source file: m1449.txt Date: Tue, 16 Jun 1998 16:34:05 -0400 Subject: Defining "Just" Intonation and "Consonance" From: "Paul H. Erlich" Benjamin Tubb wrote, >Just Intonation Ratio Limits [with respect to the denominator] The term "limit" is normally used to refer to the highest odd or prime factor to be found looking at BOTH the numerator and denominator. If the denominator alone is really intended, then it is probably not valid to use octave equivalents as you have done. >Does anyone have any comment as to why the following list of "just" intervals >isn't otherwise accepted for the most "consonant" use insofar as they are based >on the second most consonant interval of a Perfect Fifth besides the Octave. The ear doesn't care what an interval is "based" on. The various psychoacoustical models of dissonance (covered now and then on the list) essentially state that the simplest ratios will be most easily perceived, but beyond a certain point (about 17/13 or 19/13 in various members' experience) the exact ratio (if there is one) ceases to be relevant and the degree of approximation to simpler ratios is the only important factor. Thus, in your list of Pythagorean ratios, M3 8182/6561 384.36 (which should really be 8192/6561) is actually very consonant, despite its complex ratio, since it is only 2 cents off a just 5/4. >Essentially, >I'd like to know what is the definition of "just" intonation and how "should" >it be applied. Just Intonation will typically give many different ratios for a given interval, depending on how that interval is arrived at via simple, consonant ratios. The typical use of the term really means 5- (prime) limit JI, as opposed to 3- (prime) limit JI which is referred to as Pythagorean tuning, and higher limits which have no fully accepted terminology as of yet. I think it should only be applied within the limits of what it is possible to hear. Listen!