)<---|-- 49     49--|--->(______32_____)  | |  (_______4_____)<---|-- 13
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
      |    (_____________)  | |  (_______8_____)<---|-- 25         |    (_____________)  | |  (_______8_____)<---|-- 25
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [___104___][____85___][___104___]      |              |      [___104___][____85___][___104___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  37--|--->(______16_____)  | |  (_____128_____)<---|-- 73     37--|--->(______16_____)  | |  (_____128_____)<---|-- 73
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  68--|--->(______64_____)  | |  (_______2_____)<---|--  8     68--|--->(______64_____)  | |  (_______2_____)<---|--  8
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____80___][____98___][____80___]      |              |      [____80___][____98___][____80___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  20--|--->(_______4_____)  | |  (______32_____)<---|-- 56     32--|--->(_______8_____)  | |  (_______4_____)<---|-- 20
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  87--|--->(_____192_____)  | |  (_______8_____)<---|-- 32     87--|--->(_____192_____)  | |  (______32_____)<---|-- 56
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____80___][____98___][____80___]      |              |      [____80___][____98___][____80___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  44--|--->(______16_____)  | |  (_____128_____)<---|-- 80     44--|--->(______16_____)  | |  (_____128_____)<---|-- 80
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  63--|--->(______64_____)  | |  (_______2_____)<---|--  3     63--|--->(______64_____)  | |  (_______2_____)<---|--  3
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____73___][____67___][____73___]      |              |      [____73___][____67___][____73___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  15--|--->(_______4_____)  | |  (______32_____)<---|-- 51     51--|--->(______32_____)  | |  (_____________)    |
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
      |    (_____________)  | |  (_______8_____)<---|-- 27         |    (_____________)  | |  (_______8_____)<---|-- 27
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____73___][____67___][____73___]      |              |      [____73___][____67___][____73___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  39--|--->(______16_____)  | |  (_____128_____)<---|-- 75     39--|--->(______16_____)  | |  (_____128_____)<---|-- 75
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  70--|--->(______64_____)  | |  (_______2_____)<---|-- 10     70--|--->(______64_____)  | |  (_______2_____)<---|-- 10
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____64___][____88___][____64___]      |              |      [____64___][____88___][____64___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  22--|--->(_______4_____)  | |  (______32_____)<---|-- 58     34--|--->(_______8_____)  | |  (_______4_____)<---|-- 22
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  89--|--->(_____192_____)  | |  (_______8_____)<---|-- 34     89--|--->(_____192_____)  | |  (______32_____)<---|-- 58
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____64___][____88___][____64___]      |              |      [____64___][____88___][____64___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  46--|--->(______16_____)  | |  (_____128_____)<---|-- 82     46--|--->(______16_____)  | |  (_____128_____)<---|-- 82
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  65--|--->(______64_____)  | |  (_______2_____)<---|--  5     65--|--->(______64_____)  | |  (_______2_____)<---|--  5
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [___100___][___103___][___100___]      |              |      [___100___][___103___][___100___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  17--|--->(_______4_____)  | |  (______32_____)<---|-- 53     53--|--->(______32_____)  | |  (_____________)    |
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
      |    (_____________)  | |  (_______8_____)<---|-- 29         |    (_____________)  | |  (_______8_____)<---|-- 29
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [___100___][___103___][___100___]      |              |      [___100___][___103___][___100___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  41--|--->(______16_____)  | |  (_____128_____)<---|-- 77     41--|--->(______16_____)  | |  (_____128_____)<---|-- 77
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  72--|--->(______64_____)  | |  (_______2_____)<---|-- 12     72--|--->(______64_____)  | |  (_______2_____)<---|-- 12
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____70___][___108___][____70___]      |              |      [____70___][___108___][____70___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  24--|--->(_______4_____)  | |  (______32_____)<---|-- 60     36--|--->(_______8_____)  | |  (_______4_____)<---|-- 24
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  91--|--->(_____192_____)  | |  (_______8_____)<---|-- 36     91--|--->(_____192_____)  | |  (______32_____)<---|-- 60
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____70___][___108___][____70___]      |              |      [____70___][___108___][____70___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  48--|--->(______16_____)  | |  (_____128_____)<---|-- 84     48--|--->(______16_____)  | |  (_____128_____)<---|-- 84
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  67--|--->(______64_____)  | |  (_______2_____)<---|--  7     67--|--->(______64_____)  | |  (_______2_____)<---|--  7
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____64___][____74___][____64___]      |              |      [____64___][____74___][____64___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  19--|--->(_______4_____)  | |  (______32_____)<---|-- 55     31--|--->(_______8_____)  | |  (_______4_____)<---|-- 19
