Gear Ratio

The difference in the number of teeth between the DrivingGears and the DrivenGears is the gear ratio:

Note Driving Driven    Ratio
C       85    104   0.817307692
C#      71     82   0.865853659
D       67     73   0.917808219
D#     105    108   0.972222222
E      103    100   1.030000000
F       84     77   1.090909091
F#      74     64   1.156250000
G       98     80   1.225000000
G#      96     74   1.297297297
A       88     64   1.375000000
A#      67     46   1.456521739
B      108     70   1.542857143

Note that these ratios produce a very close *approximation* of the equal tempered scale. They are *NOT* exact. These ratios are used in each of the first seven octaves. The octave produced is dependant on the number of teeth on the ToneWheels. In 60Hz organs, the motor turns at 1200 RPM / 60Hz or 20 revolutions per second. The lowest octave has tonewheels with 2 teeth. The first 7 tones in the highest octave (C through F#) are produced by tonewheels with 192 teeth. For these 7 tones to be correct with only 192 teeth, they use the gear ratios for notes F through B.

The formula to calculate the exact frequency produced is:

(Motor RPM/60)*Teeth in Toneweel*(Teeth in Driving Gear/Teeth in Driven Gear)

So for the A above middle C on a 60 Hz organ:  (1200/60) * 16 * (88/64) = 440 Hz

This A tonewheel being 440 Hz actually influenced the establishment of the commonly accepted concert pitch standard as 440 Hz. Historically, concert A has wandered between 430-450 Hz. The famous Stroboconn tuner introduced in 1936 copied Hammond's use of an AC mains driven synchronous motor to spin an optical disk that also set the A above middle C at 440 Hz. Within a couple of years, Stroboconn tuners were being used globally to help tune concert orchestras. By 1939 enough orchestras had set their concert pitch to A = 440 Hz that the international concert pitch standard was established.

None of the twelve semitones on the Hammond are exactly equal tempered in their relationship to each other. The notes which are the farthest off pitch in the first seven octaves are the G#. They are .69 cents flat from the correct pitch. The top half octave is farther off pitch due to the number of teeth on the tonewheel not equaling 256. Using 192 teeth, generating the correct pitch from C7 to F#7 requires using the gear ratios for F through B. In the top half octave, the C# is the farthest off pitch, about 1.93 cents sharp:

For C#-4434:                   (1200/60) * 192 * (74/64) = 4440 Hz