1. Roland Piano Soundsources

A. Roland's piano philosophy

In 1974, Roland introduced the world's first digital piano with a touch sensitive
keyboard (EP-30). Since then, Roland has maintained its position as an innovator in the
field. Our design philosophy has always put priority on pianistic expression and making
digital pianos perfect.

We have therefore refined and commercialized stage pianos focusing on sound clarity and
dynamic range  as well as home-use pianos offering natural and realistic sonority. Our
new developments include the latest design that has become the standard for today's
digital pianos (HP-300), ism concept of MIDI-based expandability (MT series), and a
built-in FDD (HP-29000). Thus Roland has consistently ushered in new concepts in the
digital piano field.

In keeping with the development of SA and Advanced SA Synthesis techniques, the new
HP series incorporates the very latest technologies including sound generation waveform
processing and digital signal processing (DSP) to achieve new reference standards in
tonality and sonority.

B. Overview of Roland's original sound generation technologies

First generation SA soundsource (RD-1000, MKS-20, HP-3000, HP-5000, etc., 1986-1989)

The first digital sound source from Roland, was the SA (Structured Adaptive Synthesis Sound
Source) which was specially designed for digital pianos. This state-of-the-art sound source was
used in the pro-use RD-1000 and MKS-20 digital pianos and home-use for the HP-3000. These
digital pianos received much acclaim for their outstanding expressive qualities and level of
achievement as sophisticated instruments.

Around that time, PCM sound source-based sampling techniques also began to arrive in
the market. This technique apparently simulated piano sounds with an instant and
dramatic contrast to digital pianos employing an analog sound source. However, this
sampling technique showed that it was only capable of recording a naturally occurring sound
under certain conditions. It was just like taking a photograph. There were difficulties
when it came to duplicating sound having all rich and expressive timbral changes of pianos.
It is interesting to note that PCM sound sources sounded incredibly lifelike to the listener,
but caused much frustration for the players who were unable to fully express themselves
pianistically with these sound sources.

We believe that the most important factor behind musical instruments is the ability to
express the player's originality and creativity to the fullest. This philosophy was therefore
reflected in the development of the SA Synthesis Sound Source. We were committed to
developing innovative piano sound generation technology that surpassed conventional
sampling.

What really distinguishes piano tones are the rich and colorful tonal variations along the
three axes of note range, playing dynamics, and time. It is these timbral subtleties that
form so much of a piano's distinctive expressive capability.

To make such tonal variations easily controllable by the players, we knew simple sampling
(direct recording) would not be enough. We carefully examined the sources that create
various piano sound characteristics in order to create our proprietary technique. This
technique structures each element of piano sound and stores them individually into
memory, re-synthesized to obtain natural timbral changes.

A detailed look at  SA synthesis

On acoustic pianos, lower  and upper registers sound  significantly  different.

The SA Synthesis sound source is capable of recreating realistic differences in sound by
note range. It splits the key range into nearly 30 different stages (varies by tone and
model) and simulates each timbre by combining most appropriate elements. This results in
a sound source structure that is optimized for simulating each note range's timbres.
Through this process, the SA Synthesis technique can control distinctive formants* 1 and
enharmonicity*2 for the low end, the harmonics mixing balance, envelopes and resonation
on the soundboard for the midrange, as well as elements such as basic waveforms and
hammer noise for the high end, on a precise individual basis.

*1 Formants

With the SA Synthesis sound source, volume and tonal variations of transitions from
pianissimo to fortissimo and everything in between are precisely programmed for each
harmonic components and element. It also simulates dynamics curves in order to produce
smooth changes over the entire 127 levels available from MIDI, so that players can exert
precise control over sound.

Conventional sampling techniques mainly produce volume changes by varying dynamics
and adds tonal changes by switching between two recorded tones of different velocity,
changing the mix ratio for recording waveforms with three dynamic levels - hard, middle
and weak - or reducing harmonics with the Biter.

What about timbral changes over time?

The SA Synthesis Sound Source also programs each attack and decay components found in
the harmonics of acoustic pianos. Differences in sound envelopes (attack) from varying
dynamics are also programmed for each harmonic component and element of sound, in
order to recreate a soft attack for pianissimo and sharp attack for fortissimo.
With the SA Synthesis technique, the computer instantly detects how hard each key is
struck, and assigns the optimum piano waveforms to the sound source for real-time sound
re-synthesis. This results in rich and smooth timbral changes and amazing expressiveness.
Factors common to fine quality pianos were analyzed by recording sounds of fine acoustic
pianos (Steinway, Bosendorfer, Bechstein, Yamaha, etc.), were then digitally recomposed and
assembled into each element of the total piano sound.
 

