Modartt: Organteq bodily modeling

Organ pipe physics
A pipe converts quasi-steady power into oscillating power
The organ pipes belong to the so-called self-sustained instrument household. They rework a steady power (the air stream) right into a rapidly oscillating power (the acoustic vibration) due to a suggestions loop. Organ pipes are DC/AC converters!
The suggestions loop consists in an exciter and a resonator.
The exciter transforms steady power into oscillating power. Within the case of flue pipes, the air jet impacts the labium and creates the acoustic vibration. Within the case of reed pipes, the reed beats due to the upstream and creates the acoustic vibration.
The resonator is the air column of the pipe. It filters, accumulates and restores the oscillating power to the exciter and to the exterior world.

Flue pipe physics
The sound technology in flue pipe outcomes from the interplay between an air jet and the acoustic vibration of the air column of the pipe. The air jet is induced by the upstream stress when opening the valve of the pipe.

When the jet impacts the pipe labium, it injects stream from each facet of the labium. This stream injection acts as an acoustic stress supply close to the mouth of the pipe. The pipe is feed with acoustic power that may propagate via it. The pipe filters the vibration close to the frequencies it prefers: the resonance frequencies.
Whereas the acoustic vibration establishes throughout the pipe, it modulates the jet propagation: a small acoustic perturbation on the channel exit propagates and grows alongside the jet. When impacting the labium once more, the stream injection is definitely modulated by the acoustic vibration that occured earlier on the jet beginning. This closes the suggestions loop.


Throughout the propagation of the acoustic wave via the pipe, a small quantity of power is radiated exterior from the mouth and from the opposite finish. That is the sound that we hear.
In different phrases, the physics of flue pipe will be seen as an audio suggestions, or a Larsen impact, the place the jet/labium interplay could be the speaker (it produces sound) and the place the pipe could be the microphone (it shops acoustic vibration).
How the pipe form impacts the sound
The pipe acts like a reservoir which shops and restitutes power on the frequencies it prefers. These are calls resonance frequencies. The pipe can even shops power at different frequencies, however it’s much less environment friendly. The way in which the pipe is ready to retailer power for a given frequency is name the admittance: the stronger the admittance, the extra power is saved and restituted.
The dimensions of the pipe — ratio diamater/size — has a powerful impact on the resonance frequencies and on the admittance. A slim pipe has extra sharp and closest resonances than a large pipe. The resonance frequencies of a slim pipe are closest to the harmonics of the sound, than those of a large pipe. A slim pipe supplies a a lot reacher sound than a large pipe.
Gambe
Admittance of the Gambe. The grey dashed strains signify the harmonics the place the pipe is anticipated to sound.
The Gambe (slim pipe) supplies a powerful admittance virtually close to all of the harmonics. This ends in a richer sound.
Flute
Admittance of the Flute. The grey dashed strains signify the harmonics the place the pipe is anticipated to sound.
The Flute has a weaker admittance close to the harmonics. This ends in a a lot clear sound.
Bourdon
Admittance of the Bourdon. The grey dashed strains signify the harmonics the place the pipe is anticipated to sound.
The Bourdon even lacks an admittance peak on the 2nd harmonic: the following harmonic is the third (a fifth), typical sound of the Bourdon.
How the upstream stress impacts the sound
The flue pipe is a phase-locked system. The sound outcomes from a steadiness between the air jet (exciter) and the pipe (resonator). When rising the upstream stress, the jet velocity will increase too. To compensate and hold the system balanced, the propagation of the acoustic wave throughout the pipe is modified, in settlement with what the pipe permits. Within the case of a flue pipe, when rising the upstream stress, the frequency of the sound will increase in addition to its depth. As well as the distribution of the relative power among the many harmonics is modified and so the timbre.

Frequency as operate of the upstream stress, in cents (deviation with respect to the nominal frequency).

Amplitude of the 6 first harmonics as operate of the upstream stress, in dB.
Penalties for the tremulant
The tremulant is a mechanical machine that modulates the air stream and thus the upstream stress of the pipes. There are a lot of forms of tremulants. Here’s a sketch of a fundamental one:

As seen within the earlier part, decreasing or rising the upsteam stress have an effect on the pitch, the depth and the spectral content material of the sound. When the upstream stress is periodically modulated, these three elements of the sound (pitch, depth, timbre) are modulated too.
Frequency
Frequency as operate of the upstream stress, in cents (deviation with respect to the nominal frequency).
Amplitude
Amplitude of the 6 first harmonics as operate of the upstream stress, in dB.
In sample-based organ plugins, the tremulant is emulated utilizing a publish impact filter. It’s alleged to mimic the modulation described above. In Organteq, the upstream stress modulation is used as a direct enter of the mannequin. The variations of pitch, depth and timbre are generated by the mannequin itself.