# Wendell well-temperaments

[Gene Ward Smith, Yahoo tuning-math, message 6031 (Wed Mar 5, 2003 12:13 am PST)]

If we look at the brat ratios of Wendell Well, they are approximately [r, 3/2, 3/2, r, 3/2, 3/2, 3/2, r, 3/2, q, r, r] where both r and q are nearly 2, but r is a little less and q is a little more. If we solve for these under the condition that the product of the fifths comes to 128 (octave closure) then q is

320*(-27*r+18*r^2+40)/r/(2187*r^4-5184*r^3-7728*r+5760+5216*r^2)

We can relate r and q in various ways; for instance making q exactly 2, or having the average of r and q be 2. The simplest way however is to make r exactly 2, which makes q to be 580/293. This gives us the following scale:

[1, 1215/1144, 321/286, 68187/57200, 180/143, 3823/2860, 405/286, 214/143, 22729/14300, 963/572, 5107/2860, 270/143]

It is a rational intonation version of Robert's temperament.

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