Unequal Temperaments

[Billbrpt@AOL.COM]

In a message dated 6/8/00 7:58:21 AM Central Daylight Time, A440A@AOL.COM 
writes:

<< Keith writes:
 << I
 have some charts which show cents deviation from equal temperament. My
 question is, can I simply add or subtract these numbers up and down the
 complete 88-note scale or do the cents deviations change as the octaves are
 stretched?  >>
 
 Greetings,
 The cents deviations will not change over the scale.  If the numbers in your 
 machine are already such that the octaves are stretched to your taste,  
 adding cents to them will not change your octaves.  
     The easiest way to use the SAT I for this is to use your pitch change 
 buttons to add a value, such as 0 for the A, or maybe 4 cents for the F, -3 
 cents for the E, or whatever your new temperament calls for, and then, tune 
 all the A's, in one pass, then  all the F's at once and so on.  For safety, 
 zero your machine between each setting so that there is no cumulative 
 addition or subtraction of your cents deviation. 
     You may find that doing the most altered notes first to be beneficial,  
 as they may affect the soundboard like a small pitch raise.  You may need to 
 go back and change the first or second notes that you began with, 
 particularly if you will be trying the meantones with their more drastic 
 departures from ET.  
   Good luck, and remember,  judge your result with music, not 20th century 
 techniqes or expectations.  I think you will like not only the tonal palette 
 that occurs with the unequal tunings, but also,  the freedome from the 
 unrelenting beating of all the thirds.  
 Regards, 
 Ed Foote RPT
  >>

Now ask yourself, is this really any way to tune a piano?  Is this a way to 
get to know and understand what temperaments are all about?  What kinds of 
effects can be expected?  Which kind of temperament would be best to use for 
which piano under which circumstances?

Let's see, you take measurements of the difference in inharmonicity between 
two different partials on three different notes first, then wait a few 
seconds while the ETD makes a calculation for you.  Do you trust that 
calculation?  What if the piano you have has an irregular scale design?  If 
this calculation is inaccurate for ET, it most certainlay will be for 
whichever other temperament you may choose.

If the temperament you are using has irregularly tempered intervals, does it 
not also make sense that you may want to "temper" your octaves a little 
differently as well?  No smooth curve octave stretching calculation whether 
it be the FAC, RCT or Tunelab program can cope with this.  No one who likes 
to use the "deviation of a deviation", plug in in a dozen numbers (without 
making a mistake doing that, of course) method of tuning will ever admit that 
the octaves produced may not be ideal.  It would require, God forbid, an 
aural correction.

I strongly discourage this approach to the study of Histoorical Temperaments 
(HT).  It is no more productive than to have a beginner learn to tune using 
an ETD without learning to listen and to construct intervals.  Such 
individuals rarely are able to pass the PTG RPT Tuning Exam.  They cannot 
aurally recognize an error in tuning or whether the calculation is accurate 
for the piano in question.  Tuning this way loses the concept of art that it 
should, by all rights have.

Ask yourself this:  How many strings could you tune, how many intervals could 
you construct aurally during the time it would take you to do the FAC 
calculation, then plug in the deviations?  Does not tuning all the A's first, 
then cancelling out that deviation, then plugging in the next one, (making 
sure that it is correct, of course and that the sign has not been reversed or 
that the figure has not been misread from the book or chart), then tuning all 
of the A#'s or choosing the largest deviations first, as was suggested, 
remembering which ones you have done and which you haven't and going over 
some of them again, sound like an awfully awkward way to tune a piano?

What if part of your piano is even as little as 5 cents off when you start?  
If you only tune each of these notes once, do you expect them to stay where 
you tuned them by the time you are finished?  What if it is 10 cents off?  
What if it is a typical situation with an irregular scale and the pitch 
varies from 5-10 cents off to as much as 30 cents off from where it should 
be?  Would you still expect the piano to sound like it should tuning it the 
way that was suggested here?

There are no shortcuts to learning and understanding new skills.  It really 
concerns me that these ideas will be "taught" at the Convention as a valid 
way to tune the piano.  In my view, it will be the easiest way to insure that 
whoever does try this will conclude that the whole area of HT tuning is not 
worth pursuing.  How many will say, "I tried that HT stuff once and the 
results were a disaster so I just tune ET".  And among those who say that, 
how many will not recognize that the "ET" that they think they are tuning is 
not ET at all?

I suggest getting some HT tuning books from the library, practice aural 
tuning, decide which kind of temperaments work for you and your goals and 
learn to program your results into the SAT if you desire to use that device.  
That way, a thorough understanding will be developed.  There will be the 
ability to make a decision about octaves rather than relying on a calculation 
that may be less than satisfactory.  Understanding temperament concepts and 
learning to control the piano rather than hoping that some list of numbers 
will provide a satisfactory result is the way to be successful regardless of 
which combination of ideas is the goal.

Bill Bremmer RPT
Madison, Wisconsin