Hi Ric, > The only notible coincidence arithmeticaly I could find is that > 13.327/5.549= 2.401693998919 while 7.778/5.549= 1.401693998919 an EXACT > difference of 1 !. Such an exactness to the 13th place is too signifigant > to be ignored, yet what does it mean?? No coincidence at all. Think of it this way - you're describing b/(b-a) - a/(b-a)=1 Ok? Ha I figured something like this was in number teory. Without adjusting for inharmonicity, beat proportions within 12tET triads all stay the same. For instance a major triad: 5/4:6/5 ~ 1.7 5/4:3/2 ~ 11.7 6/5:3/2 ~ 20.1 8/5:3/2 ~ 23.4 here I don't know how you got your figures. Do you mean the beat rate of 5/4 divided by the beat rate of 6/5? Of course the 5/4 ratio does not exist in ET, only the coincident frequencies. The actual "3/2 ratio" or 1.5 is actually 1.49830...... Here are the same for 22tET. See if you think it qualifies proportional beats or rhythmic harmoniousness: 5/4:3/2 ~ 1.05 8/5:3/2 ~ 2.1 5/4:6/5 ~ 3.9 6/5:3/2 ~ 4.1 Of course, tuned properly it affords no tonal distinction save through enharmonic substitutions of ±~54.5 cents. Regards, Clark I am not sure what you mean by proportional beats or what rhythmic harmoniousness is. If the beats of the interval are proportional to either of the frequencies then you get a kind of resultant tone. Whether this is "reinforced" because it is proportional I don't know. But I hear these in ET 3rds quite often in certain ranges and these beats are not proportional that I know of. Not all the time so I think "conditions" must be nvolved. ---ric
This PTG archive page provided courtesy of Moy Piano Service, LLC