Just tuning and "sweetness"

[Don]

Hi Dave,

My understand is that the ratio 2187:2048 is a full syntonic comma.

The syntonic comma, also known as the comma of Didymus or Ptolemaic comma,
is a small interval between two musical notes, equal to the frequency ratio
81:80, or around 21.51 cents.	

When you ascend by a cycle of justly tuned perfect fifths (ratio 3:2),
leapfrogging 12 times, you eventually reach a note around seven octaves
above the note you started on, which, when lowered to the same octave as
your starting point, is 23.46 cents higher than the initial note. This
interval, 531441:524288 or approximately 1.0136:1, is called a Pythagorean
comma.

Have a look here for a much longer explanation:

http://members.shaw.ca/quadibloc/other/musint.htm

and

http://www.explore-music.com/music_theory/S/Syntonic_comma.html

At 12:58 AM 5/19/2005 EDT, you wrote:
>Pardon my complete ignorance here, but what is a "full comma?"  I've heard 
>the term often enough so that its about time I understood what it is 
>referring to.
  
>Thanks,
  
>Dave Stahl

>Version: 7.0.322 / Virus Database: 266.11.12 - Release Date: 5/17/2005 

Regards,
Don Rose, B.Mus., A.M.U.S., A.MUS., R.P.T.
Non calor sed umor est qui nobis incommodat

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