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MUSICAL KEYBOARD IN THE FORM OF A TWO-DIMENSIONAL MATRIX


ABSTRACT

The invention relates to music keyboard design. The music keyboard consists of keys which are organized in the form of a two-dimensional matrix and are ranged along one axis of the matrix as an arithmetic progression of the frequency of the sound produced and along the other axis of the matrix as an arithmetic progression of the period of the sound produced. The technical result is an improvement in the quality of the sound of the musical instrument through the elimination of acoustic interference, and greater ease of use of the major and minor scales.

DESCRIPTION

BACKGROUND OF THE INVENTION
a) Field of the invention.
The invention relates to music keyboard design.
b) Description of the Prior Art
It is known keyboards for keyboard musical instruments which may be divided into the following types:
a) self-sounding shock
  • celesta
б) string
  • shock-keyboards (piano and clavichord)
  • plectrum-keyboards (harpsichord and its varieties)
в) wind musical instruments
  • keyboard-wind (organ and its varieties)
  • reeds (harmonium, harmonica, accordion, melodica)
г) electronic
  • synthesizers,
  • electronic organ
An analogue of described invention is the e-key for keyboard synthesizer.
The synthesizer is an electronic musical instrument that generates (synthesizes) sound through one or more generators of the sound waves. The desired sound is achieved by changing the properties of an electric signal (analog synthesizers) or by the CPU settings (digital synthesizers).
Synthesizer, made in the form of a system-block with a keyboard, called the keyboard synthesizer. Synthesizer as a system-block without a keyboard called a synthesizer module and it controlled by MIDI-keyboard or other device for sound control, for example, MIDI-guitar. If the keyboard has a built in sequencer, synthesizer is called a workstation. Synthesizer as a computer program using a universal sound card and standard input-output devices (computer keyboard, mouse, monitor, headphones), is called software synthesizer.

The prototype of the invention is MIDI-keyboard for synthesizer module because synthesizer module allows with software and hardware generates any pitch of tone. Also synthesizer module can be connected to standard or modified keyboard.

Analogue and prototype are a software-hardware direction for development of musical instruments that gives them maximum flexibility to customize the pitch, tone, and other characteristics of the sound in frame of single musical instrument.

However, the keyboard for the analogue and the prototype are designed as a one-dimensional structure.
This one-dimensional structure is keys which are organized like equal-tempered scale typically (figure 1)

As is well known, 12- tone equal-tempered music scale is a geometric progression.
It is possible to mathematically calculate the frequency of the scale, using the formula:
f(i) = f0*2 ^i/12,
where f0 — frequency of standard tuning fork (eg A 440 Hz);
i —the number of semitones in the interval from the desired note to the standard tuning fork f0. [3]

Table 1 shows the frequencies of 12-tones equal-tempered music scale, tuned to standard tuning fork (A 440 Hz).
12-tones equal-tempered music scale

Natural scale (from Lat. Natura - nature) or overtone scale is a series of tones, consisting of the fundamental tone and harmonic overtones. The harmonic series is an arithmetic progression (1xf, 2xf, 3xf, 4xf, 5xf, ...).
In terms of frequency (measured in cycles per second, or hertz (Hz) where f is the fundamental frequency), the difference between consecutive harmonics is constant and equal to the fundamental frequency.

Natural scale corresponds to the spectrum of complex harmonic oscillator - natural sound source (eg, a string or column of air in the tube).

Table 2 shows the differencoes between the intervals equal-tempered and natural scale
differences between the intervals equal-tempered and natural scale

The table 2 shows that only octave is natural interval in the equal-tuning scale.
The difference between natural and equal-tempered intervals is the reason for the decrease of quality musical instruments with equal-tempered tuning, due to the appearance of acoustic interference.
Also, when playing major or minor tonalities, there is a need to skip certain keys that do not fall into the tonalities.

The above-mentioned disadvantages, namely: absence of natural intervals (except the octave) and a mixed arrangement of keys for major and minor tonalities are "payment" for the design of the keyboard as a one-dimensional structure.

Thus, to obtain the desired technical result, namely:
a) an improvement in the quality of the sound of the musical instrument through the elimination of acoustic interference
б) continuous and, therefore, a logical location of major and minor scales
it is proposed the design of the keyboard as a two-dimensional structure.
 The matrix of this keyboard is presented in Figure 2.

EXAMPLE

When you configure the keyboard to the standard tuning fork (the note "a" - 440 Hz), the matrix looks like shown in Table 3

Table 3. The matrix of the frequency ratio when it is tuned to standard tuning fork: note "a" - 440Hz. In parentheses there are the frequencies in Hz
matrix of the frequency ratio is tuned to standard tuning fork

This matrix keyboard design allows achieving the following technical results:
1. For horizontal or vertical movement between adjacent keys or playing a chord the dissonant intervals and acoustic interference do not appear, because the matrix is based on natural musical intervals.
2. The intermittent keys location for major and minor musical scales eliminated. Major and minor musical scales are perpendicular.
In the example, a major chord are arranged horizontally (c, e, g - 4 line from the top), minor - vertical (c, d-sharp, g - 6 column).

