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The general keyboard in the age of MIDI
© 1997 John S. Allen
This article describes the general keyboard, an alternative music keyboard which avoids many of the limitations of the conventional keyboard. The general keyboard is nothing new: examples were built in the 19th century by Bosanquet, and are described in Ellis's appendices to Helmholtz's On the Sensations of Tone; also, in the 20th century by Fokker, among others. The general keyboard never gained widespread popularity. However, today's electronic technology, and in particular the MIDI protocol, makes the general keyboard far more practical.
Desirable characteristics in an alternative keyboard
The following characteristics are desirable in an improved keyboard:
Characteristics of the general keyboard
Fulfilling all of the requirements described above may seem like a tall order, but in fact, a satisfactory design is possible. The keyboard which fulfills these requirements is the so-called "general keyboard" whose key pattern is based on series of fifths..
In the general keyboard, keys with the same intervallic relationship lie in the same geometric relationship to each other. Instruments built over the past 100 years by Bosanquet, Fokker and others typically have between 36 and 72 keys per octave, in a regular pattern.
The characteristics of such a regular pattern are described mathematically by tessellation (or tiling) theory. This describes how a surface may be fully covered with tiles of the same shape and size.
An infinite variety of tile shapes meets this requirement. Many examples of possible patterns are given in the drawings of Esscher; all, however, have their centers in triangular, rectangular or hexagonal arrays.
The width of the fingers, and the need to cross the fingers over the thumb, suggest keys of constant width, longer from front to rear than they are wide. Tiles in triangular arrays do not fulfill this requirement, since half of them must be inverted relative to the others.
This leaves rectangular and hexagonal arrays, in which the tiles can all be placed in the same orientation.
One important requirement of the keyboard narrows the choice even further. To permit playing with the extended thumb, the rows must be interleaved, and key fronts must be higher than the rears of the keys in the next row forward. This requirement dictates an array of rectangles like a brick walk with interleaved rows of rectangular bricks. The rectangles may also be visualized as degenerate hexagons, with four 90 degree angles and two 180 degree angles.
The interleaving of the rows of keys may be adjusted somewhat to skew the horizontal rows of keys, as shown in the illustration below.
The illustration below shows a sharps forward keyboard , in which a series of 12 ascending musical fifths and descending fourths, for example C to B#, is played by a sequence of keys each of which is slightly closer to the player than the previous one. At the end of that sequence, the B# key is directly in front of the C key. Conversely, the Dbb key is directly behind the C key.
Since musical fifths are approximately 1/2 octave apart, the series of fifths results in interleaved series of keys displaced from each other by approximately half the length of a key. For example, the series C D E F# G# A# B# and the series G A B C# D# E# Fx are interleaved in the keyboard shown. Interleaved rows ease playing because the keys overlap one another like those of a conventional keyboard. Like the black keys of a conventional keyboard, keys farther to the rear are elevated above the keys that are farther forward. The rearward keys can be played without unintentionally depressing the forward keys. The greater height of the rearward keys also provides a tactile pattern, as on the conventional keyboard.
In twelve-tone equal temperament, the B#, C and Dbb keys of a general keyboard all play at the same pitch. In an equal temperament whose fifths are narrower than those of twelve-tone equal temperament, the Dbb is sharper than the C, which is sharper than the B#. In an equal temperament with fifths wider than in twelve-tone equal temperament, the B# is sharper than the C, which is sharper than the Dbb.
Slight changes in the tempering of the fifths result in increasing deviations over increasing numbers of fifths, as described an accompanying article on tunings and as also described by Jeans, Yasser, Regener and others in publications listed in the bibliography on this site.
Several possible temperaments are of special interest because they closely approximate just intonation of intervals used in the music of many cultures. A 31-tone equally-tempered tuning as used by Fokker provides good approximations to natural intervals of the harmonic series and is almost identical to the historic mean-tone tuning. A diatonic scale in the key of C (in white), adjacent sharps and flats, and the corresponding natural seventh (in blue) and natural 11th (in brown) in this tuning are shown in the illustration at the left. Many other tunings are practical and useful.
The general keyboard may be applied to the unequal intervals used in many musical traditions; and also, the intervals may be made to adapt themselves under computer control. This adaptation can be more successful and far more flexible than with the traditional keyboard, since the larger number of keys reduces ambiguities between intervals. Adaptive tuning in connection with the general keyboard will be described in a forthcoming article.
A general keyboard with a sufficient number of rows from front to rear may be "split" effectively into two or three manuals from front to rear, when used with a tuning which requires half or fewer of the rows of the keyboard.
