AU610075B2

AU610075B2 - A musical calculator

Info

Publication number: AU610075B2
Application number: AU76430/87A
Authority: AU
Inventors: Pamela Joy Thomson
Original assignee: Individual
Current assignee: Individual
Priority date: 1986-07-04
Filing date: 1987-07-03
Publication date: 1991-05-16
Anticipated expiration: 2007-07-03
Also published as: AU7643087A

Description

"A MUSICAL CALCULATOR"

This invention relates to a calculator and is more specifically concerned with a calculator for enabling a musician to visualise and organise transitions between scales, modes, chords, melody lines, bass lines, fractions, colour, numerals, timber and the alphabet and to work more easily within a series of chosen scales, etc.

In co-pending Australian patent Application No. 28219/84 filed on 16th April 1984 and entitled "Sliding

Musical Scale Device" the present inventor has described a calculator comprising two flat sheets one of which provides a mask slidable over the other. The undersheet is marked with musical notation arranged in a row of parallel columns each representing a recurring cycle of notes, the starting note at the foot of each column having a pre-arranged progression, for example a fifth, with respect to the starting note of the preceding column and also shows how to transpose the modes of the Ionian Major scale into 4th/5th's from their tonic and then transposes the beforesaid modes and scale into 4th's and 5th's.

The masking sheet is formed with windows and opaque sections, also arranged in columns and each registering with a respective note position on the underlying sheet. Each row of windows and opaque sections is labelled to identify a particular type of musical, scale or mode represented by the column, and the notes visible through the windows of each column represent those used in that particular mode or scale. Although the calculator of the co-pending application is useful in enabling students of music to visualise the relationship between musical scales and modes, it has insufficient versatility for a composer who may require to change the relationship of the notes of the columns with respect to one another and to vary the order of the columns and insufficient versatility to write melody lines, bass lines etc.

In accordance with a first aspect of the invention, a calculator has musical notation in which the notes are equi-spaced and arranged in parallel rows on respective elements each of which is independently movable in the direction of the row with respect to neighbouring elements, masks overlapping respective elements and individually- movable in the direction of the row of notes on the element beneath, each mask corresponding to a particular musical scale or mode and having opaque and transparent sections alternating with one another to expose through the mask only those notes of the row beneath which are used in the scale or mode denoted by the mask. Preferably when the calculator is made in a planar configuration the length of the element is substantially greater than the length of the mask and conveniently the element is movable in either direction with respect to its length a distance of at least one complete octave. In one such arrangement the element is in a slideway six octaves long and is itself four octaves long. The mask is suitably two octaves long and may be arranged in a transparent platen which can be moved perpendicularly to the longitudinal direction of the elements beneath. In accordance with a second aspect of the invention, a calculator has musical notation arranged in circles each representing a scale or mode and in whi-ch the notes are equi-angularly spaced from one another, and masking rings superimposed over respective circles and individually rotatable about an axis common to the circles and rings, each masking ring having a circular array of transparent and opaque sections registering with the positions of respective notes in the circle beneath, so that the notes exposed in the transparent sections or windows correspond to those of the mode or scale represented by the ring.

A calculator in accordance with a third aspect of the invention has a set of rings individually rotatable about a common axis and arranged in positionally interchangeable pairs with one ring of each pair covering the other ring of the pair, each covered ring carrying at equi-angularly spaced positions notes of a chromatic scale, and the covering ring of the pair providing a mask identified as a particular scale or mode and having circumferentially distributed opaque sections and windows through which are exposed only the notes of the particular type of scale or mode represented by the masking ring.

Preferably the calculator comprises pairs of coaxially arranged cylindrical collars, the inner collars having the circle of musical notation arranged around its outside surface and the outer collar providing the mask. The inner collars have the same diameter preferably, so that any mask can be fitted over any collar. However if the collar pairs can be arranged in any order it does not matter if the collars of one pair have a different diameter or width to the collars of another pair.

