Abstract:
The invention provides methods and apparatuses for creating a two-dimensional graphical representation of music which has been analysed into a chord sequence, by evaluating a first parameter of each chord, e.g. the harmonic root, determining a first display coordinate for each chord in dependence on the evaluated first parameter, determining a second display coordinate for each chord within the sequence in dependence on the time of occurrence of each chord within the sequence, and displaying the chords graphically at positions defined by the determined.

Description:
[0001]    The invention relates to the analysis of musical harmony. In particular, the invention relates to the graphical display of chord sequences within music. 
       BACKGROUND OF THE INVENTION 
       [0002]    All music is based to a large extent on harmonic progressions, namely sequences of combinations of notes or chords which define underlying harmonic changes. However, conventional Western musical notation is based on a stave, known in the USA as a staff. An example of such notation is illustrated in  FIG. 1 , which represents in conventional musical notation the first sixteen bars of Bach&#39;s First Prelude from the Well Tempered Clavier Book I. The chord described by each section of music is shown above the stave. 
         [0003]    Musicians and composers have long known about the inadequacies of stave notation with respect to chords and harmonies. For example, the harmonic relationship between sequential chords cannot be indicated on a stave, and it is therefore difficult to appreciate any patterns that may be present within a chord sequence. 
         [0004]    Newcomers to music often find it difficult to understand and recall the appropriate patterns in chord sequences. For example, several notes may be played simultaneously to produce a chord, but if one of those notes is omitted or replaced by another note, the chord may change significantly. Such subtle differences are difficult for beginners to observe in standard musical notation. 
       BRIEF SUMMARY OF THE INVENTION 
       [0005]    In accordance with a first aspect of the invention there is provided a method of programming a computer to create a two-dimensional graphical representation of music which has been analysed into a chord sequence, such that the computer is arranged to perform the following steps: evaluating a first parameter of each chord within the sequence; determining a first display coordinate for each chord in dependence on the evaluated first parameter; determining a second display coordinate in dependence on the time of occurrence of each chord within the sequence; and displaying the chords graphically at positions defined by the determined first and second display coordinates. 
         [0006]    With such an arrangement, an aspect of the harmony of each chord within a sequence is caused to be displayed as a first coordinate within a graphical format, as opposed to merely the melody of the sequence. This enables a clear recognition of the harmonic sequence. 
         [0007]    The first parameter preferably comprises the pitch of a selected one of the notes within the chord, and this note may be selected in accordance with a predetermined algorithm and/or be the root of the chord. 
         [0008]    Since chords can usually be characterised by one of the notes of the chord, it is useful to select one of the notes for the first parameter. Thus, for example, the combination of the notes G, C and E imply a C major harmony, in which case the first parameter could be selected to be the note C. 
         [0009]    In the event that the chord comprises more than one possible root note, the chord may be represented at more than one first coordinate in the graphical representation. Thus, for example the combination of notes A and C could imply either an F major harmony or an A minor harmony, in which case the first parameter could be selected to be both F and A. Equally, the root of the chord consisting of the notes C, E flat, F sharp and A could be any one of these notes, in which case the first parameter could be selected to be all of these four notes. 
         [0010]    The scale along which the first coordinates are plotted within the graphical representation preferably defines a sequence of notes in which the interval between each pair of adjacent notes is the same. The interval is preferably a perfect fifth, since closely related chords, such as C major and G major would appear close together on the axis along which the first parameter of the chord sequence is plotted. In other circumstances, such as with jazz music, the interval may be selected to be a semitone. 
         [0011]    Each chord within the sequence is preferably indicated graphically at its respective position by an indicium which is selected in accordance with a second parameter of the chord. The second parameter may define the harmonic nature of the chord, such as: major triad; minor triad; diminished triad; augmented triad; major seventh; dominant seventh; diminished seventh; half-diminished seventh; ninth; eleventh; thirteenth; suspended second; suspended fourth; and flat and sharp alterations. 
         [0012]    When the chord is a major triad or a minor triad, a first indicium may be used when the root of the chord is the tonic of the music, and a second, different indicium may be used otherwise. 
         [0013]    A linking indicium may be displayed between each adjacent pair of chords which indicates the transition between the two chords within the chord sequence, such as: relative minor to relative major; relative major to relative minor; tritone; or dominant seventh to tonic. 
         [0014]    The first coordinate is preferably a y-axis and the second coordinate is an x-axis. 
