Wendy Galovich wrote:
<Uhhhh.. the statements you made in the paragraph to which I was
responding:
that in a literal sense it is impossible to play *exactly* in, or tune
an
instrument *exactly* to, equal temperament, because we aren't even
capable of
hearing the minute differences in pitch to enable us to do that. At
least
that is what I understood you to be saying, but if not, please correct
me.>
Comment:
Actualy that is not what I was saying. We are able to detect differences
in pitch but can't measure them. The human ear measures musical
intervals by tuning in the unison harmonics produced by the two notes.
Some are easy to do, such as the fifth, the third is more difficult, the
tempered semitone is impossible, either "exactly" as you say or
inexactly. The reason for this is that there is no unusuin harmonic in
two notes separated by the ratio 1.059 or any of its aritmetic
multiples. That is why the piano tuner tunes the instrument in the
manner I described in a previous e-mail.
<Ummmmm.. First, if you're going to quote me, I'd very much appreciate
if
you'd do me the courtesy of including enough of the quote so that what I
originally said is clear. Maybe you misunderstood the context I was
referring
to.. was that why you omitted the rest of the paragraph when you quoted
me
above? Anyway, for clarity's sake, here it is again, this time in its
entirety. Especially pertinent to the point I was trying to make is the
last
sentence:
"This is obvious if you're going to break the tempered scale down to
that
degree, but it doesn't address the context of my original comment, which
was
a response to your assertion about fiddlers playing, as you said, "out
of
tune". From the perspective of common sense it's clear that in that
context
we must necessarily speak of tempered or alternate scales as far as they
are
discernible *by the human ear*." >
Comment:
I had not intended to misquote you. My appoligies if that was what was
conveyed.
Tempered scales and alternate scales must be dealt with sepapately. The
equal tempered 12-note chromatic scale with which we are familiar is the
one defined by the ratio of a semitone being 1.095. Deviations from
this, although discernable as being a different pitch ,do not constitute
a different scale. Also "common sense" is based on a person's education,
knowledge, life expereiences, etc. In other words it is frequently not
"common" at all
<When I said "break the tempered scale down to that degree", I wasn't
being
*literal*, but simply merely pointing out that the level of precision
you're referring to is overkill in a discussion that was originally
about using alternate scales in one's playing.>
Comment:
There are two separate issues here. Firstly you are saying that playing
the notes which conforms to the ratio which defines the equal tempered
scale is "overkill". It fundamently is not. Secondly, referring back to
the type of tune which began this discussion, a tune in A, altering the
pitch of the seventh note so that it is somewhere between G and G# does
not condtitute a different scale. Similiarly playing a tune which
conforms only approximately to the tempered scale is not playing in
another scale.
Please don't be offended but I have concluded that you haven't read or
do not understand the two quotes which I included in my last e-mail.
They are based on the work of Herman von Helmholtz, who is considered
the father of the science of accoustics, who Encyclopedia Britanica
describes as "one of the greatest scientists of the 19th century" and
on subsequent work by Alexander J. Ellis and Llewelyn S. Lloyd, the
latter of whom was a Grove's consultant, writer of a text book on the
subject, and the author of approx 50 essays on the subject in learned
journals.The last line in the Turtis quote bears repeating here, "
I am concerned that we may be boring others on the list with this
discussion. If you wish to communicat further perhaps we snould do it
off list.
Alexander
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