I don't know if I'm wasting enough time on messageboards[views:1616][posts:16]___________________________________ [Dec 14,2005 10:50pm - brian_dc ""] 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. |
| _____________________________________ [Dec 14,2005 10:52pm - BornSoVile ""] what class is this? |
| ___________________________________ [Dec 14,2005 10:55pm - brian_dc ""] 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. |
| _______________________________________ [Dec 14,2005 10:56pm - Anthony nli ""] math makes my brain hurt. i never took anything more advanced than integral calculus, diff. equations and infinite series. |
| ___________________________________ [Dec 14,2005 10:57pm - brian_dc ""] 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 |
| _____________________________________ [Dec 14,2005 10:57pm - BornSoVile ""] what school do you go to? |
| ___________________________________ [Dec 14,2005 10:58pm - brian_dc ""] I'm at Providence College...all the Christ I could have ever asked for...one more semester |
| _______________________________________ [Dec 14,2005 11:01pm - Anthony nli ""] 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 |
| ___________________________________ [Dec 14,2005 11:08pm - brian_dc ""] 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 |
| _________________________________________________ [Dec 15,2005 12:04am - whiskey_weed_and_women ""] i like it when things go boom |
| _________________________________________ [Dec 15,2005 12:08am - ArrowHead nli ""] 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. |
| _______________________________________________ [Dec 15,2005 12:08am - BobNOMAAMRooney nli ""] I can draw an Euler path and do that whole Hilbert's Hotel thing. That is the extent of my mathematic ability. |
| __________________________________________ [Dec 15,2005 12:08am - SacreligionNLI ""] ohhh yeeaaahhh that's why i didn't go to college |
| _______________________________________________ [Dec 15,2005 12:09am - BobNOMAAMRooney nli ""] I've found that the best solution to any problem is to draw a torus. That failing, make a double torus. |
| ___________________________________ [Dec 15,2005 12:11am - brian_dc ""] 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. 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. |
| _______________________________________ [Dec 15,2005 12:12am - Anthony nli ""] 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 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. |
| ___________________________________ [Dec 15,2005 12:15am - brian_dc ""] yes, anthony, that is exactly what I was trying to get at with that series |