There are several ways in which the tuba and euphonium can access the world of microtonal music. The most common method is by utilizing alternate fingerings, which can exhibit certain intonation tendencies when compared to the primary method of fingering certain notes. The slides may also be used to adjust the intonation of the instrument on a micro-scale. Finally, the lips may be used to adjust notes up or down. No matter the method used, it is imperative that the performer have a strong and reliable set of ears when performing microtonally.
The capability of performers to utilize this technique varies widely from musician to musician. Advanced level microtonal performing is an art form in and of itself, and if the composer wishes for a high level of accuracy and consistency, then it is vital that they seek out a performer comfortable and capable of such techniques.
The author highly recommends the work of Dr. Luke Storm and Dr. Robin Hayward for further information on the microtonal capabilities of the tuba and euphonium. Dr. Storm’s dissertation describes in great detail the performance practice of a work written for a low brass trio that relies exclusively on microtonal writing, and Dr. Storm is additionally an expert at adapting the standard F and CC tubas to microtonal works. Dr. Hayward’s academic work, by comparison, involves the creation of an entirely re-worked valve tuning system for the tuba, which allows one to play both in standard equal temperament and in quarter-tone tuning systems. The article mentioned above by Dr. Hayward is one of the landmark pieces of scholarship on the tuba, and is worthy of extensive study in its own right.
The methods for microtonal notation are numerous enough to warrant a document in and of itself. Besides the previously-cited resources by Dr. Luke Storm and Dr. Robin Hayward, any other reputable manual on microtonal notation is acceptable.
The author highly recommends that the composer utilize a notation system that relies on the relatively well-established system of alternative quarter-tone accidentals (as in the half-flat, half-sharp, half-plus-whole-flat, and one-and-a-half-sharp). This is preferable for the simple reason that microtonal performance on the tuba is an act of approximation at its core, and in any microtonal works the tubist/euphonist is already endeavoring to find an alternative fingering for any given microtonal note. Other notation systems include ratios of intended intervals and similar mathematical formulations; these are very useful for dedicated performers of microtonal music (as Dr. Storm and Dr. Hayward both are), but may be too confusing for people that are relatively new to the technique. As such, it is recommended that simpler forms of microtonal notation (as described above) be used for the majority of works incorporating microtonal tunings.
By way of example, the works below by Liza Lim and Nicholas Deyoe use quarter-tone accidentals, and in the case of the Deyoe, specific microtonal fingerings are called for (throughout the work, several microtonal variations of middle C are specifically called for and notated; the work was written for the CC contrabass tuba, and the composer utilized the overtone charts from earlier in this guide to find several different alternate fingerings for that note). Dr. Hayward’s compositions instead utilize a mathematical notation system of his own construction; in those works, he is often the performer as well, and since he is very familiar with his own notation system, it is no large effort for him to perform them. Others unfamiliar with the system would need an extensive amount of preparation time to read such notation, which many performers would find to be a daunting task.
Advanced to Professional
Works to consider (bolded titles are particularly representative examples of this technique)
Plateau Square – Robin Hayward
…aus freier Lust…verbunden… – Georg Friedrich Haas
Plainsound Brass Trio No. 1 – Wolfgang von Scheinitz
The Green Lion Eats the Sun – Liza Lim
19 E. Main St., Alhambra, CA 91801 – Nicholas Deyoe
 Lukas Timothy Storm, “Wolfgang von Schweinitz’s Plainsound Brass Trio in Theory and Practice: A Guide for Performers” (doctoral dissertation, University of California, Los Angeles, 2017).
 Robin Hayward, “The Microtonal Tuba,” The Galpin Society Journal 64 (March 2011).