Aural Octaves

[Jim Coleman, Sr.]

Aural Octaves

The most advanced tuners prefer some stretching of the temperament 
octave such that in the 4-2 relationship (M3rd-10th test) the 10th 
beats slightly faster than the 3rd. At the present time there is 
no consensus as to the exact amount of stretch, but it seems to be 
between a 1/4 bps and a 1/2 bps wide. This octave relationship is 
usually carried on up into the 5th octave. Somewhere in the middle 
of the 5th octave the 4-2 stretch decreases to pure 4-2 (where the 
M3rd and M10th are equal in beat rate. Along the way to this point 
the 10ths and 17ths are checked to maintain smooth graduation in 
increase of beat rate. The almost zero beat of the 12ths are also 
helpful in this area (i.e. The A#3-F5 would be beatless). In this 
area one can notice that the 19ths (like C3-G5) are almost 
beatless, but on the narrow side. Here is where artful
decisions must be made. If one wishes to have triple octaves in 
tune (beatless), one must gradually transition the stretch to 
where the 12ths are slightly wide and the 19ths become beatless. 
This procedure, when done artfully, will help maintain the smooth 
graduation of the 10ths and 17ths.

By the time one gets to C7, the 17ths become extremely fast and 
therefore more reliance should be given to the 12ths and 19ths 
which are slow beating intervals and easier to hear except for 
those who have Hi-Fi
ears.

        CAUTION! For those preparing to take the PTG Tuning exam, 
        remember that it is required to 
        tune the top octave C7 to B7 as simple pure octaves (2-1 
        type?) without the additional stretch 
        which the above procedure would produce. Therfore, utilize 
        the 10th-17th test such as G#4-C6 
        and G#4-C7  to be equal in beat rate. Also F5-C6 and F5-C7 
        to be equal.

Now, back to the main presentation. As one tunes along in the 5th 
octave, it is helpful to continually
refer back to notes already tuned. While tuning C5 for example, 
after the simple octave is stretched as much as one can tolerate 
(without a noticeable beat), play the M3rd-10th test (G#3-C4 and 
G#3-C5), play the
12th interval (F3-C5) and compare these with the neighboring 
similar intervals in order to maintain evenness of graduation. 
Continue this type of comparison as you tune chromatically up to 
F5. At F5 you can use an additional type test which is called the 
M3rd,-10th-17th test. The 17th should be slightly faster than the 
10th and the 10th should be slightly faster than the M3rd (C#3-F5 
is greater than C#3-F4 which is greater than C#3-F3). Also play 
the 12th (A#3-F5) to see that it is not on the wide side. A good 
test for this is that the
C#3-A#3 is equal to the C#3-F5. If the C#3-F5 is faster, then the 
12th (A#3-F5) is on the wide side. Continue
these types of tests for each note until you get to G5

At G5, the 19th (C3-G5 also becomes available as a test. One will 
often find this interval to be slightly on the narrow side even 
though the 12th (C4-G5) test is pure. This is decision time again. 
If one prefers to have pure triple octaves eventually, it may be 
necessary to widen the 12ths slightly and slow down the narrow 
19ths gradually. In doing this, one now forces the single octaves 
to be stretched even more (somtimes even more than 1 bps) and the 
double octaves may be stretched up to 1 bps.

By the time one gets to C6 the triple octave comes into play. If 
the 12ths have been kept pure, the double octave is stretched and 
the triple octave is slightly narrow. If one wishes to have the 
triple octave pure, then the double octave will need to be 
stretched more, the 12ths will need to be widened, and the 19ths 
will need to be almost pure but on the narrow side. All of this of 
course will make the single octave stretched even more. Here again 
is a decision time. Does the tuner prefer pure triple octaves at 
the expense of the double and single octaves? What is the overall 
desired affect? Outside of unison work this is a point where ART 
enters. Who can say that Rembrandt or Renoir were wrong? Who can 
say that the Concert tuner is wrong and the Chamber music tuner is 
right? Do they each accomplish their purpose. I believe they do if 
their work shows consistency. These kinds of decisions in 
graduating the stretch CAN be accomplished with ETDs,
especially in using the SAT III and the Double Octave Beat 
control. The ART enters only from the decisions which the tuner 
him/herself makes. The rest is technique and use of the ears. ETD 
users also have ears. They should use them. I never leave home 
without them.

Next article will be on Bass Octave Tuning

Jim Coleman, Sr.