Advanced SA Synthesis Sound Source (HP models from HP-2700/3700 on, 1990~)

SA Synthesis for more natural sound

SA Synthesis was evaluated highly for its superb expressiveness and well balanced sonority
by professional and highness users. Digital pianos have also become increasingly popular
for home use as a substitute for upright pianos used by children for piano lessons, practice,
etc. The same home users have demanded more realistic and natural sound that is easy for listening.
In addition to the SA Synthesis technique, Roland has achieved technological
breakthroughs in samplers for professional use, and more memory has also become
increasingly accessible. This allowed Roland to create a new sound source that can offer
more realism in piano tones and greater pianistic expression while retaining the basic SA
Synthesis concepts. This was combined with advanced DSP technology to preserve subtle
nuances of piano performance such as sympathetic resonance and half-damper techniques.
The result is an advanced SA Synthesis piano sound source which was first employed on the
HP-2700.

This new technique uses a greater amount of memory to achieve maximum realism so it
can faithfully reproduce each element of sound as well as spatial acoustics, while also
featuring simpler architecture. As a result, the Advanced SA Synthesis technique offers
superb natural sonority as well as the SA Synthesis sound source's renowned expressive
capability, well balanced functions and ease of playing.

Advanced SA Synthesis and sympathetic resonance

When you play a note on an acoustic piano with the damper pedal down, the sound takes on
a lot of spaciousness and sounds absolutely great. What happens? Depressing the damper
pedal allows all strings to freely vibrate.

When a note is played, the string's harmonic components excite other strings having the same
frequency components as the sounding string  generating the sound. This phenomenon is
called "sympathetic resonance," a body of resonance consisting of all open strings
throughout the piano's soundboard and bridge. Clap your hands or speak near the
soundboard while depressing the damper pedal, and you'll notice an unusual reverb decay.
Based on intensive analysis of these unique reverb characteristics caused by the
soundboard / open strings combination, Roland succeeded in simulating the characteristics
with its proprietary Advanced SA Synthesis technique that uses the latest DSP technology.
HP models with the earlier Advanced SA Synthesis sound source (HP-2700 / 3700, etc.)
incorporated a dedicated DSP chip in order to simulate damper pedal resonance.
This feature added greater realism and expressiveness to Roland digital pianos which have
enjoyed much acclaim in the home use market as well as in professional live stage
applications.

C. Advanced SA Synthesis '96

Roland's SA (Structured Adaptive) Synthesis sound source has continued to be refined by
employing the latest sound processing and DSP technologies. It has also been evolving
due to the synergistic efforts of many pianists, tuning experts and musically knowledgeable
engineers. In particular, the newest HP series incorporates a brand new sound source that
draws on Roland's accumulated wealth of advanced LSI and DSP technology. What
follows are explanations of our latest achievements.

New waveforms for stereo sampling

The most important factor in the quality of piano sound created through sampling
techniques including the Advanced SA Synthesis is the basic raw material, namely the
actual waveforms.

The sound source of the new HP pianos features a 64-voice polyphony and stereo-
sampled sound that ensure the most realistic sound field. This was achieved by our work
in simulating miking. Many hours of experimentation with various microphone types,
numbers and configurations enabled us to attain an ideal microphone setup which
portrayed a lifelike sound field of a grand piano with clear localization.

Conventional stereo sampling techniques as used by competing manufacturers tend to
emphasize ambiance which produces more spaciousness, but sacrifices sound localization
which is invaluable in presenting a true acoustic piano presence. The microphone setup
we devised for stereo sampling allowed us to locate a miking point between the off-mike
and on-mike positions for each note. This allowed us to deliver rich ambiance and clear
sound localization without compromising either quality.

When we consider the acoustic piano as a source for sampling, we are well aware the high
quality elements are essential for impressive piano sounds. The new HP series is based on
a premium full concert grand that was pampered by a leading concert tuner. During
sampling, the concert tuner was on hand to continually fine tune as needed. This explains
the distinctive natural decay of Roland HP pianos that is not to be found in any other
manufacturer's product.

