WO1997020306A1

WO1997020306A1 - Keyboards for musical instruments

Info

Publication number: WO1997020306A1
Application number: PCT/AU1996/000748
Authority: WO
Inventors: Robin Sloan
Original assignee: Castlemont Investments Pty. Ltd.
Priority date: 1995-11-24
Filing date: 1996-11-22
Publication date: 1997-06-05

Abstract

A musical instrument keyboard comprises a rectangular matrix of manually operable keys, switches, buttons or the like. The pitches associated with the keys are arranged in equi-interval scales along the orthogonal axes of the matrix with rows of major thirds and columns of minor thirds being preferred. Three-dimensional versions are also claimed.

Description

KEYBOARDS FOR MUSICAL INSTRUMENTS

This invention relates to the sounding or other realization or demonstration of certain inter-note relationships in music, such as intervals and scales, and to an arrangement of controls providing for a musical instrument enabling or facilitating a player to produce new and/or remarkable sonic effects. For many centuries musical instruments have been played by manual (and pedal) keyboards - typically a row of spring-loaded levers called "keys" or, sometimes, "notes". The keys are adapted to be depressed by the player's fingers. Each key plays, or at least is given the name of, a single note i.e. a sound characterized by a single frequency. Sequential playing of different keys sounds a musical "scale" being a series of different notes of increasing ("ascending" scale) or decreasing

("descending" scale) frequencies p, p₂ p₃ bounded by notes p-_f and p_n at a fundamental interval, typically an "octave" p_n = 2p A typical "chromatic" scale consists of thirteen notes defining twelve intervals p₂/Pι p3 p₂ Pi₂ Pn P₁₃/P₁₂ which are

"tempered" to be equal. If this common interval is called N then clearly N¹² = 2.

The chromatic, "whole-tone" and suchlike are examples of the "equi-interval" scale which for present purposes may be regarded as a scale of which all pairs of successive notes are at substantially the same interval. Their frequencies are therefore in approximately geometrical progression. In the tempered chromatic scale the interval i.e. the common ratio of the progression, is r = 2^{1 /12}. We use words like "substantially" and "approximately" because the "geometrical" progressions with which this invention is concerned need not be strictly geometrical i.e. with r a consonant. The ratio r may vary to take account of non-equal temperaments and of "just" tuning wherein the tone interval could be 9/8 or 1 0/9, the notes of the diatonic scale having frequencies proportional to:- 24 27 30 32 36 40 45 48

The keys are typically of two kinds - "white notes" giving a diatonic sequence and "black notes" (normally shorter and offset rearwardly) providing the remaining notes required for a full chromatic scale of 1 3 notes. Such is a keyboard that has evolved over many centuries. Despite the offset positioning of the "black notes" and given that, exceptionally, the arrangement has been curved for ergonomic reasons, this keyboard is essentially linear in nature.

Also, this keyboard makes no distinctions such as A sharp/B flat, C sharp/D flat etc. For the purpose of this specification the "flat" terminology is avoided and "sharp" is used to denote "black notes" . It will be understood that the sharps of C, D, F, G and A could equally be referred to as flats of D, E, G, A and B respectively.

The traditional keyboard has serious drawbacks in the teaching and learning of music fundamentals. For example, an interval will generally look different, depending upon the part of the keyboard in which it is played, and standard scales (e.g. major, harmonic minor and melodic minor) generally have different aspects and require different fingerings depending upon their key or tonic note. One contrivance referred to in the literature as the "Janko

Keyboard" comprised six rows of keys of the same shape and size arranged somewhat like the keys of a typewriter. The rows were of two types each giving a whole-tone scale (1 ) C D E F sharp G sharp A sharp and C, and (2)/C sharp, D sharp, F, G, A, B, and C sharp. The two types of rows alternated. Every note was playable from three rows. Janko claimed that wide intervals could be spanned more easily than on a conventional keyboard, that all scales of the same type had the same fingering and that his keyboard made light of transposition.

