how organs work

[Hanno <shaftoe nurfuerspam de>]

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