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Subject:
From:
Dennis Johnson <[log in to unmask]>
Reply To:
Harpsichords and Related Topics <[log in to unmask]>
Date:
Mon, 21 Nov 1994 14:15:57 -0600
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At  9:21 AM 11/21/94 -0800, SIMONS, DON wrote:
 
>
>There are (at least) two ways to use an electronic tuner.  Apparently, the most
>common is to have it play the notes and tune strings in unison with it, relying
>on your ears as the final arbiter of equality.  Using this method, you are
>indeed restricted to the temperaments that have been (or can be) programmed
>into
>the device.  However, many tuners can hear the note you are playing, and tell
>you with a calibrated needle gauge how many cents the note deviates from equal
>(i.e., how many 100ths of a semitone the note is sharp or flat relative
>relative
>to equal tempered tuning).  With this type tuner and a knowledge of the desired
>offsets, you can tune any temperament you want.  That's what I do with a $80
>Seiko.  With the benefit of training in applied mechanics, I've worked out
>tables of cents deviations for many temperaments.  Apparently, not many people
>tune this way, because I haven't seen many tables like this, or discussions of
>this method.  ..........
 
---------------------------
 
        I hope that I'm not nit-picking here, but this is precisely the
method that I have a problem with.  You are on track, but how do you
account for inharmonicity?  It sounds like you caculate the theoretical
deviations from equal and tune that exactly.  Inharmonicity is the
difference between what really happens accoustically and what you caculated
on paper.  You might get something close to what you intended, but that is
why these tuners cannot tune an acceptable equal temperament.  Try this:
Take your tuner and tune each note to zero deviation from equal(equal
temperament, right?) than check to see if the thirds progress evenly up the
scale.   They will not.  If your tuner can isolate a coincident partial,
say for fifths, set it to the 3:2 partial and tune both notes of the fifth
and stop the lights (an octave above the upper note). That is a pure 3:2
fifth.  Than do the same for the 6:4 partial of the same fifth (two octaves
above the upper note).  The difference is the inharmonicity between the 6:4
and 3:2 fifths of that interval.  You cannot tune accurately without
accounting for inharmonicity,  that is why we have aural checks for these
intervals. If the major 6th and major 10th below each of these notes of the
fifth beat equally, than you have a pure 3:2 fifth, for that instrument
with inharmonicity. (C3-A3=C3-E4)  If the minor third-major third within a
fifth beat the same than you have a pure 6:4 fifth.  (A3-C4=C4=E4).  The
6:4 beats are twice as fast, an octave higher, and harder to hear- but
again the difference here is inharmonicity.  Only on the very best pianos
will these be practically the same, and never on harpsichords.  Didn't mean
to rain on you, and it is your own instrument.  But do check this out.
 
 
Dennis Johnson
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