Tone Production

Sample Rate and Bit Depth

The technology now used in most digital pianos to emulate the complex tonal behavior of the acoustic piano is called sampling. Sampling, in its simplest form, is the process of making a digital recording of a sound for later playback. A collection of samples, such as those needed to reproduce the tone of a piano, is called a sample set. There are many decisions to be made in compiling a sample set for an instrument as sonically complex as a piano, perhaps the most important being the sample rate and bit depth.

The sample rate determines how many times per second the sound will be measured. The sound must be sampled often enough to avoid missing changes that occur between sample times. This rate, in turn, depends on the frequency of the sound being sampled. The fundamental frequency of the highest note on the keyboard is 4,186 cycles per second, or hertz (Hz). But the overtones that accompany these fundamentals vibrate at multiples of the fundamental’s frequency, and must be properly recorded in order to accurately reproduce the tone. Fortunately, the inventors of the Compact Disc were well aware of this requirement, and long ago adopted the sampling rate of 44,100Hz for audio CD recordings.

The other decision is how finely to measure at each of those 44,100 times per second. Just as we don’t want to miss changes in the sound that occur between the times we measured it, we also can’t afford to miss the details of those changes. In digital recording, this is called the bit depth. The higher the bit depth, the finer the detail that can be recorded. In computers, an 8-bit number represents up to 256 levels of detail, a 16-bit number can represent 65,536 levels, and a 24-bit number tops out at 16,777,216 levels. Once again, we will bow to the decision of the developers of the Compact Disc and go with the choice of a 16-bit number as our standard.

What all of this means is that, under the audio-CD standard, every second of sound sampled is measured 44,100 times at a degree of detail that can represent up to 65,536 individual levels. This one second of sample information takes up just over 86 kilobytes (KB) of memory space. Because digital piano manufacturers do not release information about their sampling standards, there’s no basis for comparison with the audio-CD standard. However, the rates stated by developers of software pianos tend to be higher than this standard, so it’s reasonable to assume that some digital piano manufacturers may exceed these rates as well.

Looping

One interesting characteristic of a piano note is that it can sustain for several seconds, but after the first couple of seconds much of the initial complexity of the sound is gone; the remaining seconds of sustained sound go through very little change other than gradually decreasing in volume. This opens up the possibility to save some memory space, and thus some money, by introducing a process called looping. Looping involves selecting a short duration of the sound that remains essentially unchanged over a period of time, and repeating it over and over at gradually reduced volume levels. Done with care, the result is barely detectable when listening intently to the sustain of one note, and becomes completely lost in the commotion when playing normally.

Spatial Relations

The notes produced by an acoustic piano have a physical point of origin in the instrument’s strings, and can be heard moving from left to right as you play a scale from the left (bass) end of the keyboard to the right (treble) end. To preserve this spatial relationship, the samples in a digital piano are recorded in two-channel stereo. This feature, often called “panning,” adds to the realism by physically positioning the sounds in ways similar to what is heard from an acoustic piano.

Number of Notes Sampled

Now we must decide how many notes to sample. The obvious answer would seem to be “all of them,” and some manufacturers take this route. But in the interest of keeping the cost of the digital piano under control, many manufacturers seek alternatives to sampling all 88 notes.

In an acoustic piano, the tonal behavior of the longer, bass strings is different from that of the shorter, treble strings. In fact, this tonal variation goes through several changes as you play up the keyboard from the bottom. Some of these changes are due to the differences in string length, others to differences in the types and numbers of strings associated with different ranges of notes. In the lowest bass, the hammers strike a single string per note. This string is wrapped with heavy copper wire to slow its rate of vibration to produce the proper pitch. Depending on the piano’s scale design, a couple of octaves up from the bottom of the keyboard it switches to two strings per note, each wound with a lighter copper wire. Finally, by mid-keyboard, three plain-wire strings are used for each note. (Each set of one, two, or three strings per note is known as a unison because all the strings in a given set are tuned at the same pitch to sound a single note.) The subtle changes brought about by these different string arrangements also figure in the tonal variations we hear as we move up and down the keyboard.

