Conservative Octaves

[Stephen F Schell]

Hello List!

I have been reading the mail for the past month or so, and have enjoyed
it a great deal. I thought I'd weigh in on the octave stretching
discussion.

My general strategy is to widen octaves as much as possible throughout
the piano; the limit being the point where the single octave becomes too
noisy, usually at the 2:1 level. This, for me, is between 1/4 and 1/2 bps
(except the high treble and low bass), depending on the piano and how it
is voiced. The idea is to battle the tendency for the scale's
inharmonicity to seriously mistune the partial coincidences, which can
do much to strengthen the tone  if they are in close enough agreement.


Reinforcement of the piano's sound from coincident partials is a powerful
phenomenon. One can demonstrate this by "ghosting", i.e. playing a note
briefly while silently depressing another note containing partials
coincident to the note being played. The partial(s) excited this way
will sing out, often loudly. It's no wonder people often refer to the
sustain pedal as the "loud" or "swell" pedal.

Look at it from the perspective of a note on the piano, say C6. It's
first partial coincides in frequency, more or less, with the second
partial of C5, the third partial of F4, the fourth partial of C4, and so
on. The higher the inharmonicity of the scale, and the more
conservatively one expands octaves, the more these coincidences will
disagree, becoming progressively sharper to C6 down the scale. Even with
an aggressive stretching tactic, the inharmonicity wins eventually; the
16th partial of C2 may coincide with the first partial of C6 on paper,
but is often 40 cents or more sharp on a real piano. This is okay,
though; such a high partial may not be able to generate much sound
anyway. What is important is to maximize the agreement of those partials
which can contribute significantly. For my money, those are the octave
(2:1), twelfth (3:1), double octave (4:1), and triple octave (8:1). At
least those are the ones I have learned to pay attention to.

So how does one achieve a tuning where these coincidences can sing in
harmony? By expanding the octaves the maximum acceptable amount
throughout the piano. I generally like to set double octaves (at 4:1
level) about 1/2 bps wide throughout, except for the upper treble. I aim
for a pure twelfths all the way up, which usually results in a double
octave which becomes pure by about C7, then progressively but gently
narrow in the top octave. Triple octaves often remain pure to C7 or
higher, then likewise turn narrow. This seems to provide the top few
notes with maximum reinforcement; the octave is wide maybe 4bps, the
twelfth is pure, the double octave is narrow maybe 3bps.

I find that the pure twelfths approach seems to squeeze the most from a
piano's treble. Compared to the pure double octave tuning I did for
years, the sixth octave is expanded more, which really helps those
pianos tending to weakness in this area.
Sometimes, though, a compromise is necessary on a few notes around F6,
where a pure twelfth overstretches the double octave. In the top octave,
2:1s beat wide only a few bps, instead of the gritty buzz that can
develop in them with pure double octaves.

Carl Lieberman taught me a great tuning test years ago. He likes to use
both hands to play four neighboring positions of the same note ( i.e.
A3, A4, A5, A6) simultaneously, let them sing for a moment, listening
for whatever develops in the mix of sound. There are a great many
partial coincidences shared among those four notes. What is desired is
an overall solid sound, with a minimum of grumbling disagreement. This
test is useful anywhere on the piano. Curiously, an aggressive
stretching tactic will generally yield the smoothest and most powerful
sound with this test.

Does anyone around here hand out tickets for being verbose? Hope not.

Steve Schell
stfrsc@juno.com