An ‘intonation’ has two meanings:
       absolute, to making the sound timbre, voicing,
       relative, to compare different sounds in the rank, adjusting.
I concentrate on the first of them, especially on wedge tone sound generation in flue pipes. From my over twenty-five-old practise I noticed that the sound initialising (attack time) is most important to correctly recognize the specific timbres of pipes. A spectrum of aliquots in stable state is rather less important.

Below is a 'intonation graph' - the averaged results of experiments and research with smaller pipes; the sounds from f3 to d5. (Karman’s vortex sound)

            v = sqrt(2*p)         - correct to rather small pipes with small flues,

And the Reynolds number shows a kind of fluid flow:

        Re = v*s/kv

For:
0 < Re < 50 - laminar flow (nosound)
60 < Re < 1160 - Karman vortices (stabled laminar flow ) – smallest pipes
1160 < Re < 2230 - fractal vortices (stabled turbulent flow} – diskant pipes
3000 < Re < 10000 - turbulent flow (multifractal? vortices ) – rest pipes?
Re(s = 0,2mm) = 534 for d5 salicet
Re(s = 0,7mm) = 1869 for f3 principal

The A,B,C zones of my ‘intonation graph’ are not absolutely obligatory. At the first – it depends of the air jet noise spectrum from the blower, wind duct, bags, wind trunks and wind chests.

In theoretical considers most often are presumed a white noise to pipe sound generation. Real air jet noise from blower is rather between low sounds noise (as a pink noise) and the Brown noise with two explicit frequent formants:

- near 30 Hz vibrations - influence number of blower motor rotation
                                                                (Strouhall number lower frequency)
- near 600 Hz sounds - influence number of propeller blower disk blades multiply by blower
                                    motor rotation number (Strouhall number higher frequency)
 

A 3D (three dimensional) visualisation the Florens-Takens dynamical phase space as a time delay series allows more precisely different sounds and noises nature as showed below:

White noise

Pink noise

Real organ blower noise

Brownian (thermal) noise
 

A down resampling researched pipes from intonation graph (f3-d5) to c1-a3 sounds by Sound Forge application allowed to compare correctness of setting the distance between flue and the edge (lower-upper labium) in the 3D Florens-Takens dynamical phase space. As example a Principal 8’ c1 and g1 sounds (from Kwidzyn cathedral organ number 31 – II Man) were taken.

A quality spectrum of principal

31. Principal 8’- g1 from Kwidzyn cathedral organ- II Manual – sampled at 22050 Hz 16 bit. A spectrum from stable state of sound.

Principal 8’- g1 a dynamical spectrum from attack – shows ‘quinte-dump’ at the beginning time (as in B zone of intonation graph)

Principal 8’ – sound g2

Principal 8’ – initialisation time (attack) shows the growing of the amplitude in this transient just after quinte-dump

Principal 8’ – stabled state (sustaining)

Principal 8’ whole sound – the attack time and sustain time – without echo after key released.

The same sound in other time delay

A principal intoned with more noise.
 

Florian Strzyzewski – born in 1952 Kwidzyn/Poland.
Piano & organ tuner and computer science teacher in secondary high school in Kwidzyn (North Poland). Scholar of Fridrich Schwarz & Rudolf Plenikowski organ workshop. His master - F. Schwarz was a tuner in Joseph Goebel organ workshop in Danzig – before 1939.