...I happened to pick up Schoenberg's Theory of Harmony [Harmonielehre]. Schoenberg was putting forward arguments for the development of music using a much more liberal notion of consonance, and then possibly eventually of a music using a much wider range of notes (so that you could have, say, an extra four notes between C and C sharp).... I thought this was one of the most brilliant things I had ever heard in my life.
-- Helen DeWitt, The Last Samurai, Hyperion Talk Miramax Books, 2000, pages 61-62
From a New Yorker profile of composer John Adams:
In 1965, Adams went to Harvard on a scholarship and heard the surprising news that tonal music could no longer be written. Along with many other young composers of the day, he was led to believe that Schoenberg's twelve-tone method was the only way forward.... At the same time, Adams was soaking up the culture of the late sixties. He counted twelve-tone rows by day and listened to the Beatles in the dorm by night. The sense of disconnection between these worlds was so extreme that he wrote almost nothing.... The title of "Harmonielehre," which had its first performance in 1985, was aimed directly at the East Coast musical establishment. It took off from a famous text by Schoenberg, in which the inventor of atonal music set out to anatomize the preexisting tonal system and, at the same time, to demonstrate that the system had become decadent, even degenerate. "Somehow, the word really got to me -- the idea of this summa of harmony," Adams said. "I kept thinking about spiritual harmony, too. Schoenberg seemed like some religious zealot cutting off his genitals to prove how totally pure he is, how dedicated to the Lord." Adams laughed, as if surprised by the violence of his image. "Yes, 'Harmonielehre,' my version of it, is a kind of parody," he continued. "But I also reached out and embraced all of that harmony that we weren't supposed to touch." ....The feeling is one of tonality rising from the dead.
-- Alex Ross, "The Harmonist," profile of composer John Adams, The New Yorker, January 8, 2001, pages 43-44.
These quotations bring to mind a note I wrote in October 1996. See The Harmony Problem for an account of how I (re)discovered, using the square root of 25/24 as a trial root-tone, the 34-tone equal-temperament scale.
For a detailed description of the 34-tone scale, see Natural Temperament.
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