But the Janko keyboard appears not to have found favour. It is interesting to compare the seventh ( 1 947) and tenth ( 1 970) editions of The Oxford Companion to Music. The former on page 496 states of the Janko Keyboard that it "has supporters in the United States" . The latter (page 552) changes "has" to "has had" . Possibly, if the Janko idea failed, it was because whatever logic it embodied was, to traditional keyboard players, insufficient compensation for the trouble to acquire a new finger technique.

An object of the present invention is to provide a keyboard whereby chords and progressions of notes are brought with exceeding facility within the capability and dexterity of the player. Another object is to provide a rational means for the setting out, demonstration, and/or sounding of musical intervals and scales.

These and other objects and advantages will become apparent hereinafter. In one form of our invention we provide a two - or three - - dimensional control system for sounding or otherwise manifesting or representing musical notes or sounds as "played in" by an operator or player. By e.g. a switch or "key-action" of his/her finger(s), or by the interposition or insertion of fingers, control rods or the like, one or more sounds or chords can be invoked, either singly or in rapid succession. With a little practice it is believed that remarkable virtuosity could be achieved, quite incomparable with and unconfined by the limitations of known keyboards, and irrespective of whether the player were already skilled in playing a conventional keyboard. From another aspect our invention provides a keyboard musical instrument from which sounds are playable by keys arranged in a regular two - or three - dimensional pattern, lattice or matrix. The player can tune, temper or adjust the sounds ad hoc so that, in particular, keys played along imaginary lines through the lattice will independently produce sounds in unison, or desired scales or other sequences.

This independence of sound production from e.g. two keys giving the same sound or note, means that one of the two keys might be repeatedly played, and yet the repetition will be heard although the other key be continuously sounding the same note.

The keys or control elements may be "switches" (in the broad sense) such as buttons, wires, strings or other tactile members, or e.g. light beams which can be intercepted by the player's fingers, or a control rod or rods, photo-electric or other signals being generated in response to interception of the beams.

Furthermore, by analogy with a pedal keyboard or "clavier", as in a conventional organ, for example, control elements may conceivably be operated by or via the player's feet.

Advantageously we provide a two - dimensional array of control elements ("switches") each corresponding to a single musical note. The switches may be touch-sensitive devices or depressible, spring-loaded push-buttons, all of the same size and shape. The array can be wired in circuit with a sound synthesizer or suchlike sonic evice, or the elements could be purely mechanical and actuable to produce notes from strings, wind-pipes, wood or metal bars etc. Whatever the manner of sound production, each "switch" might correspond to one note.

In one form of our invention a keyboard consists of push¬ button switches located at the corners of an imaginary square grid. A simple example would be (in terms of note frequencies) :-

9 1 8 36 72 144

3 6 1 2 24 72

1 2 4 8 1 6

It will be seen that every straight line that intersects elements of this matrix e.g.

1 2 4 ... (2)

1 3 9 (3)

2 1 2 72 (6)

144 1 2 1 ( 1 /1 2) represents numbers proportional to note-frequencies of an "equi- interval scale" as herein defined, the scale interval being shown in brackets after each of the four sequences exemplified above.

The matrix of 3 x 5 = 1 5 elements referred to above is a simple example of a two dimensional "geometrical matrix" as defined below.

Considered in more general terms, we arrange the elements or switches in a square or rectangular lattice or matrix form, successive elements in each row and column sounding substantially the same interval, but the interval being different as between rows and columns. The matrix may be shown in conventional suffix notation, but commencing from the bottom left corner i.e. ^J ₄1

⁹31 ³3₂ 1 a₂₁ a₂₂ ^a23 ^aπ a₁₂ ^a! 3

In a practical embodiment of the invention, the row and column intervals may differ by one semitone. Thus, regarding the switch matrix to be directly in front of the user of the device with row 1 being the bottom row i.e. the row nearest the user and the columns numbered from 1 towards the right, the first row (an a_{1 2} a₁₃ , may be notes at intervals of a major third or 4 semitones (4s) e.g. a ₌ C, a₁₂ = E, a₁₃ = G#, a₁₄ = C, a₁₅ = E, repeating in octaves. Thus in terms of frequencies a₁₄ = 2 a , a₁₅ = 2 a₁₂ etc. The column elements may be at intervals of the minor third (3s) . That is to say, if an = C then a₂₁ = D#, a₃₁ = F#, a₄₁ = A, a₅₁ = C, a₆₁ = D# and a₅ι = 2 a _, ^aeι ⁼ 2a₂₁ a₅₂ = 2 a₁₂ etc. It follows that a rectangular module or "unit" of such a matrix will consist of 4 x 5 = 20 elements i.e. C E G# C

