DeMorgan numbers & graph

[A440A@AOL.COM]

 Greetings, 
Inre August DeMorgan's temperament, Bill writes:

<<  However, the more I study it, the more it 
really seems like a temperament created entirely in error<snip> Yet, 
I assume that it was done deliberately.
The question I have is why would anyone really want this? >>

       Why would anyone want a Pythagorean tuning with pure fifths (and 
unusable "thirds") almost all the way around the circle?  Why would someone 
want a 1/4 C meantone, Why would someone want an absolutely circular 12 ET?   
All of these tunings offer benefits not found in the others, and they all 
have their own, unique liabilities, (though the argument can be made that a 
wolf is a wolf is a wolf).  This tuning of DeMorgan's is no different.   It 
has strengths and weakness, also.   There are two considerations. 
  #1 is that all thirds are within 4 cents of ET, there is not a lot of alien 
pitch involved here.  This tuning is a mild alteration of our familiar.  150 
years ago,  I would imagine that real world temperament practice was a LOT 
less consistent,  and this tuning would not have been as shockingly atypical 
then as it appears today. 
    The other facet is more subtle and requires one to go beyond the beating 
of the thirds to understand a temperament's usefulness.  The DeMorgan 
produces five near pure fifths in the white keys, and as has been known  for 
25 centuries,  pure fifths have a strong musical attraction.  For a 
composition that uses the fifths in the melodic line or harmony, this tuning 
has something to offer.   
     Since we will be using this tuning for recording a Chopin piece this 
weekend, it has been around on some of my instruments and I have been 
watching local contemporary musicians play it.   One didn't notice it wasn't 
ET (see #1 above).   Several have liked it so much they intend to use it in 
the studio, (these are jazz people).  No one has been offended by it, (though 
a gospel enthused gentleman thought it was a little 'off", which sorta 
surprised me, but hey,  this is a new deal every day. 

Bill again:
 >>Unless, as it was  explained to me, it is really meant for someone who is 
so used to the sound  created by an erroneously constructed temperament and 
has learned to 
compensate for it in the playing that it suits the handicap.<<

  That is a definition both novel and obtuse .  I don't think it plausible 
that Mr. DeMorgan proposed this tuning for harmonically handicapped 
musicians.  Jorgensen gives an alternative, and logical, explanation of 
Chopin's possible attraction to a tuning like this, (the source of our 
current pursuit).  While the Impromptu #66 comes alive in this temperament,  
several other Chopin pieces seemed somewhat lifeless. I suppose the jury will 
be out until the recording is! (:)}
     
Bill again: 
>>  To me, Chopin, Debussy and Ravel played in the De Morgan 
would sound just as inappropriate because the music would have most of the 
energy and tension it was meant to have taken away.  The pianist could only 
compensate by playing louder and faster.  >>

      There are more ways of creating tension that by volume and speed, so 
the pianist actually could do a lot of things.  As to the "energy and tension 
it was meant to have", that is an assumption by the author that he knows the 
musical intentions of these composers. Speculative ground, at best.   I think 
 a comparison with our modern ET would be more instructive.  
     The energy and tension in ET is quite high.  I didn't realize that until 
I left it for a while and came back.  The 13.7 cent thirds produce an 
unrelenting tension in tonal music, and that is precisely the danger.  After 
a short time, the listener becomes inured to the tempering, and not only no 
longer hears it, but is also left with the lack of tonal contrast inherent in 
ET.  This acclimation actually reduces sensitivity to musical tension,  so 
the tempering and its effect can move in opposite directions at times. 
      Any of the unequal temperaments counter this lulling of the tonal 
senses by offering variety in the keys.  The movement (modulation) among 
varying levels of dissonance is stimulative,  thus unequal temperaments are 
capable of increased musical tension, even though, physically, there may be 
less overall beating occuring in the music. 
     If the comparison is made between a particular Chopin piece on a 
DeMorgan and on ET,  the level of emotive attraction may be stronger on the 
unequal one, even though by the numbers, there is more dissonance in ET.  
That is my suspicion and I intend to find out by recording a version and 
turning it loose in public (talk's cheap) I will be interested in hearing 
what the membership at large thinks about it.  
    Of course, there will be some that refuse to listen to anything that is 
outside their preconceived sense of "correct", but the loss is theirs.  They 
that have ears, let them hear. 
Regards, 
Ed Foote
(this will also be something of a learning experience inre stability, since 
we are going through 6 temperaments in 4 days.  Beginning on a mild 
Victorian, ending on a Werckmeister! wish me luck, )