[Harp-L] tuning/temperaments

[Jonathan Ross <jross38@xxxxxxxxxxx>]

First, anyone interested in tuning and temperaments for the harmonica  
should go here and read the relevant pages:

http://www.patmissin.com

Start there, read that and then go forward.  The simple answer to  
Jimmy's question is, not really.

Now to some specficis.

Michelle Le Free writes:


"My take, and Richard please jump in here if I've got this wrong, is  
that Just Intonation (JI) tunes certain notes sharp and others flat  
relative to pure Equal Temperament (ET)"


This may seem like semantics, but it can be vitally important: never  
use the term "pure Equal Temperament".  The problem is that the term  
"pure" is often used to describe beatless intervals in musical terms,  
so using it to describe the commonly found equal temperament is  
begging confusion.  Also, there is no such thing as an "impure" Equal  
Temperament--it's either an equal temperament or it isn't.  This is  
like the term "compromised just intonation", it's meaningless--it's  
either JI or it isn't.

Personally I prefer 12-Tone Equal Temperament (12TET) to just ET,  
because it is more specific (you never know, you could be talking  
about "equal temperament" to an Arabic musician and he's meaning  
24TET and you're meaning 12TET).


Vern writes:

"All instruments with fixed notes (harmonica, keyboard, etc.) must  
use equal temperament if they play in different keys without retuning."


No, as I have said on the many other occasions this has been posted,  
they may use 12TET, but they may also use many other systems.  It  
just depends on what compromises the musician wants.  I certainly  
find 12TET the most useful for the widest range of written music in  
many cases, but it is by no means the only nor the ideal solution for  
every situation.  For example, I would guess that most  
harpsichordists rarely use 12TET, in part because the music written  
for harpsichord was rarely composed for 12TET.  It depends entirely  
on usage and the instrument in question.  Listen to some Handel stuff  
in 1/4 comma or 1/6 comma meantone sometime--it becomes obvious that  
he was not writing in 12TET.  Certainly not when he wrote for English  
organs he wasn't (one prominent English organbuilder didn't switch to  
12TET from meantone until the 1870's).


fjm writes:


"12T ET can sound wonderful given the right tuning. Harmonic minors  
are not nearly as jarring chorded in 12T ET as they are in a major key."


For some odd reason, despite being farther out in absolute terms from  
the typical beatless minor third, 12TET minor thirds are not nearly  
as grating as 12TET major thirds.  It's a bit of weirdness about how  
the ear perceives things.


Iceman writes:


"when creating all 12 notes through that cycle of upward 5ths and  
inverted
intervals of downward 4ths, these perfect intervals were SQUEEZED  
smaller by 2
cents each - perfect 5ths were contracted by 2 cents and perfect  
fourths, being
inversions, were expanded by 2 cents each. The result was that your  
ending note
now matched perfectly your starting one. The intervals used became  
PERFECT
IMPERFECT intervals.

Since the human hear can't really hear a difference until 3 or more  
cents, this
2 cent shaving was not really apparent and did solve the problem of  
weird ugly
intervals and the inability to freely transpose music into any key.  
It equalized
the playing field in a compromise with Mother Nature."


Yes and no.  Perhaps the human ear can't hear a difference of 2 cents  
shaving, but it can most certainly hear the beat frequencies created  
by this shaving.  Indeed, it can hear significantly more subtle  
variations than 1 cent.  Calling the intervals in 12TET "perfectly  
imperfect" is a nice bit of propaganda, but what they really are is  
uniform.  All keys sound equally bad, with no one key (out of a  
subset of 12) sounding worse than any other.  This was the difference  
between 12TET and the other various temperaments used, which tended  
to weigh more heavily towards various keys or certain intervals.

The reason I said "not really" in answer to Jimmy's question is  
because it depends on so many other factors.  I'd bet people are more  
likely to notice if the tonal center of the harmonica (the A=440  
setting of where you begin your root note) is off than between  
something like 12TET and one of the many compromise tunings proposed,  
for instance.  Also, it depends on how you use it.  If you're playing  
a lot of chords people may hear the dissonance in the 12TET chords  
more than they hear the variance between the harmonica and the  
backing instruments even if the harp was in something like 7-limit  
JI.  Also, playing bends and overblows will add another layer of  
potential pitch relationships into the equation.

Basically, the best advice I can think of is to try a few  
temperaments and intonations out if possible and see what feels best  
to you and your bandmates (more the former, less the later) by  
listening, and then choose one system for a while and really learn  
how to use it (again by ear).  If you want to stick with whatever is  
off the shelf in your favorite harp (12TET for LOs, for instance),  
then hope for consistent tuning and learn how to use that for best  
effect.




JR Ross