Diversity of ghost notes in tubas, euphoniums and saxhorns

TL;DR

This paper investigates the ghost note phenomenon in bass brass instruments using a dynamical systems model and experimental recordings, revealing its variability and underlying bifurcation dynamics.

Contribution

It introduces a dynamical systems approach to model ghost notes and validates it with experimental data across multiple tuba types.

Findings

Ghost note intervals vary from a minor third to a perfect fourth.

The model successfully predicts the frequency intervals observed experimentally.

Ghost notes are linked to bifurcation phenomena in the instrument-player system.

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.