Equal Temperament Tuning: The Nature, Cause and Effect (original) (raw)

Approaches to tuning and temperament

The Journal of the Acoustical Society of America

Chairman's Introduction-9:00 Invited Papers 9:05 R1. Spanning the two cultures 1550-1750: Scientists and humanists seeking a quantitative account of contemporary musical scales.

Tuning the témpérament ordinaire, 2002

“Tuning the témpérament ordinaire" in Harpsichord & fortepiano, Volume 10, no. 1, pp. 22-29. UK 2002, 2002

The evolution from meantone into the 18th century French circular "tempérament ordinaire" is described. The latter is accurately reconstructed, based on the analysis of sources by Rameau, d'Alembert and Rousseau. More recently this work has been thoroughly updated, with a fully revised Rameau temperament, a detailed assessment of the differences between d’Alembert and Rousseau, and an analysis of the diverging tuning trends between pipe organs and other instruments in 18th century France. See the sections 8.3 pp. 108-112 and 21.3 pp. 418-429 of the eBook "Unequal Temperaments: Theory, History and Practice", 3rd. ed., 2013. See http://temper.braybaroque.ie/

Tuning and temperament: practice vs science 1450-2020, Roma, Gangemi, 2023

Tuning and temperament: practice vs science 1450-2020, 2023

Until now, the problem of tuning instruments has been mainly viewed as an aspect of a phylologically correct performance practice. Besides several chapters dealing with this important latter aspect, the volume also devotes ample space also to the evolution of the tuning problem from a purely scientific point of view, starting ftom the Scientific Revolution and more particularly during the Enlightenment, with the decisive development of a new science: "Acoustics". It consists of a series of articles, most already published in Italian, presented here in English translation − revised, restructured, partly rewritten, expanded (in some cases radically) − and distributed over 21 chapters.

Perceptually Based Theory for World Music Tunings

The larger research program, of which the present report is a part, involves approaching the analysis of world music from the vantage point of perception. With regard to tuning and scales, there have been three main approaches: via abstract numbers, via empirical measurements, and via perceptual responses. Since the pioneering work of Alexander Ellis in the 1880s, comparative musicologists, ethnomusicologists, acousticians, and music psychologists have measured fundamental frequencies and other partials in sonic spectra to characterize tunings empirically. Since at least as early as ca. 425 BCE, music theorists have employed abstract numbers to prescribe and describe tunings and scales. And since at least as early as ca. 1850 BCE, tunings have been prescribed and described in terms of perceptual responses. Whereas each of these three main approaches can be helpful in making sense of music, they are quite distinct. Nonetheless, these three distinct approaches have often been conflated and an aim of the present study is to disentangle them with a view to analyzing music perceptually. The present report illustrates this approach by focusing on equipentatonic tunings in general and Central Javanese sléndro in particular.

Tuning, Frequency, and Tempo in Relation to Bio-Energy, Cognition, and Natural Order

Summarizing the second chapter of his book Tuning, Timbre, Spectrum, Scale, William Sethares writes "When a tree falls in the forest and no one is near, it has no pitch, loudness, timbre, or dissonance, since these are perceptions that occur inside a mind. The tree does, however, emit sound waves with measurable amplitude, frequency, and spectral content. The perception of tone quality, or timbre, is correlated with the spectrum of the physical signal as well as with temporal properties of the signal such as envelope and attack. Pitch is primarily determined by frequency, and loudness by amplitude ." This is an interesting statement, since on the one hand Sethares states that pitch exists in the mind, while on the other hand he says that pitch is a function of frequency.