         [0015]    The centre position along the first coordinate axis preferably represents the tonic of the music. Since harmonic sequences tend to be “centred” about the tonic in the harmonic sense, this arrangement is likely to result in an efficient use of the display area, with the harmonic sequence, on average, being arranged about the centre line. Thus, for example, a piece of music in the key of C major, i.e. where C is the tonic, is likely to consist of modulations into the key of G major and also F major. Where the first parameter is plotted in fifths, this will result in chords within the sequence being plotted on the centre line, at one position above the centre line, for the G chords, and at one position below the centre line, for the F chords. 
         [0016]    The computer may further be arranged to play the music which is displayed graphically, in which case the image of the displayed chords is preferably caused to move in time with the played music, such that a chord which is played at any given time is represented within the displayed chords at substantially the same position. 
         [0017]    This arrangement provides a particularly useful teaching aid, since the student can appreciate the harmonic structure of the music, both visually and aurally. 
         [0018]    In accordance with a second aspect of the invention there is provided apparatus for creating a two-dimensional graphical representation of music which has been analysed into a chord sequence, the apparatus comprising: means for evaluating a first parameter of each chord within the sequence; means for determining a first display coordinate for each chord dependence on the evaluated first parameter; means for determining a second display coordinate for each chord within the sequence in dependence on the time of occurrence of each chord within the sequence; and means for displaying the chords graphically at positions defined by the determined first and second display coordinates. 
         [0019]    In accordance with a third aspect of the invention there is provided a method of programming a computer to create a two-dimensional graphical representation of a set of signals which define musical notes of different acoustic frequency and which have been analysed into sequence of combinations of musical notes of different acoustic frequency, such that the computer is arranged to perform the following steps: evaluating a first parameter of each combination within the sequence; determining a first display coordinate for each combination in dependence on the evaluated first parameter; determining a second display coordinate in dependence on the time of occurrence of each combination within the sequence; and displaying the set of signals graphically at positions defined by the determined first and second display coordinates. 
         [0020]    The first parameter preferably comprises the frequency of a selected musical note within the combination. 
         [0021]    The signals are preferably Musical Instrument Digital Interface (MIDI) signals. 
         [0022]    The invention advantageously enables an entire piece of music to be viewed as a whole, and structures and patterns can be recognised visually that may not be apparent simply by listening or viewing the music in standard musical notation. 
         [0023]    In a preferred embodiment, any piece of music can be analysed simply by rearranging the chords on the y-axis so that the tonic is in the middle. 
         [0024]    The invention allows chords to be read directly from a chart in the same way that a jazz musician would use a lead sheet. 
         [0025]    By studying the harmonic techniques used by composers of any kind of music using the invention, their compositional techniques are laid bare. Not only are the charts useful for analysing existing music, but also for original composition and song-writing. Entire songs can be composed simply by creating patterns and following simple visual rules. Additionally, individual styles of music can be recreated by imitating the harmonic structure of a genre or composer in a new piece. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0026]    Preferred embodiments of the invention will now be described with reference to the accompanying drawings, in which: 
           [0027]      FIG. 1  shows a conventional stave representation of the first sixteen bars of Bach&#39;s First Prelude in C major from the Well Tempered Clavier Book I; 
           [0028]      FIG. 2  shows a blank chart according to a preferred embodiment of the invention; 
           [0029]      FIG. 3  shows the chart of  FIG. 2  used to represent the first sixteen bars of Bach&#39;s First Prelude from the Well Tempered Clavier Book I; 
           [0030]      FIG. 4  shows a table containing symbols used according to the preferred embodiment of the invention; 
           [0031]      FIG. 5  shows a list of connectors which are used to illustrate the relationship between adjacent chords according to the preferred embodiment of the invention; 
           [0032]      FIG. 6   a  shows an example of a perfect cadence according to the preferred embodiment of the invention; 
           [0033]      FIG. 6   b  shows an example of a plagal cadence according to the preferred embodiment of the invention; 
           [0034]      FIG. 6   c  shows an example of an imperfect cadence according to the preferred embodiment of the invention; 
           [0035]      FIG. 6   d  shows an example of an interrupted cadence and an expected resolution according to the preferred embodiment of the invention; 
           [0036]      FIG. 7   a  shows a first interpretation of a passage from Chopin&#39;s Etude Op. 10 No. 1 according to the preferred embodiment of the invention; 
           [0037]      FIG. 7   b  shows a second interpretation of the passage from Chopin&#39;s Etude Op. 10 No. 1 shown in  FIG. 7   a  according to the preferred embodiment of the invention; 
           [0038]      FIG. 8   a  shows a first interpretation of a jazz standard known as “Rhythm Changes” based on the harmony of “I got Rhythm” according to the preferred embodiment of the invention; and 
           [0039]      FIG. 8   b  shows a second interpretation of the jazz standard shown in  FIG. 8   a  according to the preferred embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0040]      FIG. 2  shows a chart  10  for analysing the harmonic structure of a piece of music according to a preferred embodiment of the invention. Arranged vertically on the left-hand side of the chart  10  is a chord column  12  which comprises a sequence of notes. In the middle of the column resides the tonic or root note  13  of the piece of music represented on the chart  10 . For the purpose of describing the invention clearly, the chart  10  shown in  FIG. 2  does not have music represented on it. Extending above and below the root note  13  are the keys in order of ascending and descending perfect fifths respectively, according to the diatonic circle of fifths. This allows the strongest key relationships to be closest together. The skilled reader will notice that the note at the top of the chord column  12  is F sharp, which is enharmonically equivalent to the note G flat at the bottom of the chord column  12 . 
