Re: Equal Temperament

For anyone interested in hearing just temperament, Zydeco accordions are
apparently tuned like this and have a very distinctive sound. - Except
Clifton Chenier, who I have read uses an equal tempered accordion. The
little I have heard of his recent music doesn't sound like traditional
Zydeco.

The daughter of a friend of mine plays violin and has perfect pitch. She
apparently finds equal temperament slightly discordant and has to make a
deliberate effort to play in equal temperament intervals.

Tony D

"Stephen Calder" <calder9@xxxxxxxxx> wrote in message
news:431321d2$0$22634$61c65585@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> There has been some discussion on this topic and because it's complex some
> confusion surrounds it.
>
> Before Bach's time was a wild and woolly period for tuning instruments,
> and we should be glad we have equal temperament to overcome the problems
> they had then.
>
> As a matter of physics, distances between notes in a scale in any
> particular key depend on certain intervals being maintained. As a result,
> strictly speaking, C# is NOT the same as Db, but equal temperament makes
> them the same.
>
> For most purposes, and certainly for the beginner guitarist, it is of no
> consequence except for those of very sensitive ears who can hear the
> built-in "errors" that equal temperament introduces in forcing C# to be
> the same as Db. For those people, the notes below will be of interest. For
> those who wish to investigate the matter more thoroughly, here are a
> couple of links to more detailed explanations which would be out of place
> here:
>
> http://www.phy.mtu.edu/~suits/scales.html
> <http://www.phy.mtu.edu/%7Esuits/scales.html>
>
>
>
> http://hyperphysics.phy-astr.gsu.edu/hbase/music/et.html
>
> If you don't know what a harmonic is, or how to play it, post a question.
>
>
>
> The following is a reprint of THE GUILD OF AMERICAN LUTHIERS data ***
> #45.
>
> Many guitarists are frustrated because of their attempts to tune the
> guitar to pure chords (free of beats). These particular players have very
> sensitive ears that prefer pure intervals and reject the mandatory equal
> temperament. They tune their guitar beautifully pure on one chord only to
> discover that the next chord form is unacceptable. In too many instances
> they assume that there must be a flaw in the workmanship on the
> fingerboard. Their problem is not in the construction of the guitar. It is
> one of pure tuning verses equal temperament.
>
> You must accept this compromise because the guitar is an instrument of
> fixed pitch and the strings must be tuned to tempered intervals, not pure.
> Equal temperament is the name given to a system of dividing the chromatic
> scale into 12 equal half steps. Guitarists who have been trying to tune to
> one or another pure chord form must learn to understand and accept equal
> temperament. (They might be interested to know that to approximate pure
> chords on all forms would require about three dozen frets within the
> octave.) The system of equal temperament reduces the number to twelve,
> thereby making manageable all instruments of fixed pitch.
>
> Here is what all of this means to the guitarist: You must not, at any
> time, use harmonic tones at the 7th fret as a point of reference (skilled
> piano tuners could use them because they know how many beats to introduce
> between 4th and 5th). Harmonic tones at the 7th fret are pure 5ths, while
> in equal temperament each 5th must be lowered slightly. To tune by
> harmonics at the 7th fret (as occasionally ill-advised) will make the
> guitar sound entirely unacceptable on some chord forms.
>
> On the other hand, all harmonics at the 12th and 5th frets, being one and
> two octaves above the open strings, are immediately useful as explained
> below. All octaves and unisons are pure on all instruments of fixed pitch.
> Therefore, you may use harmonics at 12th and 5th as reference tones in the
> following tuning instructions.
>
> Actually this discussion and the following suggestions are for those
> players who have been tuning to pure intervals. When the steps have been
> followed correctly the guitar will be as perfectly tuned as it could be in
> the hands of a professional. Nevertheless, when you have finished, your
> sensitive ear may notice that on each major chord form there is always one
> tone slightly high. If you start adjusting a particular string on a
> certain chord form, you only compound the problem because then the next
> chord form will be completely objectionable. Tune the guitar as instructed
