Optimal meantone fifths and good best fifths

159 has a meantone fifth far too flat to be considered optimal--even
Lucy would think it flat. You can get a meantone fifth in an optimal
range ("5-limit poptimal") and a fifth within a cent of 3/2 with other
choices. One is 212, which is *four* times 53. Another is 181, which is
the smallest choice that will work, and a good 23-limit et. Still
another is 224, which is a very strong 13-limit system.

So, you think 7.5 cents deviation is too much for the transition from the Baroque fifth to the Pythagorean fifth? I personally do not think anything more precise is needed for the Qanun, or for Maqam Music Theory either. Once a satisfactory lower-limit resolution is reached, the rest of the high-granularity stuff is just detail.
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Haziran 2005 Cumartesi 22:07
Subject: [tuning] Optimal meantone fifths and good best fifths

159 has a meantone fifth far too flat to be considered optimal--even
Lucy would think it flat. You can get a meantone fifth in an optimal
range ("5-limit poptimal") and a fifth within a cent of 3/2 with other
choices. One is 212, which is *four* times 53. Another is 181, which is
the smallest choice that will work, and a good 23-limit et. Still
another is 224, which is a very strong 13-limit system.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> So, you think 7.5 cents deviation is too much for the transition
from the Baroque fifth to the Pythagorean fifth? I personally do not
think anything more precise is needed for the Qanun, or for Maqam
Music Theory either. Once a satisfactory lower-limit resolution is
reached, the rest of the high-granularity stuff is just detail.

You're the maqam expert. Anyway, the fifth actually works as a
meantone fifth; I just don't think it is optimal.