Non-Equal Temperaments

[Corte Swearingen]

Ron,

I guess I didn't realize that all machine-generated temperaments tune the
octaves in the same way as ET - it's just the intervals that are slightly
altered.  That makes very good sense.  Thanks for the clarification.

Corte


                                                                                                        
                      "Ron Koval"                                                                       
                      <drwoodwind@hotma        To:       pianotech@ptg.org                              
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                      Sent by:                 Subject:  Non-Equal Temperaments                         
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                      04/02/2004 03:06                                                                  
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Hey Conrad,

I'm guessing this is just a case of over-re-simplificating, but when you
wrote this:
<snip>
I never said all fifths were pure. The fact that they _can't_ all be pure
is why we have to temper in the first place!

All the methods of tempering are efforts to split that difference.  The
more times you split the difference, the fewer pure intervals until you get
to ET, where there are none.
<snip>

It might have been a bit more clear to observe that there are a great many
temperaments that do not have ANY pure fifths, yet produce key color.  The
Wells and Victorians value a range of dissonence, rather than just "good"
or
"bad".

But back to Corte's question..... Hmmmm, do they "ripen" quicker?  What
normally goes out first?  Unisons.  There shouldn't be any difference
there.
  Next, if you live in a variable climate, I guess the octaves start
getting
spread, or contracted, around the break.  All of the machine-generated
temperaments set the octaves the same way as ET, so there shouldn't be any
difference there, either.  Only in the EBVT, by Bill Bremmer, do the octave

widths get tempered, based on the tempering of the octave 5th.

So we are down to the other intervals going out..... Here's the weird
thing.
  ET has all of the beat speeds of intervals, from real slow in the bass,
to
real fast in the treble.  Moderate temperaments share many of the same
beatspeeds, just in a different order than an ET tuner would expect.  It's
easy to find a third out of place in ET by using a chromatic progression.
Since the thirds are already "out of order" in an alternate temperament,
there might actually be a little more movement allowed, before the
differences are enough to alter the character of the temperament.  But
remember, we are already way down the list past the unisons going out
before
any of this comes into play.  Once the unisons get ripe, all bets are off!

So my guess would have to be that ET is the quickest "ripening"
temperament,
due to the minute tolerances required to actually achieve a true ET.

Ron Koval
Chicagoland

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