Bohlen-Pierce scale

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The Bohlen-Pierce scale , also known as the BP scale , is a tone scale that divides the duodecime into thirteen steps . It was discovered independently by Heinz Bohlen, Kees van Prooijen, and John R. Pierce from 1972. While in the classic western tone system the octave , which corresponds to a frequency ratio of 2: 1, is divided into twelve tone levels, here the duodecime, frequency ratio 3: 1, is divided into thirteen tone levels. Pierce invented the term tritave for 3: 1 .

The Bohlen-Pierce scale can be both tempered and fully tuned , but is usually played on tempered instruments in the compositions that use it.

Harmony

The initial idea of the three discoverers of the scale was to replace the major triad , which appears in pure tuning as 4: 5: 6, with 3: 5: 7. These simple, odd-numbered intervals , which for the most part do not appear in the tempered western twelve-tone system , are also contained in the Bohlen-Pierce scale in its tempered form to a good approximation. The resulting scale has a step size that is between a semitone and a whole tone . In a tempered mood, the step is 146.3  cents .

In the western tone system, the tempered major third is reached after four tone steps and the fifth after seven tone steps . In the non-tempered Bohlen-Pierce scale, 3: 5 is reached after six tone steps (the major sixth in non-tempered form), after ten tone steps 3: 7. The wide range of interval possibilities is indicated by the web links below.

Instruments

Aerophone with a cylindrical bore, e.g. B. clarinets and pan flutes , have an overtone spectrum , which consists of the fundamental and its odd overtones. You don't overblown like B. Recorders in the octave, but in the duodecime. Because of their odd-numbered spectrum, these instruments are particularly suitable for the harmonic possibilities of the BP scale. The Canadian instrument maker Stephen Fox built the first Bohlen-Pierce clarinets at the suggestion of Georg Hajdu , which have been used in concerts since 2008. He also produces metallophones in this scale.

Compositions and concerts

Charles Carpenter released the progressive rock album Splat in 1996, which contains 10 instrumental pieces on the Bohlen-Pierce scale. Further compositions come from Elaine Walker from 2005.

A first concert with Bohlen-Pierce clarinets took place on March 20, 2008 at the University of Guelph , Ontario, Canada. Musicians Tilly Kooyman and Stephen Fox performed new works by Owen Bloomfield and Todd Harrop. A second concert took place on June 13, 2008 at the Hamburg University of Music and Theater , which was followed by a workshop. The composers were Georg Hajdu, Sascha Lino Lemke , Manfred Stahnke , Fredrik Schwenk and Peter Michael Hamel , the interpreters Anna Christina Bardeli and Nora-Louise Müller.

symposium

Organized by the composer Georg Hajdu (University of Music and Theater Hamburg) and the Boston Microtonal Society, the first Bohlen-Pierce Symposium took place from March 7th to 9th, 2010 in Boston . The event was supported by the Goethe-Institut Boston, Berklee College of Music , Northeastern University and the New England Conservatory of Music . The participants gave 20 lectures on the history and properties of the Bohlen-Pierce scale, performed over 40 compositions with this system and presented a number of new instruments.

literature

  • Rudolf Wille : Mathematics and Music Theory. Preprint. Darmstadt University of Technology, 1975.
  • Rudolf Wille: Music and Numbers. Publishing house for systematic musicology, Bonn-Bad Godesberg 1976, pp. 233–264. With the first reference to Heinz Bohlen's scale.
  • Heinz Bohlen: 13 pitches in the duodecime. In: Acustica. Vol. 39, no. 2. Hirzel, Stuttgart 1978, pp. 76-86 (manuscript December 1975, submitted in September 1976).
  • Kees van Prooijen: A Theory of Equal-Tempered Scales. In: Interface. Vol. 7, No. 1. Swets & Zeitlinger, Lisse 1978, pp. 50-51 (filed February 1978).
  • Max V. Mathews, LA Roberts, John R. Pierce: Four New Scales Based on Nonsuccessive-Integer-Ratio Chords. In: J. Acoust. Soc. Amer. 75, 1984, p10 (A).
  • Nora-Louise Müller, Konstantina Orlandatou, Georg Hajdu: Starting Over - Chances Afforded by a New Scale In: 1001 Microtones , ed. Sarvenaz Safari & Manfred Stahnke, von Bockel Verlag, Hamburg 2014, pp. 127–174
  • Todd Harrop: Just Chromatic BP Scales and Beyond In: 1001 Microtones , ed. Sarvenaz Safari & Manfred Stahnke, von Bockel Verlag, Hamburg 2014, pp. 181–203

Web links