To take maximum advantage of these superb sound elements, substantial wave memory is
used for piano sounds. Memory capacity is a full three times that of models equipped with
previous Advanced SA Synthesis (HP-2700/3700, etc.) and more than 10 times that of
models using the first SA Synthesis sound source (HP-3000, etc.).

New 64-voice soundsource LSI  (polyphony)

All Roland digital pianos prioritize pianistic expression. The new 64-voice sound source
LSI eliminates sound dropouts or any shortage in simultaneously produced notes (voices),
while also enabling stereo sampling. This is just one indication of how Roland is
constantly trying to accomplish more.

Conventional 32-or 28-voice sound sources are not held in high regard by serious players
with elaborate songs due to the lack of simultaneous voices available. But 64 voices
should be more than enough to solve this problem. When compared with competing
products in the same price range (16 voices, stereo), Roland new HP pianos feature twice
the number of simultaneous voices.

The soundfield is crucial for pianistic expression. Roland new stereo sampling approach
faithfully recreates the spacious piano soundfield. The substantial 4-voice sound source
was the key to achieving this technological breakthrough.

DSP resonance

The DSP technology that simulates the resonance occurring naturally in acoustic pianos
when the damper pedal is depressed has been a part of Advanced SA Synthesis from the
start. On the new HP series, parameters have been reworked to deliver more realistic
effects that better suit the new stereo waveforms.

Pedaling timing has also been improved. The natural resonance in the highest note range
is singly breathtaking.

For all players, but especially for children, it is important to confirm variations regarding
note duration, sustain, sonority and tone characteristics that vary with pedal action with
then- own ears. Songs with difficult pedaling are not needed for beginner lessons, but it's
still important for those beginners to understand just how to control sound through
pedaling for greater pianistic expression.

Newly developed formant filter

Generally, digital pianos use a filter to control tonal variations present in pianissimos and
decay sounds. It was usually a synth filter, which usually made it difficult to obtain
genuine tonal variations found in acoustic pianos. Roland had developed a special filter to
recreate genuine piano sounds.

Instrument sounds generally consist of several harmonics. Piano tones in particular
contain several distinctive harmonics called 'formants" along the frequency axis. The
original shape and balance of the formant components must be maintained if authentic
piano sound is desired.

The conventional synthesizer filter is very effective for creating tonal changes from.
pianissimo to fortissimo for non-piano sounds. But for piano sounds specifically, a filter
exhibiting constant decay characteristics at - 12dB / Octave often causes too great an
attenuation of the upper harmonics, particularly for pianissimo sounds (when the cut-off
frequency is lowered). This often causes highs to be cut excessively, deviating formant
shape and balance.

Roland has developed a special formant filter in order to produce the natural tonal
variations of a piano without formant corruption. This filter is capable of controlling
piano tone while maintaining the original formant shape and balance. Regarding tonal
variations by key strike force (velocity), this filter eliminates the excessive filter effect that
occurs in pianissimo sounds for an authentic recreation or original acoustic pianissimo
sounds. How about tonal variations up to fortissimos? With acoustic instruments, the upper
harmonics tend to increase in a gradual curve starting with the formant of pianissimo
sounds. The formant filter is capable of simulating this gradual inclination and shows a flat
at the fore notes - ideal filter characteristics It can also emulate natural tonal variations
over time - the higher the degree of harmonics the faster the decay occurs, and vice versa.
These outstanding characteristics allow the formant filter to offer incredibly natural tonal
variation.

Spectrum comparison

 

Dynamic range

Dynamic range is an important factor in creating impressive piano sound. Roland uses a
new approach for this as well and makes it effectively follow the player's expressive style.
Conventionally, pianissimo sounds were created by making maximum use of the filter
which often sacrificed formant components. To solve this, the new HP series uses
dedicated pianissimo sound waveforms. By controlling these waveforms with the formant
filter, a very natural pianissimo control is obtained. In addition, individual waveforms are
used to simulate different attacks between pianissimo and fortissimo, to achieve more
precise pianistic expression. Attack dedicated waveforms are also added for fortissimos
(which are rarely used in actual playing) to gain maximum clarity in the sound. By
effectively matching these waveforms with the player and keyboard, the ideal dynamics
control has been achieved.

