Meantone, my personal adventure-test for pure 3rd

[Billbrpt@AOL.COM]

In a message dated 3/19/99 5:23:11 PM Central Standard Time,
pianotoo@imap2.asu.edu writes:

<< Hi Bill:
 
 In your response to Richard you said and I quote:  "There is no test for a 
 pure 3rd the way there is for a 4th, 5th or octave."
 
 You might want to try an augmented 4th below the bottom note which becomes
 a minor 7th below the upper note. It is a faster interval, but could be
 slowed down by moderating the test note on the sharp side to slow down
 the beats. 
 
 I discovered this by using 3 Coleman Beat Locators. It's amazing what I 
 have discovered over the years with my own invention.
 
 Now, I am in need of some education. You have mentioned the 11th comma
 MEANtone temperament as being EQUAL temperament. It was my understanding
 that it takes 12 equal half steps to make equal temperament and so my
 logic seems to demand dividing the ditonic comma into 12 parts. Where did
 I go wrong?
 
 Jim Coleman, Sr.  >>

Thank you VERY much for the pure 3rd test.  I had been told by those who
taught me about the HT's that there was none, I should have known better than
to just accept a statement like that without trying to prove it otherwise.  It
would be a very valuable test for a serious aural tuner but I'd have to say
that it is the absolute *weirdest* test note  and pair of intervals I've ever
heard of.  I can see how it would work though and I do think that moving the
test note to a point of *convenient* listening speed would be necessary.

It seems that no matter what someone puts forth as an absolute truth in this
business, someone eventually comes along who can prove that notion false.  I
can imagine that the test would be only useful to a very skilled and
perceptive aural tuner but anyone who attempts something like the 1/4 Comma
Meantone for a serious musician should have the highest level of skill.  In
order to compensate for inharmonicity, you would want that test to show a very
slight difference on the wide side but for the 3rd to still *sound* apparently
beatless.  This would put a width of less than a cent in the interval.

As for the other question:  All of those meantone temperaments are named based
upon the Syntonic Comma, the one which relates to 3rds and whose value is 21.5
cents.  If you divide 21.5 by 11, you get 1.95, a virtual ET 5th.  What you
are thinking about is the Ditonic Comma, the one related to 5ths and whose
value is 23.5 (virtually 24) cents.  In that case, of course, ET might be
described as a 1/12 Ditonic Comma Meantone.  It's all academic but I do know
that this has caused some confusion.

I like to call ET a 1/11 Syntonic Meantone Temperament just as a joke, as in,
"What would you like your piano tuned in today, Ma'am, a nice Well-Tempered
Tuning or the 1/11th SYNtonic MEANtone?"  It puts the often heard statement,
"I've NEVER had anyone ask for anything but ET" into perspective.  It's all in
the presentation.  A good salesman can sell whatever he/she has to sell if the
right spin is put into it.

Regards,
Bill Bremmer RPT
Madison, Wisconsin