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New site? Maybe some day.
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my metal good. your metal bad. dick comparison.
I gotta work on this stuff instead:
acoustic Consonance and Dissonance
C&D must be considered in two different categories: contextual and non-contextual. Many scholars confuse these two, falling into the fallacy of equivocation. Acoustic C&D is non-contextual, i.e., it considers individual sounds isolated from any musical context. Theories of of acoustic C&D are commonly restricted to intervals and come under three categories:
1. Pythagorean Theory. Consonant intervals are those with simple number ratios, although what constitutes "simple numbers" varies from author to author. The original Pythagoreans (5th Century BC) apparently restricted these to the numerals 1, 2, 3, and 4, whereby, 2:1 is the octave (P8), 3:2 is the perfect fifth (P5), and 4:3 is the perfect fourth (P4). Intervals having number ratios beyond that were considered dissonant; e.g., 5:4 the major third (M3), 6:5 the minor third (m3), etc. Later authors, e.g. Zarlino, expanded the consonant interval numbers to include those up to 6, with their inversions. This would include the perfect unison (1:1), P8, P5, P4, M3, m3, M6, m6. Other intervals would be dissonant.
2. Harmonic Series or Beat Theory. This theory is represented by Helmholtz {2} and is often cited as the "beat theory", or "roughness theory". Consonant intervals are those without perceptible beats; e.g., an in-tune octave or fifth has no beats. The end results of this theory are not much different from the Pythagorean Theory. Carl Stumpf offered a convincing refutation of this theory in 1898{3}.
3. Fusion Theory. Carl Stumpf {4} offered this theory. It is psychoacoustical, and assumes that amateurs will confuse various intervals for a unison. In his experiment, subjects are asked whether they perceive an interval as one or two sounds. Hence, the fusion theory may be aptly called the "confusion theory". Experiments by Stumpf yielded the following results, showing the percentage of confusion by amateurs:
o P8 75%
o P5 50%
o P4 33%
o Thirds 25%
o Tritone 20%
o Seconds 10%
The problem with this theory is its subjective nature. Results vary wildly.
All these theories suffer from a lack of musical context. Even an octave can become dissonant within certain musical contexts. Therefore, a contextual definition of C&D is essential for music. |
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physics of sound and music...the whole course was actually really easy but I wanted to challenge myself on the paper...and now I'm running into a brick wall...going insane and stuff. |
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math makes my brain hurt. i never took anything more advanced than integral calculus, diff. equations and infinite series. |
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I'm a math major...but I'd say that it stopped being easy for me with "Modern Algebra" this stuff is easy...just proportions |
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what school do you go to? |
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I'm at Providence College...all the Christ I could have ever asked for...one more semester |
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brian_dc said: I'm a math major...but I'd say that it stopped being easy for me with "Modern Algebra" this stuff is easy...just proportions |
can't you express some musical harmony as an infinite series? it's "Sigma, infinity, n=1, 1/n"... i think |
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it's probably "Sigma, infinity, n=1, n+1/n" that should give you the fundamental series up to a point....but I'm so unsure about that it's ridiculous....nah, theoretically I'm already not digging it...when you'd get to n=6 things get shaky and outside of the western music scales |
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i like it when things go boom |
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brian_dc said: when you'd get to n=6 things get shaky and outside of the western music scales |
Isn't that the point? Outside of western scales, things sound dissonant to us. You could correlate eatern musical scales and theory with the percieved dissonance in corresponding western scales, and use this math to verify it.
I took physics of music when I was in school, but I doubt I coud help. It was over 8 years ago.
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I can draw an Euler path and do that whole Hilbert's Hotel thing. That is the extent of my mathematic ability. |
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ohhh yeeaaahhh that's why i didn't go to college |
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I've found that the best solution to any problem is to draw a torus. That failing, make a double torus. |
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ArrowHead nli said: brian_dc said:when you'd get to n=6 things get shaky and outside of the western music scales |
Isn't that the point? Outside of western scales, things sound dissonant to us. You could correlate eatern musical scales and theory with the percieved dissonance in corresponding western scales, and use this math to verify it.
I took physics of music when I was in school, but I doubt I coud help. It was over 8 years ago.
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it's totally doable and worth it...but this is a paper in the hindsight of a presentation where I only covered that as a passing thought. My hand is pretty well forced as far as what I can talk about in this. |
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ArrowHead nli said: brian_dc said:when you'd get to n=6 things get shaky and outside of the western music scales |
Isn't that the point? Outside of western scales, things sound dissonant to us. You could correlate eatern musical scales and theory with the percieved dissonance in corresponding western scales, and use this math to verify it.
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i think he was talking about a series that would represent stacked harmonic intervals (something along the lines of an overtone series), so I don't think it's supposed to wind up creating dissonance. |
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yes, anthony, that is exactly what I was trying to get at with that series |
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