More about commas

[Billbrpt@AOL.COM]

In a message dated 8/8/00 8:11:49 AM Central Daylight Time, 
remoody@midstatesd.net (Richard Moody) writes:

<< A series of pure fifths would  tune out resulting in C--E
 (81/64);  E--G#(81/64) and leaving G#--c slightly smaller than 5/4.  If the
 series were continued, (G#--D#--A#--E#);   D#--G, A#--C, and E#--A should
 all sound as pure 3rds.   Crazy eh?  Of course the "wolf" fifth caused by
 the pythagorean comma would then be between "F" (actually E#)  and
 .  ---ric >>

I'm not sure that you had this all as you intended but I get the idea.  What 
it does illustrate is the importance of studying the various kinds of tunings 
and temperaments: so that the tuner-technician really understands the 
consequences of errors and particularly of cumulative errors.

Many tuner-technicians today like the sound of a pure or nearly pure 5th but 
dismiss the idea of tuning anything but Equal Temperament (ET) on the modern 
piano.  I often hear technicians say something like, "I concentrate on 
getting pure 5ths and don't care about the 3rds".  While this same person 
scoffs at the notion of tuning a Well-Tempered Tuning or Meantone Temperament 
and makes no effort to learn or understand either, the result may easily be 
some kind of Pythagorean or Quasi-Pythagorean type.

Unfortunately, there is not much music at all which features open 4ths or 
5ths.  Tuning those intervals as pure only sounds good when the 
tuner-technician is playing them.  The kind of mixed up, chaotic, unfocused, 
reverse polarity kind of harmonies that are the actual result of wildly 
uneven 3rds go completely unnoticed. 

I can tell you from personal experience that I have heard many a pure or 
nearly pure Ab-C 3rd and a screaming fast C-E 3rd in someone's temperament as 
a consequence.  The tragedy is that the person doing this cannot recognize 
nor understand the error or what its consequences are on virtually all music 
that will be played.  That same person is likely to dismiss the idea of 
studying the various kinds of temperaments and go through a lifetime of 
professional experience repeating the same errors.

Bill Bremmer RPT
Madison, Wisconsin