         [0041]    The chord column  12  represents a y-axis of the chart  10 , and extending orthogonally from the middle of the y-axis is an x-axis  14  along which time is plotted. Time is measured in bars as indicated in a bar row  15  which extends orthogonally from the top of the y-axis parallel to the x-axis  14 . Vertical lines  16  indicate the beginning of each bar subsequent to the first bar. 
         [0042]    The first sixteen bars of J. S. Bach&#39;s First Prelude in C major from the Well Tempered Clavier Book I is displayed on the chart  10  in accordance with the invention in  FIG. 3 . This piece is in the key of C major, and the harmony of the first bar is C major, as indicated by a filled square  20  placed next to the root note  13  in the area of the chart  10  defined as the first bar of the piece. As will be appreciated by the reader, chords come in many types, such as major, minor, diminished, etc. The table shown in  FIG. 4  illustrates the corresponding symbol used in the preferred embodiment of the invention for each type of chord. Of course, these symbols may be substituted by other symbols, as desired by the user. 
         [0043]    Moving now to the second bar of the chart  10  shown in  FIG. 3 , the root of the chord played here is D minor. Therefore, as designated by the table in  FIG. 4 , an unfilled diamond  22  is placed in the second bar section of the chart  10  and positioned at the y-coordinate defined by the note D in the chord column  12 . A straight line  21  is drawn between the filled square  20  and the unfilled diamond  22 , as explained below. 
         [0044]    Similarly to the first and second bars, the chord played in the third bar of the piece is indicated by placing a symbol in the third bar section of the chart  10 . In this case, the harmony of the chord is G dominant 7 th . Therefore, a partially filled square  24  is placed in the third bar section of the chart  10  and positioned at the y-coordinate defined by the note G in the chord column  12 . A straight line  23  is drawn between the unfilled diamond  22  and the partially filled square  24 , again as explained below. 
         [0045]    For the sake of brevity, the remaining chords of the piece will not be described, since the method of the invention described above is used for all chords of the piece. 
         [0046]    The relationship between adjacent chords is displayed diagrammatically by the use of connectors. A list of connectors used to do this is shown in  FIG. 5 . 
         [0047]    Dominant 7 th  chords are usually followed by a major or minor chord a perfect fifth below, e.g. a dominant 7 th  chord on G is usually followed by a C major or minor chord. However, in the event that the subsequent chord is not the expected chord, the expected chord is indicated in dashed outline on the chart, and a suitable connector, also in the form of a dashed line, is included. 
         [0048]    The skilled reader will be aware that a dominant 7 th  chord is crucial to the establishment of a new key and is nearly always present just before a modulation. This relationship is known as a perfect cadence. Referring back to  FIG. 3 , the partially filled square  24  which represents a G dominant 7 th  chord of the piece is followed by a C major chord, indicated in the appropriate position by a filled square  26 . This chord change constitutes a perfect cadence, and, referring to the list in  FIG. 5 , a single-headed arrow  25  is drawn from the partially filled square  24  to the filled square  26 . As can be clearly seen from  FIG. 3 , the next perfect cadences occur in bars six to seven, and ten to eleven, and these serve to establish a new temporary tonic for the piece. 
         [0049]    Using the list shown in  FIG. 5 , a relative major/minor connector in the form of a double-headed arrow  27  is used between bars four and five, and another relative major/minor connector  35  is used between bars  8  and  9 . The remaining connectors will be self-explanatory by referring to  FIG. 5 . 
