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This is a little
tuning exercise
(right click and choose "save link as")
similar to the commercially-available "Tuning CD." I did it
with the Harmony Director keyboard, so all the pitches are
perfectly tuned to a standard of A=440.
It could be used in either of two ways:
1) Simply play along — it's 13 notes from concert Bb to the
octave above — trying to match pitch as closely as possible.
2) Hook your instrument up to a tuner. Don't look at the
tuner during the first four counts, then look at see how
successful you were in matching. If you've got a tuner, but not
a hookup, try using headphones; the tuner will pick up only your
instrument and not the recording.
I'd suggest you do it throughout the full range of the
instrument. It's a wonderful ear-training technique that I'm
sure you'll find beneficial.
This
exercise is for a perfect 5th. A tempered 5th, of course is
seven half-steps (700 cents) wide. A true, beatless 5th, is
actually 702 cents wide. This exercise, then, is intended to
refine the player's concept of a beatless 5th in just
intonation.
You'll hear 13 major triads, ascending chromatically from Bb to
Bb. After the first four beats, the other notes drop out,
leaving only the 5th. The idea is to play the fifth (concert F
to start with), then look at the tuner to see if you're matching
the 5th after the other notes stop. The tuner should be
calibrated to 441 for this exercise. You might find the needle
just slightly to the left of zero.
Here's the
major 3rd. A
tempered 3rd is 400 cents wide, but a beatless major 3rd in just
intonation is 14 cents lower, or 386 cents wide. The routine
here is the same as the last one. Bb triad for four beats, then
the 3rd alone for four.
Some of you might be as skeptical as I was about this at first.
A major third 14 cents flat? Come on! But then when I heard
two triads side by side, one in tempered intonation and one in
just intonation, I was astonished at how much better the lowered
third sounded.
True, most of the time we're not even aware of what chord tone
we're playing. My hypothesis is that the best musicians are
simply listening constantly to make whatever note they are
playing at any given moment sound "right," and that if it's a
chord tone sustained for any duration, they naturally favor
lowered major 3rds and raised minor 3rds (and we're assuming, of
course, that others playing the same pitch is doing exactly the
same thing).
The tuner should be calibrated to A=437 for major 3rds.
Here's the
minor 3rd, which
is actually 16 cents higher in just intonation than in equal.
You could calibrate your tuner to A=444 for this one. These
calibrations, incidentally, are not really dead on, but they're
as close as we can get and the difference is so slight as to be
negligible.
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