But the tonal changes from one note to the next are not always noticeable; sometimes, all that changes is the pitch. It turns out that it’s a fairly simple matter for the digital piano to play back a sample at a different pitch. This makes it possible to save memory space by using one sample as the basis for two or three consecutive notes. Taken too far, this would result in obvious tonal problems. But if at least a third of the notes are sampled, with careful attention to areas of the keyboard where there are more noticeable changes, these shared samples can produce a convincing, if basic, tonal progression.

Sampling Dynamics

One more source of tonal variation — the effect of dynamics (variation in volume or loudness) — must be dealt with before we move on from our basic sample set. Striking a string harder results in a larger number and greater prominence of higher overtones, which, in addition to making the sound louder, give the tone more “edge.” Currently, in all but the least expensive instruments, digital pianos use from three to five dynamic samples. As you play with varying degrees of force, the digital piano selects the closest appropriate dynamic sample for playback. Entrylevel pianos that use a single sample level for dynamics also use variable filtering of a note’s overtones to simulate these tonal differences, sometimes with remarkable success.

Sampling Other Effects

Many digital pianos incorporate additional types of samples aimed at capturing more of the nuance of an acoustic piano. At this time, the two most common such samples are string resonance and damper effect. As with so many features, different manufacturers seldom use the same terms for the same effects. String resonance is related to the strings’ overtones. Each of the overtones generated by a vibrating string are at, or close to, the fundamental frequencies of higher notes whose frequencies bear a mathematical relationship to the one played. This results in a weak sympathetic or resonant vibration of the strings of the related notes, and adds another dimension to the sound. (To hear this effect, slowly press the keys of a chord — for this discussion, let’s make it a C chord — without actually sounding them. While holding these keys down, quickly strike and release the C an octave below the held chord and you’ll hear, faintly, the sympathetic resonance of the C chord above.)

In an acoustic piano, a note’s felt damper moves away from the string(s) when its key is depressed, and returns to stop their vibration when the key is released. The effect on the sound is not instantaneous; it takes a fraction of a second for the strings’ vibration to stop. During this time the tone is altered as its overtones rapidly decay. Damper-effect samples are triggered by releasing a key, and add another subtle dimension to the digital piano’s sound.

Polyphony

Finally, we have to consider how many notes the instrument can play at once, which is expressed as its polyphony. A quick glance at your hands may suggest that 10 ought to be plenty. But consider what happens when you play a series of chords, or an arpeggio, while holding down the sustain pedal. Each note that continues to sustain takes up one note of polyphony. If you press the sustain pedal and play a three-note chord with both hands, then repeat those chords three more times in successively higher octaves, you will now be sustaining 24 notes. Played with layered voices (a combination of two different voices, such as piano and strings), that example would require 48 notes of polyphony. Some models of digital piano have 32 notes of polyphony, but most current models have 64 or more.

A cautionary note: As you delve into the specifications of digital pianos, the temptation to rank instruments based on numbers — how many notes were sampled, how much memory the sample set takes up, and so on — will be high. And the results would be highly unreliable. Designing a digital piano involves choices driven by economics (e.g., how much a model will sell for), by the intended customer’s needs (beginner or professional), and, in no small part, by the engineering talent at the manufacturer’s disposal. Engineering creativity, or lack of it, can turn the numerical specifications on their head, resulting in an instrument that sounds better — or worse — than its numbers would suggest.

Controlling Tone — The Keyboard

Just as in an acoustic piano, the role of the keyboard is to provide the player with intimate, reliable control of the instrument’s tonal resources. But just as there is no single correct tone, there is no single correct feel; rather, there is an acceptable range of touch characteristics.

Touch Weight

As in an acoustic piano, the action of most digital pianos is primarily an arrangement of levers, but the digital action is far less complex and doesn’t require regular adjustment. Players use a few definable criteria to judge an action. Some are easily measured, others are largely subjective. Among the most frequently debated by digital piano buyers is touch weight.

