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Au ra l T u n i n g
The two-octave "A" temperament may be tuned aurally with exactly the same note-tuning
sequence. This makes it easy to check an electronic tuning aurally at every step--very helpful in
avoiding errors. Aural tuners can study and possibly improve their tuning by using the Accu-
Tuner to measure the width of tuned intervals after setting this two-octave temperament very
carefully by ear.
S tep 1. Tune A4 to 440 Hz. Use F2 as test note, 17th to fork should beat same as 17th to A4.
Tune A3 from A4 as a 2-4 octave, 1\2 beat wide. That is, the tenth should beat 1\2 beat per
second (bps) faster than the third.
S tep 2. Tune A2 from A3 as a 3-6 octave 1\2 beat wide. That is, the major sixth should beat 1\2
bps faster than the minor third.
S tep 3. Check the double octave, a 1-4 interval to be less than 1 beat wide. That is, the 17th
beat should be less than 1 bps faster than the third. If the double octave is too wide, compromise
both octaves slightly to get and acceptable double octave.
S tep 4 . Divide the A2-A3 octave into three equal parts by tuning C#3 and F3. These thirds can
be tested very accurately with the contiguous thirds test. This test states that two contiguous
thirds must have relative beat rates in the ratio of 4 to 5, that is 4 beats of the lower one require
the same amount of time to complete as 5 beats of the upper one. This test then does not require
knowledge of beats per second, only a good sense of rhythm or tempo. In this case, C#3 and F3
are correctly tuned when 4 beats of A2-C#3 occur at the same tempo as 5 beats of C#3-F3, and in
addition, 4 beats of C#3-F3 occur at the same tempo as 5 beats of F3-A3.
S tep 5. Now tune C#4 and F4 to divide the A3-A4 octave into three equal parts with thirds. You
may have to taper the width of the thirds downwards slightly in the upper octave on account of
the inharmonicity of the piano.
S tep 6 . Check that the three major tenths formed on the seven notes tuned so far also in the
ratio of 4 to 5. Also check the C# and F octaves with both the third-tenth and minor-third-sixth
tests. Scale problems will show up at this stage, and it may be necessary to compromise slightly
the perfectly rising thirds to get satisfactory octaves and tenths.
S tep 7 . Fill in the six untuned notes between F3 and C#4 to get a nine-note mini-temperament,
but be sure not to change already tuned notes. Tune up a fourth from F3 to A#3, down a third
from A#3 to F#3, up a fourth from F#3 to B3 and stop. Then tune down a fourth from C#4 to G#3,
up a third from G#3 to C4, down a fourth from C4 to G3 and stop. Check the G3-B3 third, which is
the test interval for this tuning. If it is too small, you must expand your fourths, and vice versa.
With just nine notes to worry about, it is always possible to get five perfectly rising thirds and
four matched fourths no matter how poorly scaled the piano may be. The beat rates may not be
very close to theoretical, but they will be right for the given piano and its inharmonicity
characteristics. So tune the piano, and let the beat rates fall where they may!
S tep 8 . Tune down to A2 and up to A4, and use the contiguous third test to place each note
initially. Check each note with the fourth and fifth, and then the major sixth and octave as they
become available. The final result should be two octaves tuned with rising thirds all the way,
with all fourths quite even and acceptable, and with all fifths nearly pure.
APPENDIX F
C o nt i g u o u s- I n te rval T u n i n g Te st s f o r E le ct r o n i c P ia n o T u ne r s
By D r . A . E . Sa n de r s o n
Two contiguous musical intervals are intervals that touch each other, in other words, share the
note in the middle. Tests that use contiguous intervals are easy to learn and use, and tell the
tuner explicitly which notes are at fault and what to do to correct them.