I have recently encountered something on the web that piqued my curiosity.

For a short time, some Hammond tonewheel organs utilized a second tone generator unit which produced slightly different frequencies than the main one, as a way of producing a chorus effect.

The service manual for Hammond organs does not give the details of the gear ratios used in this unit, but it does note the following:

Some notes are sharp, and others flat, by about the same amount;

For frequencies 56 to 67, the difference in frequency is 0.8%;

For frequencies 68 to 91, the difference in frequency is 0.4%.

Middle C is frequency 37, and the frequency numbers increase by one for each semitone higher in pitch a tone is.

The following diagram illustrates the frequency numbers, from 1 to 91, used in the service guides for the Hammond organ:

Also note that in this diagram, white keys change to yellow, black keys change to blue, and brown keys change to green, to indicate frequencies 10, 20, 30... up to 90.

Note that the additional drawbars of the later models of the Hammond tonewheel organ are also illustrated. As well, while the keyboards illustrating the connections of the frequencies for the original drawbars have the keys corresponding to frequencies above 91 shown in a different color, to indicate that foldback is taking place, since the later models with those two additional drawbars had tone generators which went up to frequency 96, foldback is indicated for those drawbars above that frequency instead.

Some of the higher frequencies were not generated by the tonewheels; just using frequencies that the tonewheels did generate an octave or two away, instead, is called "foldback". Some models of the Hammond organ also omitted frequencies 1 through 12, or just frequencies 1 through 9, from the tone generator, and thus there was foldback at the bottom of the range as well as the top. (This is oversimplified; in some cases, frequencies 1 through 12 were not omitted, but they were produced by "complex tonewheels", which produced a sound with harmonics already present, for use with the pedals only.)

The Hammond organ had stops from 16' to 1', and it had the normal 61-key organ keyboard; this, nominally, would require 61 frequencies, one for each note, plus an additional 48 frequencies: 12 frequencies to extend the range downwards by one octave, as the 16' stop would require, being one octave below the nominal pitches of the keys, considered to be those associated with the 8' stop, and 36 frequencies to extend the range upwards by three octaves, as the 1' stop requires.

Given what we know of the frequencies used for the regular frequency generator in a Hammond organ:

Equal Hammond C 261.63 261.54 85 104 277.18 277.07 71 82 D 293.66 293.70 67 73 311.13 311.11 105 108 E 329.63 329.60 103 100 F 349.23 349.09 84 77 369.99 370 74 64 G 392.00 392 98 80 415.30 415.14 96 74 A 440 440 88 64 466.16 466.09 67 46 B 493.88 493.71 108 70

is it possible to hazard a guess (of course, there are extant Model BC Hammond organs out there which could be examined, even if I hadn't initially been able to find the information on the web) as to how producing the chorus tones, 0.4% or 0.8% higher and lower, was done at a reasonable cost?

Only the highest seven frequencies produced by the tone generator of the Hammond organ, frequencies 85 to 91, were produced using 192-tooth tonewheels, so this doesn't account for the change from 0.8% to 0.4%, eliminating one possible way to achieve a difference in frequency offsets.

It is noted, as well, that while the gears moved at twelve different speeds in the main tone generator, they were on twenty-four driveshafts, not twelve, with pairs of driveshafts moving at the same speed. In the chorus generator, it is specifically noted that the driveshafts move at twenty-four different speeds. Each driveshaft has two gears on it, thus producing two frequencies.

Since twelve frequencies (from 56 to 67) are produced with the 0.8% offset, and twenty-four frequencies (from 68 to 91) are produced with the 0.4% offset, one possibility that might suggest itself is the change in offsets is produced by the driveshaft speeds. However, the twenty-four frequencies with 0.4% offsets were all produced by dual tonewheels, and each driveshaft had one dual tonewheel and one regular tonewheel for the other twelve frequencies on it.

One thing some accounts do not note is that the chorus generator produced two additional tones for each frequency. Of the 48 tonewheels it contained, twenty-four of them were "double" tonewheels, so that two frequencies were generated at once; the other twenty-four were normal single tonewheels, but were connected in pairs to produce the two additional tones for the frequencies with which they were used.

At this point, it seems reasonable to suspect that the double tonewheels were used to produce the twenty-four frequencies with an 0.4% offset, and that the single tonewheels in pairs were used to produce the twelve frequencies with an 0.8% offset; this has been confirmed by a photograph of the tone generator that I have seen.

This regular setup, though, doesn't leave room for seven tonewheels having 192 teeth, accompanied by five dummy tonewheels, for producing the highest seven frequencies.

As a first guess, let us suppose that the tonewheels in the chorus unit would nominally have 128, 64, and 32 teeth.

100.4% of 64 is 64.256, and 99.6% of 64 is 63.744. This shows us that the dual tonewheels would all have to have about 125 teeth; for example, 126 and 125 teeth or 125 and 124 teeth.

This site gives information from the Hammond patent, U. S. patent 2,159,505, for the chorus generator. Originally, when I looked at that site and the patent referenced, it seemed to me that the gear ratios in the patent don't seem to be applicable to the chorus tone generator in its production form as it seemed that the design was more elaborate, requiring more resources, than the one used in production. However, I have since realized that this was a mistaken impression. However, I thought that some of the gear ratios from the table there, those which drove wheels with 32 teeth, could have been used in the production unit if it has the design I have reconstructed.