In addition, matrix keyboard design has the following properties:
1. Tonic (keynote) is the diagonal of matrix. In the present example the tonic note “C” has the frequency of 264 Hz. (Figure 5)
2. The matrix contains all 12 chromatic intervals (Figure 5).
3. The matrix design may increase its axis without losing their properties, but in terms of psychoacoustics the square 8x8 (64 keys) matrix is optimal, and the square 4x4 (16 keys) matrix is minimum (figure 3)
4. The range of the matrix (8x8) is 6 octaves and it can be shifted at least to one octave. In the example, the range of the matrix is from “contra-octave” to the beginning of “4-line octave”.
5) The changing of tonic (keynote) pitch requires reconfiguring the matrix.

This matrix keyboard design is a technical presentation of the following definitions:
1. The “natural minor” is a scale built like a vertical arithmetic progression of all periods of the matrix’s top row. The arithmetical ratios are these periods. In turn, this matrix’s top row is an arithmetic progression of the tonic frequency . The 6, 5, 4 members of the “minor progression” form a minor chord (see figure 2 and figure 5).
2. The “natural major” is a scale built like a horizontal arithmetic progression of all frequences of the matrix’s left column. The arithmetical ratios are these frequences. In turn, this matrix’s left column is an arithmetic progression of the tonic period. The 4, 5, 6 members of the “major progression” form a major chord. (see figure 2 and figure 5).
Matrix keyboard design for musical instruments keeps its advantages and features of the case turns on its axis.

SUMMARY OF THE INVENTION

An object of the present invention is to provide the music keyboard design for
a) improvement in the quality of the sound of the musical instrument through the elimination of acoustic interference,
b) remove mixed arrangement of keys for major and minor scales
According to the invention there is provided:
a) the music keyboard consisting of keys which are organized in the form of a two-dimensional matrix and are ranged along one axis of the matrix as an arithmetic progression of the frequency of the sound produced and along the other axis of the matrix as an arithmetic progression of the period of the sound produced,
b) a method for producing of musical intervals are ranged like in the described matrix.

BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1. Keyboard for equal-tempered scale
Figure 2. The relationship of the periods and the frequencies of the sound produced
Figure 3 Strict keyboard design
Figure 4. Keyboard design with selected tonic (keynote).
Figure 5. The matrix of the frequency ratio when it is tuned to standard tuning fork: note "A" - 440Hz. In parentheses there are the frequencies in Hz


DESCRIPTION OF THE PREFERRED EMBODIMENT

It is known audio control device - keyboard for musical instruments, in particular, the keyboard for synthesizer. Technically easy to change the design of the keyboard and transform it into a matrix. In particular, the design of the keyboard, in the simplest case, may look like shown in Figure 3 or Figure 4.
Since the keyboard is a sound control device, for example, for synthesizer module that is selected like the prototype, there are standard hardware and software tools to perform basic operations on matrices.
In this case, it is the multiplication matrix to number. These operations will expand the functionality of a musical instrument and arbitrarily set the value of the tonic. The using of this keyboard is more convenient than a standard keyboard for piano or synthesizer. To simplify the perception of musical intervals should mark out all tonics, the diagonal of the tonic and major-minor chords as in Figure 3 and 4.

CLAIMS.

1. The music keyboard, comprising keys which are ranged by the frequency of the sound produced, characterized in that the music keyboard keys are organized in the form of a two-dimensional matrix and are ranged along one axis of the matrix as an arithmetic progression of the frequency of the sound produced and along the other axis of the matrix as an arithmetic progression of the period of the sound produced.
2. A method according to claim 1 characterized in that the musical intervals are ranged like in described matrix (2).

Figure 1. Keyboard for equal-tempered scale
Keyboard for equal-tempered scale
Figure 2. The relationship of the periods and the frequencies of the sound produced
The relationship of the periods of the sound produced by the keys represented by the arithmetic progression on the vertical axis.
1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8
2/1 2/2 2/3 2/4 2/5 2/6 2/7 2/8
3/1 3/2 3/3 3/4 3/5 3/6 3/7 3/8
4/1 4/2 4/3 4/4 4/5 4/6 4/7 4/8
5/1 5/2 5/3 5/4 5/5 5/6 5/7 5/8
6/1 6/2 6/3 6/4 6/5 6/6 6/7 6/8
7/1 7/2 7/3 7/4 7/5 7/6 7/7 7/8
8/1 8/2 8/3 8/4 8/5 8/6 8/7 8/8

Since the period of sound oscillations is a value inverse to the frequency the matrix can be presented differently.

The relationship of the frequencies of the sound produced by the keys represented by the arithmetic progression on the horizontal axis.
1/1 2/1 3/1 4/1 5/1 6/1 7/1 8/1
1/2 2/2 3/2 4/2 5/2 6/2 7/2 8/2
1/3 2/3 3/3 4/3 5/3 6/3 7/3 8/3
1/4 2/4 3/4 4/4 5/4 6/4 7/4 8/4
1/5 2/5 3/5 4/5 5/5 6/5 7/5 8/5
1/6 2/6 3/6 4/6 5/6 6/6 7/6 8/6
1/7 2/7 3/7 4/7 5/7 6/7 7/7 8/7
1/8 2/8 3/8 4/8 5/8 6/8 7/8 8/8

Figure 3 Strict keyboard design

Strict keyboard design
 
Figure 4. Keyboard design with selected tonic (keynote).
Keyboard design with selected tonic (keynote).

Figure 5. The matrix of the frequency ratio when it is tuned to standard tuning fork: note "A" - 440Hz. In parentheses there are the frequencies in Hz
matrix of the frequency ratio


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