Forum.RttP{I don't know if I'm wasting enough time on messageboards}

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.