So I started with the topmost seven notes as the basis, to which we apply 0.8% changes in either direction, and came up with some possible gear ratios that could have worked:

Equal Hammond + 0.8% Hammond - 0.8% G 392.00 392.31 85 104 395.6 75 91 389.33 73 90 415.30 415.61 71 82 419.15 62 71 412.5 55 64 A 440 440.55 67 73 444 74 80 436.85 81 89 466.16 466.67 105 108 470.59 50 51 462.86 81 84 B 493.88 494.40 103 100 498.23 82 79 490.32 95 93 C 523.25 523.64 84 77 528 77 70 519.53 92 85 554.37 555 74 64 559.12 106 91 550.4 86 75 A 587.33 588 98 80 592.5 79 64 583.38 79 65 622.25 622.71 96 74 627.69 102 78 617.14 9 7 B 659.26 660 88 64 665.14 97 70 654.55 15 11 F 698.46 699.13 67 46 704.68 69 47 693.33 52 36 739.99 740.57 108 70 746.67 70 45 734.69 75 49

However, it seems as though it is not necessary to rely on the hypothetical reconstruction above, or wait for someone with a physical example of the organ in question to examine it. As it happens, a later patent, U. S. patent 2,498,367 describes a chorus generator which seemed to me to correspond more closely to the descriptions of the actual one which went into production.

While it indicates that I was mistaken in thinking that the tonewheels had 48, 96, and 192 teeth, but instead they were in the neighborhood of 32, 64, and 128 teeth, there are still some complications that required further analysis before I came up with the hypothetical gearing for the chorus tone generator, derived from that patent, that is shown below; for one thing, it seems to still include information for the additional "theater" chorus generator referenced at the web site noted above; for another, instead of each driveshaft having one dual tonewheel and one simple tonewheel, as described in the service manual, twelve driveshafts have two dual tonewheels on them from the description in that patent.

At first I thought that possibly these gear ratios from that later patent were used in the production unit:

Equal Hammond Hammond + 0.8% - 0.8% G 392.00 392 98 80 394.77 33 107 388.6 415.30 415.14 96 74 418.46 34 104 411.92 A 440 440 88 64 443.08 36 104 436.15 466.16 466.09 67 46 469.73 40 109 462.39 B 493.88 493.71 108 70 497.78 42 108 490 C 523.25 523.08 85 104 527.72 47 114 519.47 554.37 554.15 71 82 558.55 48 110 549.82 D 587.33 587.4 67 73 591.7 49 106 582.45 622.25 622.22 105 108 627.2 49 100 617.4 E 659.26 659.2 103 100 665.1 53 102 654.71 F 698.46 698.18 84 77 704 55 100 693 739.99 740 74 64 746.67 63 108 735

The gear ratios in the column marked "Hammond + 0.8%" would have been used with two dual tonewheels on each driveshaft, one with 63 and 64 teeth, and the other with 126 and 128 teeth, to make the pair of tones, one 0.8% higher, and one 0.8% lower, than the normal tone. The - 0.8% column shows the frequency, moved down into the central octave, for the tone generated by 63 or 126 teeth.

This applies to the frequencies from 44 to 67.

The patent also shows another possible version of how the frequencies from 44 to 67 could be generated, using dual tonewheels. In that version, the frequency deviations are wider; this is the "theater" version of the chorus tone generator, rather than the "church" version, which was not put into production, its sound being found to be unacceptable.

Dual tonewheels are also shown in that patent as being used for the frequencies from 68 to 91. Wherever dual tonewheels are used, the octave is divided into two groups of six notes:

x y u v p q g h G 64 69 G 110 88 G 61 98 G 76 98 D 57 58 D 90 68 D 62 94 D 60 73 A 75 72 A 77 85 A 58 83 A 81 93 E 85 77 E 104 70 E 57 77 E 60 65 B F 90 77 B F 85 54 B F 69 88 B F 85 87 C 78 63 C 100 60 C 54 65 C 58 56

The notes in column x are reached from the following gear ratios with dual tonewheels with 84 and 85 teeth, and the notes in column y are reached from the following gear ratios with dual tonewheels with 119 and 120 teeth.

Similarly, the notes in column u are reached from the following gear ratios with dual tonewheels with 125 and 126 teeth, and the notes in column v are reached from the following gear ratios with dual tonewheels with 177 and 178 teeth.

For the theater version of the chorus unit only:

The notes in column p are reached from the following gear ratios with dual tonewheels with 31 and 32 teeth, and the notes in column q are reached from the following gear ratios with dual tonewheels with 44 and 45 teeth.

Similarly, the notes in column g are reached from the following gear ratios with dual tonewheels with 50 and 51 teeth, and the notes in column h are reached from the following gear ratios with dual tonewheels with 71 and 72 teeth.