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  86--|--->(_____192_____)  | |  (_______8_____)<---|-- 31     86--|--->(_____192_____)  | |  (______32_____)<---|-- 55
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____64___][____74___][____64___]      |              |      [____64___][____74___][____64___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  43--|--->(______16_____)  | |  (_____128_____)<---|-- 79     43--|--->(______16_____)  | |  (_____128_____)<---|-- 79
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  62--|--->(______64_____)  | |  (_______2_____)<---|--  2     62--|--->(______64_____)  | |  (_______2_____)<---|--  2
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____82___][____71___][____82___]      |              |      [____82___][____71___][____82___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  14--|--->(_______4_____)  | |  (______32_____)<---|-- 50     50--|--->(______32_____)  | |  (_____________)    |
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
      |    (_____________)  | |  (_______8_____)<---|-- 26         |    (_____________)  | |  (_______8_____)<---|-- 26
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____82___][____71___][____82___]      |              |      [____82___][____71___][____82___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  38--|--->(______16_____)  | |  (_____128_____)<---|-- 74     38--|--->(______16_____)  | |  (_____128_____)<---|-- 74
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  69--|--->(______64_____)  | |  (_______2_____)<---|--  9     69--|--->(______64_____)  | |  (_______2_____)<---|--  9
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____74___][____96___][____74___]      |              |      [____74___][____96___][____74___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  21--|--->(_______4_____)  | |  (______32_____)<---|-- 57     33--|--->(_______8_____)  | |  (_______4_____)<---|-- 21
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  88--|--->(_____192_____)  | |  (_______8_____)<---|-- 33     88--|--->(_____192_____)  | |  (______32_____)<---|-- 57
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____74___][____96___][____74___]      |              |      [____74___][____96___][____74___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  45--|--->(______16_____)  | |  (_____128_____)<---|-- 81     45--|--->(______16_____)  | |  (_____128_____)<---|-- 81
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  64--|--->(______64_____)  | |  (_______2_____)<---|--  4     64--|--->(______64_____)  | |  (_______2_____)<---|--  4
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [___108___][___105___][___108___]      |              |      [___108___][___105___][___108___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  16--|--->(_______4_____)  | |  (______32_____)<---|-- 52     52--|--->(______32_____)  | |  (_____________)    |
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
      |    (_____________)  | |  (_______8_____)<---|-- 28         |    (_____________)  | |  (_______8_____)<---|-- 28
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [___108___][___105___][___108___]      |              |      [___108___][___105___][___108___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  40--|--->(______16_____)  | |  (_____128_____)<---|-- 76     40--|--->(______16_____)  | |  (_____128_____)<---|-- 76
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  71--|--->(______64_____)  | |  (_______2_____)<---|-- 11     71--|--->(______64_____)  | |  (_______2_____)<---|-- 11
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____46___][____67___][____46___]      |              |      [____46___][____67___][____46___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  23--|--->(_______4_____)  | |  (______32_____)<---|-- 59     35--|--->(_______8_____)  | |  (_______4_____)<---|-- 23
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  90--|--->(_____192_____)  | |  (_______8_____)<---|-- 35     90--|--->(_____192_____)  | |  (______32_____)<---|-- 59
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____46___][____67___][____46___]      |              |      [____46___][____67___][____46___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  47--|--->(______16_____)  | |  (_____128_____)<---|-- 83     47--|--->(______16_____)  | |  (_____128_____)<---|-- 83
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  66--|--->(______64_____)  | |  (_______2_____)<---|--  6     66--|--->(______64_____)  | |  (_______2_____)<---|--  6
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____77___][____84___][____77___]      |              |      [____77___][____84___][____77___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  18--|--->(_______4_____)  | |  (______32_____)<---|-- 54     30--|--->(_______8_____)  | |  (_______4_____)<---|-- 18
      |           |         | |         |           |              |           |         | |         |           |
      |---------------------------------------------|              |---------------------------------------------|
      |     ______|______   | |   ______|______     |              |     ______|______   | |   ______|______     |
  85--|--->(_____192_____)  | |  (_______8_____)<---|-- 30     85--|--->(_____192_____)  | |  (______32_____)<---|-- 54
      |       ___|_|___  ___|_|___  ___|_|___       |              |       ___|_|___  ___|_|___  ___|_|___       |
      |      [____77___][____84___][____77___]      |              |      [____77___][____84___][____77___]      |
      |     _____|_|_____   | |   _____|_|_____     |              |     _____|_|_____   | |   _____|_|_____     |
  42--|--->(______16_____)  | |  (_____128_____)<---|-- 78     42--|--->(______16_____)  | |  (_____128_____)<---|-- 78
      |           |         | |         |           |              |           |         | |         |           |
       ---------------------------------------------                ---------------------------------------------

