On Fri, 28 Mar 2014, Hlöðver Sigurðsson wrote:
> You could try using Audacity to plot spectrograph of organ tone. There you
> have the dB values and formant peaks. 

I spent some time doing that a few months ago and found it quite
educational.  There are clean samples of many different stops available
from the Encyclopedia of Organ Stops at http://www.organstops.org/ .

It matters what kind of pipe you're simulating.  Flue pipes have much less
harmonic content than reed pipes, and then there are hundreds of more
specific classes of pipes. For a very simple open diapason sound (classic
middle-of-the-road organ pipe) it suffices to just use fixed ratios of
fundamental and the first few harmonics.  You could probably even get away
with just using a pure sine wave for each pipe!  I was going a bit fancier
(before I got interested in other things and shelved the project) and
extracted the following four tables by measuring a selection of samples
from the Encyclopedia.  My code interpolates between them depending on the
note being played (a for low, b in the middle, c for high), but I doubt
that's really necessary.

gitfluea ftgen 100,0,4096,10, \
   ampdb(0),ampdb(-9.5),ampdb(-18),ampdb(-22),ampdb(-36),ampdb(-33), \
   ampdb(-43),ampdb(-44),ampdb(-46),ampdb(-57)
gitflueb ftgen 101,0,4096,10, \
   ampdb(0),ampdb(-16),ampdb(-29),ampdb(-32),ampdb(-25),ampdb(-35), \
   ampdb(-36),ampdb(-43),ampdb(-49),ampdb(-57),ampdb(-60),ampdb(-57)
gitfluec ftgen 102,0,4096,10, \
   ampdb(0),ampdb(-15),ampdb(-20),ampdb(-33),ampdb(-25),ampdb(-45),\
   ampdb(-54)

Playing any of those with a simple wavetable oscillator sounds like one
pipe alone, but people don't play organs that way.  Normally, you'd use
several oscillators corresponding to different stops:  two or three near
the written frequency of your note, detuned a few Hertz from each other,
and then more at octaves above or below.  The characteristic sound of an
organ comes more from the interaction of multiple ranks of pipes at close
but not exact unison, and from tremolo, than from the spectra of single
pipes.  I included more harmonics in my tables than are probably needed,
but with wavetable oscillators that costs nothing.

Hammond tonewheel organs don't sound the same as pipe organs, but it's
worth looking at their spectra.  The Hammond draw bars correspond directly
to harmonics, and the output of the organ (*before* you start modulating
it with a rotary speaker cabinet...) is pretty close to a pure sine wave
for each drawbar.  Registration "88 8000 000" equates to three sine waves
of roughly equal amplitude at the first, second, and third harmonics of a
note one octave below the score (i.e. 0.5, 1.0, and 1.5 times the written
pitch).  And if you just play three equal sine waves at those frequencies,
especially with moderate amplitude and frequency modulation (both
modulated by sine waves at the same low frequency, preferably the two
modulating sine waves 90 degrees apart in phase... this is a first-order
approximation of what a Leslie does) the result sounds recognizably like
a rock'n'roll tonewheel organ, even if it's not good enough to satisfy a
purist fanatic.

> The Hammond draw bars correspond directly to harmonics...

Slightly off-topic, but IIRC, this is incorrect. A Hammond has only 96
tonewheels. The drawbars correspond to the nearest equal-tempered
equivalents of the harmonics, because they use existing tonewheels. They
will only be perfect harmonics with the octave drawbars.



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And I guess the tone wheels are not producing pure sinusoids either, I would expect. 
========================
Dr Victor Lazzarini
Senior Lecturer
NUI Maynooth, Ireland
victor dot lazzarini at nuim dot ie




On 28 Mar 2014, at 16:07, Jim Aikin  wrote:

>> The Hammond draw bars correspond directly to harmonics...
> 
> Slightly off-topic, but IIRC, this is incorrect. A Hammond has only 96
> tonewheels. The drawbars correspond to the nearest equal-tempered
> equivalents of the harmonics, because they use existing tonewheels. They
> will only be perfect harmonics with the octave drawbars.
> 
> 
> 
> --
> View this message in context: http://csound.1045644.n5.nabble.com/organ-spectrum-tp5733607p5733612.html
> Sent from the Csound - General mailing list archive at Nabble.com.
> 
> 
> Send bugs reports to the Sourceforge bug trackers
> csound6:
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> Discussions of bugs and features can be posted here
> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"
> 
> 



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On Fri, 28 Mar 2014, Jim Aikin wrote:
> > The Hammond draw bars correspond directly to harmonics...
>
> Slightly off-topic, but IIRC, this is incorrect. A Hammond has only 96
> tonewheels. The drawbars correspond to the nearest equal-tempered
> equivalents of the harmonics, because they use existing tonewheels. They
> will only be perfect harmonics with the octave drawbars.

Because the tonewheels all have integral numbers of teeth and are driven
by a common shaft, they can't really be equally tempered; and half the
drawbars are octaves anyway.  However, you're right that the gear ratios
are chosen to approximate equal temperament, wheels are reused between
different drawbars (and even between different notes on the same drawbar -
the instrument doesn't necessarily really cover the entire keyboard
range), and the harmonics won't be exact.  By "correspond directly to" I
didn't mean "produce perfectly just."