A general keyboard with rows interleaved in more than two steps per key length is conceivable, but its layout is more complicated for the player, and its keys can be depressed less far before falling before the level of keys in the next row forward. Two interleaved rows are therefore most practical.
Left-rising, right-rising and horizontal-row
The sharps-forward general keyboard already described is a left-rising keyboard. The rows of keys trend upward from right to left, so that keys an octave apart (for example a C and the C an octave higher) are at the same distance from the player, while enharmonic keys with more sharps (for example, B# in its relation to C) are closer to the player.
The layout of a right-rising keyboard is the same as the left-rising keyboard, except that the key locations are reversed from front to rear. Keys an octave apart are at the same distance from the player, just as in the left-rising keyboard, but the rows of keys trend upward to the right.A right-rising keyboard is also a flats forward keyboard, assuming that the higher pitches are, as usual, toward the right side of the keyboard. The B# is farther from the player than the C, and the Dbb is closer to the player than the C.
A third possibility is a horizontal-row keyboard. In this keyboard, of which the Fokker Keyboard, whose layout is shown below, is an example, the rows of keys a whole tone apart, such as C D E F# G# A# B# or G A B C# D# E# Fx, lie straight across from right to left, and the octaves lie in a diagonal array.
|On the right-rising and left-rising keyboards, notes an octave apart are at the same
distance from the player in every octave. There is little practical difference in playing
qualities between the left-rising and right-rising keyboards, though fingerings differ
between them, as will be described later in this article.
The octaves of the horizontal row keyboard are skewed diagonally across the keyboard. The same notes in different octaves are found in different rows. For this reason, horizontal "splits" into separate manuals are not very practical on this keyboard. Since the octaves are diagonal, the wrists must be rotated to span the octave.
The horizontal-row keyboard does have advantages. It is more flexibly configurable, since it is symmetrical in more ways. A horizontal-row keyboard can be mapped with the sharps toward the front or toward the rear, at will. Different fingerings result, which may be preferable depending on the tuning used and the music to be played. The horizontal-row key pattern is more adaptable to patterns of organization not based on musical fifths, and to purposes not related to the mapping of musical pitch.
The left/right symmetry of the horizontal-row general keyboard makes it possible to use mirror-image key assignments on different parts of the same keyboard or of two identical keyboards. The same possibility exists with the conventional keyboard, as described in an earlier article in this series.With a left-rising or right-rising general keyboard, mirrored fingering is only possible by using another keyboard which rises toward the other side for the other hand.
However, playing music with two hands on one keyboard is the most usual situation, and in this case the fingerings will be different for the two hands even on a horizontal-row keyboard. The advantages of the left-rising or right-rising keyboard then prevail. Skills learned on a left-rising or right-rising keyboard can be transferred to a horizontal-row keyboard with very little adjustment; whether the converse is true depends on the configuration in which the player learned to use the horizontal-row keyboard.
Fingerings on the general keyboard
The fingering of the general keyboard depends on the keyboard pattern chosen and on the tuning for which the keyboard is configured. When playing diatonic music, however, all of the possible fingerings for scales and arpeggios (though not always for chords) are the same as familiar fingerings on the conventional keyboard.
For this reason, skills learned on the conventional keyboard transfer easily to the general keyboard. If the octave span is the same as on a conventional keyboard, then conventional diatonic and chromatic scales and chords on the general keyboard are almost immediately accessible to a keyboardist trained on the conventional keyboard. Furthermore, the general keyboard is extremely easy to learn despite its unfamiliar appearance, because fingering is the same in every key.
In a thirds-in-sequence tuning such as 12, 19 and 31-tone equal temperament (see accompanying article on tunings):
In a thirds out-of-sequence, diatonic-comma-preserving tuning such as 29, 41 or 53-tone equal temperament (to be described in a forthcoming article):
A horizontal-row keyboard may be configured to play in any of these fingerings, with the wrists rotated somewhat since keys an octave apart are displaced diagonally relative to one another. However, when the horizontal-row keyboard is used to play a twelve-tone scale, the enharmonic equivalents are exact, and so octaves may be played without this displacement.
Exotic, non-diatonic intervals fall into key relationships which depend on the particular tuning and keyboard array. The smaller the number of pitches in a tuning, the closer the exotic intervals are to the home row, but the fewer are available. As a practical matter, the thirds-in-sequence tuning of 31 tones, as Regener has pointed out, and the thirds-out-of-sequence, diatonic comma-preserving tuning of 41 tones (shown at right) are the smallest ones which accommodate the use of exotic intervals based on partials up to the natural 11th with minimal ambiguity.
The more tones in a tuning, the more keys per octave, and the more forward-to-back arm motion is necessary to play them. On a right-rising or left-rising keyboard in the tunings just described, diatonic scales require no forward-to-back arm motion, and practical scales incorporating exotic intervals need require no more forward-to-back arm motion than is needed on a two-manual harpsichord or organ.
