Bohlen-Pierce Fugue for 3 Clarinets in 41EDO BPS[9] sLsLsLsLs "Moll II/Pierce" скачать в хорошем качестве

Bohlen-Pierce Fugue for 3 Clarinets in 41EDO BPS[9] sLsLsLsLs "Moll II/Pierce"

Bohlen-Pierce (BP) is a classic microtonal scale that divides the 3 to 1 frequency ratio, or tritave, into 13 equal parts. This is a choice that challenges the foundations of most harmonic systems, which are based instead on the octave or (2 to 1 frequency ratio) often to the point where notes an octave apart are considered the same note. In this fugue, I use an octave based system to notate and tune pitches in the BP system: The octave is divided into 41 equal parts, then taking every 5th note results in a series of pitches which is close enough to BP to be indistinguishable to the human ear. I do this both for convenience, and to illustrate correspondences between intervals in BP and those in other forms of music (e.g. the tritave corresponds to an octave plus a perfect 5th). This fugue is the 3rd in a planned series of 9 fugues illustrating the modes of a 9 note scale repeating at the tritave consisting of 5 small steps (s) and 4 large steps (L). This scale, called Bohlen-Pierce-Stearns[9], or BPS[9], was first discovered in the context of BP where s is 1 BP step, and L is 2 BP steps, but there are many possibilities for the relative size of these two intervals (some of which are used in other fugues in the series.) Since I am using strict BP in this fugue, I make various musical choices that reinforce the original motivation for BP. In addition to the tritave, BP gives excellent approximations of frequency ratios of odd harmonics (e.g. 9/7,7/5,5/3, and 7/3) but does not give good approximations to frequency ratios of even harmonics (such as the octave.) As such, in addition to basing the harmony of the fugue around ratios of odd harmonics, I use exclusively the timbre of the Clarinet, which basically lacks any even overtones. The mode I use, "Moll II", sLsLsLsLs was a favorite of one of the two namesakes of the system, so it is sometimes named "Pierce" in his honor.