historical vs. equal temperament

[Jim Coleman, Sr.]

Hi Orlando:

Several months ago I wrote about tuning the pure 5ths Temperament, and it
was also published in the Piano Technicians Journal. Basically it involved
widening the temperament octave by around 1.5 to 2.0 cents at their 4th 
partials. This makes the octave about 1 bps wide. No problem, We've been 
listening to 4ths which are 1 bps wide for a long time. The initial thought
scares people, but in listening to the music afterward, it is quite 
acceptable. The 4ths will be wider also. In fact all of the wide intervals
as a consequence are slightly wider and all of the narrow intervals are
slower. It is still equal temperament with the final addition of tempering
the octaves. Some people think of it a Pythagorean tuning, but it 
nothing of the kind except for the pure 5ths. No pythagorean 3rds or 6ths.
Everything is smooth and even.

In constructing such a tuning, you must start out with the widened octave.
Please refer to the Aug '97 Journal for the details. Or better yet, attend
my class in Providence and get the detailed notes on how to do it by ear.

Jim Coleman, Sr.

On Fri, 3 Jul 1998, Orlando Fiol wrote:

> So, Jim, I'm quite intrigued by your pure fifths tuning, since, believe it
> or not, I had never heard of it before.  How is it done?  Does one start
> from a given point and just tune pure fifths all around?  Of course, that
> couldn't be right, silly me, since it would give a rather wide fifth
> somewhere around A-flat to E-flat.  so, what did you mean by the thirds not
> being Pythagorean in a pure fifths temperament?
> 
> Thanks,
> Orlando
> 
>