The heart of the Leslie effect is a rotating horn loudspeaker. The rotating horn from a Model 600 Leslie can be seen mounted on a microphone stand in Fig.5.7. Two horns are apparent, but one is a dummy, serving mainly to cancel the centrifugal force of the other during rotation. The Model 44W horn is identical to that of the Model 600, and evidently standard across all Leslie models [190]. For a circularly rotating horn, the source position can be approximated as

where is the circular radius and is angular velocity. This expression ignores any

By Eq. (5.3), the source velocity for the circularly rotating horn is

Note that the source velocity vector is always orthogonal to the source position vector, as indicated in Fig.5.8.

Since and are orthogonal, the projected source velocity Eq. (5.4) simplifies to

Arbitrarily choosing (see Fig.5.8), and substituting Eq. (5.8) and Eq. (5.9) into Eq. (5.10) yields

In the far field, this reduces simply to

Substituting into the Doppler expression Eq. (5.2) with the listener velocity set to zero yields

where the approximation is valid for small Doppler shifts. Thus, in the far field, a rotating horn causes an approximately

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University