Acoustic design

The best in design and sound output. This is the goal Roland has sought - how the digital
piano can improve sound quality and output through cabinet design. Most competitors
take a more audio-oriented approach through speaker and speaker box configurations to
achieve flat frequency response. However, the new HP series is designed to simulate the
vibrational response of a complete piano, just as is found in acoustic pianos or other
acoustic instruments. We noticed the beneficial effect of key vibration. When you press a
key on an acoustic piano, vibrations are conveyed to the finger and has a beneficial effect
on performance. What we have done is to install a large diameter speaker on the same
board that the keyboard mounts to in order to integrate speaker, cabinet and keyboard.
This benefit is instantly noticeable if you compare the sound with headphone sound. To
augment bass, the blindboard height was also adjusted so that sound can be better heard at
remote locations. The bottom board and rear panel are securely attached with tight
screws to enhance powerful speaker low notes (HP-530).

Final touches

For digital pianos, "no need for tuning" has been the most prominent benefit. This means
factory preset tuning has been everything. For the new HP series, the digitally controlled
tuning was performed at the final stage, and an expert, German trained concert tuner was
consulted for this process. The same approach was used on the top-of-the-line HP-7700
to considerable acclaim. This tuning process encompasses more than mechanical tuning
aspects, covering the characteristics of every single note, and adding pleasant ambiance to
the sound.

Performance was compared before and after tuning. Although the difference in data was
minor, the difference in terms of the spaciousness of sound and how chords sounded
surprised us. When we set sound parameters, the sound was repeatedly auditioned and
compared with a grand piano installed right beside the HP. The master timer was also in
attendance to ensure we got the most realistic sound.

D. Hammer action keyboard for the digital piano

Regarding the grand piano keyboard mechanism and construction

The hammer action of a grand piano is widely considered the ideal keyboard touch.
Illustration A (below) shows the superior attributes of the grand piano's keyboard mechanism.
When a key is pressed, the hammer which rests horizontally moves from the lower to the
upper position, striking the string. When the key is released, the hammer returns to its
original position, as the result of its own weight.

This design offers these features:

Illustration A
 

Roland Hammer Action Keyboard

Roland's epoch making hammer action for digital pianos has been  designated to reproduce the
superior attributes of the grand piano key (see illustration B below). The Roland Hammer Action Keyboard is
specially constructed to concentrate the weight on the tip of the key without using springs
or a long hammer, and is carefully designed to react to variations in key touch, thus
producing a variety of sound responses.

The fine keyboard action of a grand piano requires regular attention in order to maintain
its exceptional characteristics. However, the Roland Hammer Action Keyboard is
designed to retain its superior characteristics without any tuning or significant
maintenance.

Illustration B
 

The touch of the grand piano key

1) What does it mean when the touch of a piano key is heavy or light?

If the keys have not been tuned or adjusted for a long time, the touch of a key may feel
heavy due to keys sticking together. You may be unable to get the fortissimo sound you
expect when you hit the key strongly. By contrast, if a perfectly adjusted grand piano key
is pressed, the superior response and clear sound combine to offer a touch that feels light.
As with the example above, the true key touch is judged by the total feel of the keyboard,
including sound performance. A piano tuner not only adjusts the piano mechanically but
tonally as well improving the quality of sound helps to create a key touch which is
comfortable to play.

So what are the mechanical reactions when a key is played?

2) There are two different reactions that occur when a key is touched.

One is a static weight reaction which is felt when touching a key delicately to create a
pianissimo sound. The weight at which the key starts to sink when you touch it softly is
called "first-load." The first-load of a grand piano is usually adjusted to be between 50 to
55 grams.

The other effect is called "dynamic-load" which occurs when striking a key with a strong
force to create a fortissimo sound. This effect is a result of the weight of the hammer and
its inertia.

3) First-load and dynamic-load (moment inertia)

The illustration of a see-saw (C) is the simplest way to explain these two kinds of weight.
On see-saw A, a 1 kg weight is placed on one side. On see-saw B, a 31 kg child and 30
kg child are on opposite sides of the see-saw.

By applying a 1 kg force, both see-saws A and B can be moved slowly. This reaction is
caused by the first-load weight.

What should happen if you try to move a see-saw by pushing it down with a quick, strong
stroke at one end?  See-saw A will move easily, but a very strong force is needed to
quickly move see-saw B. We can say that this 1 kg difference is the first-load, while the
reaction felt when you try to move it quickly is the dynamic weight (dynamic-load).

Illustration C
 
 

4) The most important element of key touch

The most important element of key touch is the dynamic weight. As the difference
between the first-load and dynamic-load becomes larger, the key touch control increases,
enabling richer sound egression.

