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 an 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 A-440 on a 60Hz organ:  (1200/60) * 16 * (88/64) = 440Hz

The A notes are the only notes on the Hammond which agree exactly with the equal tempered scale. 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) = 4440Hz