Klarinet Archive - Posting 001562.txt from 1999/01

From: Richard Bush <rbushidioglot@-----.net>
Subj: Re: [kl] Tuning while playing
Date: Sun, 31 Jan 1999 07:25:16 -0500

Jdclar@-----.com wrote:
>
> I hear a lot on the list about tuning while playing. Incredible statements (to
> me) about knowing which cord you are playing so that you can adjust your
> tuning depending on whether you are playing the tonic or some other note in
> the chord. This morning I experimented with a few notes and my tuner seeing
> how much I could "lip" the notes. I could see no appreciable change sharpening
> but I could flatten a note about 5 cents but the tone became worse. I know
> that something must work because I have heard small groups resolve a note
> between them and it makes a great difference. So how do you do this? When do
> you do this? I can't believe that you do this in 32nd notes but certainly must
> at the end of a piece or passage on a sustained note.
> Thanks,
> Jack Dannenberg
> jdclar@-----.com

Wind and string players live and work within several tuning systems. The
two most common are the equally tempered tuning system and the just
tuning system.

Starting somewhere around the time of J. S. Bach, a system that equally
spaced all twelve pitches started to gain favor. While much of the
"color" or personalities of playing in different keys was lost, the
advantage, as music and tonalities were become more chromatic in nature,
was that playing in ANY key was no more out of tune (nor no more in
tune) than any other key. While imperfect in many regards, we have come
to accept this equal spacing of all half steps as is found in the
equally tempered scale. We have become conditioned to it, hearing it
every day.

Fixed pitch instruments, all keyboards and mallet instruments use the
equally tempered scale, though there are slight deviations because of
the tricks our ears and minds play on us.

The just tuning system is that other system that orchestras, bands and
other groups use to sound beautifully in tune and sonorous. It is an
amazing trick to subtly shift from one to the other. Indeed, the two
systems are strange bed fellows that musicians live with and learn to manage.

Think of the just tuning system as being derived from the rungs of a
ladder. The first two or three rungs of this ladder are very far apart.
If you were to climb this ladder (considering the ground to be step one)
the first rung would be so high that one would need to get a boost or a
lift just to reach it. That distance, in the overtone series is the
octave jump from the fundamental (the ground) to the second partial or
the first overtone. In musical terms, this octave is perfectly in tune.
If the sounding pitch is 220 cycles per second, the octave will clock in
at 440 cycles per second.

The next rung is within reaching distance. This second overtone (or
third partial of the overtone series) is the distance of a perfect
fifth. As it occurs naturally, it is very close to the assigned
placement in an equally tempered scale, sounding only 1/50th of a
semitone or half stem higher than where it is tuned in an equally
tempered scale.

The next rung is still closer, or a lessor distance. This overtone is a
perfect fourth higher and represents a pitch two octaves above the
ground and one octave above the first rung. If spelled as notes, using
C=550 Hz, as the ground or fundamental, the first rung (overtone) is
C=1040, the G (second rung) is G=1558 in equal temperament and G=1560 in
a just tuned scale, and the next overtone, is C@-----. Notice that the
even numbered partials (octave C and double octave C are perfectly in
tune with each other being doubles or halves of each other).

The next partial is where the two tuning systems really start to pull
apart. It also represents some of the tuning problems that start to
become obvious on many wind instruments over blow to this partial.

The fifth partial is a major third higher than the previous (double
octave C), being an E natural. This tone is quite a bit lower than where
it it tuned, placed or found in an equally tempered scale. Instead of
being E@-----. That
represents a difference of 20 cycles per second. That is a lot of beats.

If three players are trying to perfectly tune a simple major triad of
C-E-G, to play them in just tuning, the third, the E must be a two
octave lower version of the E that is generated by the person playing
the C. That means that the overtone E of 2600 Hz is now an E of 650 Hz
or cycles. This E is 5 vibrations per second lower that the equally
tempered E of 655. To put it in other terms, it must be lowered 1/7th of
a half step.

Skipping the next overtone after this high E, which is a G, perfectly in
tune with the two below it, we come to a Bb. This is the seventh partial
and is very much lower than a Bb on the piano. This Bb is also the exact
tuning that needs to be inserted into a C major triad that has been
expanded to become a C7 chord or a C chord with a flatted 7th. This Bb
must be lowered 1/3 of a half step or 33 cents from tempered.

You see, it is important to hear what chord member you might be playing.
You need to know and be able to hear if you have the third or the
flatted 7th. You can then react quickly, move the right direction and be
in tune (assuming that the other people playing the other members of the
chord are also in tune with each other.

In fast passages, and/or unison runs, the plan is to "school" like fish
and be in tune with each other. That would indicate going for the
generic equally tuned scale.

All of this is fairly complicated and takes a long time to learn and to
do, but good musicians do it every time they play. Get yourself the
theory background. Get yourself the ear training, learn what the tuning
tendencies are on your instrument and then just listen, listen, listen.

All of the above explanation can be boiled down into one simple
statement, when it is as clear and pleasing as possible, when the beats
have been eliminated (assuming we are talking about a consonant chord)
then you are playing by mother natures rules and making the overtone
series work for you.

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