[HAM] The beauty of Tonewheels - an alternate view

[pj geerlings]

FWIW, here are the Hammond ratios according to the Scala Archive.

 C#   71.0/82.0   -2.03
 D     67.0/73.0   +0.66
 Eb   35.0/36.0   +0.71
 E     69.0/67.0   +0.66
 F    12.0/11.0    -1.63
 F#   37.0/32.0   +0.01
 G    49.0/40.0    +1.67
 G#   48.0/37.0  -1.63
 A    11.0/8.0     +0.66
 Bb   67.0/46.0   +0.71
 B    54.0/35.0   -0.04
 C    85.0/52.0   +0.25

The signed numbers to the right are the errors (in cents) from what the 
ratio "should" be - it is pretty darn close to 12 tone equal!

I did quite a lot of research before designing my Tonewheel synthesis 
engine. I did include the above tuning just for purists ;)

peace,
pj geerlings
nubi3.com

----- Original Message ----- 
From: "Drew Hoelscher" <dahoelscher at charter.net>
To: "The Hammond Forum" <hammond at zeni.net>
Sent: Friday, February 02, 2007 2:09 AM
Subject: Re: [HAM] The beauty of Tonewheels - an alternate view


> Good point.  It should also be said that the Hammond is not tuned like a
> piano (12edo - mean tuning, or as most of us prefer, a "stretch" tuning
> based on the mean tuning) (edo = equal division octave).  Hammonds are
> tuned to a rational intonation scheme - based on large integer ratios
> (mainly caused by the effect of using gears to set the speed of the tone
> wheels).  This also contributes to the unique sound.  (I hate to re-word
> what other posters have said, but one of pj's points is (by extension)
> that the sound of a Hammond is (or the complex sounds generated by a
> Hammond are) synthetic and not a natural harmonic series).
>
> Interestingly enuf, for those who think human beings can't be fooled by
> approximations of sound, the Hammond sounds like 12edo to our brains.
> So, as in gospel music, the piano, with its stretch tuning and the
> Hammond, with its RI tuning, sound in-tune with each other!
>
> -Drew
>
>
> pj geerlings wrote:
>> In the recent discussion about Tonewheels the focus seemed to be firmly 
>> on
>> waveform. I won't dispute that the waveform is not pure sinous and it is
>> probably not valuable here to weight the merits of individual differences
>> between extant units - this has already been covered.
>>
>> What I haven't noticed in the discussion is a recognition of the one 
>> thing
>> that is constant in the Hammond design. This is something I would call
>> "harmonic reinforcement".
>>
>> Everytime you play a chord on a tonewheel organ the harmonics that make 
>> up
>> each note are *always* in perfect alignment. This is because (for 
>> example)
>> the same tonewheel that is used to sound at the 5 1/3' pitch for the root 
>> of
>> the chord is also used to produce the fudimental of the fifth of the 
>> chord.
>> The net result is that are simply no harmonic pitches that would tend to
>> fight with each other.
>>
>> Yes, I know that the harmonic sequence is "off" and frankly, IMO, it is a
>> very small price to pay for *that* sound.
>>
>> peace to all,
>> pj geerlings
>> nubi3.com
>>
>>
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>>
>>
>>
>
>
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