source file: m1441.txt Date: Mon, 8 Jun 1998 21:18:05 -0400 Subject: Re: magic chord From: "Paul H. Erlich" >> Here's my problem with that: the 28:25 is represented in 31TET by 193.5 >> cents, and that interval by itself doesn't really evoke a consonant 9:8. >> If one really hears intervals at the 9-limit or higher, then both 9:8 >> and 10:9 must be considered consonant, and there should be a dissonant >> point about halfway between them. >I don't agree with this reasoning. Is the 22-equal 7/5 similarly >at a dissonant point? Yes, it is, and it requires other notes to support either the 7/5 or the 10/7 interpretation. The mechanism for supporting ratios is the root in the otonal case and the common overtones in the utonal case. I don't claim that there is any similarity between these two mechanisms. >Or is the just 11/9 at a dissonant point >between 6/5 aand 5/4? Yes, unless the conditions are sufficient for hearing the 11-limit, which may be rather often. But the simplest interval between the 9/8 and the 10/9 is the 19/17 and conditions are rarely sufficient for hearing the 19-limit. >> There are many chords in 31TET where the 9:8 is clearly >> evoked, because other ratios are supporting that interpretation. But in >> this chord, that doesn't happen. >Granted, the 9/8 isn't "clearly evoked" but it can still function >as a 9-limit consonance. How so? Think about triads in 12-equal. Even though all the intervals in the augmented triad can function as consonances in major and minor triads, the augmented triad is dissonant. And the thirds aren't even close to any simple ratios other than the 5-limit ones. Can you say that all three intervals in an augmented triad are functioning as 5-limit consonances? >Besides, how do the other ratios >support 10/9??? They don't support either. They support 28/25, which is too complex to be psychoacoustically relevant.