Touch weight is the amount of force, typically measured in grams, required to depress a key. A touch weight in the range of 50 to 55 grams is generally considered normal for an acoustic piano. The resistance offered by the key is a combination of friction and the mass of the parts being moved. Both of these factors behave slightly differently in acoustic pianos than in digital pianos. Measuring the touch weight of an acoustic piano is typically done with the sustain pedal fully depressed, which removes the weight of the dampers and reduces the force required to depress the key. The problem is, digitals don't have dampers, so the digital manufacturer has to decide between the higher weight the pianist will feel when the dampers are being lifted by the key, and the lighter weight when the dampers have been lifted by the sustain pedal. There is no single right answer — just design choices.

Friction is also a bigger factor in the action of an acoustic than in a digital piano. Most of the friction in an acoustic action is due to various hinge points and bearing surfaces, many of which have cloth or felt bushings. Over time, these bushings wear away or become compacted, reducing friction and the amount of force required to depress a key. Another factor is humidity. Felt and wood parts readily absorb and release moisture, effectively increasing or decreasing friction with changes in the amount of moisture in the air. Because digital actions contain far fewer felt parts and — with the exception of a few upperend actions sporting wooden keys — no wooden parts at all, changes in friction due to wear and fluctuations in humidity are substantially reduced.

Yet another aspect of touch weight is that it varies from one end of the keyboard to the other. In an acoustic piano, the hammers are significantly heavier at the bass end of the keyboard than at the treble end, which results in heavier touch weight in the bass and lighter touch weight in the treble. Enter the graded hammer action: To replicate the touch weight of the acoustic piano keyboard, most digital piano actions employ in their designs the equivalent of graduated hammer weights. Rather than using 88 different weights across the span of the keyboard, which would be cost-prohibitive and of questionable value, it’s common to use four different touch-weight values, each one used uniformly throughout one touch-weight zone.

Key Design

Some high-end digital pianos employ wooden keys to subtly move you closer to the feel of an acoustic action. The physical properties you may detect would be a slight flexing of the key, a difference in the mass of the key, and possibly a very slight difference in the shock absorption of wood vs. plastic when the key is depressed and bottoms out (although this is mostly masked by the felt pad under the key).

Another aspect of key design is the tactile property of the keytop material. Ivory is so prized (and missed) by acoustic piano players not for its appearance, but for the fact that it’s porous, and thus offers a degree of “grip” that slick-surfaced plastic keytops don’t. This grip is particularly valued when the playing gets serious and the pianist’s fingers become sweaty, which typically occurs during demanding passages, when the pianist’s accuracy and control are pushed to their limits. Ivory substitutes, such as Kawai’s Neotex, Roland’s Ivory Feel, and Yamaha’s Ivorite, provide the positive properties of ivory without the discoloring, cracking, and chipping for which ivory is equally famous. Other manufacturers have since added this feature, and it’s one worth considering when comparing instruments.

Dynamic (Velocity) Sensors

The final aspect of the digital piano action we’ll explore is how it measures the force the player’s fingers apply to the keys. This is typically done using two electrical contact switches that are closed in rapid succession as the key is depressed. Alternatively, some high-end digital hybrids use optical sensors to sense the key’s motion — a small flag attached to the key breaks a beam of light as it descends. However, what these sensors actually measure is not force — that is, how hard the key is depressed — but the speed or velocity with which it is depressed. This is why you’ll sometimes see the term velocity sensing in the keyboard specifications. As the key moves to the bottom of its travel, the instrument measures how much time has elapsed between the signals received from the first and second sensors. A longer time indicates that the key was traveling slowly and tells the instrument to produce a softer tone; a shorter time means a faster, harder keystroke, and thus a louder tone — it’s that straightforward. Some actions employ additional switches to trigger other sample types, such as the damper effect mentioned earlier.

Some digital pianos now employ three sensors (“Tri-Sensor” or “Triple-Sensor” keys) instead of the usual two. The additional sensor greatly improves the repetition speed by allowing the player to retrigger a note without the key having to fully return to the top of its stroke. The third sensor also improves the instrument’s response to legato passages.

The Pedals

Modern acoustic pianos have three pedals. Let’s take a look at how they work, and how their functions translate to the digital piano.

