Generalized keyboards are musical keyboards, a type of isomorphic keyboard, with regular, tile-like arrangements usually with rectangular or hexagonal keys, and were developed for performing music in different tunings. They were introduced by Robert Bosanquet in the 1870s, and since the 1960s Erv Wilson has developed new methods of using and expanding them, proposing keyboard layouts (and some notations) including any scale made of a single generator within an "octave" (or more generally, period) of any size.
The generalized keyboard is one kind of symmetrical arrangement that represents pitches according to their relationship to each other - rather than their positions in specific scales such as in the familiar piano and organ keyboard - as well as in sequence of pitch, unlike arrangements such as duet systems for concertinas and the array system keyboard. Bosanquet used chains of fifths to generate the mapping of the keys, with the pitches transposed into the space of an octave (or more generally, period) so that pitch determined the lateral position of keys, and the number of fifths, or any other interval used as generators, from the starting pitch its vertical position in the keyboard.
The coordinates of a key can be calculated using the size of the generator (in cents), where the vertical position is the number of generators away from the starting pitch, (positive or negative depending on whether they are in the sharp or flat direction), which Bosanquet rounded to the nearest semitone, giving 12 vertically aligned rows of keys in each octave. Wilson introduced alternate arrangements with combinations of seven or five (and in some cases, i.e., a division of the octave in 13 tones, eight) vertical lines of keys, and so Bosanquet keyboard sometimes is used to distinguish the original arrangement.
The angle between keys originally depended on the shape of the key and relative size of the generating fifth, but Bosanquet discovered fingering could sometimes be improved by reversing this angle; the angle can also be straightened out, or the spacing changed to better represent the keys' pitches, which alters vertical alignment. Generalized keyboards usually duplicate pitches mapped close to the front and rear edges of the arrangement in order to organize pitches for consistent fingering. This can result in very large arrangements depending on the shape of the keys and any modifications made to the basic design.
The possibility of the duplication of pitches occurs because the generalized keyboard is, in principle, a mapping of pitches onto a closed space in which intervals and chords have fixed shapes under transposition across the keyboard; thus a generalized keyboard is a useful tool for the analysis of harmonic structures.
Bosanquet's 1873 harmonium has rectangular keys more or less horizontal and aligned vertically with 12 lines in each octave. The width of octaves is slightly compressed from usual, and the keys are narrow and undercut at the front.
Arthur von Oettingen's 1914 Omnitonophonium harmonium has keys similar to Bosanquet's, but which aren't undercut (like Jankó's 1883 patent for his 12-tone keyboard).
Arthur Fickénscher patented a keyboard in 1941 with rectangular keys overlapping in 12 staggered diagonal rows each representing the same named tones.
Larry Hanson devised keyboards in 1942 with rectangular, as well as staggered "7"-shaped keys. [1]
Adriaan Fokker's 1951 31-tone organ used relatively short rectangular keys with sides relieved toward their fronts to form T-shaped playing surfaces, as well as longer rectangular keys in a concave arrangement for a pedalboard.
Erv Wilson patented a keyboard in 1967 with five perpendicular chromatic lines of keys in an octave, using fourths as generators. Robert Moog built a prototype with undercut round front rectangular keys.
Herman van der Horst built the first of four staggered square key Archiphones in 1970 for Anton de Beer.
George Secor's 1974 generalized keyboards for the Motorola Scalatron used oval keys skewed in diagonal rows.
Scott Hackleman and Erv Wilson designed a 19-tone generalized keyboard clavichord with oblong hexagonal keys in 1975, and marketed it as a kit. [2]
Michel Geiss, fr:Christian Braut and Philippe Monsire built the Semantic Daniélou, a 36-tone (out of 53 just intonation notes listed in the book "Sémantique Musicale" by Alain Daniélou) electronic instrument, on behalf of the author, using staggered square key button keyboards from two Cavagnolo Midy 20 master keyboards, where each parallel row of keys offers a transposition by one comma.
Harold Fortuin's 1994 Clavette midi controller uses straight alternating rows of switches which can be customized for different tunings by programming and with key overlay sheets. Bert Bongers built versions with 122 and 124 keys.
Harvey Starr manufactures Wilson Microzone skewed row hexagonal key midi controllers in 248 and 810-key models that can be programmed and the key surfaces organized into generalized as well as many other arrangements.
Lumatone Inc. manufactures a 280-key MIDI controller with skewed hexagonal keys based on designs by Siemen Terpstra. This has now become the Lumatone Keyboard. [3]
Hex is a free software MIDI sequencer, which uses a generalized keyboard in place of the standard piano keyboard. Lanes are extended from the keys and MIDI notes can be drawn into each lane, and edited, with the mouse (as in a standard MIDI sequencer like Logic, Reaper, SONAR, etc.). The layout can be sheared to ensure that the vertical height of each key (and note lane) is proportional to its pitch height—regardless of the tuning used. A wide variety of isomorphic layouts are possible, including Bosanquet and Wicki. [4]
A musical keyboard is the set of adjacent depressible levers or keys on a musical instrument. Keyboards typically contain keys for playing the twelve notes of the Western musical scale, with a combination of larger, longer keys and smaller, shorter keys that repeats at the interval of an octave. Pressing a key on the keyboard makes the instrument produce sounds—either by mechanically striking a string or tine, plucking a string (harpsichord), causing air to flow through a pipe organ, striking a bell (carillon), or, on electric and electronic keyboards, completing a circuit. Since the most commonly encountered keyboard instrument is the piano, the keyboard layout is often referred to as the piano keyboard.
