HT tuning checks

[Billbrpt@AOL.COM]

In a message dated 11/4/98 8:58:13 AM Central Standard Time, A440A@AOL.COM
writes:

<< Jerry asks:
 >In tuning Major 4th's and 5th's pure, are the M3-M6 and M10-M6 checks
 >valid for checking that the interval is pure. That is, testing that
 >M3=M6 or M10=M6.
 
 Greetings, 
     For pure fifths, the m3-M3 has proven to be a useful test.  Going to the
 tenth is, imho, not as necessary for pure intervals as tempered ones.  This
 may be just a personal preference.  Actually, my personal pref. is the SAT!
 It makes these tunings, (and there are many), as easily provided as ET.  
 Good luck, 
 Ed Foote  >>

The tests that prove that an ET 5th is tempered, M3-m3 and M10-M6 and for the
ET 4th, M3-M6 were originally tests for *pure* intervals.  When tuning ET, you
are looking for a very slight discrepancy between the two that prove that the
interval is *not* pure.  If the tests reveal a pure, widened or overly
tempered interval, you know to correct it.

The difference between the two tests for the 5th is that the M10-M6 is for a
lower set of coincident partials,  3:2 and the M3-m3 is for the higher audible
set, 6:4.  In lower inharmonicity pianos, there would not be much difference
but in the higher inharmonicity instruments, the results will lead you towards
a slightly different outcome.  The lower set is usually easier to hear because
the beats are stronger.

For the most part, it seems to be more useful to use the lower set in all
cases.  When Ed says he uses the SAT, he probably has it reading on the lower
set.  I also use the SAT to really lock in a perfectly pure 5th when that is
what I want.  In the octaves above the temperament section, these 5ths become
slightly widened.  In ET, the very slightly tempered 5ths become virtually
pure and even widened in the high treble.  A slightly widened 5th is a very
appealing and acceptable sound regardless of the temperament used.

There is only one test for a 4th because there is only one set of audible
coincident partials.

When tuning aurally, the M3-m3 test for the 5th is a little more convenient to
use for quick reference.  You simply find the note which makes a minor triad
between the two notes which form the 5th.  To use the test for the lower
coincident partials, you drop that note down an octave.

These tests are really only useful when doing the very finest tuning.  Your
test notes must be virtually where they should be when the tuning is completed
in order for you to be able to use them.  It is another example of how "You
can't tune a piano unless it is already in tune".

Sincerely,

Bill Bremmer RPT
Madison, Wisconsin