Tuning

[Michael Jorgensen]

Hi Jonathan,
     Bill Bremmer hits it right on the nail.  Tuning a temperament
without using thirds and sixths would likely be pretty hard if not
impossible.  The important thing is that the thirds and sixths increase
at a steady rate.  This may mean an F-A third of about 7.3 bps on a
concert grand or around 5 bps on a Baldwin Hamilton studio, even lower
on smaller pianos.   I don't count beats per second on fifths as it
would take to long to wait for.  Simply listen for pure and shoot for
alittle bit of unclarity on the FC fith. 
      If you're not sure if you're fifth is narrow, listen to the note a
major sixth below the lower note with that note of the fifth and compare
to the upper note which should beat alittle slower, assuming that sixth
is wide.  To test a forth, compare the beats formed by the wide Major
third below the lower note to the upper note which should be alittle
faster.  Listening for slow beats on most pianos would be a challenge as
the pitch/tone is very transient, very short, and usually false.  P4 B-E
is about as slow as I might bother counting, about 1 bps.
-Mike Jorgensen

    
Bill Bremmer wrote
> 
> You need to learn the very valuable 4:5 ratio of contiguous 3rds test.  This
> does not mean "beats per second" but a proportionate amount.  Contiguous 3rds
> are any two 3rds which share a common note in the middle such as FA and AC#.
> To have the relationship be correct, for every 4 beats you hear from the lower
> 3rd, you should hear 5 from the upper.
> 
> For a beginner, this may seem to be an extremely fine amount to distinguish
> and that it is.  You can use your 4ths and 5ths temperament and once you get
> to a place where you can use the 4:5 ratio test, try it to hear the results.
> You may look at it this way:  it is easier to hear when the ratio is *not*
> correct than when it is.  If the two intervals are the *same*, there is
> something wrong, if the lower one is faster than the upper one, there is
> something wrong.
> 
> That is the value of this test:  it tells you when there is something out of
> order.  When the test reveals an incorrect ratio, go back to the 4ths and 5ths
> you have tuned and try to find the error.  Is one of them too pure?  Is one of
> them too fast?  Usually you will find both.  Ask yourself, "Which note can I
> move up or down which will correct the situation?"
> 
> This relationship was discovered by PTG's own members, Bill Garlick RPT who
> worked with Dr. Al Sanderson RPT (Golden Hammer Award winner and inventor of
> the very popular Sanderson Accu-Tuner).  Garlick had the idea and Sanderson
> proved it out mathematically.
> 
> It has been for me the most valuable diagnostic interval ever for
> constructing, correcting and proving an Equal Temperament (ET).  I use it when
> I serve as a Certified Tuning Examiner when I prove or disprove an error on
> the RPT Tuning Exam.
> 
> The danger in relying solely on 4ths and 5ths is that your 3rds can easily be
> chaotically uneven.  I have seen over the years that many tuners end up tuning
> what they believe to be an ET but because of no good way to listen to, check
> and correct the 3rds, they end up creating an inverted version of a Well
> Tempered (WT) tuning (WT and ET are *not* synonymous).  This will make all
> music from the piano sound a bit sour and unfocused, yet it is a very common
> occurrence.  You can do better by learning to use this very valuable tool.
> 
> Bill Bremmer RPT
> Madison, Wisconsin