Tuning

[Billbrpt@AOL.COM]

In a message dated 10/17/98 9:19:13 PM Central Daylight Time,
jpage@capecod.net writes:

<< No one has mentioned the test of a major triad
 canceling out the rolling beats of the fifth.
  >>
It is my understanding that this will only occur with a more tempered 5th than
ET allows for.  This happens in both the Victorian and 1/7 comma Meantone
temperaments that I frequently tune as well as in many other HT's.  But an ET
5th must be anything but "rolling".  When the 5th comes this close to being
pure, anywhere from 1.8¢ to 0.8¢ narrow (data from a sampling I did of a
Master Tuning for an RPT Exam), the Equal-Beating effect of canceling out some
of the rapid beats does not occur.

This is the reason that many of the Ht's make harmony sound "clearer" than in
ET.  Conrad mentioned the Marpurg Temperament earlier in this thread.  It has
9 of its 5ths absolutely pure while the remaining three are noticeably wobbly
in comparison.  I believe they are 1/6 ditonic comma 5ths which would place
them at 4¢ narrow, twice the tempering of an ET 5th.

This creates a very interesting combination:  The 9 triads with pure 5ths
sound very "clean".  All 3rds and 6ths progress at the same rate as in ET.  In
fact, if you listen to the 3rds and 6ths alone, they sound identical to ET.
The remaining tempered 5ths have that canceling out effect of the tempering in
the 5th.  This is a way of getting the most pure 5ths that you can without
making the octave overly wide as you must do in the ET with pure 5ths.

I use the very properties you speak of in each of the 24 distinctly different
major and minor tonalities of my Equal-Beating Victorian Temperament (EBVT).
Not a single triad bears the exact same characteristics of an ET triad.  The
5ths are either pure or tempered.  The tempered 5ths cause the major triads to
bear the characteristics you speak of.

Bill Bremmer RPT
Madison, Wisconsin