Suitably, an indexing mechanism is provided to enable the masks and collars beneath to be individually located in any one of a number of predetermined angular positions. This may be achieved by providing each collar with a circular groove on its inside surface from which protrude sections of an undulating steel spring. The collars are conveniently threaded on a cylindrical former provided with longitudinally-extending flutes corresponding to the number of indexed positions required. The collar is then positively located in any one of those positions by the engagement of the protruding sections of the spring with the flutes.

The invention will now be described in more detail, by way of examples, with reference to the accompanying drawings, in which:-

Figure 1 shows parts of a cylindrical calculator; Figure 2 shows the calculator partially exploded and partially cut away to illustrate internal detail; Figure 3 shows in developed form a pair of superimposed collars or rings used in the calculator; and. Figures 4 to 6 show respectively a planar form of calculator: in diagrammatic form partially broken away; exploded; and, in plan, the legend which appears on two sliders used in the calculator;

Figure 7, shows a preferred method of interlocking the movement of parts of the calculator of Figure 4; and Figure 8, shows a calculator of another embodiment used for translation of notes or chords, scales, modes, etc. for guitars.

The calculator 1 of figures 1 and 2 has a cylindrical former 2 internally threaded at its ends and carrying pairs of separately rotatable superimposed rings 4 and 5. Inner ring 4 is externally marked at equi-angularly spaced positions with the twelve notes making a recurring cycle in the Lydian mode, as is clearly shown in figure 3. Each ring 4 is provided at one end with an outwardly-radial flange 6 having a knurled rim which projects beyond the ring 5 and enabling the ring 4 to be individually turned to any angular position. An indexing or detent mechanism (not shown) which is easily overcome by finger pressure, holds the ring in any position to which it is moved. The mechanism is conveniently of the watch bezel type referred to earlier in this specification, and using an undulating steel spring captured in a circular groove formed around the inside of the flange. Protruding sections of the spring can engage in respective notches formed by grooves extending lengthwise of the former in its external surface.

The outer ring 5 of the pair is formed as a mask having circumferentially spaced windows and opaque sections, as shown in figure 4, and carrying legend indentifying the scale or mode represented by the ring 5. In one example of the invention the masking rings 5 are respectively identified as:

LYDIAN MODE

IONIAN MAJOR SCALE

MIXO-LYDIAN MODE DORIAN MODE

AEOLIAN MINOR MODE

PHRYGIAN MODE

LOC IAN MODE

CHROMATIC SCALE HARMONIC MINOR SCALE

BLUES SCALE

SCRIABINS MYSTIC SCALE

WHOLE TONE RAJA SCALE It will be appreciated that other scales or modes may also be used, such as JAPANESE SCALES, HEJAZ, PENTATONIC, etc or modes of these scales. The ring 4 denoting the Lydian Mode, is shown in figure 3. It will be appreciated that any chord may be used such as major, minor, diminished, augmented, etc. You may also form your own scale, mode, chord, melody line or bass line, etc with spare clear plastic strips and an erasable pen. The masking ring 5 is provided on one rim with an inwardly-directed rim flange 15 which abuts against the adjacent edge of the inner ring or collar 4 at its end opposite its outwardly extending flange 6. The collar 15 has on its inside surface an annular groove (not shown) housing the undulating spring providing a indexing mechanism referred to earlier and already described with reference to the ring 4.

A retaining cap 14 is screwed into each end of the former 2 to hold the sets of rings in place.

The calculator is used by arranging the pairs of rings on the former in the order in which the user is to progress from one mode or scale to the next. This is simplified by the ring pairs forming units which can individually be removed from and returned to the former. To facilitate the replacement of the ring units, the end of the former can be bevelled so that the protruding sections of the springs of the mechanisms which locate the rings in chosen angular positions, slide smoothly onto the bevelled end of the former. The user then turns the underlying collars or rings by means of their radial flanges, to bring their starting positions into alignment with a chosen progression, and finally moves the masking rings individually to the desired positions to tell him the order of the notes in the scale or mode in which he is working.

