[sdiy] Hammond Tuning /was: Re: Observations of synthesized

[Donald Tillman]

On Apr 10, 2010, at 5:25 AM, JH. wrote:

>
>> in order to make relatively static tonewheels sound better, hammond  
>> used slightly altered tunings that make more of the common
>> chords sound better -- like G >major for example -- at the expense  
>> of other less popular chords. these inter-harmonic relationships
>> have defined a whole genre of playing styles that was only  
>> >enhanced by the application of overdrive, vibrato and leslie  
>> speakers.
>
> That's interestig! I used to think the approximations were because  
> of technical reasons (forgot what I thought it was exactly) ...
> But you say it's like these old church organ tunings then?

Hmm, I'm finding it hard to believe.

The Hammond tonewheel tuning is determined by the ratio of the number  
of teeth between pairs of gears, and those teeth number between 46 and  
108.  The details can be found in the original patent.

The result is that the Hammond tonewheel pitches are all within a  
spread of 0.9 cents -- that's the peak-to-peak deviation from equal  
temperment.

(Compare that to the classic Top Octave Generator chips with a spread  
of 2.4 cents.  That's 35 years of progress for ya!   The reason is  
that the TOG is a single divisor while the Hammond is a ratio.)

But alternate tunings deviate from equal temperment by more than an  
order of magnitude than that.   For instance, a major third ratio is  
-13 cents off of equal temperment.  A minor third ratio is +16 cents.   
A dominant 7th ratio is -31 cents.

   -- Don

--
Don Tillman
Palo Alto, California
don at till.com
http://www.till.com