A C# F A

F# A# D F#

D# G B D#

C E G# C

Theoretically the matrix can be extended indefinitely i.e. to the right, left, up or down. In general, for a rectangular array or matrix a,,, denote the row interval by K and the column interval by L, then clearly if a corresponds to a frequency P i.e. a_u = P then a₁₂ = PK, a₁₃ = PK² a,, = PK^1"1 a₂₁ = PL a₃₁ = PL² a_n = PL^1"1 and a, = PK L' ¹

Therefore, for any K and L, the frequency "of" (i.e. corresponding to) each element is a function of its position vector

(i, j) relative the the datum zero an = P.

To achieve repetition by octaves, it is clear that the row and column intervals must be integral divisors of the octave so that 2 - K^m and 2 = Lⁿ where m and n are (different) whole numbers. In the embodiment particularly described herein i.e. K = major third, L

= minor third, one has, in the tempered system K³ = 2, L⁴ = 2. By extending the matrix or module shown above, it will be seen that if the elements are notionally located at the points of a square grid, then imaginary straight lines at various angles can intersect the elements representing different "equi-interval" scales.

Thus "horizontal" lines (in the direction "i") intersect notes at the interval of a major third, and "vertical" lines (in the direction "j") intersect notes at the interval of a minor third. Conveniently, the element a may be regarded as a pole, with lines drawn through it at various angles θ to the horizontal.

Thus θ = O (parallel to vector i) and θ = 90° (j) represent, respectively, equi-interval scales at the major and minor third; θ =

45° (i + j) is seen to represent a scale of fifths C G D A etc: whereas θ = minus 45° (i - j) is the chromatic scale C C# D D# etc.

Other lines can be drawn in like manner. For example, lines going approximately "north-north-west" (parallel to 2j-i) will intersect notes such as C, D, E...forming a "whole-tone scale" and j-2i, like i + j, is a scale of fifths. We call a matrix of this kind i.e. through which imaginary straight lines intersect elements whose values are in geometrical progression, a geometrical matrix.

For the purposes of this specification a "geometrical matrix" is a two - or three - dimensional array of elements each with a corresponding number and arranged such that the numbers of sequences of elements intersected by imaginary straight lines through the matrix are in substantially geometrical progression.

Thus "geometrical matrix" includes a three-dimensional matrix through which imaginary straight lines intersect geometrical progressions of elements and planes intersect elements arrayed in a two-dimensional geometrical matrix.

A significant advantage of our switch array is that compared with a conventional keyboard, the notes comprising standard scales, chords and the like, can be provided within a relatively short compass, and wide chords for example are thereby rendered easily amenable to "playing" by the fingers of one hand. A further advantage is that the switch array of our invention is amenable to be "played" using various attitudes of the hand. This is in contrast with the traditional keyboard which constrains the performer's hands into substantially the same attitude.

The accompanying drawings show practical embodiments of the invention. In the drawings :-

Fig.1 shows part of an array or matrix with the elements in the Iower left labelled according to the double-suffix terminology referred to above;

Fig. 2 shows the key - names corresponding to the elements of Fig. 1 when an is the note C and the ratios K and L are such that K³ = 2, L⁴ - 2; Fig. 3 is a logarithmic representation of the matrix part wherein the numbers represent the number of semitones above the polar note a = O;

Fig. 4 shown portion of the array, in polar form, showing a number of lines representing equi-interval scales θ = O : ascending major thirds (K) augmented fifths (K²) octaves (K³) θ = 90° : ascending minor thirds (L) diminished fifths (L²) sixths (L³) octaves (L⁴) θ = 45° ascending fifths θ = - 45° ascending chromatic θ = artan (-2) ascending whole tone θ = artan (^~ 4/3) unison line The lastmentioned is called a "unison line" because it joins points related to the same frequency. Thus in Fig . 3, for example, the line joining notes " 1 2" is a unison line, as are all lines parallel to it. Clearly they all have a gradient 4/-3 with respect to the

Cartesian axis system shown.

