Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: Pythagoreans and music
Posted:
Apr 18, 1996 10:36 AM


On 18 Apr 1996, Daniel A. Asimov wrote:
> In article <960417183558_193158113@emout15.mail.aol.com> Marksaul@aol.com writes: > >In a message dated 960416 18:58:40 EDT, you write: > > > >>I think that that (2^(6/12) in equaltempering) is part > >>of what's known as the Devil's Triad, AKA a diminished 7th; > >>at any rate, a nice refernce is _The Myth of Invariance_ > >>by McSomebody. > > > >I've never heard of the Devil's Triad, but the Devil's interval is an > >augmented fourth (or diminished fifth: they're the same in the tempered > >scale). The ratio is 2^(6/12). It's the interval you hear in the solo > >violin at the beginning of SaintSaen's Danse Macabre. >  > > A solo violin is often played so its scales are NOT eventempered, > but Pythagorean (or so I've heard). > > So  in for example SaintSaens's "Danse Macabre", just what interval > is actually played by the violin for this "Devil's interval" ? > > Is is really 2^(6/12) = sqrt(2) = 1.414..., or is it an approximating > rational number like 7/5 = 1.4 ? > > Dan Asimov > After joining this conversation this morning, it occurred to me that (of course) the MOST dissonent interval will be that corresponding to the Golden ratio 1.618... . Then around noon, I opened a paper someone had sent to me, and found it to contain the words:
"Although many contemporary music composers have been intending to gain control of the golden section, ... ... the golden section gives the critical dissonance."
Quite a coincidence! Does anyone know of any "traditional" name for the "golden section interval"?
John Conway