         [0050]    The invention enables other cadences to be easily viewed. For example,  FIG. 6   b  shows an F major chord  102  moving to a C major chord  104 , and the representations of the two chords  102 ,  104  are connected by a connector  103 . This is an example of a plagal cadence.  FIG. 6   c  shows a C major chord  106  moving to a G major chord  108 , which is an example of an imperfect cadence. Again, the representations of the two chords  106 ,  108  are connected by a connector  107 .  FIG. 6   d  shows a G dominant 7 th  chord  110  moving to an A minor chord  112 , which is an example of an interrupted cadence, where the representations of the two chords  110 ,  112  are connected by a connector  111 . In the example shown in  FIG. 6   d , the expected move to the tonic root is shown with a dashed-line arrow  113 . Thus, expected movement which does not occur or alternative movement can be highlighted by the invention. 
         [0051]    For the purposes of illustration, Bach&#39;s First Prelude from the Well Tempered Clavier Book I has been used to describe the invention. Of course, any other piece of music may be analysed using the invention, and further examples are discussed below. 
         [0052]    Thus, an example of another piece of music which has been analysed according to the invention is shown on a chart  200  in  FIG. 7   a . The more complex harmonic movement of Chopin&#39;s Etude Op. 10 No. 1 is displayed. A feature of this piece is the diminished chords  202 ,  204 ,  208 ,  210 ,  212  which are often harmonically ambiguous. The two diminished chords  202 ,  204  in bar  74  act like dominant 7 th  chords  216 ,  218  a fifth below. These suggested dominant 7 th  chords  216 ,  218  have been added as small symbols which imply a harmonic movement descending down to C major in bar  75 . 
         [0053]    As will be appreciated by the skilled reader, diminished chords do not necessarily have an obvious root note. The invention advantageously allows all four notes of the diminished chords  208 ,  210 ,  212  to be shown on the chart  200  in bars  76  and  77 . For example, the four notes of diminished chord  208  are F sharp  208 , A  222 , C  224 , and E flat  226 . Connectors  207 ,  209 ,  211  show one possible interpretation of the harmonic movement, namely a tritone jump from C to F sharp, followed by descending perfect fifths between diminished chords  208 ,  210 ,  212  in bars  75  to  77 . 
         [0054]    Chart  200  also contains a minor 6 th  chord  214 . Minor 6 th  chords can also be ambiguous as they can be interpreted alternatively as half-diminished chords and vice versa. For example, the F sharp minor 6 th  chord  214  can be interpreted as an E flat half-diminished chord  220 . Often the lowest note of the chord will help in determining the identity of a chord, but it can be equally useful to add both chord symbols to the chart as shown in bar  78 . 
         [0055]      FIG. 7   b  shows a different interpretation of the piece shown in  FIG. 7   a . In  FIG. 7   b , the suggested harmony is indicated by dashed-line connectors  300  in bar  74 . Also, a different route has been taken through bars  77  to  79 , as shown by dashed-line connectors  302 . In contrast, the harmony moves in a chromatic fashion as seen in bars  77  to  78  of  FIG. 7   a . The “correct” interpretation is clearly open to discussion, but, without the visual aid of the invention, it would be far more difficult to see the different interpretations available. 
         [0056]      FIG. 8   a  shows a further piece of music using a representation in accordance with the invention. A chart  350  shows the suggested tritone counterparts of the chromatic shifts using dashed-line connectors  354 . The invention allows the complex harmonic movement&#39;s true nature to be clearly shown as it descends slowly back towards the tonic root  352 . 
         [0057]    However, sometimes it can be useful to rearrange the chords along the y-axis with chromatically ascending and descending chords. In the interpretation shown in  FIG. 8   b , the suggested substitutions are omitted. In  FIG. 8   b , the chromatic movements of the chords E  354 , A  358 , D  356  and G  360  are clearly shown. 
         [0058]    In a further preferred embodiment, a piece of music is played through one or more loudspeakers of a computer, and the harmonic sequence of the music being played is displayed dynamically on the computer screen such that the displayed chords move horizontally along the computer screen in time with the music. An indicium is also displayed which indicates the position of the chord being played through the loudspeakers. 
         [0059]    Having described preferred embodiments of the invention, it is to be appreciated that these embodiments are merely exemplary, and that variations and modifications including modifications made to the chart or symbols, such as those that will occur to those possessed of the appropriate knowledge and skills, may be made without departure from the spirit and scope of the invention as set forth in the appended claims.