The ranges of frequencies to which these apply can be seen by looking up the number of teeth in the tonewheels in the table below:

Church chorus Theater chorus Frequency Numbers Teeth on Frequency Teeth on Frequency Tonewheels Deviation Tonewheels Deviation 44 - 49 63, 64 +/- 0.8% 31, 32 +/- 1.6% 50 - 55 44, 45 +/- 1.0% 56 - 61 126, 128 +/- 0.8% 50, 51 +/- 1.0% 62 - 67 71, 72 +/- 0.6% Either version 68 - 73 84, 85 +/- 0.6% 74 - 79 119, 120 +/- 0.4% 80 - 85 125, 126 +/- 0.4% 86 - 91 177, 178 +/- 0.3%

which is somewhat similar, involving 24 driveshafts moving at different rates, each with two tonewheels on it, to the description of the production unit in the service manual. One important difference is that the production unit only provided the chorus effect for frequencies 56 to 91, not frequencies 44 to 91, so instead of all the tonewheels being dual tonewheels, the claim that half of them were single tonewheels must have been correct.

If the description in that patent corresponds to how frequencies 68 through 91 were actually generated in the production unit, could single tonewheels on those same driveshafts obtain deviations of +/- 0.8% for frequencies 56 to 67? That is the natural question that occurs here, but that would result in a unit in which the driveshafts rotated only at twelve distinct speeds, contradicting the description in the service manual.

But tonewheels with 43, 59, 31 and 45 teeth, for example, could perhaps serve in such a design.

So, could *this* be how the chorus unit worked:

x y u v -0.6% +0.6% +1.8% -0.4% +0.4% -1.2% -0.4% +0.4% -1.2% -0.3% +0.3% +1.5% 84 85 43 119 120 59 125 126 31 177 178 45 G 389.57 394.2 398.84 551.88 556.52 547.25 64 69 G 390.63 393.75 387.5 553.13 556.25 562.5 110 88 412.76 417.67 422.59 D 584.74 589.66 579.83 57 58 413.6 416.91 410.29 D 585.66 588.97 595.59 90 68 A 437.5 442.71 447.92 619.79 625 614.58 75 72 A 437.5 441 434 619.5 623 630 77 85 483.64 469.16 474.68 E 656.82 662.34 651.3 85 77 464.29 468 460.57 E 657.43 661.14 668.57 104 70 B 490.91 496.75 502.6 F 695.45 701.3 689.61 90 77 B 491.9 495.83 487.96 F 696.53 700.46 708.33 85 54 C 520 526.19 532.38 736.67 742.86 730.48 78 63 C 520.83 525 516.67 737.5 741.67 750 100 60 68-73 56-61 74-79 62-67 80-85 56-61 86-91 62-67 (/4) (/2) (/4) (/2) (/8) (/2) (/8) (/2)

Again, the frequencies are normalized, all being put in the same octave to facilitate direct comparison. The applicable frequency numbers, and the factor by which they are divided to carry out this normalization, are shown in the bottom two rows of the table above.

On further reflection, taking a look at the earlier patent again, it seems that I may have dismissed it too hastily, and it could be that it, rather than the later patent, does contain the gearing used in the chorus generator for the production units.

Equal Hammond Hammond + 0.4% -0.4% +0.4% Hammond - 0.4% -0.4% +0.4% 32 127 128 63 126 127 (Teeth on tonewheel) DG DN DG DN DG DN G 392.00 392.31 85 104 393.52 91 74 390.44 393.52 390.33 57 92 390.33 393.42 415.30 415.61 71 82 416.84 99 76 413.59 416.84 413.64 65 99 413.64 416.92 A 440 440.55 67 73 441.38 80 58 437.93 441.38 438.26 48 69 438.26 441.74 466.16 466.67 105 108 468.15 79 54 464.49 468.15 464.21 70 95 464.21 467.89 B 493.88 494.40 103 100 495.77 110 71 491.90 495.77 491.92 57 73 491.92 495.82 C 523.25 523.64 84 77 525.37 110 67 521.27 525.37 521.11 67 81 521.11 525.25 554.37 555 74 64 556.52 120 69 552.17 556.52 552.13 78 89 552.13 556.52 A 587.33 588 98 80 589.47 105 57 584.87 589.47 585 65 70 585 589.64 622.25 622.71 96 74 624.52 121 62 619.64 624.52 619.67 60 61 619.67 624.59 B 659.26 660 88 64 662.07 120 58 656.9 662.07 656.62 74 71 656.62 661.83 F 698.46 699.13 67 46 701.28 103 47 695.8 701.28 695.45 85 77 695.45 700.97 739.99 740.57 108 70 742.86 130 56 737.05 742.86 736.98 62 53 736.98 742.83 56-67 80-91 56-67 68-79 (Frequencies covered) (/2) (/8) (/2) (/4)

This does call for one octave to be generated with two simple tonewheels for each note, and two octaves to be generated with one compound tonewheel for each note. But working out two sets of slightly discrepant gear ratios, so as to generate the two octaves with simple tonewheels in different ways, although it could be beneficial by adding to the realism of the sound, still seems excessive.

However, the two blank columns in the diagram, blank because they would be redundant, illustrate one problem with the design in that patent: since 126 is equal to 63 times two, and 128 is equal to 32 times four, some of the "+0.4%" or "-0.4%" frequencies would be the same, except for being in a different octave, as the "+0.8%" and "-0.8%" frequencies.

If the "-0.4%" frequency is really a "+0.4%" frequency, though, then a +0.8% frequency
would still complete the set of three frequencies at 0.4% spacing, and, similarly, if the
"+0.4%" frequency is really a "-0.4%" frequency, then a -0.8% frequency would complete
the set. *That* was a trick, though, at which the service manual did not hint.