In the common three-pedal arrangement of an acoustic piano, the pedal on the right is the sustain pedal. In the case of digital instruments having only one pedal, it is the sustain pedal. Some refer to this as the damper pedal, because its mechanical function on an acoustic piano is to lift the dampers away from the strings. On a digital piano, the sustain pedal is an electronic switch. When depressed, it tells the instrument to allow played notes to gradually decay as they would on an acoustic piano.

The most frequent question about a digital piano’s sustain pedal is whether it can perform a function called half pedaling. The acoustic piano’s sustain-pedal mechanism can move the dampers from a position of rest on the strings to a position completely clear of the strings — or anywhere in between. Between these two positions is the highly useful half-pedal position, which allows the player more control of tone and sustain. While half-pedal capability is now commonly found on upper-end digitals, it is not always present on lower-priced instruments, where the sustain pedal is more likely to be a simple on/off switch that allows full sustain or no sustain, but nothing in between. Some lower-priced digitals come with a separate square plastic or metal foot switch rather than something that looks like a piano pedal. However, even if the piano itself is capable of half-pedal control, the foot switch may provide only on/off sustain. The same may be true even with some pedals that have the appearance and movement of a piano pedal. It’s always worth checking the specifications to be sure that both instrument and pedal are capable of half-pedal control.

At the left end of the three-pedal group is the soft pedal. The proper term for this in an acoustic grand piano — una corda, or “one string” — relates to its function. In an acoustic grand, this pedal, when depressed, laterally shifts the entire action — from keys to hammers — slightly to the right. Recall (from “Tone Production,” above) that, on an acoustic piano, most notes have two or three strings associated with them. When the action is shifted to the right by the soft pedal, the hammer strikes only two of the three strings in each three-string unison. This has two effects: it reduces the volume of the sound, and it slightly alters the tonal quality.

As with the sustain pedal, the digital version of this pedal is simply an electronic switch that activates an equivalent effect. Since the digital piano action can play at much lower volumes than the acoustic piano, the practical importance of this pedal for reducing sound volume is considerably lessened. However, its ability to alter tonal quality remains relevant — assuming it actually does so. Most do not.

The mysterious center pedal is the sostenuto. The easiest way to think of the sostenuto’s function is as a selective sustain pedal. Play one or more keys anywhere on the keyboard and, while holding these keys down, press and hold the sostenuto pedal. The sostenuto mechanism will hold the dampers for these keys away from the strings, sustaining them even after you release the keys, but any subsequent keys played will not sustain when released (unless you also use the sustain pedal). Clear? The bottom line is that all three-pedal digital pianos incorporate this feature exactly as it works on an acoustic piano. In written music, the sostenuto pedal is called for in only a few pieces of classical music. If you need it, it’s there, but chances are you never will. In digital pianos, the middle pedal is often assigned another function, discussed in Part 2 of this article.

The Audio System

The final component of most digital pianos is the audio system — its amplifiers and speakers — which perform the same job as an acoustic piano’s soundboard: making the piano’s sound audible at useful volume levels. I say most digital pianos because some instruments designed specifically for stage use lack an onboard audio system, as they will always be connected to a sound-reinforcement, or public address (PA), system.

The digital pianos currently on the market offer anywhere from 12 to 360 watts (W) of output power, channeled through from two to twelve speakers. To understand why there is such a wide range of options, we need to look at how the system’s power-output capability (and the type, number, and placement of speakers) relates to what we hear.

The smallest change in volume that most people can detect is 3 decibels (dB), and to achieve a 3dB increase in volume requires a doubling of the output power in watts. With these relationships in mind, let’s look at some numbers.

Based on measurements of three of the most frequently encountered concert grand pianos — Bösendorfer model 290, Steinway & Sons model D, and Yamaha model CFIIIS — I arrived at a model dynamic range. This range extends from the softest note possible, at 64dB, to the loudest chord I could produce, at 103dB. Assigning a modest 0.015W — we’re assuming a very efficient audio system — to produce the softest (64dB) note, the chart below traces the progression of amplifier power required to keep up with the increasing volume to the top of the piano’s dynamic range. Different audio systems will have different starting points, depending on the size and number of speakers being powered, the efficiency of those speakers’ use of power, and the notes played (bass requires more power to match the treble volume). Dynamic markings have been added to bring some musical perspective to the numbers.