But there is a limit to how strongly the key can be depressed, so the important thing is
how light the first-load is. The grand piano's first-load, which is recognized as an ideal key
touch, is 50-55 g, and Roland digital pianos' first-load (models incorporated with the
hammer action keyboard mechanism) is 65-75 g.  The digital pianos of a competitors' first-load,
for instance, is 100-120 g, significantly heavier than that of the grand piano. This "heavy
touch" not only places an unnecessary burden on the player's hands, but also narrows the
player's range of expression because the difference between the first-load and the dynamic
weight is too small.

To create the pianissimo sound, one need only to place a finger on the keyboard, causing the
key to play due to the light first-load weight and smooth hammer action.

For fortissimo sounds, concentrate all the weight on the tip of the finger, and the desired
"strong" sound can be created because of the dynamic weight reaction and force is
continuously applied on the hammer.

The ability to play lightly (for pianissimo) or heavily (for fortissimo) and the ability to
precisely control the sound is what is most desired in a fine piano keyboard.
 

Features of the Roland Hammer Action Keyboard

The Roland Hammer Action Keyboard has a unique construction that features the first-
load and dynamic-load weights at levels close to what is considered ideal for acoustic
piano keyboards.

Graph D (below) shows the sound level from pianissimo (ppp) to fortissimo (fff) on the
horizontal axis and the reaction when you hit the key on the vertical axis.

The difference in this reaction is the dynamic range of the mechanical  (physical) key's
weight (feeling of touch). The bigger the difference between these levels, the easier it is to
express the loudness of sound and create various expressions.

The Roland Hammer Action Keyboard has a first-load and large dynamic-load weight
close to that of a grand piano, which as you can see, is most suitable for a wider range of
piano sound expressions.

When test-playing the keyboard at the store, compare the key touch of not only mezzo
piano sounds but also fortissimo chords as well. In this way you will be able to feel the
superior key touch of the Roland Hammer Action Keyboard.

Mechanical Dynamic Response  Graph D

 

Points of improvement for the Roland Hammer Action Keyboard

The following improvements have been made since the inception of the keyboard:

    Decreased the mechanical noise of keys
    Decreased the boundary of the returning key
    Increased the uniformity of key touch for all keys
    Improved durability
    Smoothed key operation

E. Future directions

Semiconductor technology will continue its rapid progress and we can expect more
technological advances that will enable us to take advantage of more sound generators and
memory as well as high-speed microcomputer (CPU) control Roland remains committed
to creating a truly innovative sound sources that preserve the original SA Synthesis
concept and offer increasingly realistic and expressive piano sound to better accommodate
playing techniques. Once developed, this innovative sound source will respond to a
player's touch dynamics and playing techniques to an amazing degree in speed of response
and accuracy. Players are freed from all restraints and will be able to give their musical
expressiveness full rein. We can foresee using a lot of memory and waveforms to create
more delicate expressive nuances. Many sound generators (oscillators) and high-speed
CPUs will also be employed to their full potential

In addition, we aim to reinforce the piano's total response everything from keyboard
playing dynamics to speaker configurations and sound systems. Our aim is to make a
direct connection between the player's playing touch and the sound that is actually heard.

2. Temperaments and stretched tunings

A. What is a temperament?

Temperaments refer to tuning methods for pianos and harpsichords. In general, modem
keyboard instruments such as acoustic pianos and electronic organs most often use the
tuning method known as "equal temperament." This tuning theory was already established
in Johann Sebastian Bach's time (1685 ~ 1750), but its practical use was discovered much
later (see chart below comparing the history of temperament).

Consonant chords in Western music have a pure and beautiful sound. With an ensemble
that only consists of instruments with freely adjustable playing pitch such as string and
wind instruments, the pitch of each note that makes up a chord for each instrument's part
is fine tuned to maintain the harmony among different parts. For example, take a chord
consisting of A, C# and E. The frequency ration between A, C# and E is 4:5:6. The ratio
between A and E at the interval of a pure fifth is 4:6, or 2:3.

If tuning keeps fifths such as A-E, E-B, B-F#, and F#-C# at an exact ratio of 2:3, the
tuning of the last D and A will cause note A to be pitched higher than original pitch (the
pitch at tuning start). Conventional keyboard instruments avoid this by equally
diminishing each true fifth (2:3) by a slight amount. This is "equal temperament."
Equal temperament maintains a constant frequency ration for all pitches by equally
distributing one octave at a ration of 12/2 based on a purely mathematical calculation.
Although consonant chords sound slightly ambiguous, this ambiguity is the same for any
key to allow transposition. This significant advantage had made equal temperament the
most common tuning method for current keyboard instruments.

