Harmonic table note layout
Encyclopedia
The Harmonic Table note-layout, or tonal array, is a key layout for musical instruments that offers interesting advantages over the traditional keyboard layout.
Its symmetrical, hexagonal pattern of interval sequences places the notes of the major and minor triads together. It is sometimes called the Melodic Table note-layout, and more rarely the Triad note-layout. It is related to the Wicki-Hayden based keyboards
and other isomorphic keyboard
s, both of which can be utilized on the jammer keyboard
musical interface.
, the Harmonic Table is topologically equivalent to Euler's Tonnetz
, discovered by the Swiss mathematician Leonhard Euler
in 1739. The two pitch arrays are trivially obtained from each other by direct shear mapping. This note layout created by Euler is utilised in Neo-Riemannian theory
to geometrically model its musical ideas.
The Harmonic Table keyboard layout was used in a keyboard harmonica called the Harmonetta, invented by Ernst Zacharias
and manufactured by Hohner
from the early 1950s through the mid-1970s.
The modern layout was proposed in 1983 by inventor Peter Davies, who obtained an international patent for its use in instruments in 1990. Davies coined the term Melodic Table to refer to the layout. It was afterwards renamed to Harmonic Table by the first major manufacturer, C-Thru Music and publicized by the company. This layout is used in the sonome family of keyboards, currently commercially manufactured as the Axis and Opal keyboards. It can also be found implemented in iOS devices such as the iPad, Musix is an example application.
note-assignments possible; however, the Harmonic Table format is unusual in the musically important intervals it uses:
Ergonomically, the harmonic table format is exceptionally compact: all notes of the major and minor scales fall under the fingers, and all common chords can be played with one or two fingers.
and Jordan Rudess
who find that it gives them a novel view of music, which is reportedly very useful in composing. It also works well with novel tunings such as the Bohlen-Pierce scale
.
It is in use for ongoing research into microtonal scales by music researchers and composers, in particular Carlo Serafini, Elaine Walker and Dr. Richard Boulanger.
Its symmetrical, hexagonal pattern of interval sequences places the notes of the major and minor triads together. It is sometimes called the Melodic Table note-layout, and more rarely the Triad note-layout. It is related to the Wicki-Hayden based keyboards
Wicki-Hayden note layout
In music, the Wicki-Hayden note layout is a key layout for musical instruments that offers some advantages over the traditional keyboard layout.-History:...
and other isomorphic keyboard
Isomorphic keyboard
An isomorphic keyboard is a musical input device consisting of a two-dimensional array 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...
s, both of which can be utilized on the jammer keyboard
Jammer keyboard
A jammer is a new musical instrument characterized by#at least one isomorphic keyboard, and#thumb-operated and/or motion-sensing expressive controls.The instrument is designed to be fast to learn to play, very fast to play and very expressive....
musical interface.
History
The structure and properties of the Harmonic Table have been well known since at least the 18th century. Indeed, as a pitch spacePitch space
In music theory, pitch spaces model relationships between pitches. These models typically use distance to model the degree of relatedness, with closely related pitches placed near one another, and less closely related pitches placed farther apart. Depending on the complexity of the relationships...
, the Harmonic Table is topologically equivalent to Euler's Tonnetz
Tonnetz
In musical tuning and harmony, the Tonnetz is a conceptual lattice diagram representing tonal space first described by Leonhard Euler in 1739....
, discovered by the Swiss mathematician Leonhard Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
in 1739. The two pitch arrays are trivially obtained from each other by direct shear mapping. This note layout created by Euler is utilised in Neo-Riemannian theory
Neo-Riemannian theory
Neo-Riemannian theory refers to a loose collection of ideas present in the writings of music theorists such as David Lewin, Brian Hyer, Richard Cohn, and Henry Klumpenhouwer...
to geometrically model its musical ideas.