The octave span of a general keyboard is preferably the same as for a conventional keyboard, approximately 6.5 inches (165 mm) to allow the fingers to fit comfortably between keys and to be familiar to trained keyboardists.
The keys extend forward and rearward like those of a conventional keyboard. The keys of the general keyboard which form a diatonic scale overlap one another in their front-to rear dimension. The longer the keys, the greater the overlap and the easier the finger placement is for diatonic chords.
However, longer keys also place non-diatonic pitches farther from the home row of keys. Consider the following four categories of key length:
Depth of key depression; concave key array
Each key of the general keyboard must not depress so far that a thumb laid across it will unintentionally depress a neighboring key. For this reason, the depression depth of a key must not exceed its height above adjacent keys to its right or left when at rest. This is the same requirement as with the black keys of a conventional keyboard.
Since the general keyboard has interleaved rows of keys, it follows that the allowable depression depth is about half of the step height between each key and the one directly in front of it. Step height is one of the factors restricting a general keyboard to two interleaved rows. With three interleaved rows, each key could depress to only about 1/3 the step height.
As already described in the discussion of the conventional keyboard, use of concave keys minimizes the step height by bringing a depressed key level with adjacent keys which are not depressed. A step height of 5/8 inch (16 mm) and a depression depth of approximately 3/8 inch (9.5 mm) at the front of the key are optimum for a general keyboard. These are typical for black keys of a conventional keyboard.
On organs with three or four manuals, it is common to tilt the rear manual somewhat toward the player, to bring it closer and flatten the wrist. Reaching forward and back with the arm to place the hand over different keys on a general keyboard is like shifting a hand from manual to manual on a conventional harpsichord or organ. The depth of a general keyboard from front to rear can be similar to that of an array of three or four conventional organ keyboards, and it is advantageous for the keys at the rear of the general keyboard to tilt toward the player. The tilt is achieved by increasing the concavity of the keys so the entire key array is concave around a horizontal axis. The optimum concavity is the greatest which avoids contact between the elbow and keys at the front of the keyboard while allowing the playing of keys at the rear with a flat wrist.
Because the keys of a general keyboard are arranged in tiers, their front ends are angled upward considerably with respect to the plane of the array, and the concavity can be considerably greater than it would be with keytops that are all in the same plane. With keys 3.9 inches (100 mm) long, a radius of approximately 34 inches (0.85 meter) is optimal for adult players. This arrangement places as many as 64 keys within the reach of a typical adult player. With shorter keys, the angle of the keys becomes greater and the radius may be decreased, though at the expense of ease of playing.
The following drawings show the geometric relationships that have just been described. First, a side view of a general keyboard whose tiers of keys have parallel keytops. The outlines of two adjacent columns of keys are shown, one in black and the next in red. The step height must be twice the depression depth when keys depress until their fronts are at the same height as the tops of adjacent keys.
|When keys are pivoted behind the playing surface, the depression depth is smaller at the rear of the playing surface. Flat-topped keys then produce a convex array if angled so a key, when depressed, is level with keys one row closer to the player. The step height is reduced.|
|Making each key surface concave retains the reduced depression depth, and permits a plane array of pivoted keys.|
|Increasing the concavity of the keys results in a concave array and a more comfortable hand position over keys at the front and rear of the keyboard.|
Overcoming the historical impediments to the general keyboard
Nothing like a general keyboard has ever been used widely in the past -- except with concertinas and the bayan accordion -- but the general keyboard stands a chance of becoming far more successful in connection with today's electronic, computer-controlled means of tone generation.
Mechanoacoustical tone generation imposes severe design limitations on general keyboards. A microtonal piano or harpsichord is out of the question because the large number of closely-spaced keys does not provide enough room for the strings and sounding mechanism. Tuning any mechanoacoustical instrument with dozens of pitches per octave is a time-consuming chore that requires specialized training. While Bosanquet and Fokker each built at least one pipe organ, most experimental instruments with general keyboards have been reed organs, since reeds are compact and economical. The accordion, with its closely-spaced chord buttons, uses the same solution to the same problem -- an accordion, after all, is also a reed organ.
A computer-controlled instrument does not need a tone-generating mechanism for each key. Rather, it only needs as many tone generators as the number of keys which are to sound at the same time. 16 voices are sufficient for all of the notes which a keyboardist can play with both hands. 32 or 64 voices are sufficient with a sustain pedal.