The history of temperaments
 

Keyboard instruments such as harpsichords and clavichords used for pre-Bach Baroque
music easily went out of tune due to limitations in construction. This made it necessary
for players to tune their instruments right before performance to obtain the most
acoustically pure scale to suit the key of the pieces to be performed. However, the
possibility of playing only one key caused a problem- This led to various tuning methods
being developed that would maintain acoustically pure sounds even after transposition.

B. HP-530/330 temperaments

Equal

This tuning method divides an octave into 12 equal parts. Most often used for modem
music, equal temperament makes performance in any key sound the same. Most post-
Roman Pieces were composed assuming performance in equal temperament, and so -
naturally this method is used for most modem keyboard instruments.

Pythagorean Scale

As the name indicates, this method was developed by the famous Greek philosopher,
Pythagoras. Eliminating "Wolf' fourths and fifths, this method makes melody sound
beautiful, but makes chord thirds sound ambiguous. This tuning method made its way
over from Greek to Rome, where it was used for a very long period at churches as the
scale for the Gregorian chants. Until the development of the mean tone temperament, this
tuning method had the most relevance in classical music.

Just

This tuning method eliminates "wolf" fifths and thirds to make fundamental chords sound
beautiful without any beats. However, the unequally distributed scale makes it unsuitable
for melody. As the keynote (basic note for the scale) must be changed according to the
key you are playing in, this method is not suited for transposed pieces. As the tonic must
be changed for both the major and minor, the HP pianos provide a choice of major and
minor. This tuning method has significance in the study of music history, but is hardly used
for modem piano performance due to its major limitations.

Mean Tone

Also known as the "quarter-comma mean tone", this system was advocated by Peitro
Aarron (1490-1545) in 1523, the mean tone temperament was an adaptation of just tuning
principles, reworking some features to allow transposition. This temperament works well
for music that keeps modulation within three flats and two sharps of a tuning's tonic,
allowing chords to sound similar to just temperament chords. Thanks to 'wolf thirds
having been eliminated, this tuning method replaced the Pythagorean temperament, and
dominated the music world until well-tempered tuning was introduced. Essential tuning
for Renaissance music, mean tone tuning was also used to good effect by Handel and
Vivaldi.

Werckmeister

The Werckmeister Technique #l. Temperament #3. Advocated by Andreas Werckmeister
(1645-1706) in 1691, this tuning combines mean tone and Pythagorean tunings to allow
playing in any key. Pieces with fewer key signatures sound harmonically, and those with
may key signatures sound melodically. This tuning method was prevalent in the Bach and
Haydn era.

Kirnberger

The Kimberger Temperament #3. This tuning method was advocated by Johann Philippe
Kimberger (1721-1783), one of Bach's pupils, in 1766 or 1779. This method refined mean
tone and just temperament features for more flexible transposition to enable performing in
any key. Since equal temperament tuning was yet to be established in the age of Mozart
and Beethoven, Werckmeister and Kimberger tunings were the most popular.
 

C. Well-Tempered tunings

Temperaments like Werckmeister and Kimberger are called "well-tempered tunings."
These classical temperaments were clearly distinguishable from the earlier methods
because they allowed playing in any key. Thus well-tempered tunings were often confused
with equal temperaments. Bach's "Well-Tempered Clavier" was presumably composed for
playing in the Werckmeister tuning. If this piece is played on an instrument tuned using the
Werckmeister, chords will sound differently in each key. * I

Pianos became popular after the Bach era, specifically in the age of Mozart. Equal
temperament was theoretically established at the time, however, the well-tempered tunings
were most commonly used because there was no well-estabhshed technique for accurately
measuring intervals at the time. Only in the 19th century was equal temperament first
implemented on pianos. *2

* 1 Some theorists claim Bach perfected equal temperament tuning or that his
        compositions were created assuming use of equal temperament tuning. Established theories
        regard such claims result from a misunderstanding of well-tempered tuning and equal temperament tuning.

*2 The first book on the equal temperament ("Harmonic universelle" Parise 1636) was written by
        Marin Mersenne (1558-1648). Research by Herman Ludwig Ferdinand von Helmoholtz (1824-1894)
        among others led to the systematic theory for practical use of the equal temperament, which in
        turn allowed it to be widely disseminated. The first piano tuned in equal temperament was marketed in 1842.
 

