temperaments

[Ron Koval]

Thanks for continuing the discussion, ric M.  I think I see where this is 
going again, so let me answer this:

You asked what methods, I have the words of James Broadwood himself how
to tune ET in 1811.
<snip>

I'm going to start over.  Forget anyone saying anything about any historical 
temperaments.


A growing body of technicians have been discovering the joys and musicality 
of tuning an earlier version of equal temperament.  This temperament, known 
as Broadwood's best, has been used successfully in homes, in recording 
studios, and on the stage around the world.  With a maximum offset from the 
"sterile, clinical" modern equal temperament of only 5/100ths of a half 
step, all keys are playable, while retaining the preferences of musical 
development and harmony valued by western music.  Others of us have been 
instrumental in developing new versions of this more musical equal 
temperament for everyday use.  Consider the Equal Beating Victorian, the 
Coleman 11 and the Koval Variable temperaments as those developed using both 
the best of the aural tradition and modern spreadsheet technology.  By 
removing the biases introduced in the middle of the 20th century by the 
development of tuning technology, we've rediscovered the extra connection to 
the music that these tunings can bring.

>From Mr. Broadwood himself:

Farey's critique piqued James Broadwood's interest and he responded---

To the Editor of the Monthly Magazine
	SIR,
If Mr. Farey will peruse again the article on Tuning, in your Magazine of
September, he cannot but perceive my object to be, not to advocate the
correctness of any system of temperament, but to point out  "the best 
practical method of tuning keyed stringed instruments."  I gave instructions 
to produce the interval of a proper fifth in the temperament called the 
equal temperament, from its being in most general use, and because of the 
various systems, it has been pronounced the
best deserving that appellation, by Haydn, Mozart, and other masters of
harmony.
<snip>

The modern twist to these tunings has been the study of the beat ratios 
between the intervals in the early equal temperaments.  In fact the ratio 
between the M3 and the m3 in a triad is the only thing equal in a "sterile" 
modern temperament.  By manipulating this ratio to get a whole number ratio, 
extra vibrance and resonance is added to the tuning.  Surprisingly enough, 
it was the development of the modern tuning machines that allows easy 
experimentation with more responsive tunings.

Ron Koval

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