Re: [Phys-l] Exotic harmonies

["Kilmer, Skip" <kilmers@greenhill.org>]

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu]On Behalf Of Jack
Uretsky
Sent: Tuesday, May 30, 2006 7:56 PM
To: Forum for Physics Educators
Cc: Nancy Seese; Bill Mathews; T.K.Wang and Mary Brooks;
HornCabbage@aol.com; Bryan Mumford
Subject: Re: [Phys-l] Exotic harmonies


Hi bc-
 	Plese ask your friend if he is familiar with the tempered scale -
used by all piano tuners since about the time of Bach.  You can find the 
ratios on the web, through Google - probably in the Wikipedia.
 					Regards,
 						Jack

On Tue, 30 May 2006, Bernard Cleyet wrote:

> My friend, the crackpot inventor sent me the msg below.
>
> I'll mail the MP3 files to which he refers upon request.
>
> As obvious from the header, I'm sending this to musician friends and a
> Physics of music expert in addition to the list.
>
> bc
>
> ----------------------------------
>
> I've been studying music scales and I've been tabulating some inherent
> harmonies not recognized by western music. This came about as a result
> of my "Harmonic Visualizer", which is just a fancy Lissajous pattern
> generator. See:
>
>
> http://www.bmumford.com/art/visualizer.html
>
>
> My device easily shows many mathematical patterns that are not musical
> harmonies in the western scale, but are inherently harmonic because of
> the low value integer relationships (like 7:4, 11:8, 13:8, 14:8).
>
> For example, there are ratios of halves (3:2 = perfect fifth), thirds
> (4:3 = perfect fourth), quarters (5:4 = major third), fifths (6:5 =
> minor third), sixths (see thirds and halves), and eighths (9:8 = major
> second, 15:8 = major seventh).
>
> But there are no ratios of sevenths. Even though 8:7, 9:7, 10:7, etc.
> are pretty low ratios and, in theory, ought to be pleasant harmonies.
> And they are, in fact, relatively soothing harmonies, which you can hear
> below:
>
> [nope]
>
>
> <>Yet none of these notes (outside the root and octave) are in western
> music.  Furthermore, if you diagram out the notes of our scale and the
> ratios that produce them, there are some major harmonies missing. Like
> 7:4, which falls between A and A#. A is 5:3 and A# is 9:5. But 7:4 is a
> pleasant harmony BETWEEN A and A#:
>
> [nope]
>
> It just seems odd. One wonders what sort of music might be possible by
> using more of the mathematical harmonies, or by using only (for example)
> ratios of 7.
>
> Since there is nothing new under the sun, one wonders if someone has
> already made music using these exceptions.
>
> One also wonders if any non-western music explicitly uses these
> additional harmonies.

-- 
"Trust me.  I have a lot of experience at this."
 		General Custer's unremembered message to his men,
 		just before leading them into the Little Big Horn Valley



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