Wind instruments differ one each other mainly in the type of exciter used (reed, double reed, mouthpiece, …) but the physics of the resonator, which in the case of wind instruments is a pipe, it is quite clear and different types can be distinguished by some variants such as closed pipe vs. open pipe, cylindrical vs. conical, coullisse vs. holes, material (wood, metal, other …).
In the SWAM woodwinds instruments there is no a real exciter because the sound is sampled and the most modeled part is the pipe.

Physics of the cylindrical open pipe.

Cylindrical open pipe instruments produce tones with a full spectrum (having both even and odd harmonics), so they are able to produce overtones multiple of the fundamental.

In practice: the fundamental, the first overtone that produces a tone one octave higher than the fundamental (+12 semitones), the second overtone that produces a tone a twelfth higher than the fundamental (+19 semitones), the third overtone that produces a tone 2 octaves higher the fundamental (+24 semitones ), etc.

Flutes are instruments having cylindrical open pipe (see below).

Physics of the cylindrical closed pipe (at one end)

Cylindrical closed pipe instruments produce tones whose spectrum is characterized by containing mainly odd harmonics (especially for the lower frequencies), consequently also the overtones will be more “rarefied ” (odd overtones).

The first overtone produced is one twelfth above the fundamental (+19 semitones).

Clarinets are instruments having cylindrical closed pipe.

Physics of the conical closed pipe (at one end)

Conical closed pipe instruments behave similarly to the cylindrical open pipe instruments, being able to produce a full spectrum (with both even and odd harmonics).

Saxophones are instruments having conical open pipe.

A note about flutes

As specified above, flutes behave accordingly to the cylindrical open pipe physics, so it can produce tones and overtones full spectrum (having both even and odd harmonics).

We want to highlight an important aspect of the flute that gives it a particular behavioural characteristic. Many of the higher tones are not always produced by shortening the pipe (by means of a coulisse, for example, or using holes like in the standard flutes) but through of overtones.

An overtone is a harmonic sound whose fundamental frequency is a multiple of the one produced by the full pipe.

During dynamic or pitch changes, the sound is often contaminated by the overtones; such interference is an important element that characterizes the timbre of the instrument, giving it its typical character.

In sampled libraries this behaviour is “photographed”, so despite being very faithful it cannot interact with the expressiveness of the musician. In the SWAM Flutes, instead, in spite of the sound is also sampled from a real instrument, such behaviours are played dynamically and in real time using special algorithms (taken from physical modeling) that interact with the musician’s expressiveness, giving to the sound much more vividness and responsiveness.

We can therefore say that SWAM is a true hybrid between physical modeling and sampling.

Bowed Strings

The bow allows the player to continuously input energy and so to maintain a note. This affects the timbre, too: after a pluck, the high harmonics fade away quickly, leaving only the fundamental and some weak lower harmonics, while bowing maintains the rich harmonic spectrum.

The action of the bow which drives the strings is a regular cycle of stick-slip-stick-slip. This involves some interesting properties of friction, the force that makes things difficult to slide.

The bow string interaction is important for another aspect. Over a limited range of pressure applied by the player, the cycle of stick and slip is governed by the standing wave in the string. When this happens the motion of the string is nearly exactly periodic, and it therefore makes a sound with an almost exactly harmonic spectrum. This means that any inharmonic effects of the string are reduced by bowing, which is not the case when the string is plucked.

Helmholtz motion is the name given to the idealised motion of the string during stick and slip cycles.

SWAM-S bowed strings model this complex system using the Digital Waveguide Synthesis conceived by prof. Julius O. Smith, exploiting a complex friction model and adding several elements taken from the SWAM technology created for the Woodwinds instruments.