The Pulse Forming Process

In the years 1966/67 one founds out, that the sound generating function of double-reed woodwind instruments is a chain of pressure pulses, which determines the envelope of the sound spectrum: The spectral envelope gets  minima (socalled valleys) and between these valleys spectral maxima  (socalled formants).

(Formant = formants are stable areas of the spectrum, where the amplitude of the partials is particularly strong, independent of the pitch of the fundamental. These areas or spectral maxima are characteristic for each instrument and are responsible for the impression of the instruments timbre).

It could be shown that all wind instrument timbres are generated after this principle. The characteristic timbre of a wind instrument is only a result of the chain of pulses. In the original wind instruments these pulse chains are generated by the valve function of the reed or  lips: The pulses go in similar intervals through the lips  or (double)reeds into the connected tube/pipe and cause its vibration. The steady opening and closing of the reeds or lips is modeled by the pulse forming process: Instead of a short opening of the lips/reeds is a equal shaped electronic  pulse.

After the theory of the creation of cyclical spetra with the help of pulse chains there are  the following principles to modify the shape of the spectrum:

The basic condition for stable formant areas are constant opening and closing times of the reeds/lips, independent of the pulse frequency. This means: The speed or frequency of the pulse chain does not matter. Only the width of the pulses must be constant.
The smallest change of the pulse width causes a micromodulatoric change of the timbre, which is typical for musical instruments. With other words: constant pulse widhts cause constant  formant arreas and constant valleys in the spectral envelope. Minimal changes of the pulse width cause audible changes of the spectrum.
This is the principle: By a pulse width of t and a cycle of T one can find the valleys (minima) of the spectral envelope at the partials 1/t (or 1/T-t, if the constant cycle T-t <= T)(this corresponds to the principle of formant areas, discovered by Karl Erich Schumann in the 1920ies). 

In the case of timbres played in p the shape of the pulses is rounded. This means for the spectrum, that the higher partials are not so strongly marked as normal.
In the case of timbres played in f the shape of the pulses is squared. This means for the spectrum, that the higher partials are more strongly marked as normal.
With other words: The more squared ist the shape of the pulses  the stronger are the amplitudes of the higher partials.

In the case of a minimal shortening of the pulse width the spectral minima (valleys) and maxima (formants) move to higher partials. This is the case by crescendo playing wind instruments and corresponds the the principle of shifting formant areas found by Karl Erich Schumann in the 1920ies. 
(one hase the reverse case by decrescendo playing wind instruments (longer pulse width cause a shifting of the spectral minima and maxima to lower partials)). 

The pulse forming process of the Variophon and of the Martinetta works with rectangle pulses. This is not the case in the sound generation of real instruments: Here one gets only rectangle pulses in the sound generating process, when the opening and closing times of the reeds/lips are infinite small. But this is not the case: Between the "open" and "close" state is a small transitory distance. So one must speak of cosinus or triangle shaped pulses in the sound generating process of wind instruments to be absolutely correct. But the rectangle shaped pulses work very well for the wind instrument simulation.

The following principles are valid for the puls forming process with triangle shaped pulses:

The distribution of the minima in the spectral envelope is dependent on the attack  and decay time (t1 and t2-t1) of the triangle shaped pulse inside a  cycle (T): As long as the decay time (t2-t1) has a harmonic ratio to the whole cycle (T) and as long as the ratio between attack and decay time (t1 and t2-t1) stays constant, remain the positions of the spectral maxima and minima constant also.

The ratio between the decay time (t2-t1) and the whole cylcle (T) causes the main maxima and minima of the spectral envelope, whereas the ratio between the attack time (t1) and the whole cylcle (T) causes the minor spectral maxima and minima between the main maxima and minima of the spectral envelope.