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@@ -646,16 +646,16 @@ <p> Within a Pythagorean tuning system, each scale can sound highly - distinctive, since the notes will not be distributed evenly within the + distinctive, since the notes will not be distributed evenly across the octave. In a sense, 12-tone equal temperament "bends" all of the notes - so they are evenly spaced. Fifths in equal temperament are not quite - pure but close enough, making it easy to modulate between keys. By - comparison, thirds are quite out of tune compared to a pure ratio - (5:4). Equal temperament invokes irrational numbers, creating - in-between intervals which do not exist on the Lambdoma. (Notes in - equal temperament are separated by an irrational ratio of 1 to the - 12th root of 2 (1:<super>12</super>√2), which can only be approximated - by pure fractions.) + so they are evenly spaced. Fifths in equal temperament are all nearly + pure, making it easy to modulate between keys. By comparison, thirds + are quite out of tune compared to a pure ratio (5:4). Equal + temperament invokes irrational numbers, creating in-between intervals + which do not exist on the Lambdoma. (Notes in equal temperament are + separated by an irrational ratio of 1 to the 12th root of 2 + (1:<super>12</super>√2), which can only be approximated by pure + fractions.) </p> <p> |