First, before we even can start, many organs are not tuned
"wohltemperiert".
They are tuned harmonic from a certain starting point. This
means we have to
have a simple midi command or a table where we can change
the frequency for
every note.
Otherwise we would have problems to simulate many existing
organs. More you'll
find here (in german): http://
members.aol.com/ReinerJank/home-de.htm
At this time I wont elaborate this and first concentrate on
harmonics.
In past I mentioned that it will be useful (no, its
imperative!) to have a
harmonic generator. This comes more than true if we try to
simulate organs.
Because organs are really harmonic simulators.
Some thoughts about this to start:
I assume the lowest frequencys man can hear is around 15 Hz,
some organs even
go below that, but lets start here. The highest are around
20 kHz.
We count the ocataves that are:
1 - 15
2 - 30 -2
3 - 60 -4
4 - 120 -8
5 - 240 -16
6 - 480 -32
7 - 960 -64
8 - 1920 -128
9 - 3840 -256
10- 7680 -512
11-15360 -1024
12-30720 -2048
Thats 12 ocataves. In harmonics thats from the second up to
the 2000th
harmonic max that are relevant.
Its not that much what we need, I just wanted to make a
point for
calculations. But with control over 2000 harmonics we'd be
able to build
every possible simple (unchanging) sound through additive
synthesis. The
upper harmonics usually are configured through the SOUND of
the pipe. You can
build pipes with soft sounds with hard sounds with or
without much harmonics
or with "gedackte" pipes you kill all even
harmonics (sounds a bit more like
rectangle, trapez -a triangle with atan-distortion- or
something like this,
I'd presume). Easy going.
This is by the way the (yet poor) possibilities in the
dav-module tries to do
this. "brass", "flute" and
"reed" - thats not enough. We have to put in there
a vast number of possible waveforms, maybe we calculate them
to simulate
roughly the sound of certain pipes. But first back to
harmonics.
For organs we seldom need more than control over 10-15
harmonics (for real
organs there are certain mechanical limits) and I tell you
now which are the
most used.
Basetone
1 (8" = prinzipal)
Octave
1/2 (4")
1/4 (2")
1/8 (1")
1/16 (1/2")
Quint
1/3 (2 2/3")
1/6
1/9 (8/9" - "None")
8/3 (21 1/3") - deeeeper, only pedals
4/3 (10 2/3") - even deeper than Gross Nasard, only on
pedals
2/3 (5 1/3") - only in great organs "Gross
Nasard"
2/9
Terz
1/5 (1 3/5")
1/10
2/5 (3 1/5") (Grosse Tierce)
Sept
1/7 (1 1/7")
1/14
2/7 (2 2/7")
None
1/9 (8/9" see Quint)
2/9 (1 7/9")
Higher harmonics
1/11 (8/11") undezime
2/11 (1 5/11") tredezime (only pedals)
1/13 (8/13") quindezime
1/15 (8/15") see Terz
1/17 (16/17") kleine Sekunde (only pedals)
1/19 (16/19") reine Mollterz (only pedals)
Inharmonics
9/40 (1 4/5") moll Terz
With this we have more or less all harmonics most organs
will do. If I forgot
one, we have to fix that. Some of the tones only make sense
on deeper
frequencys, but with this the organ module would be much
more rounded up.
I will fire more about organs next. When I have more about
making special
sounds. The pipes in the registers will create sometimes
harmonics itself,
sometimes they only play more or less sinewavs. That one I
will specify more
precisely in future.
hope that helps
Hanno
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