Meantone temperament is a musical temperament, that is a tuning system, obtained by narrowing the fifths so that their ratio is slightly less than 3:2, in order to push the thirds closer to pure. Meantone temperaments are constructed the same way as Pythagorean tuning, as a stack of equal fifths, but it is a temperament in that the fifths are not pure.
The Jankó keyboard is a musical keyboard layout for a piano designed by Paul von Jankó, a Hungarian pianist and engineer, in 1882. It was designed to overcome two limitations on the traditional piano keyboard: the large-scale geometry of the keys, and the fact that each scale has to be fingered differently. Instead of a single row, the Jankó keyboard has an array of keys consisting of two interleaved manuals with three touch-points for every key lever, making six rows of keys. Each vertical column of three keys is a semitone away from the neighboring ones, which are in the alternate rows. Thus within each row the interval from one note to the next is a whole step.
The spaces described in this article are pitch class spaces which model the relationships between pitch classes in some musical system. These models are often graphs, groups or lattices. Closely related to pitch class space is pitch space, which represents pitches rather than pitch classes, and chordal space, which models relationships between chords.
A pedalboard is a keyboard played with the feet that is usually used to produce the low-pitched bass line of a piece of music. A pedalboard has long, narrow lever-style keys laid out in the same semitone scalar pattern as a manual keyboard, with longer keys for C, D, E, F, G, A and B, and shorter, raised keys for C♯, D♯, F♯, G♯ and A♯. Training in pedal technique is part of standard organ pedagogy in church music and art music.
An enharmonic keyboard is a musical keyboard, where enharmonically equivalent notes do not have identical pitches. A conventional keyboard has, for instance, only one key and pitch for C♯ and D♭, but an enharmonic keyboard would have two different keys and pitches for these notes. Traditionally, such keyboards use black split keys to express both notes, but diatonic white keys may also be split.
Hans Luedtke was a German inventor in the field of music.
George Secor was an American musician, composer and music-theorist from Chicago. He was the discoverer of miracle temperament and eponym of the secor.
In music theory and tuning, an Euler–Fokker genus, named after Leonhard Euler and Adriaan Fokker, is a musical scale in just intonation whose pitches can be expressed as products of some of the members of some multiset of generating prime factors. Powers of two are usually ignored, because of the way the human ear perceives octaves as equivalent.
Henry Ward Poole (1825–1890) was an American surveyor, civil engineer, educator and writer on and inventor of systems of musical tuning. He was brother of the famous librarian William Frederick Poole, and cousin of the celebrated humorist, journalist and politician Fitch Poole.
Robert Holford Macdowall Bosanquet was an English scientist and music theorist, and brother of Admiral Sir Day Bosanquet, and philosopher Bernard Bosanquet.
In music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET or 31-EDO, also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equal-sized steps. Play (help·info) Each step represents a frequency ratio of 31√2, or 38.71 cents.
Mayer Joel Mandelbaum is an American music composer and teacher, best known for his use of microtonal tuning. He wrote the first Ph.D. dissertation on microtonality in 1961. He is married to stained glass artist Ellen Mandelbaum, and is the nephew of Abraham Edel.
In musical tuning systems, the hexany, invented by Erv Wilson, represents one of the simplest structures found in his combination product sets.
An isomorphic keyboard is a musical input device consisting of a two-dimensional grid of note-controlling elements on which any given sequence and/or combination of musical intervals has the "same shape" on the keyboard wherever it occurs – within a key, across keys, across octaves, and across tunings.
Dynamic tonality is a paradigm for tuning and timbre which generalizes the special relationship between just intonation and the harmonic series to apply to a wider set of pseudo-just tunings and related pseudo-harmonic timbres.
The Wicki–Hayden note layout is a compact and logical musical keyboard layout designed for concertinas and bandoneons.
The Harmonic Table note-layout, or tonal array, is a key layout for musical instruments that offers interesting advantages over the traditional keyboard layout.
In musical tuning, a lattice "is a way of modeling the tuning relationships of a just intonation system. It is an array of points in a periodic multidimensional pattern. Each point on the lattice corresponds to a ratio. The lattice can be two-, three-, or n-dimensional, with each dimension corresponding to a different prime-number partial [pitch class]." When listed in a spreadsheet a lattice may be referred to as a tuning table.
The Semantic System is based on a microtonal musical scale tuned in just intonation, developed by Alain Daniélou.