Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Pythagoreans and Music
Replies: 13   Last Post: Oct 23, 1997 12:11 PM

 Messages: [ Previous | Next ]
 John Conway Posts: 2,238 Registered: 12/3/04
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 96-04-16 18:58:40 EDT, you write:
> >

> >>I think that that (2^(6/12) in equal-tempering) 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 Saint-Saen's Danse Macabre.

> ------------------------------------------------------------------------
>
> A solo violin is often played so its scales are NOT even-tempered,
> but Pythagorean (or so I've heard).
>
> So -- in for example Saint-Saens'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