CLASS C:
Lower note is the reference note. If the beat rate between the test note and the upper note is
too slow
as
compared to the beat rate of the test note and the reference note,
lower the upper note
. If the beat rate with the upper
note is
too fast, raise the upper note
.
CLASS D:
Upper note is the reference note. If the beat rate between the test note and the lower note is
too slow
as
compared to the beat rate of the test note and the reference note,
lower the lower note
. If the beat rate with the lower
note is
too fast, raise the lower note
.
The object in each case is to obtain an equal beat rate between the upper and lower notes of the octave, and the test
note. Each test is given a name corresponding to the intervals employed in the test. In naming the intervals, "P" denotes
a so-called "Perfect" interval, "M" denotes a "Major" interval, "m" denotes a minor interval, "A" denotes an "Augmented"
interval, and "d" denotes a "diminished" interval. It must be noted that some of these intervals are very hard to hear in the
bass region of the piano. These checks, however, are still valid. To make use of these checks, hold down one of the
octave notes and the test note without playing them. (You may have to use the sostenuto pedal in some cases). Play the
strike note with a staccato blow. Repeat this procedure with the other octave note and the test note. When the two beat
rates are the same, the type of octave which has been tested for will have been tuned. The strike note in all cases is the
note listed in the electronic setting instructions for that particular type of octave.
APPENDIX H
DUAL SYSTEMS FOR SMOOTHING OUT THE STRINGING BREAK
By J. Coleman, Sr.
Often we encounter a piano with wound strings in the tenor section. In older piano design where inharmonicity was not
considered, the highest wound strings had much lower inharmonicity than their neighboring plain strings, which usually
had very high inharmonicity. This has always caused some difficulty in achieving smooth interval beat speeds. There is a
way to help out this situation by tuning the lowest plain strings a little flatter than usual and tuning the upper wound strings
a little sharper.
For an example: A spinet piano might have wound strings on F3 and F#3 and then have plain steel strings from G3 on
up. The difference between the 4th and 8th partials of F3 and F#3 may be something like 8 or 9 cents whereas the
difference between the 4th and 8th partials of G3 and G#3 might be somewhere from 18 to 14 cents. If all of these notes
are tuned by their 4th partials to any smooth curve pattern, the major 3rds based on F3 and F#3 will beat faster than
normal and the major 3rds based on G3, G#3 and A3 will beat slower than usual. This is due to the differential of
inharmonicity between the upper and lower note of the intervals. This is how it works: A string with lower inharmonicity
has less difference between its 4th and 5th partials. The opposite is true of a string with higher inharmonicity. If each
note is tuned on the basis of keeping the 4th partials on a smooth curve, then when the lower note of a major 3rd has less
relative inharmonicity than the upper note does, the smaller distance between the 4th and 5th partials causes the interval
to have a slightly faster beat. This is more easily understood by the fact that the lower note was tuned by its 4th partial,
but its 5th partial is the cause of the beat with the 4th partial of the upper note. With the 5th partial of F3 being closer than
normal to the 4th partial of F3, this makes the 5th partial of F3 flatter in respect to the 4th partial of A3 than it would have
been in a more normal situation.
When you look at the situation of the greater inharmonicity of the upper note (A3), since it is tuned by its 4th partial, its 4th
partial is right where it belongs according to the stretch curve being used. However, the beat speed of F3-A3 could be
helped some if the A3 were tuned slightly flatter. In fact several of the intervals involved with plain strings vs. wound
strings which occur in the tenor section can usually be helped by lowering the upper plain strings on a graduated basis.
One way to tell if some correction is helpful is to look at the tenor bridge to see if it flares out like the end of a hockey stick.
If it does, then some lowering to the pitch starting where the "hockey stick bend" begins will help. In the past, this has
been done rather arbitrarily. Now with the advent of FAC stretch numbers on the newest SAT's, one can let the computer
in the SAT do the figuring. Here's one way to do it: If during the measuring of the F3 plain string stretch, you notice that it
is unusually high (such as 14-25 cents), you can increase the stretch number by 1 to 2 cents before storing it in the usual
fashion (your call). This will keep the beat rates from slowing down too much as the 3rds descend from C4 down to F3.
When the lower notes of the plain string section have a relatively higher inharmonicity (more distance between the 4th and
5th partials of F3) the sharper 5th partial of F3 decreases the beat produced with the 4th partial of A3, the upper note.
In similar fashion one can cause the upper wound strings to be tuned slightly sharper by selecting a stretch number that is
slightly lower than what was measured.