wow! that surprises me. after all, the fourth is the interval between the fifth and the octave above it. doesn’t the “amen” at the end of a hymn often go from the fourth to the tonic? I thought that was quite old in Western music. - Cris
On Jan 17, 2018, at 9:36 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Cris Moore's comment that the major third was considered dissonant in medieval music was a surprise to me. I know, however, that well into the Baroque, the perfect fourth was considered a dissonance, and its avoidance was part of the standard rules of counterpoint of the time. Mathematically, the fourth is even more consonant than the major third, since it corresponds to a 4:3 ratio.
On Wed, Jan 17, 2018 at 9:55 PM, Cris Moore <moore@santafe.edu> wrote:
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").
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Cristopher Moore Professor, Santa Fe Institute Why should we be deported? This is very, very hard for a family. What will our fellow citizens think if honest subjects are faced with such a decree — not to mention the great material losses it would incur. I would like to become a Bavarian citizen again. Your most humble and obedient, Friedrich Trump (1905)