How has non-classical tuning and temperament influenced Western classical music? How has music notation changed to reflect changes in the music it represents? Classical temperaments have employed twelve distinct pitches in each octave, whether regularly or irregularly spaced. These notes are almost always the only that appear in classical musical works; sometimes in unequal temperaments, changes of keys lead to flats and sharps with different pitches. However, this paradigm has been broken increasingly often from the Romantic period to today.
There have been three main non-classical tuning advances, each more ambitious and powerful than the last. The first is quarter-tones, first used classically in the early 1800s, which simply extend twelve-tone equal temperament and include the harmonic seventh. The second is equal-temperament microtonal music, which divided the octave in more than 12 equal steps, often to better approximate just intervals. The third breaks from the idea of dividing the octave entirely, allowing access to all frequencies and intervals.
So far, I have focused my research on the Bohlen-Pierce scale, which can be equally or justly tempered, and in the former form consists of thirteen equal steps in a “tritave” (3:1 frequency ratio). The tritave serves much the same role that the octave does in classical music; it is the largest fundamental interval, usually not stretched, and it defines pitch classes: an H# transposed one tritave up is again an H#. The Bohlen-Pierce scale is sometimes referred to as macrotonal because the smallest intervals are greater than a classical half step.
This paper has three parts: the first is about changes in music notation caused by microtonal and atonal music, the second is about other innovations made in classical music notation, and the third is about novel forms of music notation that abandon traditional ideas like the staff or signs for lengths of a note. Because
There have been three main non-classical tuning advances, each more ambitious and powerful than the last. The first is quarter-tones, first used classically in the early 1800s, which simply extend twelve-tone equal temperament and include the harmonic seventh. The second is equal-temperament microtonal music, which divided the octave in more than 12 equal steps, often to better approximate just intervals. The third breaks from the idea of dividing the octave entirely, allowing access to all frequencies and intervals.
So far, I have focused my research on the Bohlen-Pierce scale, which can be equally or justly tempered, and in the former form consists of thirteen equal steps in a “tritave” (3:1 frequency ratio). The tritave serves much the same role that the octave does in classical music; it is the largest fundamental interval, usually not stretched, and it defines pitch classes: an H# transposed one tritave up is again an H#. The Bohlen-Pierce scale is sometimes referred to as macrotonal because the smallest intervals are greater than a classical half step.
This paper has three parts: the first is about changes in music notation caused by microtonal and atonal music, the second is about other innovations made in classical music notation, and the third is about novel forms of music notation that abandon traditional ideas like the staff or signs for lengths of a note. Because