Composers who follow this school are interested in the natural resonance of sounds, causing them to write notes in their music with very specific tunings, also outside of Equal Temperament
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.
In this connection, Koukal points out that today's equal temperament
, within which the octave is divided into iq equal semitones, asserted itself gradually during the course of the 19th century, and the concert pitch set at 440 Hz was only officially agreed as the international standard in 1939.
While it listens to you play, your pitch is charted in relation to equal temperament
His two published books, How Equal Temperament
Ruined Harmony (and Why You Should Care) and Shakespeare's Songbook, have gained international renown.
38a (tuned in Kellner) and two portatives built by David Petty & Associates, one in equal temperament
and the other in meantone.
This is the four decimal approximation of 2(1/12), which is the incremental ratio between the frequencies of adjacent notes in an equal temperament
tuning scale, which is used on most modern musical instruments.
He pairs music and math concepts such as scales and modular arithmetic, octave identification and equivalence relation, intervals and logarithms, equal temperament
and exponents, overtones and integers, tone and trigonometry, and tuning and rationality.
It might happen to prick up your ears from a purely avant-garde perspective, but it still doesn't add anything new to our understanding of Bach's lessons in well-temperament as a technological, namely reproducible way forward in musicking (and which incidentally was itself eventually supplanted by the modern system of true equal temperament
, which is also what makes playing Das wohltemperierte Klavier on the piano such an ironic exercise to begin with).
How Equal Temperament
Ruined Harmony: And Why You Should Care, by Ross.
And third, there is a noteworthy irony in setting 72-equal in opposition to just tuning: 72-equal contains the best approximations, as I recall, to just intervals of the 3, 5, 7, and 11 identities of any double-digit equal temperament
Curiously, the theatricality of mobile horns and thejuxtaposition of natural and equal temperament
tuning seemed peripheral to this intriguing interplay of instrumental textures and dialogue.