The other volumes will be: lit'ap to Expand the

Harmonic Series, covering instruments that use methods such as slides, finger holes, and keys to fill in notes outside the

harmonic series; Valves Evolve, covering the development of various valve mechanisms in the nineteenth century; Heyday of the Cornet; and The Modern Trumpet, covering twentieth-century trumpet development.

Alternatively, the external gravitational potential can be modeled by

harmonic series expansions (e.g., Rummel et al., 1988).

The piece gets its unmistakable fanfare sound by confining its palette to the capabilities of valveless brass instruments such as bugles, which can play only the limited pitches of the

harmonic series. The melody leaping from pitch to pitch accompanied by simple, folk-like harmonies, is reminiscent of bugles on the battlefield, giving the fanfare an air of pride and nobility.

Coverage includes elementary and advanced tests for convergence or divergence as well as information about the

harmonic series, the alternating

harmonic series, and closely related series.

He explains the tuning process and related issues, historical factors, and theories including frequency, ratios, cents, fixed intonation, and the

harmonic series. Sixteen temperaments are discussed and compared in detail.

As in the Green functions approach, the problem of computing the infinite

harmonic series [34] and [36] may be considered.

In the new tuning system the major third was an imperfect consonance that could be directly equated with the

harmonic series.

Additionally, ratios are an appropriate descriptive language for the pitch relationships of the

harmonic series, which Helmholtz discussed at length in his influential book On the Sensations of Tone.(5) Thanks to his encounter with Helmholtz's work, the

harmonic series formed a major source of Partch's investigations in the years 1923-28, when his theoretical ideas were crystallizing.

The slide trumpet (illus.2) filled in the gaps in its

harmonic series with its single slide, which offered a pitch-change of up to one and a half tones (more with some note-bending and imagination).

The title refers to my association between the natural

harmonic series, which I use as the harmonic basis of the work, and the full spectrum of light as one would observe refracted by a prism.

The symbol [f.sub.o] was agreed upon, written with a lower case f and a subscript "o," not "zero." The reason given was that a "zero" frequency does not ft into the

harmonic series of the sound source.

Not to be missed catch Deerhunter tonight at The Button Factory as part of a new

Harmonic series. Tickets: EUR20.