I don’t know the answer to this question, but I note that the 5th and 4th are more like 0.1% off, while the major 3rd is 1% off. Also, quoth Wikipedia: "The older concept of a ditone (two 9:8 major seconds) made a dissonantly wide major third with the ratio 81:64." - Cris
On Jan 17, 2018, at 10:14 AM, Tomas Rokicki <rokicki@gmail.com> wrote:
Was the major third dissonant for them because they tuned their instruments differently? Or was it just a matter of perception?
On Wed, Jan 17, 2018 at 9:03 AM, Cris Moore <moore@santafe.edu> wrote:
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").
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- -- http://cube20.org/ -- http://golly.sf.net/ -- _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun