more on this temperament thing

[Ron Koval]

Hello all 'temperers' out there.

It's been a while since I've written on the temperament issue, but I'd like 
to restate some of the ideas I've posted before. (this time no graphs, I 
promise)

I hear from other tuners, that they would like to appreciate HT's, but the 
dissonences just get in the way.  I'm not surprised, considering the choice 
of temperaments listed; Young, Kirnberger III, and the Coleman XI are all 
pretty strong choices!  There is an 'aquired' aspect to tuning in 
temperaments, and it becomes easier to accept 'stronger' temperaments the 
more they are heard.

But back to the three listed temperaments.  Imagine someone trying Thai food 
for the first time and unexpectedly gets a VERY spicy dish.  They may decide 
not to eat Thai again, because it's too spicy.  Now, there are many Thai 
dishes that are not spicy, but because of the introduction, they may decide 
to play it safe and not eat Thai anymore.
Temperaments can be thought of like spice; it's best to start out easy, and 
not get pushed away by too strong of a tuning.

So...... to review, in ET, every third is tuned almost 14 cents wide of 
pure.  Once a third gets to more than 20 cents wide of pure, most first 
timers will squirm at the sound, because it's something new.  In our scale 
from 1 to 20, ET major thirds are more than half way to unacceptable, giving 
the 'busy' sound that most of us are accustomed to hearing.

In the Young, the biggest offset from an ET tuning is 5.9 cents, which 
allows the major thirds to progress from around 6 cents, to 22 cents from 
pure thirds.

In the Kirnberger III, the biggest offset from an ET tuning is around 9 
cents, causing the major thirds to progress from 0 cents(pure) to around 22 
cents from pure thirds.

Now at first look, these may seem to be similar, with the Kirnberger having 
more purity.  WRONG!  This is where graphing the major thirds can help to 
preview the temperament.  The Young progresses evenly through the keys, 
while the Kirnberger has three pure thirds, (C,G,D) Two kindof ET thirds 
(A,F) and 7 thirds up around 20 cents from pure!

The Coleman XI is the weakest of the three, with the biggest offset from an 
ET tuning of 5 cents, giving a progression from around 8 cents to around 18 
cents from pure.  However, when playing triads, instead of just major 
thirds, the Emaj triad SOUNDS out of progression.  I think that this has 
something to do with beats combining and influencing each other.  In a 
triad, there is a major third, a minor third, and a fifth sounding together. 
  All the beat rates combine to influence the overall effect of the chord. 
(Even the octave, if included has an effect on the temperament, as Bill 
Bremmer uses in his tunings.)

So what to use for a first 'taste test'?  Good ones to try are the Moore, 
with the biggest offset being 3 cents, major thirds range from around 10 
cents to around 16 cents from pure.   Ab is the chord that sticks out in 
this tuning.  Or, try an equal beating Victorian type.  One that works with 
offset tuning is:

C  2.7
C# -1.3
D  1.8
D# 1.8
E  -.2
F 1.7
F# -1.5
G  3.8
G# 0
A  0
A#  .6
B  -1.4

This one has the largest offset of 3.8 cents, with the major thirds 
progressing from aound 8 cents to around 16 cents from pure.

There are many mild temperaments to start the journey, and all temperaments 
can be 'diluted' as well to maintain the flavor, while reducing the impact.  
Remember, for offset tunings to work, your machine of choice must be able to 
calculate a good ET first.  If you find that you have to make adjustments to 
a machine tuning to get ET right, (like at the break) it's best to work off 
of an 'adjusted' saved tuning to create an alternate temperament.

Happy tuning!

Ron Koval

Chicagoland


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