If you’ve not seen this sort of table before, the results are startling. It’s the last three or four steps of volume that really demand power from the amplifiers.

When the audio system attempts to reproduce a sound louder than it can accommodate, it goes into “clipping” and produces a distorted version of the sound. One thing to remember is that even the most powerful instruments can be driven into clipping if played loudly with the volume turned all the way up. Aside from distorting the sound, overdriving the system can damage the speakers and amplifiers. The key is to set the volume no higher than 75 to 80% of its maximum level.

If you’ve already peeked at the specification charts toward the end of this book, you know that only a few digital pianos produce 100-plus watts of output power per channel (left and right). Many of the models that do have that much power also separate the low-demand treble frequencies from the power-hog bass frequencies by providing each frequency range with its own amplifier and speaker(s). A very few go so far as to divide the audio system into three separate subsystems, for the bass, midrange, and highs. These designs, called “bi-amped” or “tri-amped,” can make a noticeable difference in sound and power efficiency by using amplifiers and speakers optimized for specific frequency ranges rather than sending the entire frequency spectrum to a single full-range audio system.

Speakers

Because all of the digital pianos we’ll consider in this publication have stereo audio systems, all discussions of speakers will assume matching left and right channels.

The least expensive digital pianos employ a single full-range speaker per side. While these speakers are typically described by the manufacturer as “full-range,” they are in fact a compromise dictated by cost and, in the case of the most compact designs, space. While a full-range speaker may reproduce much of the 20Hz–20kHz frequency range required by the piano samples, those frequencies will not be treated equally. The frequency response of a speaker is judged not only by its range, but also by its “flatness,” or accuracy. If we send to a speaker multiple signals at different frequencies but at the same volume level, then measure the speaker’s output volume when producing those sounds, we will see the speaker’s “frequency-response curve.” The full-range speaker will usually be acceptably flat through the middle of the frequency range, but will fall off in volume at the upper and lower reaches of the spectrum. In other words, the speaker will not accurately reproduce the full range of the signal sent to it. This is not the result of poor speaker design. As a matter of fact, I’m frequently amazed at what the engineers can coax out of these speakers. But the fact remains that they are inaccurate, and in ways that color our perception of the instrument’s sound. Even the best sample set is rendered unimpressive if the sparkling highs and thunderous lows are weak or missing.

For this reason, most upper-end models use three speakers, one of each optimized for the bass, midrange, or treble frequencies. Ac-curate reproduction of bass frequencies requires the movement of a great deal of air. This is accomplished by combining a relatively large surface area with a high degree of in-and-out movement.  These bass speakers, or woofers, are largely responsible for our impression of an instrument’s “guts.”

At the opposite end of the frequency spectrum is the highfrequency speaker, or tweeter. The tweeter, which is physically quite small, is responsible for reproducing the nuances of the upper range of the instrument. Besides the obvious frequency difference between the outputs of the woofer and tweeter, they also differ in their placement requirements. Whereas low frequencies tend to radiate in all directions, the higher the frequency of the sound, the more directional it is, which means that the precise placement of the tweeter is much more important.  Most of the low- and mid-frequency speakers on digital pianos are located below the keyboard because there’s plenty of room there. The more directional nature of the high frequencies requires pointing the tweeters directly at the player’s head, usually from somewhere on the instrument’s control panel.

The newest twist in speaker systems — one that appears to be unique to digital pianos — is the soundboard speaker. This technology will be discussed in the article “Hybrid Pianos,” elsewhere in this issue.

So we now have all the makings of a digital piano: a sound source, and the means to control and hear it. But none of the current crop of digital pianos stops there; all of them have additional capabilities. These extras range from a handful of additional voices to direct Internet access. Even if your current needs don’t extend past the basics, you should understand the other features present on your instrument, and how they might surprise and lure you into musical adventures you’ve never contemplated. To continue, please read “Digital Piano Basics, Part 2: Beyond the Acoustic Piano.”