alt=Notation for the Bohlen-Pierce scale.|thumb|upright=1.5|Notation for the Bohlen–Pierce scale. It was first described in the 1970s. Instead of dividing the [[octave like a traditional scale, it spans an octave plus a perfect fifth.

Background

Heinz Bohlen was curious why the octave should govern scales. After reading Paul Hindemith's explanation of tonality in The Craft of Musical Composition, Bohlen remained skeptical. He settled on combination tones as a model for a scale that would span a perfect twelfth. In 1972, Bohlen developed a version of the scale in just intonation and equal temperament.

Bohlen wrote about his invention in 1978. That same year, software engineer Kees van Prooijen independently discovered the same scale. In 1984, John R. Pierce, Max Mathews, and Linda A. Roberts published their own discovery of the scale. Pierce was the primary investigator of the project. Like Bohlen, he was also an electronic engineer by trade.

Structure

thumb|upright=0.9|The 13 notes of the BP scale. The 9-note equal tempered version is marked in [[Roman numerals.

The equal tempered version of the BP scale only has 9 steps. Heinz Bohlen developed his own 9-step modes of the scale which he named after Greek letters. Mathews and Pierce were certain that the scale was conducive to clear and memorable melodies. They were indifferent about its potential for counterpoint and functional harmony.

  • Jon Appleton.
  • Richard Boulanger, Solemn Song for Evening (1990).
  • Georg Hajdu
  • Juan Reyes, ppP (1999–2000).
  • Ami Radunskaya, "A Wild and Reckless Place" (1990).
  • Charles Carpenter, Frog à la Pêche (1994) & Splat.
  • Elaine Walker, Stick Men (1991), Love Song, and Greater Good (2011).

See also

  • Double reed
  • Square wave
  • Other non-octave repeating scales:
  • Gamma scale

References

  • Bohlen–Pierce scale on Xenharmonic Wiki
  • "The Bohlen–Pierce Scale" Research, ZiaSpace.com.
  • "Stephen Fox Clarinets", Bohlen-Pierce clarinets and other instruments, SFoxClarinets.com.
  • "The Bohlen–Pierce Site: Web place of an alternative harmonic scale", Huygens-Fokker.org.
  • "Kees van Prooijen: 13 tones in the 3rd harmonic", Kees.cc.
  • Song in Bohlen Pierce Scale: "17tppp4 Walker Love Song", Xenharmonic.Wikispaces.com.
  • "The Bohlen–Pierce Symposium", Bohlen-Pierce-Conference.org.
  • "Bohlen–Pierce Scale Symposium, Boston 2010" [playlist], YouTube.com.
  • Stredici, a Bohlen–Pierce string instrument by David Lieberman, University of Toronto.