Bohlen–Pierce scale

The Bohlen-Pierce scale is a tone scale, which divides the twelfth to thirteen pitches. It was discovered independently by Heinz Bohlen, Kees van Prooijen, and John R. Pierce in 1972. While the octave, which corresponds to a frequency ratio of 2:1, is divided into twelve pitches in the classical Western tonal system, here is the twelfth, frequency ratio of 3:1, divided into thirteen pitches. Pierce invented for 3:1 the term " Tritave ". The Bohlen-Pierce scale can be both tempered as voted or not pure, but is usually played in the compositions, which they use on tempered instruments.

Harmonics

The Bohlen-Pierce scale also contains in its tempered form a good approximation the simple odd intervals that do not appear mostly in the temperate western twelve-tone system, for example, integer interval sequences as 3:5:7:9. The starting idea of the three discoverers of the scale was to replace the major triad, which appears as 4:5:6 in just intonation by 3:5:7. The resulting scale has a step size that is between a half and a whole step. In equal temperament, the move is up to 146.3 cents.

In the western sound system of four -tone steps the tempered major third is reached and after seven sound steps the fifth. In the non-tempered Bohlen-Pierce scale is reached after six -tone steps 3:5 ( major sixth in untempered form), after ten sound steps 3:7. The variety of intervallic options passed to the below links.

Instruments

Aerophones with cylindrical bore have a harmonic spectrum, which consists of the root and its odd harmonics. Examples are e.g. Clarinets. You have not blown in the octave such as Recorders, but in the twelfth. These instruments are suitable because of their odd spectrum especially for the harmonic possibilities of the BP scale. The Canadian instrument maker Stephen Fox has built on a suggestion by Georg Hajdu towards the first Bohlen-Pierce clarinets, used since 2008 in concerts.

Concerts

A first concert of Bohlen-Pierce clarinets was held at the University of Guelph, Ontario, Canada on March 20, 2008. The musicians Tilly Kooyman and Stephen Fox led to new works by Owen Todd Bloomfield and Harrop. A second concert was held on 13 June 2008 held at the University of Music and Theatre in Hamburg, where a workshop was connected. The composers were Georg Hajdu, Sascha Lemke, Manfred Stahnke, Fredrik Schwenk and Peter Michael Hamel, the interpreters of Anna Christina Bardeli and Nora -Louise Müller.

Symposium

Organized by the composer Georg Hajdu ( University of Music and Theatre in Hamburg ) and the Boston Microtonal Society was held from 7 to 9 March 2010 in Boston, the first Bohlen-Pierce Symposium. Was co-sponsored the event by the Goethe -Institut Boston, Berklee College of Music, the North - Eastern University and the New England Conservatory of Music. The participants held 20 lectures on the history and characteristics of the Bohlen-Pierce scale, resulted in more than 40 compositions on this system and presented a number of new instruments.