> below and let it stand. How to help your ear accept equal temperament: It
> is easier to face a problem if we are prepared in advance and expect it.
> If you are one of those persons who is sensitive to pure intervals, here
> is what you are going to notice on an absolutely perfectly tuned guitar in
> equal temperament: Play an open E major chord. Listen to G# on the third
> string and you most likely will want to lower it very slightly. Don't do
> it. Ignore it. Enjoy the overall beauty and resonance of chord just as
> does the pianist.
>
> That troublesome second string: Play an open position A major chord.
> Listen to the C# on the second string and you may want to lower it
> slightly. Play a first position C chord and listen to the E on the first
> string and fourth string at 2. These tones are slightly higher than your
> ear would like.
>
> Now play an open position G chord. Listen to B on the second string. Yes,
> it would sound a little better if lowered ever so slightly. Why not try
> it? Slack off the second string a couple of vibrations and notice what
> beautiful G chord results. Now play the C chord and with that lowered
> second string, and you are going to dislike the rough C and E a lot more
> than before. Take the open B, second string back up to equal temperament
> so that it will be equally acceptable on all forms. Learn to expect and
> accept the slight sharpness of the major third in each chord (and
> oppositely, the flatness of the minor third in each minor chord). Train
> your ear to accept tempered intervals and you will be much happier with
> your guitar.
>
> *PROCEDURE:*
>
> Tuning the 1st and 6th strings: The E, open 1st string, must be in pure
> unison with the harmonic of the E, 6th string at the fifth fret. When
> these two strings have been properly tuned with each other, continue as
> follows. Tuning the 4th string: Play a harmonic on the (in tune) 6th
> string at twelve, and as this harmonic sounds, adjust the 4th string until
> the tone E on the second fret is in pure unison. Now you have the E, open
> 1st string, 1st on the 4th string at two, and E, open 6th string tuned
> pure (permissible because they are octaves).
>
> Tuning the 2nd string: Play a harmonic on the (in tune) 4th string at
> twelve. As this sounds, adjust the 2nd string until D at the third fret is
> in pure unison. As you have used two fretted tones for references and as
> the frets are positioned for tempered intervals, you now have the open
> 1st, 2nd 4th and 6th strings in tempered tuning.
>
> Tuning the 3rd string: As it is easier to adjust a string while listening
> to a continuous reference tone, you may first try the following: Play a
> harmonic on the (in tune) 4th string at twelve and as this sounds, adjust
> the 3rd string until D at the 7th fret is in pure unison.
>
> Double check: Now make this check to see if you have been accurate or if
> the instrument plays tune when fretted at seven. Play a harmonic on the
> (now tuned) G string at twelve, and as this tone sounds, play G on the 1st
> string at three. The two tones should be in pure unison. If they are not,
> either you are at fault or the instrument doesn't fret tune at seven. Go
> back to the beginning and carefully check each step up to this point. If
> the tones are still faulty, then readjust the 3rd string until the
> harmonic at twelve is in unison with the 1st at three. Do not tamper with
> the 1st and 4th strings because it is the 3rd string you are trying to
> bring in tune. When you have the 1st, 6th, 4th, 2nd and 3rd strings in
> tune, in that order, continue with the remaining 5th string.
>
> Tuning the 5th string: Play the tone A on the (in tune) 3rd string, at the
> second fret. Listen to this pitch carefully and now adjust the 5th string
> until the harmonic at twelve is in pure unison. When the foregoing steps
> are followed correctly, the strings will be tuned perfectly to equal
> temperament. No further tuning adjustments are permissible.
>
> THE GUILD OF AMERICAN LUTHIERS is a non-profit organization formed, in
> 1972, to promote the art of the string instrument maker. This is done
> through it's quarterly journal - AMERICAN LUTHIERS,
> convention/exhibitions, and the DATA SHEETS, one of which you have just
> read. The G.A.L. is an information sharing system. Membership is not
> restricted to practicing instrument makers.
>
> For more information on GUILD publications, membership, and activities,
> write:
>
> GUILD OF AMERICAN LUTHIERS
> 8222 South Park Avenue Tacoma, WA 98408
> (206)472-7853
>
>
> --
> Stephen
> Byron Bay, Australia


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