That *would*, though, explain the accounts that imply that the chorus unit
provided only one additional frequency, either above or below the ordinary note, but not
both, as that would contain some truth and would be an understandable result of the
confusion such an arrangement could be expected to create.

However, we can see from the table that this is not what was done; the various frequencies are either above or below the primary frequency as nominally intended. Instead, it seems that the "0.4%" deviations and the "0.8%" deviations do not differ in size, at least in this design.

Furthermore, actual photographs of gears from the chorus tone generator, made available on this web site, seem to force one to the conclusion that a gearing arrangement of this type was used, and the additional measures described below to have the unit correspond to its description, and use a +/- 0.8% deviation for the lowest of the three octaves covered could not have been taken.

In any event, here is a schematic diagram of how the gears, the tonewheels, and the magnetic pickups are laid out in the tone generator and the chorus tone generator, with the number of teeth on the gears and tonewheels, including their hypothetical values for the chorus tone generator (the location of the pickups for the different frequencies is attested to from the service manual):

Tone Generator Hypothetical Chorus Tone Generator --------------------------------------------- ------------------------------ | ______|______ | | ______|______ | | | | ______|______ | 61--|--->(______64_____) | | (_______2_____)<---|-- 1 | | | (___126/127___)<---|-- 68 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [___104___][____85___][___104___] | | [____57___][____92___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 13--|--->(_______4_____) | | (______32_____)<---|-- 49 | | | (______63_____)<---|-- 56 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | | (_____________) | | (_______8_____)<---|-- 25 | | | (______32_____)<---|-- 56 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [___104___][____85___][___104___] | | [____91___][____74___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 37--|--->(______16_____) | | (_____128_____)<---|-- 73 | | | (___127/128___)<---|-- 80 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 68--|--->(______64_____) | | (_______2_____)<---|-- 8 | | | (___126/127___)<---|-- 75 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____80___][____98___][____80___] | | [____65___][____70___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 20--|--->(_______4_____) | | (______32_____)<---|-- 56 | | | (______63_____)<---|-- 63 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 87--|--->(_____192_____) | | (_______8_____)<---|-- 32 | | | (______32_____)<---|-- 63 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____80___][____98___][____80___] | | [___105___][____57___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 44--|--->(______16_____) | | (_____128_____)<---|-- 80 | | | (___127/128___)<---|-- 87 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 63--|--->(______64_____) | | (_______2_____)<---|-- 3 | | | (___126/127___)<---|-- 70 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____73___][____67___][____73___] | | [____48___][____69___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 15--|--->(_______4_____) | | (______32_____)<---|-- 51 | | | (______63_____)<---|-- 58 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | | (_____________) | | (_______8_____)<---|-- 27 | | | (______32_____)<---|-- 58 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____73___][____67___][____73___] | | [____80___][____58___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 39--|--->(______16_____) | | (_____128_____)<---|-- 75 | | | (___127/128___)<---|-- 82 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 70--|--->(______64_____) | | (_______2_____)<---|-- 10 | | | (___126/127___)<---|-- 77 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____64___][____88___][____64___] | | [____74___][____71___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 22--|--->(_______4_____) | | (______32_____)<---|-- 58 | | | (______63_____)<---|-- 65 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 89--|--->(_____192_____) | | (_______8_____)<---|-- 34 | | | (______32_____)<---|-- 65 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____64___][____88___][____64___] | | [___120___][____58___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 46--|--->(______16_____) | | (_____128_____)<---|-- 82 | | | (___127/128___)<---|-- 89 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 65--|--->(______64_____) | | (_______2_____)<---|-- 5 | | | (___126/127___)<---|-- 72 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [___100___][___103___][___100___] | | [____57___][____73___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 17--|--->(_______4_____) | | (______32_____)<---|-- 53 | | | (______63_____)<---|-- 60 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | | (_____________) | | (_______8_____)<---|-- 29 | | | (______32_____)<---|-- 60 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [___100___][___103___][___100___] | | [___110___][____71___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 41--|--->(______16_____) | | (_____128_____)<---|-- 77 | | | (___127/128___)<---|-- 84 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 72--|--->(______64_____) | | (_______2_____)<---|-- 12 | | | (___126/127___)<---|-- 79 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____70___][___108___][____70___] | | [____62___][____53___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 24--|--->(_______4_____) | | (______32_____)<---|-- 60 | | | (______63_____)<---|-- 67 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 91--|--->(_____192_____) | | (_______8_____)<---|-- 36 | | | (______32_____)<---|-- 67 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____70___][___108___][____70___] | | [___130___][____56___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 48--|--->(______16_____) | | (_____128_____)<---|-- 84 | | | (___127/128___)<---|-- 91 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 67--|--->(______64_____) | | (_______2_____)<---|-- 7 | | | (___126/127___)<---|-- 74 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____64___][____74___][____64___] | | [____78___][____89___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 19--|--->(_______4_____) | | (______32_____)<---|-- 55 | | | (______63_____)<---|-- 62 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 86--|--->(_____192_____) | | (_______8_____)<---|-- 31 | | | (______32_____)<---|-- 62 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____64___][____74___][____64___] | | [___120___][____69___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 43--|--->(______16_____) | | (_____128_____)<---|-- 79 | | | (___127/128___)<---|-- 86 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 62--|--->(______64_____) | | (_______2_____)<---|-- 2 | | | (___126/127___)<---|-- 69 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____82___][____71___][____82___] | | [____65___][____99___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 14--|--->(_______4_____) | | (______32_____)<---|-- 50 | | | (______63_____)<---|-- 57 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | | (_____________) | | (_______8_____)<---|-- 26 | | | (______32_____)<---|-- 57 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____82___][____71___][____82___] | | [____99___][____76___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 38--|--->(______16_____) | | (_____128_____)<---|-- 74 | | | (___127/128___)<---|-- 81 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 69--|--->(______64_____) | | (_______2_____)<---|-- 9 | | | (___126/127___)<---|-- 76 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____74___][____96___][____74___] | | [____60___][____61___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 21--|--->(_______4_____) | | (______32_____)<---|-- 57 | | | (______63_____)<---|-- 64 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 88--|--->(_____192_____) | | (_______8_____)<---|-- 33 | | | (______32_____)<---|-- 64 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____74___][____96___][____74___] | | [___121___][____62___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 45--|--->(______16_____) | | (_____128_____)<---|-- 81 | | | (___127/128___)<---|-- 88 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 64--|--->(______64_____) | | (_______2_____)<---|-- 4 | | | (___126/127___)<---|-- 71 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [___108___][___105___][___108___] | | [____70___][____95___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 16--|--->(_______4_____) | | (______32_____)<---|-- 52 | | | (______63_____)<---|-- 59 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | | (_____________) | | (_______8_____)<---|-- 28 | | | (______32_____)<---|-- 59 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [___108___][___105___][___108___] | | [____79___][____54___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 40--|--->(______16_____) | | (_____128_____)<---|-- 76 | | | (___127/128___)<---|-- 83 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 71--|--->(______64_____) | | (_______2_____)<---|-- 11 | | | (___126/127___)<---|-- 78 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____46___][____67___][____46___] | | [____85___][____77___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 23--|--->(_______4_____) | | (______32_____)<---|-- 59 | | | (______63_____)<---|-- 66 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 90--|--->(_____192_____) | | (_______8_____)<---|-- 35 | | | (______32_____)<---|-- 66 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____46___][____67___][____46___] | | [___103___][____47___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 47--|--->(______16_____) | | (_____128_____)<---|-- 83 | | | (___127/128___)<---|-- 90 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 66--|--->(______64_____) | | (_______2_____)<---|-- 6 | | | (___126/127___)<---|-- 73 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____77___][____84___][____77___] | | [____67___][____81___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 18--|--->(_______4_____) | | (______32_____)<---|-- 54 | | | (______63_____)<---|-- 61 | | | | | | | | | | | |---------------------------------------------| |------------------------------| | ______|______ | | ______|______ | | | | ______|______ | 85--|--->(_____192_____) | | (_______8_____)<---|-- 30 | | | (______32_____)<---|-- 61 | ___|_|___ ___|_|___ ___|_|___ | | ___|_|___ ___|_|___ | | [____77___][____84___][____77___] | | [___110___][____67___] | | _____|_|_____ | | _____|_|_____ | | | | _____|_|_____ | 42--|--->(______16_____) | | (_____128_____)<---|-- 78 | | | (___127/128___)<---|-- 85 | | | | | | | | | | | --------------------------------------------- ------------------------------

