This chapter discusses the Fourier series representation for continuous-time signals. This is applicable to signals which are either periodic or have a finite duration. The connections between the continuous-time Fourier transform (CTFT), the discrete-time Fourier transform (DTFT), and Fourier series are also explained. Properties of Fourier series are discussed and many examples presented. For real-valued signals it is shown that the Fourier series can be written as a sum of a cosine series and a sine series; examples include rectified cosines, which have applications in electric power supplies. It is shown that the basis functions used in the Fourier series representation satisfy an orthogonality property. This makes the truncated version of the Fourier representation optimal in a certain sense. The so-called principal component approximation derived from the Fourier series is also discussed. A detailed discussion of the properties of musical signals in the light of Fourier series theory is presented, and leads to a discussion of musical scales, consonance, and dissonance. Also explained is the connection between Fourier series and the function-approximation property of multilayer neural networks, used widely in machine learning. An overview of wavelet representations and the contrast with Fourier series representations is also given.

The history of sodomy carries a long association with magic, the occult, and alternative forms of knowledge. This connection persists in relation to homosexuality, most obviously in the figure of the fairie (with its associations of enchantment) and with the poetic experience of “magic” or “mystical” forms of alternative knowledge in queer countercultures. This chapter explores the way that two gay San Francisco Bay Area groups — the Beats and the Berkeley Renaissance — took magic, spiritualism, and other forms of alternative knowledge as central to their poetics and authorial practice. Mystical forms of sexuality offer modes of contact at a time when physical intimacy was outlawed and heavily policed in midcentury America. Further, this chapter argues, contemporary poets writing in the wake of these midcentury movements offer new ways to understand how these mystical forms of sexuality constitute institutional critique.

Combinations of tones that are consonant (“nice”) are those that exhibit no slower beats. Beats occur when two periodic signals are close to the same frequency. For sinusoidal signals, the beat frequency is simply the difference between the two signals. For complex signals, one must also consider differences between multiples of the signal frequency. Thus, consonant combinations are those where the ratio of the frequencies is equal to a rational number. Of particular importance are rational numbers involving the ratio of small integers. The musical fifth corresponds to a frequency ratio of 3 to 2 and is an important part of music. A set of note frequencies used for a musical scale can be justified based on consonant combinations, and variations of the details of those choices, known as temperaments, are useful in music for practical reasons. In particular, the equal-tempered scale used for keyboards, based on multiples of the 12th root of 2, is very common.

Mailer’s philosophy of the Hipster is one of his most provocative: Outlined most clearly in “The White Negro,” “Reflections on Hip,” and “Hip, Hell, and the Navigator,” his figuration of the Hipster is an existentialist rebel, an “urban frontiersman” who lives in “the undercurrents and underworlds of American life” amongst “the defeated, the isolated, the violent, the tortured, and the warped.” Mailer’s characterization of the Hipster is the foundation for more than one of his later characters, and is reflective of his place on the periphery of countercultural groups like the Beats.

In 1912 Ezra Pound set himself in opposition to one particular sonic form: ‘the sequence of a metronome.’ With its symmetrical ticking or beating, the metronome became for Pound and some of his contemporaries an apt figure for a metrical tradition, often equated with an outmoded Victorian versification based on a regular succession of beats. In fact, the figure of metronome had been structuring debates about the appropriate sonic form of poetry for roughly a century before Pound issued his pronouncement about it. From the early decades of the nineteenth century, when Johann Maelzel’s musical chronometer began to offer a standard of temporal measurement for musical and vocal compositions, the metronome and practices attuned to its ticking featured regularly in elocutionary and prosodic literature. From the first tick of Maelzel’s machine to the modernism of Pound, a dispute about the practice of reading and reciting verse, as well as composing in it, found an apt correlate in the figure of the metronome. This chapter suggests that Pound’s anti-metronome modernism belongs to an evolving debate about a culture of sing-song and deliberately repetitive prosody.

This chapter tracks the fascination with mid-twentieth century New York black American culture through a reading of influential works by white writers. The second half of the chapter explores the role that New York–based African American writers Ted Joans and LeRoi Jones played in the development of the Beat Generation, a movement which began in New York City. While the Beats have long been associated with the triumvirate of white American writers who met at Columbia University in the late 1940s–Jack Kerouac, Allen Ginsberg and William Burroughs–African American writers played an important role in the development of what became known as the Beat Generation. As this chapter explores, while Mailer and Kerouac in particular viewed jazz as the quintessential sound-track for post-war New York culture, Baldwin, Jones and Joans developed a new jazz aesthetic in their writing which further explodes the myth of the Beat Generation as a quintessentially white phenomenon. And while Baldwin in particular was dismissive of the Beats’ interest in jazz, this chapter traces a less rigid trajectory between white and black culture, suggesting that bebop, arguably more than literature, became a vital text where issues of race, class, gender and authenticity were played out.