It was commonly used, then it was considered dissonant, then it wasn't. It is still dissonant today "in two-tone textures or if the interval occurs above the bass in a chord with three or more notes." The involvement this statement with Common Lisp is left as an exercise to the reader. Hilarie
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)