Thus, in the box at the upper left corner of the diagram, for example, we see an 85-tooth brass gear on the driveshaft driving two 104-tooth Bakelite gears, which cause four tonewheels to rotate with 64, 2, 4, and 32 teeth; these tonewheels produce the signals for frequencies number 61, 1, 13, and 49 respectively.

Given that 126 and 127, and 127 and 128, differ by about 0.8%, which, given appropriate gear ratios, is suitable for producing -0.4% and +0.4% frequency deviations, how could this design be modified so as to provide the larger deviation for the lowest octave that was specified?

While the schemes below involve techniques that I now know not to have been used on the actual chorus tone generator, I will note that one last possibility for a wider frequency deviation for the bottom octave covered does remain. If the chorus tone generator provided additional tones of -0.6% and +0.2% for one of the upper octaves (frequencies 68 through 79 in the diagram above, since there a 63-tooth tonewheel corresponds to the 126-tooth lower track on the dual tonewheel), and -0.2% and +0.6% for the other, then the lower octave could have chorus tones of -0.6% and +0.6%.

In effect, one would like to replace the tonewheel with 32 teeth by one with 32 1/8 teeth, and the tonewheel with 63 teeth by one with 62 3/4 teeth.

Well, one could follow the technique used for the frequencies from 85 to 91 in the regular tone generator, and replace the tonewheel with 63 teeth by five tonewheels with 94 teeth, and seven tonewheels with 47 teeth. That would allow a close approximation to the -0.8% deviation.

The same trick, though, doesn't work for the +0.8% deviation. However, if one switches around which driveshafts are used for +0.8% and -0.8%, perhaps we would have better luck.

In that case, we would want to replace the tonewheels with 32 teeth by ones with 31 5/8 teeth, but that leads to a requirement for seven tonewheels with about 47 1/2 teeth; that doesn't work, even if five tonewheels with 95 teeth would be achievable. For the other bank, we would be replacing the tonewheels with 63 teeth with ones with, ideally, 63 3/4 teeth; the perfect fifth trick gives us a requirement for tonewheels with 95.625 teeth, to which 96 teeth is not quite a good enough approximation.

