Time-domain simulation of the flute
John W. Coltman · The Journal of the Acoustical Society of America · 1992
A time-domain simulation of the flute dealt entirely with volume velocities or currents. The pipe was driven by jet current inserted at the end correction, while the jet shape characteristic was approximated by a truncated saturating cubic function of the delayed mouth current. An empirically derived reflection function yielded a pipe frequency response closely approximating that of a real flute. Jet offset was provided. At zero offset, near-triangular waveforms of three lower modes resulted. Their frequencies as a function of blowing velocity matched those calculated in the frequency domain. An edgetone curve produced by the model was properly tangent to the lower ends of the mode curves. With high jet offset and high blowing velocity large second harmonic content resulted. The maximum second harmonic achievable diminished sharply when mode shrinking was used rather than the mode stretching afforded by the original reflection function.