Non-Equal Temperaments

[A440A@aol.com]

Greetings, 
<< >>My question is this.  I'm wondering if unequal temperaments tend to sound

>>like they are going out of tune quicker than equal temperament.  My

>>reasoning is that if some of the notes are already altered from equal

>>temperament, isn't there less of a "window" of pitch shift before the piano

>>starts to sound out of tune?  Does this seem to be a valid question and/or

>>concern?

     Yes, it is a valid question, however, there are some other 
considerations.  One is that since ET is totally out of tune, the ear stops listening to 
the beating and doesn't notice out of tuneness so much.  It has been my 
experience that musicians that become familiar with the WT's often begin to regard ET 
as sounding out of tune, even when it is freshly and accurately tuned! 
    It is rare that a piano will go "out of tune" by having a few notes here 
and there move around, so the concept of a note moving and causing a highly 
tempered interval to become too far out to accept is unlikely.  The far greater 
occurance is the spreading or compressing of octaves in relation to humidity 
or temp changes.  I am going to disregard the unison question, here.  
    I believe that the mild WT's stay "in tune" longer, and the customers of 
mine that use them agree.  These temperaments are already somewhat "organic", 
as opposed to the scientific and rigid ET.  Thus, a slight loosening of their 
structure usually goes totally unnoticed. 


Conrad  writes:
>>Unequal temperaments frequently have PURE fifths, fourths and/or 

thirds.  Therefore, if the tuning starts to slip and one of these pure 

intervals is beating, it is IMMEDIATELY recognisable as being out of tune.<<

No ifs, ands, or buts.  It _is_ or it _isn't_ PURE. << 

     In musical use,(as opposed to tuner's examinations),  a third which is 
tempered only 4 cents is heard as very Just.  In the Broadwood tuning, for 
example, you have the C-E tempered 7 cents, which is half as busy as ET.  The four 
most expressive keys have their thirds tempered only 18 cents, which is only 
30% more than ET.  That means that there is less dissonance produced, in sum, 
by the Broadwood, if you play exactly the same amount in ALL 12 keys.  
However, this is very unlikely, since the majority of music is written in the five 
simplest keys.  Which means, far more consonance is available from a WT in the 
music written before 1900. 

>>Also, that pure interval is frequently the other side of one which is real 

close to being a "wolf".  One common note slipping can not only "temper" a 

pure interval, but create a REAL nasty interval out of one which had been 

only borderline nasty.<< 

   Here we have to decide how close to being a "wolf" is.  Historically, the 
syntonic comma (21.5 cents) was the upper limit in the WT's and in more modern 
WT's like the Coleman 11 or Broadwood, 18 cents is the limit.  This is hardly 
a wolf.  
 

>>Can you listen to a major third which theoretically should beat at 9.7, but 

happens to be beating at 9.6 or 9.5, and IMMEDIATELY tell that it is slow 

without a machine or using several checks?<< 

     You might not hear that it is beatin slower, but the third on the 'other 
side' will be beating noticeably faster! 

>>There is more "wiggle room" in equal temperament than in a temperament 

which uses pure intervals.>>

    I feel that the opposite is true.  There is only one ET, and deviations 
from it are obvious when comparing chords.  It takes very little imbalance to 
make one key sound different than another.  In the WT's,  the keys are all 
different to begin with, and any shift will only change the relative balances.  

Corte then asks: 

>>Since most of my clients only tune 1-2 times per year, it sounds like I'd

be doing them a disservice by tuning anything other than ET.  Of course, a

lot of my clients own small spinets and consoles and claim that they can't

tell when it's out of tune (even when it's terribly out of tune).<< 

     I don't think it would be a disservice, at all.  The clients that own 
small spinets and consoles have pianos that are almost impossible to get a real 
even ET on to begin with, but more importantly,these customers will,  by and 
large, never be playing the literature that uses more than 4 accidentals. For 
them,  a tuning such as the Broadwood or Coleman 11 will make their piano sound 
far more harmonious than ET.  And if they perchance venture into a simple, 
expressive, Chopin piece, the added color of a non-ET will create a dimension 
that is musically effective.  .  

 
Andre writes: 
   Some time ago I was in Bergen Norway and Richard Brekne, who lives and 

works there, asked me to listen to a Bill Bremmer tuning he had just 

tuned. I played the instrument for a bout a minute and told Richard that to 
me 

it sounded awful to me and that it sounded like it was in need of a 

tuning. It means that a. people used to ET may have a problem with un-ET, and 

it could also be that when an un-ET tuning goes off, it will only cause 

more 'problems'.<< 

    If I remember correctly, Richard tuned a Broadwood's temperament for his 
department chair and it was very well received.  We have to remember that the 
musician doesn't listen to the same thing as the tuner does.  We tend to judge 
a temperament by how close it is to what we are familiar with, while the 
musician listens to how the music sounds.  There is a difference between these 
two. 
    For the record, I have found far more customers that prefer non-ET 
tunings that those that want to stay with ET.  This includes not only the expected 
Classical pianists, but also the jazz musicians and songwriters around here.   
Many times, when they call, they are amazed how long it has been since I 
tuned, last. 
Regards, 
Ed Foote RPT







Ed Foote RPT 
http://www.uk-piano.org/edfoote/index.html
www.uk-piano.org/edfoote/well_tempered_piano.html