Figures 5 and 6 show the major scale as a zig-zag course across vertical and horizontal lines respectively. Clearly they are playable simply by suitably orienting the hand and adopting a "rocking" motion using appropriate fingers - in sharp contrast to the

"thumb-under" technique generally required for playing scales on a conventional keyboard.

The scales are shown as having C as tonic, but evidently the configuration is the same whatever the key. Similarly, on our matrix, chords of the same kind have the same "shape" and "fingering" irrespective of their root or fundamental note. Figures 7 and 8 show some examples, "X" being the relative position of the keynote with respect to the chord.

Although the invention has been particularly described by reference to a 4s/3s tuning along right-angled axes, we have found that for many purposes it is preferred that the "horizontal" axis (θ = 90°) be tuned to the chromatic scale, and the "vertical" axis (θ = 90°) to a major (4s) or possibly a minor (3s) third.

The s/4s tuning appears particularly suited to the playing of so called "classical" or diatonic music. Our keyboard is particularly suited to use with a system of musical notation wherein note symbols are located/centred at points of which the distances from a fixed datum, corresponding to e.g. "middle C", represent or are proportional or substantially proportional to the intervals of the respective notes with respect to the datum note.

This is at marked variance from the ordinary staff notation wherein the unit staff distance (e.g. between the nth line and the nth space) can be as little as one semitone(s) or as much as six semitones (6s) depending upon signs of inflexion applied to one or both notes.

This aspect of our invention in a preferred form adapted to the "equally tempered" scale provides for representing music by note-symbols whose distance from a fixed straight line is proportional to the number of semitones in the interval of the note with respect to the datum note.

Typically, as in conventional notation, the datum line is "horizontal" i.e. the direction in which the music progresses in time. Thus in a Cartesian sense, the "ordinate" of a symbol represents the pitch of the note, and its "abscissa", may indicate the point of time at which it is (to be) heard. Not only does such a system do away with the need for showing sharps, flats or other "accidentals", but it renders transposition very easy by a system according to our invention of showing stave lines separately from note symbols e.g. on a transparent sheet displaceable relatively "vertically" to a "note- sheet". Moving the stave sheet "up" by one unit relative to the note sheet will effectively transport the music down by one semitone, assuming the stave lines are separated by two units. The stave lines can be grouped in any desired manner and number. Clearly it is immaterial whether the staves or notes are on the upper sheet, as long as the two are capable of being placed and read in appropriate registration.

Just as our keyboard finds particular application to the notation system just described i.e. wherein the "vertical" distance between notes on the stave is proportional to the musical interval between them, so is our keyboard particularly suited for use with a "staveless" system of musical notation such as described in our Australian patent application PO 1 782 of 21 st August 1 996, in which intervals are shown by the shape and/or colour of a symbol or tactile element suitably positioned relative to a datum.

It will be evident to those skilled in the art how our keyboard can be connected to conventional synthesizers, computers and the like such as by MIDI (Musical Instrument Digital Interface) equipment or in any other known manner. It should also be appreciated that in the "planar" (two- dimensional) keyboard particularly described herein, it is by no means essential that all the key surfaces be or remain exactly coplanar. For example, before a particular chord or scale is played, it may be desirable to "raise" the relevant keys (or to "Iower" the others), and provision can be made for this. Additionally or alternatively, of course, keys may be selectively illuminated ad hoc to highlight the keys required for a particular chord or scale.

