Re: Voce V3, H Vibrato Scanners (harmonic error discussion)

[dlkerl@cmack.b11.ingr.com (Dan Kerl)]

Re: tone generation harmonic error

As I understand it, the sound of the Hammond organ is primarly a product
of the fact that all 'harmonics' are in fact borrowed from the nearest
pitch available in the equally-tempered scale.  Since equal temperment
pitches are based on fractional powers of two (e.g., G would be 2^(7/12)
* (the frequency of the C below it)), it makes sense that all of the odd
'harmonics' (black drawbars) will be a little 'off'.  All pitches
available from the tonewheels (alternators) in the tone generator bank
are used as fundamentals somewhere on the keyboard, so they have to be
equally tempered.

For example, if A440 is selected as a fundamental, the correct third
harmonic would be three times this, or 1320 Hz. The nearest equal
temperment pitch to this is 440*2^(19/12) Hz, or 1318.51 Hz, which
constitutes a .113% error.  I've read that this is the reason that
no seventh harmonic drawbar exists, since the error would be large
enough to be objectionable. (let's see.. 440 * 7 = 3080 Hz, 
closest wheel below this: 440 * 2^(33/12) = 2960 Hz, a 3.9% flat error,
next wheel higher: 440 * 2^(34/12) = 3136 Hz, a 1.8% sharp error) Yep -
this looks large. 

I'm happy with this error, since it's what makes the Hammond organ sound
like it does - the sound of a unique instrument.  Any electronic
simulation would require similar behavior.

BTW, did anyone hear a segment on NPR a while back where Don Leslie was
interviewed (at least a year ago)?  As I recall, it had some interesting
anecdotes about the develoment of the Leslie speaker, as well as some
run-ins he had with Laurens Hammond.  If anyone has a copy of this
broadcast, I'd like to arrange a copy of my own.

                                        Dan Kerl
                                        dlkerl@ingr.com
                                        wheelhead third class.