D. Temperaments for specific music

Equal temperament grew in popularity after the late Romantic composers, and so musical
ideas came to be developed assuming equal temperament was to be used. For instance,
Debussy pieces with impressionistic nuances take advantage of the ambiguous harmony
unique to equal temperament, and these would not have resulted if classical tunings had
been used.

Even today, using early tunings adds excitement to playing classical music. For instance,
you can really appreciate the beautifully sounding chords of early music by playing Handel
in mean tone temperament and Bach in Werckmeister. Or try playing pieces of the
romantic composers using Werckmeister or Kirnberger and compare them to playing in
equal temperament. This provides a good look at how the composers fared in the era
covering the transition to equal temperament tuning. These experiments can heighten
musical enjoyment and knowledge.

On an acoustic piano, such experiments are hard if not impossible to do. Selectable temperaments can be a
significant point of appeal for digital pianos. In fact, pianists tend to concentrate more on
performance itself rather than tunings. They also tend to be very conservative, so this digital
advantage needs to be pointed out repeatedly.

E. Stretched tuning

What is stretched tuning?

Stretched tuning is a tuning method unique to pianos.
Piano tuners usually start by tuning a central octave of a piano keyboard using a standard
tuning fork or tuning meter to match the concert pitch in equal temperament. The central
octave is then expanded outward to cover the entire key range. In this way, it should ideally
be possible to tune all piano keys to pitches of equal
temperament. Due to physical characteristics induced by vibrating strings, however, subtle
pitch deviations occur; higher notes are pitched slightly higher and lower notes are pitched
slightly lower in relation to the equal temperament pitches. This type of tuning is called
"stretched tuning" meaning a tuning in pitches that are stretched.

Stretched tuning -why is it necessary?

As a piano produces sound, its hammers cause the strings to vibrate, and the resulting
vibrations are released into the air through the soundboard, generating sound. At this point,
pitch is set by the fundamental wave determined by string length and tension. Complex
string vibrations, however, cause  partial vibrations at 1/2, 1/3, and 1/4 points of string
length, and so forth. These harmonic byproducts determine the tonality of piano sounds,
the pitches interfering with piano tuning.

Piano strings are thick, rigid and not flexible, thus creating non-vibrating parts at the
dividing points of the strings when partial vibrations occur. This means that the harmonics
(more divisions), the shorter the wavelength to the integral multiples of the original
frequency.

If the reference key and a key 1 octave higher are tuned to eliminate beats, a harmonic's
frequency twice that of the reference key it matched to the basic frequency of the 1-octave
higher key, resulting in the 1-octave higher key being tuned slightly higher than the 1-
octave interval (frequency exactly doubled).

As a result, the acoustic piano's unique tuning curve includes lower notes that are slightly
lower in pitch and higher notes slightly higher in pitch, in comparison to the
mathematically equal temperament.

Each acoustic piano has its own tuning curve according to each string's length and gauge. Piano tuners do not refer to a list of standard stretched tuning frequencies, but decide on the tuning pitch only after the piano in question is encountered.

For an easier explanation, we have only covered tuning adjustments for octaves. In reality, however, tuning involves adjustments of beats at various intervals of fifths, fourths, and thirds.

Also taking into consideration how human hearing relates to pitch (slightly higher pitches for the high range and slightly lower pitches for the low range are more comfortable), fine adjustments may be carried out for stretched tuning.

In fact, the factory preset setting is the most natural tuning for HP pianos that is free from beats. More stretched tuning curved may cause chords to sound slightly unnatural. Despite this fact, we employed stretched tuning curves on the new HP pianos because we received customer feedback that the "low range sounds higher and high range sound lower" for the previous HP series. Through adjustments that better satisfy hearing preferences, we believe our new HP pianos offer maximum satisfaction to a greater number of customers. Unless a special case arises, we recommend the factory preset tuning to be used. Stretched tuning can easily be used or disengaged depending on one's preference.

• Relationship with temperaments As mentioned above, piano tuning uses a stretched tuning curve as the piano's physical properties require it. Although the HP-530/330 features selectable temperaments, varied tuning nuances depending on the selected temperament will be incorporated into the stretched pitches.

Vibraphones and electric pianos with no possibility of stretched pitches principally are played back in mathematically calculated perfect equal temperament, to which a selected temperament will be added.

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