Melodic and harmonic octaves

[Jim]

Dear Larry:

Because you asked me to repeat my post on Melodic-Harmonic octaves
and because I could not find a copy of my last comments on this
subject, I did another study (on just one note).

If you play A3 a couple of times to get the pitch firmly in your mind
and then after a moment of silence, you try to tune an octave
accurately purely by ear and memory, the results will surprise you.
We call this melodic sense of hearing which means one note after
another.  You can do the same thing for each of the octave partials.

Each time you do this test on yourself, set the note to be tuned
deliberately sharp a few beats or flat a few beats before trying
to bring it to pitch.  Be sure and let the reference tone become
perfectly quiet before attempting to tune a higher octave with
the respective partial of the reference note (in this case A3).

Here are some results:   A3 fundamental or 1st partial tuned to 0.0.

Reference Note tuned = A-37  |  Note estimated and tuned is below
Harmonic or partial below    |    Melodic octave fundamental

 2nd at A4 =   .2 cents           A4        1.3, 10.7,  5.9,  9.0, 4.1

 4th at A5 =  2.9 cents           A5        1.8,  7.8,  7.8,  6.4, 5.9

 8th at A6 = 13.0 cents           A6       35.4, 35.6, 33.8, 32.4 17.0

In the above example there are 5 tuning samples for each of the single
double and triple octaves. they were tuned listening only melodically.  This
utilizes strictly subjective judgments.  First you will notice a great deal
of variation in the tuning estimates.  But the second thing you notice
is that notes tuned are considerably higher than the respective partials of
the reference tone A3.

Before you say "Coleman is getting too old, he's a violinist or he can't hear,
try it yourself.  Then try it before an audience of tuner-technicians.
I have done this many times in classes which I have taught.  I would let the
class tell me when they thought my estimate for a triple octave was correct.
We always came out with results quite similar to the above.  See, this wasn't
just my ears making decisions.

>From the above, it is quite obvious that we can't tune that sharp, and still
have good harmony, or matching of partials.  We will never be able to
satisfy this kind of melodic pitch requirement.  The octaves would sound
awful.  However, by giving a little more stretch than a pure matching of
certain partials would require, we can approach satisfaction.  Remember,
Musicians do not listen to the same things to which we listen.  They listen
musically and often melodically.  Don't be afraid to stretch yourself a
little.  but remember, I said "a little".

I hope many people will take up this challenge and do the test on themselves
or with a group of technicians.  It will help you justify yourself in trying
to stretch your upper octaves more and even the middle octaves a little bit.

Jim Coleman, Sr.

PS You might want to read again my article on Chasing the Wolf in the June
'96 issue of the Journal if this whets your appetite.