Although our keyboard is essentially portable in nature, it is not generally intended to be used portatively, as were certain e.g. organs of a past age. Rather it will normally be used positively i.e. on a stationary support. Placed on a suitable table, a square keyboard i.e. of square keys arranged on a square lattice pattern, may afford interesting possibilities to four players seated one at each side of the table. Usually, however, there will be only one player. A base¬ board or the like upon which the keys are mounted may have markings appropriate to the keys. Normally these markings will not represent frequencies as such, as may happen on a conventional keyboard. Rather is it desirable that they show intervals with respect to a "pole" or "orgin" a as in Fig. 3 for example. Thus the player may set a to a desired frequency e.g. 256 herz, and may "tune" the keyboard as a whole e.g. to 4s/3s as in Fig. 4 He/she then knows that key a₂₃, for example, will be [(2- 1 )x3] + [(3-1 ) x 4] = 1 1 semitones above an ■ If desired the pitch and/or tuning of the keyboard pro tern can be displayed on a conventional screen or other visual display unit (VDU) .

Additionally or alternatively the keys themselves may be marked and/or coloured. For each tuning it is desirable to cross-identify keys sounding notes of the same pitch or at octave pitches, by the same colour or otherwise.

It will be evident that our keyboard is applicable not only to electronic organist, synthesizers and the like, but might also be adapted for use with a mechanical - style instrument such as the conventional piano or pipe-organ. This might be done by the use of appropriate motors, levers etc.

It will also be appreciated that just as conventional "linear" keyboards need not necessarily be straight (for example some manual and/or pedal keyboards of a kind known per se are concave and/or radiating with respect to the player) our two - dimensional keyboard might possibly be curved, for ergonomic or other reasons.

Provision might also be made for changing the gauge or key separation. It may also be desirable that the key - movement trigger different sonic functions. For example, a sideways pressure on the key could superimpose tremolo or vibrato effects upon a note sounded by the key. Additionally or alternatively, a "double-touch" for example might be provided, so that a first pressure on the key will produce one sound, and a further pressure will produce a different or additive sound.

Our keys may be square, hexagonal or other suitably shaped buttons located at the points or vertices of an imaginary net, lattice or graph to form a two-dimensional keyboard capable of being played by the fingers (including the thumbs) of a performer.

The non-linear nature of our keyboard permits of substantial flexibility of key size and spacing. Therefore it may be readily adapted to be played e.g. by sticks or mallets, as is a conventional xylophone for example.

Claims

CIAIMS

1 . A keyboard for a musical instrument, characterized by keys arranged as a geometrical matrix, as hereinbefore defined.

2. A keyboard as claimed in claim 1 characterized by keys located in a rectangular array whereby the position of each key is defined by three numbers representing co-ordinates with respect to a set of three mutually orthogonal axes with an arbitrary origin.

3. A keyboard as claim in claim 2 wherein the keys are substantially coplanar, that is to say, one of said co-ordinates is constant over the array.

4. A keyboard as claimed in claim 3 wherein the keys are located substantially at the corners of an imaginary square grid, forming a rectangular matrix of m rows and n columns, such that keys played along rows sound scales at the interval of the major third, and keys played along columns sound scales at the interval of the minor third.

5. A keyboard musical instrument from which sounds can be independently produced in response to keys arranged in a regular two- or three - dimensional lattice or pattern on imaginary lines along which the playing of keys produces substantially equi-interval scales adjustable by the player.

6. An instrument as claimed in claim wherein the playing of each key sounds a musical note, and the interval between the notes sounded by respective keys is a function of the position vector of one with respect to the other.

7. An instrument as claimed in claim 6 wherein the lattice is a grid of first and second mutually intersecting sets of lines, the interval along the lines of the first set being different from the interval along those of the second set, the intervals being selected from one(s) two(2s) three(3s) four(4s) and six(6s) semitones (s), whereby every twelfth, sixth, fourth and second note, respectively, is at the octave.

8. An instrument as claimed in claim 7 wherein keys along each of a further or unison set of lines sound the same note, and therefore the interval of the set is 1 , or (o x s) in logarithmic terms.

9. A keyboard musical instrument substantially as herein described.

10. A keyboard substantially as herein described with reference to the accompanying drawings.