In the case of the Locrian Mode, Chromatic and Harmonic minor scales, some of the note positions on the underlying rings carry two notes instead of one. This occurs when the same note position in the scale can be represented in either of two ways according to the scale in use. Any scale mode etc may be used with these double notes. Also certain ring configurations may be denoted as a "#" (sharp) column or ring or as a "b" (flat) column or ring.

The invention is of particular value in programming electronically synthesized music as it enables the composer to use computer programmes by applying the logic derived from the calculator.

The calculator shown in figures 4 and 5 is of planar form and comprises a rectangular flat base 20 having shallow parallel walls 21 on its upper face defining the sides of a set of channels providing slideways 22 in which are respectively located twenty-five strip sliders 23. Each slider 23, two of which are shown in figure 5, is four octaves long and has its upper face provided with musical notation as shown in figure 6. Each of the slideways 22 is six octaves long which allows the slider 23 within it to be slid one octave in either direction from a central position.

The top of the base is covered by a sheet 24 having a central window 25 formed in it extending the length of the base and arranged perpendicularly to the slideways 22. The width of the window 25, measured in the direction of a slideway 22, is two octaves. Two opaque rectangular areas 26 & 27 of the sheet 24 respectively flank the window and have the same dimensions as it has. The areas 26 and 27 each have a parallel channel 28 extending the length of the window 25 and disposed adjacent to it. Two further channels 28 are provided of respective ends of the window 25. The channels 28 provide guides for a transparent platen 30 able to move along or across the , window 25. The platen 30 has ridges 31 extending along each edge and arranged to engage the channels 28 as shown in Figures 7 and 8. Figure 7 shows the sheet 24 fitted to the base 20. Figure 8 illustrates the under side of the platen 30 showing the ridges 31. The channels and ridges allow the platen 30 to move either across the sheet 24. If the platen is to be moved along the sheet, the ridges along the shorter sides of the platen are disengaged from their associated channels and the platen moved sideways sufficiently to allow the ridges to clear the channels and replaced in contact with the sheet such that the long ridges and their associated channels are still engaged. The platen may now slide freely along the sheet guided by the ridges engaged with the channels of the sheet. Similar steps are taken if the platen is to be moved across the sheet with the other ridges being disengaged from their associated channels.

The upper face of the platen 30 is formed with parallel walls 32 arranged parallel to the slideways 22 and defining the sides of channels 33 each two octaves long. The tops of the walls 32 are slightly enlarged laterally, to retain within the channels respective masking sliders 34 which are of the same width as the sliders 23 beneath, as shown in figure 6. One of the masking sliders 34 is shown in plan in figure 6 from which it will be seen to comprise a line of opaque and transparent sections which denote a particular musical scale or mode identified in writing on one end of the masking slider. The length of the masking slider 34 is two octaves. The order of the opaque and transparent sections on the masking sliders 34 will differ from one scale or mode to another.

The sliders 23 are first fitted into the slideways 22 and slid along them to appropriate positions to bring a desired order of notes on the sliders 23 into alignment with the lower edge of the window 25. A slight stiffness in the slideways 22 ensures that the sliders 23 remain in any position to which they are moved although, of course, they can be slid by finger pressure to different positions if desired.

The ^"masking slides 34 are next slid into the channels 31 in the platen 30 in the order of progression of the scales and modes required by the user. The masking sliders expose in their windows only those notes relevant to the scale or mode marked on it. Finally the platen 30 is slid along the rails 28 until the first masking slider 34 is over the slider 22 the user wishes to employ first. By sliding the mask left to right, up or down over 20 and 24 you are able to transpose scale, mode, chord, melody lines, bass lines, etc, to any desired key.

The planar calculator of figures 4 and 5 has the advantage that the user can see at all times the complete progression of scales and modes he wishes to employ in the portion of the composition he is working on. Also as it is flat, it is easily transported in bulk. Another form of the invention as shown in Figure 8, resides in a calculator used to calculate the required notes or chords to be played on a standard six string guitar. The calculator has a slider 101 which is slidable within a mask 102, the slider has depicted on its upper surface, the notes playable on the guitar. The notes are also arranged in order of play so that the slider also represents the location of the notes on the neck of the guitar. The mask 102 is opaque with a series of transparent window arranged to reveal the notes depicted on the slider in a predetermined manner. By this arrangement, notes, chords, melody lines, bass lines, etc of one scale or mode may be transposed into another key as denoted by the mask being used. The calculator may be configured similarly for a 12 string guitar, violin, etc, in fact, any string instrument. This particular embodiment is a refinement of the previous embodiment as it should be appreciated that the previous embodiment can be arranged to represent the same configuration as each note position is changeable to represent any particular note or chord as required by the user. Likewise, the mask is also changeable to suit the translation or transposition required by the user.

