The "devil's interval" of sqrt(2) was certainly considered dissonant. But I never heard that about the major third, whose ratio is 1.25, which is more like 10% off sqrt(2) than 1%. —Dan ----- That is a famous tritone (in the equal-tempered scale, the square root of 2) but I don’t think it’s a joke. Another classic use is in the Tristan chord. I was surprised to learn from a friend that in the middle ages, the major third was considered very dissonant. We consider it quite consonant, and associate it with the ratio 5:4. In the 12-tone scale this is about 1% off from the cube root of 2. Cris

On Jan 17, 2018, at 9:36 AM, Henry Baker <hbaker1@pipeline.com> wrote:

Leonard Bernstein famously (in musical circles, at least) included a musical joke in "West Side Story" with the first two notes of the song "Maria", which form a *tritone* (the two "Ma ri" notes of the "Ma ri a").