Today's electronic musical synthesizers are inexpensive, and thanks to the MIDI interfacing standard, they can be separate from the keyboard assembly itself. Therefore, it is no longer necessary to build an entire instrument to experiment with tunings, but rather, only the keyboard and an interfacing computer module. Synthesizers can produce a good approximation of the timbre of many different types of mechanoacoustical instruments, as well as other timbres which can not be generated mechanoacoustically.
Today, with computer technology, tuning can be preconfigured, and any of a large number of tunings can be selected at will. Computer control also allows adaptive tuning (accompanying article on tunings yet to be posted).
Meeting design requirements
In the context of modern tone-generating apparatus, how well does the general keyboard meet practical requirements?
The general keyboard is extremely versatile. It allows full freedom of modulation and transposition in any of a very large number of tunings.
Relationship to existing literature
Most existing keyboard literature is playable using the general keyboard. The literature through the Baroque and early Classical periods which was written to be played in mean-tone tuning is especially well adapted to a general keyboard. This literature can be played as written while avoiding the problems of "wolf intervals." In mean-tone tuning, traditional, correct spelling of musical intervals corresponds to the correct keys for playing.
Some keyboard literature uses idiomatic fingerings and voicings which may be difficult to play on the general keyboard. The one significant technical problem for the player that sometimes occurs, fingering of chords, may be solved through adaptive intonation.
Hand positioning by sight or by touch
The general keyboard does not have an inherent, tactile pattern that repeats with each octave. Such a pattern may be provided by means of a tactile cue such as a different surface texture.. The positioning of keys in interleaved columns assures that the lateral spacing between any two keys which can be mistaken for one another in rapid playing is greater (6 per octave) than with the white keys of the conventional keyboard (7 per octave). If the keys of the general keyboard are of black-key length, the front-to-rear spacing of the interleaved rows of keys makes approximately as much room for the extended thumb as with the heads of white keys of the conventional keyboard.
Learning fingering technique is easier than on the conventional keyboard, because fingering is the same in every key.
Hand positioning and ease of fingering
Ease of fingering has been discussed in the section on key length, above. Hand positioning is somewhat more constrained than with the conventional keyboard, since all of the keys are of black-key length rather than some keys' being longer, like the white keys. Note that this constraint does not apply when playing a general keyboard in conventional 12-tone tuning, as all of the keys in each column then play the same pitch. Adaptive intonation, in addition, can resolve some of the more difficult hand positions by allowing key substitutions.
On the conventional keyboard, the hand span determines the range of pitches which one hand can play at the same time. On the general keyboard, the hand span also determines how far forward and back from the diatonic "home row" the hand can reach to play exotic intervals. Rotation of the wrist to stretch the thumb or a finger toward the front or rear of the keyboard becomes a more significant factor in technique for the general keyboard than for the conventional keyboard. Certain idiomatic chord voicings will result, particularly when exotic intervals are used. These will be different depending on the tuning, though they will be consistent in every key signature in a given tuning. Clearly, the limitations of the hand span give an advantage to tunings which place the desired pitches close to the home row.
In 12-tone tuning, the general keyboard not only makes hand positioning easier, but also makes it possible to play unisons, which are not possible on the conventional keyboard. This possibility also exists in other closed equal temperaments if the keyboard has enough keys, and it may also be achieved through adaptive intonation.
On the general keyboard, finger rolls are possible from any scale degree to any other. Except when playing in 12-tone tuning, some of these rolls start with from slightly detuned notes - however, since these are usually short grace notes, the detuning is not very noticeable. The detuning also may be corrected through adaptive intonation (see accompanying article on tunings yet to be posted).
Glissandos are inherently different on the general keyboard, though more versatile. A diatonic glissando may be played in any key signature, but it must be played with alternation of fingers, since the keys of a diatonic scale are at varying levels.
A chromatic glissando may be played by dragging each of two fingers across a separate row of keys at the same time, as on the conventional keyboard. Short chromatic glissandos may also be played by dragging one finger diagonally down the keyboard from rear to front. A chromatic glissando surface is not practical on the general keyboard.
As mentioned earlier, the general keyboard is not right/left mirror symmetrical except in its horizontal-row version. For this reason, it is necessary to have either a horizontal-row keyboard or a right-rising and a left-rising keyboard, mirror images of each other, to use the same fingerings with both hands.
Size and Weight
The general keyboard is inherently larger and heavier than a conventional keyboard, though the weight can be minimized through careful design.
One possibility with today's ability to reassign pitches is to shift key assignments forward and backward electronically. Along with a tuning which places the required keys close to the home row, this trick makes it possible to use a keyboard with fewer keys and a short forward-backward reach. In this way, any practical tuning can be accommodated within the depth of a conventional two-manual organ or harpsichord keyboard.
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Last revised 10 March 2004