Although the present invention in the description of the preferred embodiment, has been described with reference to scales and modes using musical notation, the inventor envisages the calculator as being able to be used to transpose all manner of different notations including, but not limited to scales, modes, chords, melody lines, bass lines, colour, number, fractions, alphabetic character and timber grains.

Claims

THE CLAIMS DEFINING THE INVENTION ARE AS FOLLOWS:

1. A calculator having musical notation in which the notes are equi-spaced and arranged in parallel rows on respective elements each of which is independently movable in the direction of the row with respect to neighbouring elements, masks overlapping respective elements and individually movable in the direction of the row of notes on the element beneath, each mask corresponding to a particular musical scale or mode and having opaque and transparent sections alternating with one another to expose through the mask only those notes of the row beneath which are used in the scale or mode denoted by the mask.

2. A calculator as claimed in claim 1, in which the elements comprise rectangular strip sliders and the masks also comprise sliding strips.

3. A calculator as claimed in claim 1 or claim 2, in which the masks and elements lie in respective parallel planes and the masks are mounted in a platen which is movable perpendicularly to the strips and sliders.

4. A calculator having musical notation arranged in circles each representing a scale in which the notes are equi-angularly spaced from one another, and masking rings superimposed over respective circles and individually rotatable about an axis common to the circles and rings, each masking ring having a circular array of windows and opaque sections registering with the positions of respective notes in the circle beneath, so that the notes exposed through the windows correspond to those of the mode or scale represented by the ring.

5. A calculator having a set of rings individually rotatable about a common axis and arranged in positionally interchangeable pairs with one ring of each pair covering the other ring of the pair, each covered ring carrying at equi-angularly spaced positions notes of a chromatic scale, and the covering ring of the pair providing a mask identified as a particular scale or mode and circumferentially distributed opaque sections and windows through which are exposed only the notes of the particular type of scale or mode represented by the masking ring.

6. A calculator as claimed in claim 4 or claim 5, in which the rings are coaxially-arranged cylinders.

7. A calculator as claimed in claim 6, in which the rings are rotatable around a cylindrical former passing coaxially through them.

8. A calculator as claimed in claim 7, in which the former has a removable end cap holding the rings in place but permitting the rings to be removed and re-arranged on the former in a different order when required.

9. A calculator as claimed in claim 8, in which the former is" formed with notches for cooperating with an indexing mechanism on each ring for holding it in a desired position while adjacent rings are being moved.

10. A calculator as claimed in claim 9, in which the former has longitudinally extending grooves formed in its external cylindrical surface, and the rings have mechanisms which resiliently engage with the grooves to hold the rings in chosen positions from which they may be turned by hand pressure.

11. A calculator as claimed in claim 10, in which each ring has a radial flange at one end which is formed on its internal cylindrical surface with an annular groove containing an undulating spring steel loop parts of which protrude from the groove to register with grooves in the former to locate the ring positively in a chosen position, one end of the former being bevelled to allow the rings to be slid onto it without the protruding parts of the spring abutting the end of the former.

12. A calculator as claimed in claim 1, arranged and adapted to be used substantially as hereinbefore described with reference to the accompanying drawings.

13. A calculator for changing the key of a tune to be played on a guitar comprising: a slide depicting all the notes playable on a guitar arranged in rows along the slide, each row representing a string of the guitar; and a mask having opaque and transparent windows, wherein the windows are arranged to align with predetermined respective ones of the notes displayed on the slider to indicate the particular note or chord to be played when changing from one key to another as indicated by the mask.