As a sound engineer, I’ve known and worked with many accomplished piano
players, and I’m an avid pianist myself. But until I started down the
path of tuning pianos, I had no clue that the concept of a piano being
perfectly “in tune” does not actually exist. Most of us know when
unisons and intervals are way off. But what constitutes “in tune” in
terms of being musically pleasing? The answer lies in understanding two
key factors: temperament and inharmonicity.
It’s a String Thing
Piano strings exhibit inherent inharmonicity. This means that the fundamental pitch, let’s say the note A
vibrating at precisely 440Hz, will exhibit harmonic content (also
called overtones or partials) that is not evenly distributed as in say, a
pipe organ, a Hammond organ, some synths, or many
other instruments. The second harmonic, which in theory should be
880Hz, will in fact be slightly higher in pitch than twice the
fundamental. The third, fourth, fifth and other ascending harmonics will
rarely, if ever, be exact arithmetic multiples of the fundamental.
Moreover, when a piano string is struck by the hammer, it
becomes physically displaced, causing an initial and temporary pitch
change in its fundamental and harmonic frequencies. This is
difficult to hear because the pitch displacement in the fundamental is
small, yet magnified in the harmonics that are multiples of the
fundamental frequency. The result of this inharmonicity is
usually perceived as harshness, but not always. In addition to what you
can hear, seeing the pitch visually wandering on an Electronic Tuning
Device (ETD) readily shows what’s happening.
Shorter upright pianos, spinets, and baby grands all have
short strings that exacerbate inharmonicity—so will low-quality string
material. Conversely, the longer strings on medium- and full-sized grand
pianos, along with their typically higher quality metal alloys, are
much more forgiving; partials are more closely in-tune with each
string’s fundamental pitch. Less inharmonicity equates to purer sound
quality, but that’s not always the goal of a piano manufacturer.
Harmonic content can be part of a piano’s unique tonality.
The “scale” of a piano—that is, the string length in
relation to string tension, intended pitch, and resultant harmonic
content—is a huge element that distinguishes one piano from another.
Variations on scaling include the duplex scale, invented by Theodore
Steinway. This is a short “non-speaking” segment of the string length,
isolated from the string’s “speaking” length by a bridge and roughly
tuned to an octave or fifth above the note. In some pianos the
non-speaking strings can be tuned; in others they can’t.
Exactly how partials present themselves in a given string
is not readily predictable, and it’s only one of many factors in a
piano’s character. Were it not for the highly complex interaction of the
strings, the bridge, the soundboard, the hammers, and the structure of
the piano case itself, then all pianos of a given size would sound
pretty much the same. But they don’t, and we revel in that fact.
Temperament is the frequency relationship of each interval
to another within the “temperament octave” that dictates the pitch of
all upper and lower octaves, and one size does not fit all!
Numerous forms of temperament range from equal to ancient. To name just a
few: 14th-century Pythagorean (1373), DeMorgan unequal (1843), Moscow
equal-beating, William Hawkes Improved (1807), and the list goes on.
Temperament can be (and often is) set by ear by skilled
piano tuners who count beats—audible oscillations between
not-quite-in-tune notes—though the modern-day preference of many
professional tuners is to hand this task over to an ETD. Fifths can be
made perfect (no beating) at the expense of fourths and thirds, or the
opposite can be true. One aural tuning guide, authored by W. Dean
Howell, specifies 6.93 beats per second (bps) between F33 and A37. Under this same guidebook, A37 to the higher E44
should beat at 0.74 bps to achieve a perfect fifth. Point being, there
is no such thing as beat-free intervals throughout the scale.
Electronic Tuning Devices
Modern electronic tools give professional tuners a whole
new way to work. Pianists who can’t afford to pay a tuner to show up
every week might also take advantage of these, but they’ll need to work
through the rather steep learning curve of handling a tuning lever (also
called a tuning hammer) to properly set the tuning pins. It’s not easy,
but it’s not rocket science, either. If you just move the lever until
you hear the desired pitch without “setting” the tune, stability will be
elusive. This involves torquing the tuning pin upward in pitch, then
relieving the torque, and then carefully adjusting each string’s tension
ETDs range from dedicated hardware such as Peterson’s
industry-standard strobe tuners to modern apps that run on laptops, iOS,
and Android. I was privileged to try out two leading apps while
repeatedly tuning a year-old Yamaha upright piano in a small church—an
application that many professional tuners might encounter. Both were
easy to learn, yet sophisticated.
| || |
| Fig. 1. TuneLab’s primary display. The black bars move left or right to
indicate fine pitch, while the graph below indicates coarse pitch.||Fig. 2. One of Verituner’s main displays showing the inharmonicity table
(left), pitch in cents (center), current note, settings, and the
inharmonicity I-beam (right).|
TuneLab. I started with TuneLab (tunelab-world.com),
an app I ran on an iPhone 4S. The display shows an FFT-style coarse
pitch graph, while simultaneously providing a series of black bars that
move either left (for flat) or right (for sharp), to establish fine
pitch.. The coarse pitch graph lets you see
two or more unisons at the same time that are not in-tune, due to its
excellent resolution. This is a very helpful feature, especially in the
upper octaves. TuneLab can also sample strings in order to identify
their inharmonicity and thus calculate the projected inharmonicity of
the entire piano’s scale.
Verituner. Next was Verituner (veritune.com),
a product with significant design depth. It runs on iOS or Windows PCs,
and is also available as a standalone device called Verituner Pocket. I
loved Verituner’s relative initial simplicity, combined with its
ability to make complex adjustments to the prescribed starting points,
thus giving the professional tuner a broad palette of possibilities. The
display depicts a rotating icon including several additional elements. Coarse pitch is shown much like a speedometer
needle; fine pitch is depicted by a spinning rotor. Inharmonicity is
displayed as a table for each string, providing valuable information
about a given piano’s harmonic quirks. Verituner looks at string
inharmonicity in the background as each note is tuned. It doesn’t
extrapolate, but rather, makes a direct calculation for each string.
Partials (ascending harmonics) tend to skew sharp in piano
strings. So if each fundamental frequency were the only basis for a
tuning strategy, most pianos would sound lifeless. For this reason, most
by-ear tuners and most ETDs will “stretch” the upper and the lower
octaves in relation to the reference “temperament tuning octave.” Both
the TuneLab and Verituner ETDs do the work for you. You simply specify
stretch tuning and you’ll get it, without having to count beats per
second. Both apps allow adjustments to the stretch parameters, which is
important for making a piano sound the best it can.
Piano tuning is an art form backed by decades of
scientific research. But science and the mathematical analysis of
harmonics can never tell us what to enjoy when we listen to
music. While we can analyze frequency content, we have yet to bridge the
gap between objective analysis and why one subtle difference in tuning a
piano might make all the difference in how a performer responds to the
instrument. ETDs bring us much closer to this understanding, though none
should ever be taken as a substitute for listening.
Ken DeLoria has had a 45-year relationship with music in
general and pianos in particular. He works in the audio industry as an
engineer, most notably as the founder and CEO of loudspeaker maker
Apogee Sound Inc. He can be reached at firstname.lastname@example.org.