Editing Bohlen–Pierce scale (section)

==Timbre and the tritave==
[[File:BP Klarinettenfamilie.jpg|thumb|140px|Bohlen-Pierce clarinet family: soprano, contra(bass) and tenor]]

3:1 serves as the fundamental harmonic ratio, replacing the diatonic scale's 2:1 (the [[octave]]). ({{Audio|Octave.ogg|play}}) This interval is a perfect twelfth in [[diatonic scale|diatonic]] nomenclature ([[perfect fifth]] when reduced by an octave), but as this terminology is based on step sizes and [[diatonic function|functions]] not used in the BP scale, it is often called by a new name, '''''tritave''''' ({{Audio|Tritave.ogg|play}}), in BP contexts, referring to its role as a [[pseudooctave]], and using the prefix "tri-" (three) to distinguish it from the octave. In conventional scales, if a given pitch is part of the system, then all pitches one or more octaves higher or lower also are part of the system and, furthermore, are considered [[octave equivalency|equivalent]]. In the BP scale, if a given pitch is present, then ''none'' of the pitches one or more octaves higher or lower are present, but ''all'' pitches one or more tritaves higher or lower are part of the system and are considered equivalent.

The BP scale's use of odd integer ratios is appropriate for timbres containing only odd harmonics. Because the [[clarinet]]'s spectrum (in the [[Clarinet#Range|chalumeau]] register) consists of primarily the odd harmonics, and the instrument overblows at the twelfth (or tritave) rather than the octave as most other woodwind instruments do, there is a natural affinity between it and the Bohlen–Pierce scale. At the suggestion of composer [[Georg Hajdu]], clarinet maker [[Stephen Fox (clarinet maker)|Stephen Fox]] developed the first Bohlen–Pierce soprano clarinets and began offering them for sale in early 2006. He produced the first BP tenor clarinet (six steps below the soprano) in 2010 and the first epsilon clarinet (four steps above the soprano) in 2011. A contra clarinet (one tritave lower than the soprano) is now (2020) played by Nora Mueller, Luebeck, Germany.