In terms of music history, particularly valuable is the chapter "Equal temperament
--a history of disputes and errors", giving an account of the development of musical tuning, ranging from various types of unequal temperament up to the currently standard most common 12-tone equal temperament
He preaches that there's nothing natural about equal temperament
, or "ET" as he refers to it.
Yes, we just-tuning composers have attacked the deficiencies of 12-equal (one complaint about equal temperaments
that echoes Werntz is that they are an arbitrary, "scientific"--thus "inhuman"--way of producing musical intervals, themselves ipso facto "inhumanely" irrational), and there may be a natural impulse to counter-attack just tuning in response.
Zaragoza may not have been aware of the experiments of Juan de Espina and Giovenardi, but, as is clear from the above, he did know about the organ presented by Pomar to Philip IV, moreover, it was his idea to introduce equal temperament
on an organ in the royal chapel, following in Falco's steps in Valencia.
The long, slowly modulating drones on Tony Conrad's box set Early Minimalism Volume One (Table of the Elements) are totally uncompromising, even if they do relax the listener over time; the electrified violins that produce the sounds attack tiny intervals across the audible spectrum with slightly wobbly intonation, never applicable to the equal temperament
of the piano.
Thus, the twelve equal temperament
level of hearing provides the basis for the diatonic level of hearing, in the same way that the beat level of hearing provides the basis for the metre level of hearing: we cannot hear the diatonic scales if the distances among the pitches are uneven and disproportionate.
The challenge of achieving pure intonation has been unjustly neglected in the age of equal temperament
, which, as Max Weber wrote, has had "an extensively dulling effect upon the delicacy of listening ability.
Pesic's last case study, on Max Planck's (1858-1947) consideration of natural tuning versus equal temperament
In an attempt to reconcile their findings with contemporary practices of equal temperament
, two genera of tetrachords were identified: diatonic and chromatic (Examples 1 and 2).
The Seventh Dragon: The Riddle of Equal Temperament
," is a book on the philosophy of piano tuning that won the Western States Book Award for creative nonfiction in 1986.
Ten years later I am responding with some thoughts of my own, as one of a small minority of microtonalists referred to by Douglas Keislar in his introduction: composers who use microtones for no reason other than to obtain the stimulating sonorities that are available with the added pitches, and who employ distinct, functional, expanded forms of equal temperament
to this end.
The keys of the first manual will produce a 19-note octave, while the second manual is tuned a diesis higher; combined with the first manual, the 31 steps to the octave are each a diesis apart, which produces a kind of equal temperament
The analyses themselves are not uniformly convincing or penetrating, while much of the technical writing concerning Harrison's obsession with intonational systems other than equal temperament
will be lost on all but the most mathematically minded (or temperamentally inclined) readers.
usually some version of meantone or its variants or, when necessary, equal temperament
Thursday and Friday), Equal Temperament
Percussion Duo (7:30 p.