The Harmonic Table keyboard layout was used in a keyboard harmonica called the Harmonetta, invented by Ernst Zacharias
Ernst Zacharias
Ernst Zacharias is a German musician and engineer. In the 1950s and 1960s, he invented various electro-mechanical musical instruments for the German musical instrument manufacturer Hohner, including the Cembalet, the Clavinet, the Guitaret, and the Pianet...
and manufactured by Hohner
Hohner
Hohner Musikinstrumente GmbH & Co. KG is a company specialising in the manufacture of musical instruments. Founded in 1857 by Matthias Hohner , Hohner is identified especially with harmonicas and accordions. The Hohner company has invented and produced many different styles, and most of the...
from the early 1950s through the mid-1970s.
The modern layout was proposed in 1983 by inventor Peter Davies, who obtained an international patent for its use in instruments in 1990. Davies coined the term Melodic Table to refer to the layout. It was afterwards renamed to Harmonic Table by the first major manufacturer, C-Thru Music and publicized by the company. This layout is used in the sonome family of keyboards, currently commercially manufactured as the Axis and Opal keyboards. It can also be found implemented in iOS devices such as the iPad, Musix is an example application.
Special features of the Harmonic table
There are a large number of isomorphicIsomorphic keyboard
An isomorphic keyboard is a musical input device consisting of a two-dimensional array 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...
note-assignments possible; however, the Harmonic Table format is unusual in the musically important intervals it uses:
- Note-values ascend by the musical interval of a perfect fifthPerfect fifthIn classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...
along the vertical axis. - On one diagonal axis notes ascend by four semitones (a major thirdMajor thirdIn classical music from Western culture, a third is a musical interval encompassing three staff positions , and the major third is one of two commonly occurring thirds. It is qualified as major because it is the largest of the two: the major third spans four semitones, the minor third three...
or diminished fourthDiminished fourthIn classical music from Western culture, a diminished fourth is an interval produced by narrowing a perfect fourth by a chromatic semitone. For example, the interval from C to F is a perfect fourth, five semitones wide, and both the intervals from C to F, and from C to F are diminished fourths,...
). - On the remaining diagonal axis notes ascend by three semitones (a minor thirdMinor thirdIn classical music from Western culture, a third is a musical interval encompassing three staff positions , and the minor third is one of two commonly occurring thirds. The minor quality specification identifies it as being the smallest of the two: the minor third spans three semitones, the major...
or augmented secondAugmented secondIn classical music from Western culture, an augmented second is an interval produced by widening a major second by a chromatic semitone. For instance, the interval from C to D is a major second, two semitones wide, and both the intervals from C to D, and from C to D are augmented seconds, spanning...
). - The notes of commonly played chords (except the octave) are clustered close together.
- Any major triad and minor triad, in root position, can be played with a single finger
Ergonomically, the harmonic table format is exceptionally compact: all notes of the major and minor scales fall under the fingers, and all common chords can be played with one or two fingers.
Uses
This key layout has attracted the attention of numerous professional musicians, including Brian MayBrian May
Brian Harold May, CBE is an English musician and astrophysicist most widely known as the guitarist and a songwriter of the rock band Queen...
and Jordan Rudess
Jordan Rudess
Jordan Rudess is an American keyboardist best known as a member of the progressive metal band Dream Theater and the progressive rock supergroup Liquid Tension Experiment.-Biography:...
who find that it gives them a novel view of music, which is reportedly very useful in composing. It also works well with novel tunings such as the Bohlen-Pierce scale
Bohlen-Pierce scale
The Bohlen–Pierce scale is a musical scale that offers an alternative to the octave-repeating scales typical in Western and other musics, specifically the diatonic scale. Compared with octave-repeating scales, its intervals are more consonant with certain types of acoustic spectra. It was...
.
It is in use for ongoing research into microtonal scales by music researchers and composers, in particular Carlo Serafini, Elaine Walker and Dr. Richard Boulanger.
External links
- Sonome, ‘Tiem’ Taxonomy of Realtime Interfaces for Electronic Music Performance, Compiled by Jon Drummond and Garth Paine.