Is there a trick to comparing the fast beating thirds (or sixth's for
that matter)?
Dear Jonathan,
Yes there are tricks, the first one is to listen carefully to each third
going up chromatically and then listen carefully to the sixths going up
chromatically. ALso listen critically to chromatic tenths and minor
thirds.
As one becomes familiar with the sounds and the beats the variations
become obvious. When the differences can be told one from the other
then they can be used to improve one's tunings.
Major thirds and sixths increase in beat rate about 1/2 beat per second
ascending chromatically. This being said then a major third will have
about the same beat rate as a major sixth 1 whole to lower, i.e., G-B
and F-D.
If you compares the F-A and F-D the degree of tempering of the A-D
fourth came be accurately determined. The difference in the third and
the sixth is about 1 beat per second.
Octaves are counted from note #1 A0, note #4 C1, note #88 C8.
If you compare the tenth to sixth which encompasses a fifth (C3-E4
tenth, C3-A3 sixth) you con determine the temper of the A3-E4 fifth.
THe difference is the tenth is slightly slower than the sixth at less
than 1/2 beat per second.
A properly stretched octave will have three contiguous major thirds
whose beat ratio will be 4:5 rising or descending always. i.e., F3-A3,
A3-C#4, C#4-F4 as follows.
F-A 4 bps in one time frame (say 1/2 second)
A-C# 5 pbs in these time frame.
This is easiest counted by counting to four, subvocally, while playing
the F-A then counting to five in the same time frame while playing the
A-C#. It takes practice but this is a most valuable tool.
When you have mastered these techniques then you will be ready to go on
to the next phase which is integrating these techniques into tuning the
perfected equal temperament developed by Baldisen and Sanderson.
I look forward to seeing you reach that new plateau.
Newton J. Hunt
nhunt@jagat.com
This PTG archive page provided courtesy of Moy Piano Service, LLC