But the same principle could be applied with other choices of ratio. Thus, we could use the tritone instead of the perfect fifth, for example, and use six tonewheels of one type, and half a dozen with twice as many teeth.

Then, if we don't switch driveshafts, we do get a very good approximation. Replace the twelve tonewheels with 32 teeth by three tonewheels with 54 teeth, thus generating the highest three notes of the octave (from G to F#) on the driveshafts for the lowest three notes, and nine tonewheels with 27 teeth, and replace the twelve tonewheels with 63 teeth by five tonewheels with 94 teeth and seven tonewheels with 47 teeth, as that possibility, derived before, can't be improved upon.

With that technique, we finally do obtain a possible setup for the production unit that would produce the desired frequencies:

Equal Hammond Hammond + 0.8% -0.4% +0.4% Hammond - 0.8% -0.4% +0.4% 54/27 127 128 94/47 126 127 (Teeth on tonewheel) DG DN DG DN DG DN G 392.00 392 98 80 664.05 91 74 390.44 393.52 D 582.39 57 92 390.33 393.42 415.30 415.14 96 74 A 703.42 99 76 413.59 416.84 617.17 65 99 413.64 416.92 A 440 440 88 64744.8380 58 437.93 441.38 E 653.91 48 69 438.26 441.74 466.16 466.09 67 46 B 395 79 54 464.49 468.15 F 692.63 70 95 464.21 467.89 B 493.88 493.71 108 70 C 418.31 110 71 491.90 495.77733.9757 73 491.92 495.82 C 523.25 523.08 85 104 443.28 110 67 521.27 525.37 G 388.77 67 81 521.11 525.25 554.37 554.15 71 82 D 469.57 120 69 552.17 556.52 411.91 78 89 552.13 556.52 D 587.33 587.4 67 73 497.37 105 57 584.87 589.47 A 436.43 65 70 585 589.64 622.25 622.22 105 108 E 526.94 121 62 619.64 624.52 462.3 60 61 619.67 624.59 E 659.26 659.2 103 100 F 558.62 120 58 656.9 662.07 B 489.86 74 71 656.62 661.83 F 698.46 698.18 84 77 591.7 103 47 695.8 701.28 C 518.83 85 77 695.45 700.97 739.99 740 74 64 G 626.79 130 56 737.05 742.86 549.81 62 53 736.98 742.83 56-67 80-91 56-67 68-79 (Frequencies covered) (/2) (/8) (/2) (/4)

As it happens, though, there is one additional source of information that I had not plumbed.

The service manual for the models of organ in question, while it did not include the gear ratios, would still provide a clue as to whether such a technique as this was employed from the wiring diagram indicating how the chorus tone generator was connected.

And, by appearances, this technique was not the one used.

So, how could the chorus tone generator have been constructed to use a straightforward wiring pattern?

If a dual tonewheel with 127 and 128 teeth has frequencies which are about -0.4% and +0.4% from the standard frequency of each given note, then the gearing would be set up to produce that frequency for a tonewheel with 127 1/2 teeth. And 126 1/2 teeth would be -0.8%, and 128 1/2 teeth would be +0.8%. Exactly the same problem exists with a dual tonewheel with 126 and 127 teeth.

This would continue to be true if the tonewheels had 124 and 125 teeth or 125 and 126 teeth, for a more exact approach to an 0.8% difference between the two chorus tones.

The situation is not *entirely* hopeless. If we reverse the use of the 126 and 127 tooth
double tonewheels and the 127 and 128 tooth double tonewheels from that given in the earlier patent,
using the 126 and 127 tooth tonewheels for frequencies 80 to 91, and the 127 and 128 tooth tonewheels
for frequencies 68 to 79, then using a 32 tooth tonewheel with the 126 and 127 tooth tonewheels
produces a tone with a +1.2% frequency, and using a 63 tooth tonewheel with the 127 and 128 tooth
tonewheels produces a tone with a -1.2% frequency. So, having a wider frequency deviation in
the lowest octave is achievable, even though that deviation is not the one specified. (Note that
the reversal is required because 126 is not divisible by 4.)

Equal Hammond Hammond + 1.2% -0.4% +0.4% Hammond - 1.2% -0.4% +0.4% 32 126 127 63 127 128 (Teeth on tonewheel) DG DN DG DN DG DN G 392.00 392 98 80 396.52 57 92 390.33 393.42 387.36 91 74 390.44 393.52 415.30 415.14 96 74 420.2 65 99 413.64 416.92 410.33 99 76 413.59 416.84 A 440 440 88 64 445.22 48 69 438.26 441.74 434.48 80 58 437.93 441.38 466.16 466.09 67 46 471.58 70 95 464.21 467.89 460.83 79 54 464.49 468.15 B 493.88 493.71 108 70 499.73 57 73 491.92 495.82 488.03 110 71 491.90 495.77 C 523.25 523.08 85 104 529.38 67 81 521.11 525.25 517.16 110 67 521.27 525.37 554.37 554.15 71 82 560.9 78 89 552.13 556.52 547.83 120 69 552.17 556.52 D 587.33 587.4 67 73 594.29 65 70 585 589.64 580.26 105 57 584.87 589.47 622.25 622.22 105 108 629.51 60 61 619.67 624.59 614.76 121 62 619.64 624.52 E 659.26 659.2 103 100 667.04 74 71 656.62 661.83 651.72 120 58 656.9 662.07 F 698.46 698.18 84 77 706.49 85 77 695.45 700.97 690.32 103 47 695.8 701.28 739.99 740 74 64 748.68 62 53 736.98 742.83 731.25 130 56 737.05 742.86 56-67 80-91 56-67 68-79 (Frequencies covered) (/2) (/8) (/2) (/4)

So, if we instead set up the gear ratios for dual tonewheels of 177 and 178 teeth, accompanied by a single tonewheel of 44 teeth, we could get +0.3%, -0.3%, and -0.9%; although the larger deviation is now three times the smaller deviation, the nominal values of 0.4% and 0.8% are at least approximated.

