Relationship between Bohlen–Pierce and octave-ful temperaments: Difference between revisions

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	Just as conventional music theory is associated with multiple temperaments (the [[rank]]-1 temperament [[12edo\|12EDO]] and the rank-2 temperament [[meantone]]), the [[Bohlen-Pierce]] system is based on at least two different temperaments. The first is [[13ed3\|13EDT]] (13ED3), the rank-1 temperament where 3/1 is divided into 13 equal parts. Many explanations of Bohlen-Pierce simply state that this equal division '''is''' Bohlen-Pierce. But just as a description of conventional music theory wouldn't be complete if you just said it's 12 equal divisions of 2/1 and left it at that (ignoring diatonic scales, key signatures, and so on), the Bohlen-Pierce system is also strongly associated with the rank-2 temperament (of the 3.5.7 [[just intonation subgroup\|subgroup]]) tempering out [[245/243]]. This temperament has been referred to by various names including "Lambda temperament" or "BP Diatonic temperament".		Just as conventional music theory is associated with multiple temperaments (the [[rank]]-1 temperament [[12edo\|12EDO]] and the rank-2 temperament [[meantone]]), the [[Bohlen-Pierce]] system is based on at least two different temperaments. The first is [[13ed3\|13EDT]] (13ED3), the rank-1 temperament where 3/1 is divided into 13 equal parts. Many explanations of Bohlen-Pierce simply state that this equal division '''is''' Bohlen-Pierce. But just as a description of conventional music theory wouldn't be complete if you just said it's 12 equal divisions of 2/1 and left it at that (ignoring diatonic scales, key signatures, and so on), the Bohlen-Pierce system is also strongly associated with the rank-2 temperament (of the 3.5.7 [[just intonation subgroup\|subgroup]]) tempering out [[245/243]]. This temperament has been referred to by various names including "Lambda temperament" or "BP Diatonic temperament", although the standard name by which it is referred to on this wiki is [[Bohlen-Pierce-Stearns]].

	== Relationship of 13EDT to octave-ful temperaments ==		== Relationship of 13EDT to octave-ful temperaments ==