Relationship between Bohlen–Pierce and octave-ful temperaments: Difference between revisions
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== Relationship of rank-2 Bohlen-Pierce-Stearns temperament to octave-ful temperaments == | == Relationship of rank-2 Bohlen-Pierce-Stearns temperament to octave-ful temperaments == | ||
The rank-2 temperament under discussion here is the 3.5.7 temperament known as [[BPS]] that tempers out only 245/243 (not any other commas such as 3125/3087). Its mapping matrix is {{val|1 1 2}}, {{val|0 2 -1}} and the two generators are ~1902 cents (the period, [[3/1]]) and ~440 cents (which represents a sharpened 9/7, two of which make a 5/3 because | The rank-2 temperament under discussion here is the 3.5.7 temperament known as [[BPS]] that tempers out only 245/243 (not any other commas such as 3125/3087). Its mapping matrix is {{val|1 1 2}}, {{val|0 2 -1}} and the two generators are ~1902 cents (the period, [[3/1]]) and ~440 cents (which represents a sharpened 9/7, two of which make a 5/3 because 245/243 vanishes.) In 3/1-equivalence world, its MOS sequence goes 4, 5, 9, 13..., and the 9-note MOS is known as the BP "Lambda" scale. | ||
If we add the prime 2 back into this system, we get a rank-3 system that has been given the name "[[octarod]]". | If we add the prime 2 back into this system, we get a rank-3 system that has been given the name "[[octarod]]". | ||