The tonewheel and pickup for frequency 13 was only included on the model M-100 spinet, and not the model M, M-2, and M-3. Why just one frequency was omitted can be seen from the diagram below:

This shows how the 61-key manuals on the console model Hammond organs related to those on the spinet organs, and to the pedal keyboards.

Except for very early models of the Hammond console organs, instead of frequencies 1 through 12 being used for the 16' stop for the lowest octave of the upper and lower manuals, those keys were wired for that stop to frequencies 13 through 24. This was done because the shape of the tonewheels for the lowest octave of the tone generator was changed so that they produced a signal that contained harmonics (thus, they were called the "complex tone wheels").

In the diagram, the top three keyboards illustrate the console model Hammond organs, and the bottom three keyboards illustrae the spinet model Hammond organs. The pedal keyboard for the spinet models is that of the M-100; on the Model M, M-2, and M-3, the topmost key, for the second C to complete the octave, was omitted.

The top two keyboards illustrate a typical console model; below them, the pedal keyboard of the concert model Hammond organs, which provided for an additional octave, is illustrated.

While the lower manual is shown as shifted down an octave relative to the upper manual in the diagram for the spinet organs, the two manuals were actually wired in almost the same way. The shifting was actually achieved by re-labelling the drawbars for the lower manual, as shown in the following table:

Upper   BR  BR  W   W   BK  W   BK  BK  W
Manual       1'          2'      3'  1'
        16' 5-  8'  4'  2-  2'  1-  1-  1'
             3           3       5   3
        |     \/    |     \   \   \ |
        |     /\    |      \   \   \|
Lower   W   W   BK  W   BK  BK  W   BK
Manual           2'      3'  1'
        8'  4'  2-  2'  1-  1-  1'  II
                 3       5   3

The 1 3/5' drawbar for the lower manual was achieved by wiring the tone generator to that manual with a novel displacement. The drawbar combining the 10th and 12th harmonics was not, of course, actually labelled "II", but it was equivalent in function to the drawbar with that label on the later model Hammond organs, since that drawbar on those organs controlled a combination of those same two harmonics.

Spinet organs had only one drawbar for the pedals, controlling their volume; the console organs had two drawbars for the pedals, each controlling a combination of harmonics. This is what made the complex tone wheels useful for the lowest octave, as by generating combined harmonics, they reduced the amount of wiring needed, given that the harmonics in question were to be combined in any event.

This is the circuit that combined the harmonics to produce the signals controlled by the two drawbars for the pedals:

The resistors shown in red were not present in earlier versions of the circuit; in the earliest, the 10 ohm resistor was also absent. The Model E had a much more complicated circuit for its two drawbars for the pedals; on the other hand, the model H-100, which had four drawbars for the pedals, still had a circuit of this general type:

Incidentally, the chorus tone generator was eliminated from the Hammond organ when the vibrato circuit was introduced. The vibrato unit came in a number of different forms; on the spinet organs, there were only two settings instead of three. The following is a common form of the circuit, the one found on the famed B-3 organ:

Note the switch at the bottom right. When that switch is open, so that the resistor is not shorted out, the delay line floats at the input voltage, so that the delayed signal, the selection of different forms of which by the rotary switch gives rise to the vibrato, becomes mixed with some of the undelayed signal. This is the simpler chorus effect attainable at a minimal cost that the later organs provided.

The switch scanned the contacts at a rate of 412 RPM, just under seven times a second. The earlier tremolo feature, which only affected amplitude, involved a scan rate of 360 RPM, six times a second.


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