The lower octave (of those handled by dual tonewheels, frequencies 68 through 79) would then be handled, for example, by dual tonewheels of 176 and 177 teeth, accompanied by a single tonewheel of 89 teeth.

From the later patent, we at least have six of the twenty-four gear ratios required, and, in fact, if we use 178 and 179 teeth instead on the other set of dual tonewheels, we can obtain six more gear ratios from those used with dual tonewheels with 44 and 45 teeth in that patent for a larger deviation; in that case, the accompanying single tonewheel has 90 teeth.

Equal Hammond Hammond - 0.9% -0.3% +0.3% Hammond + 0.9% -0.3% +0.3% 44 177 178 90 178 179 (Teeth on tonewheel) DG DN DG DN DG DN G 392.00 392 98 80 388.67 53 60 390.88 393.08 395.33 47 107 390.93 393.13 415.30 415.14 96 74 411.79 73 78 414.13 416.47 418.81 47 101 414.16 416.48 A 440 440 88 64 436.27 117 118 438.75 441.23 443.66 35 71 438.73 441.2 466.16 466.09 67 46 462.22 104 99 464.85 467.47 470.15 35 67 464.93 467.54 B 493.88 493.71 108 70 489.68 69 62 492.46 495.24 497.87 26 47 492.34 495.11 C 523.25 523.08 85 104 518.81 79 67 521.75 524.70 527.59 17 29 521.72 524.66 554.37 554.15 71 82 550 110 88 553.13 556.25 560.2 61 98 553.98 557.09 D 587.33 587.4 67 73 582.35 90 68 585.66 588.97 593.62 62 94 587.02 590.32 622.25 622.22 105 108 616 119 85 619.5 623 628.92 58 83 621.93 625.42 E 659.26 659.2 103 100 653.71 104 70 657.43 661.14 666.23 57 77 658.83 662.53 F 698.46 698.18 84 77 692.59 85 54 696.53 700.46 705.68 69 88 697.84 701.76 739.99 740 74 64 733.33 100 60 737.5 741.67 747.69 54 65 739.38 743.54 56-67 80-91 56-67 68-79 (Frequencies covered) (/2) (/8) (/2) (/4)

This, I suspect, at least takes us closer to the gear ratios in the production unit, although there are many other possibilities for those in the portion of the octave from G through C, for which that later patent could not be used as a source.

However, the later patent shows us a way to achieve +0.8% and -0.8% using dual tonewheels on twelve driveshafts for frequencies 44 through 67, in addition to the earlier patent showing us how to achieve +0.4% and -0.4% on frequencies 68 through 81 with dual tonewheels. Since the description of the production unit has it producing frequencies 56 through 67 with +0.8% and -0.8%, and frequencies 68 through 81 with dual tonewheels, with those deviations, why not just combine what the two patents provide?

The difficulty is that three sets of gear ratios would be required in that case, one applying to ome set of twelve dual tonewheels, instead of two sets of simple tonewheels, for frequencies 44 to 67, and one applying to each of two sets of twelve dual tonewheels. Both descriptions of the production unit, and the wiring diagram, show clearly that it contains twenty-four driveshafts, each with one simple tonewheel and one dual tonewheel. Thus, the simple tonewheels and the dual tonewheels must be compatible and share the same set of gear ratios.

Basically, it seems as if I have proven it impossible to construct the chorus tone generator as it was specified. However, one last possibility does remain. While 192-tooth tonewheels were used in the original Hammond organ with 91 frequencies, because making tonewheels with 256 teeth was not possible initially, eventually the Hammond organ went to 96 frequencies.

Given that the main tone generator did not come in two pieces, and all the driving gears were on one axle, unlike the situation outlined in the original patent where the driving gears turned at half speed for the second half of the range, this means that the production of 256-tooth tonewheels was eventually mastered.

One way to achieve this would simply have been to make the chorus tone generator physically somewhat larger than the normal tone generator, so that the tonewheels could be larger. Then a 256-tooth tonewheel could have teeth the same size as the teeth on the 192-tooth tonewheels of the regular tone generator.

So, for example, the dual tonewheels could all have 253 and 255 teeth, rotating at a speed such that one with 254 or 127 teeth would produce a note exactly on the equal-tempered scale. One set of single tonewheels would have 64 teeth, producing the +0.8% signal, and another set of single tonewheels would have 126 teeth, producing the -0.8% signal.

