Just made a short series of videos exploring some additive synthesis techniques with the fundamental modules.
Saw some users asing questions about the tuning and setting of harmonics that the hammond uses.
I actually don’t know much about the specific design of the hammond, but if it behaves according to the laws of acoustics … then it’s useful to think about (at least) two different aspects that combine make the instrumental characteristics:
A choir (of registers) will be in tune to some temperament. In the case of the fundamental modules this temperament happens to be 12TET.
Discrete registers are set or built according to the principle of the harmonic series. So, that means that when employing certain registers (duodecime, duotessaron, etc…) there will be some very slight deviation from equal tempered tuning.
Obviously the haromonics are just g(x)
where x is the partial number and g is the fundamental.
to calculate 12TET
**fn = f1 * pow(q, (n-1))**
| n | number of the wanted tone |
| fn | frequency of the wanted tone |
| f1 | frequency of the reference tone |
| q | 2 ^ ( 1 / 12 ) when the wanted tone is higher |
| q | ½ ^ (1 / 12 ) when the wanted tone is lower |
| n-1 | means the number of the wanted tone -1 |
You can see the deviations in the table below
a4 = 442Hz as a reference
a2 = 221Hz is the fundamental for the different registers
so g(1) = a2 = 221Hz
From what I just read it’s as close as they could accomodate with mechanical cogs that needed to have a whole number of teeth. When discussed further, it seems like it only makes one cent of difference if I read correctly. More the discussion is the even temperament - if input in to Cheby is even-tempered will the harmonics out be even tempered? I may be asking a completely dumb question.
Not a dumb question at all. And, no, the outputs of Chebyshev are not even tempered at all. Waveshapers (of which Chebyshev is one) can only generate perfect integer multiples of what you put into them. So the outputs are exactly 1x, 2x, 3x, 4x, 5x, etc… Some of those perfect harmonics are pretty far from even tempered.
okay, apologies - I haven’t investigated in detail the mechanics behind the hammond and how the tonwheel system is working, I also can’t ever remember actually playing a hammond. So, my almond organ is very much a design built to illustrate a number of things:
the divergence between just intonation and equal temperament systems
In the almond organ, each “register” is tuned in 12TET. The registers themselves are laid out according to the harmonic series. Therefor there is nothing particularly special about playing any individual register, other that the fact that it is equal tempered, note also that the midi info coming in on vcv rack is by default equal tempered, so this is actually hard to avoid without some digging around.
The subtleties emerge when you start to combine registers, because then you are blending equal tempered and just intoned intervals.