Diversity of ghost notes in tubas, euphoniums and saxhorns

Abstract

The ghost note is a natural note which can be played exclusively on bass brass instruments with a predominantly-expanding bore profile such as tubas, euphoniums or saxhorns. It stands between the pedal note – the lowest natural note playable, or first regime – and the instrument’s second regime. However, if the interval between the pedal note and the second regime remains close to an octave regardless of the instrument, the interval between the pedal note and the ghost note vary from a minor third to a perfect fourth. References about this note are very scarce, and it is not commonly known among tuba players. This study shows that an elementary brass model describing the player coupled to the instrument is capable of bringing both the ghost and the pedal note to light. Here, we adopt a dynamical systems point of view and perform a bifurcation analysis using a software of numerical continuation. The numerical results provided in terms of frequency intervals between pedal note and ghost note are compared with frequency intervals experimentally inferred from recordings of seven different types of tuba, each of them being played by two professional tuba players.

One pedal note can hide another

“…dance with the value predicted by the bifurcation diagram [7]. This agreement between the picture displayed by bifurcation diagrams and the experiments is all the more interesting as the physical model used is very simple, with a single degree-of-freedom model for lips.…”

“…S1 ′′ corresponds to the saddle-node bifurcation point at which the stable regime of the pedal note arises from the isolated branch (lime green). Figure from [7]. This tool also makes it possible to revisit earlier work and understand why approaches based on time integration or linear stability analysis, although they provided some interesting insights, could only lift one corner of the veil on these "strange peculiarities" mentionned a century ago by Bouasse [1].…”

“…The most recent answers to date concerning pedal notes and ghost notes regimes have been proposed in [6,7].…”

“…In memory of Joël Gilbert (1963Gilbert ( -2022 and his careerlong efforts to advance this research topic.…”

Brass player’s mask parameters obtained by inverse method

“…To reduce the amount of parameters that must be calibrated, the model chosen in the present article is the simplest one described by (1), with only three equations (cf. [16]), that proved to replicate many of the properties of brass instruments (see e.g., [17]). It relates the mouth pressure p m to the mouthpiece pressure p and the opening h through a spring-mass-dashpot equation describing the lips, a valve effect computing the flow u through the lip from the difference of pressure, and the expression of the input impedance:…”