I wish that Doug Leedy had devoted more of his response to explaining his enigmatic statement about equal temperaments
being "scientific" and "inhuman." Then we might have had a stimulating discourse about, for example, what is "human" in music, or the role in art of "irrationality" (in either its mathematical or psychological sense).
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.
Pythagoras created a numerical system that led over the centuries to twelve-tone equal temperament
; he claimed it to be in tune with the workings of the universe.
9) that the lute and viol were tuned exclusively in equal temperament
during the sixteenth, seventeenth, and eighteenth centuries.
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.
One choice is rejected because it "would depart too much from the 12-tone equal temperament
that was standard practice for Webern's compositions" (p.
Thursday and Friday), Equal Temperament
Percussion Duo (7:30 p.m.
with Crosses of Fire) which was commissioned by the Michigan Music Teachers Association, and Sun Dogs for a new CD by the percussion duo, Equal Temperament
(Eric and Stacey Jones).The CD, called "Parhelion" has just been released on the Eroica label.
But it is clear that he responded to two common themes: the conflict between Pythagorean theory and Bizcargui's division of the tone and the equal temperament
of the vihuela.
In addition, the argument between Rameau and Bollioud-Mermet was not exactly as reported in note 107 on page 202; the event is clarified in Albert Cohen, 'Rameau, Equal Temperament
, and the Academy of Lyon: a Controversy Revisited', French Musical Thought 1600-1800, ed.