If the pattern of the designs we've seen in the patents was followed, the design would have been slightly more complicated, with the tonewheels rotating at 24 different speeds. The chorus tones for frequencies from 80 to 91 could perhaps have been generated by dual tonewheels with 253 and 255 teeth, which would be accompanied by simple tonewheels with 64 teeth to generate the signal at a +0.8% deviation for frequencies 56 to 67. The chorus tones for frequencies from 68 to 79 could then have been generated by dual tonewheels with 251 and 253 teeth, which would be accompanied by simple tonewheels with 125 teeth to generate a signal at a -0.8% deviation for frequencies from 56 to 67.

However, if we let all the dual tonewheels have the same number of teeth, it would not be necessary to use any gear ratios that we have not already seen from actual patents. And so we get this design for the chorus tone generator, which, I had thought until recently, just possibly, could have been the actual one used:

Equal Hammond Hammond + 0.8% -0.4% +0.4% Hammond - 0.8% -0.4% +0.4% 64 253 255 126 253 255 (Teeth on tonewheel) DG DN DG DN DG DN G 392.00 392 98 80 394.75 66 107 390.14 393.22 388.6 33 107 390.14 393.22 415.30 415.14 96 74 418.46 34 52 413.56 416.83 411.92 34 104 413.56 416.83 A 440 440 88 64 443.08 36 52 437.88 441.35 436.15 36 104 437.88 441.35 466.16 466.09 67 46 469.72 80 109 464.22 467.89 462.39 40 109 464.22 467.89 B 493.88 493.71 108 70 497.78 42 54 491.94 495.83 490 42 108 491.94 495.83 C 523.25 523.08 85 104 527.72 47 57 521.54 525.66 519.47 47 114 521.54 525.66 554.37 554.15 71 82 558.55 48 55 552 556.36 549.82 48 110 552 556.36 D 587.33 587.4 67 73 591.7 49 53 584.76 589.39 582.45 49 106 584.76 589.39 622.25 622.22 105 108 627.2 49 50 619.85 624.75 617.4 49 100 619.85 624.75 E 659.26 659.2 103 100 665.1 53 51 657.3 662.5 654.71 53 102 657.3 662.5 F 698.46 698.18 84 77 704 55 50 695.75 701.25 693 55 100 695.75 701.25 739.99 740 74 64 746.67 63 54 737.92 743.75 735 63 108 737.92 743.75 56-67 80-91 56-67 68-79 (Frequencies covered) (/2) (/8) (/2) (/4)

And, as it turns out, the twenty-four pairs of tonewheels do turn at twenty-four different speeds, because twelve turn twice as fast as the ones corresponding to them in the previous octave (of dual tonewheel notes), this being achieved by changing the gear ratios following the lead of the original Hammond patent rather than splitting the main driveshaft in two.

Of course, though, changing the gear ratios in that fashion might have made it possible to avoid the need to make 256-tooth tonewheels to achieve a 96-frequency tone generator as well, so the conclusion that the 96-frequency tone generator proves that the 256-tooth tonewheel was achieved becomes flawed...

Since I have learned that there was only one tooth difference between the two tonewheels on the real tone generator, is there any way that going up to 256-tooth tonewheels could have helped achieve the specified frequency deviations?

As it turns out, one possibility exists. Instead of 253 and 255 teeth, 255 and 256 teeth would produce +0.4% and +0.8%, and instead of 253 and 255 teeth, 252 and 253 teeth would produce -0.8% and -0.4%. This would lead to the right separation between the three tones in every octave, even though now the center tones of the two upper octaves would be shifted.

However, this trick, too, was not actually used, since the photographs I have seen of an actual chorus tone generator clearly show that the number of teeth on the dual tonewheels is four times and two times that of the associated single tonewheel, not eight times and four times, so they are instead in the range of 128 teeth or so.

Also, note that A above middle C is frequency 46. Up until now, I have been neglecting octaves when carrying out my calculations.

So it is a 16-tooth tonewheel, connected to a 64-tooth gear driven by an 88-tooth gear, which produces a 440 Hz tone. Hence, the driveshaft of the tone generator is rotating 20 times each second, or at a speed of 1200 RPM.

The +0.8% tone for frequency 66 is exactly 704 Hz, and it is produced by a 64-tooth tonewheel connected to a 50-tooth gear driven by a 55-tooth gear. Thus, the driveshaft in the chorus tone generator as depicted here is rotating 10 times each second, or at a speed of 600 RPM. The gear ratios as given, therefore, might need to be adjusted so that the driveshaft would instead rotate at the same 1200 RPM as that of the main tone generator.

Given the way that the tonewheels are distributed, replacing the 192-tooth and blank tonewheels with 128-tooth tonewheels instead of 256-tooth tonewheels to produce 96 frequencies, if the design were not otherwise modified, would result in the 8, 16, and 128-tooth tonewheels becoming 4, 8, and 64-tooth tonewheels respectively, while the 2, 4, 32, and 64-tooth tonewheels remained as they were; so it would not be as simple as dividing the number of teeth in the tonewheels for the upper half of the instrument's range in two.

However, since this was written, I have encountered a web site (a site in tribute to the organist Ken Griffin) with some pictures of the chorus tone generator, and it noted that the dual tonewheels have a one-tooth difference between their two parts. So the solution shown above is not possible either. Examining the pictures shows, too, that the relation between the single tonewheel and the dual tonewheel is either a factor of two or a factor of four, and so my solution with modified wiring is definitely not the case either.