Abstract:
A music composition, editing, and playback system and method provides a user interface design based on geometric interpretation of music theory replacing traditional modern music notation with geometric shapes including chords represented by polygons that are colored with colors or hues.

Description:
PRIORITY AND INCORPORATION BY REFERENCE 
     This application claims the benefit of Prov. Pat. App. No. 62/101,982 filed Jan. 9, 2015 which is incorporated herein in its entirety and for all purposes. This application incorporates by reference, in their entireties and for all purposes, U.S. Pat. No. 6,570,584 filed May 15, 2000, U.S. Pat. No. 7,519,603 filed Nov. 27, 2002, U.S. Pat. No. 6,320,112 filed May 18, 2001, U.S. Pat. No. 6,353,170 filed Sep. 3, 1999 and U.S. Pat. App. Nos. 20080055479 A1 filed Sep. 4, 2007 and 20060285136 filed Mar. 13, 2006. 
    
    
     BACKGROUND OF THE INVENTION 
     The tasks of composing and editing musical compositions have long been tedious work characterized by use of modern staff notation. Generations of composers and musicians have learned this method of composing, memorializing, and/or playing various works. However, many fail to attempt or master the rigors of reading and writing in modern staff notation. For example, The Beatles, Jimi Hendrix, and Eric Clapton became famous, although they were arguably “illiterate” musicians because they could not read music. The music of many less famous musicians has likely been lost for lack of the ability to record it in traditional modern staff notation. A solution to this problem is to replace modern staff notation with a more accessible technique for composing and memorializing musical works. 
     FIELD OF INVENTION 
     This invention relates to machines, articles of manufacture, and processes. In particular, a computer based aid for composing, editing, and playing music is provided. 
     DISCUSSION OF THE RELATED ART 
     The scholar and music theorist Isidore of Seville, writing in the early 7th century, considered that “unless sounds are held by the memory of man, they perish, because they cannot be written down.” Since music&#39;s Classical period, from about 1750 to 1820, music notation including a multi-line or five-line staff has been known and adapted in what has been called a system of “modern” music notation. Known and used by Chopin and Taylor Swift alike, the term “modern” appears misplaced as there has been only little improvement during the last two centuries. In particular, this ancient system of music notation has been an impediment to both those who would compose new music and those learning to play music presented in this format. 
     SUMMARY OF THE INVENTION 
     Embodiments of the present invention provide one or more aids for composing, editing and playing musical works. 
     In an embodiment, a music composition, editing, and playback system comprises: a processor and one or more input/output devices including a display or displays which may include a touch sensitive display screen; the processor for executing a computer readable code for music composition, editing, and playback; musical notes and chords are visualized in one or more note circles, each note circle including an octave of notes; each chord visualization derived from one or more of seven base vector triads, has a particular polygonal shape colored with a particular hue, differs from visualizations of other chords for at least one of a different shape or a different hue, and includes an indication of the chord root note; visualizations of musical rhythms created by aggregation of plural ones of the visualized notes and chords in a time circle; time circle circumference equal to a particular musical distance and a time marker for moving around the circle; and, the aggregation of notes and chords visualized in the time circle in accordance with a user selected rate or scale of the time marker. 
     Embodiments of the invention provide a computing, internet, and/or cloud based platform for musical expression, collaboration, creativity &amp; content sharing, with a user interface design based on a geometric interpretation of music theory. 
     In an embodiment, the user interface design for music shaper translates western music theory into a notation of shape and color, allowing the user to easily and intuitively express themselves through touch interactions. 
     In an embodiment, the invention is an enabler for writing music without detailed knowledge of music notation. This enabler avoids the music notation of the present centuries old system which delays learning by, among other things, obfuscating the mathematical structures present in music. This representation removes obfuscations, and enables user interfaces for intuitive operation. 
     Music Shaper can benefit society because it will help more people experience and write music in a new and fun way. It will share concepts from upper division and graduate mathematics, graphically, with the general public. By helping people through the learning curve for music writing, it opens up commercial potential for new economic interactions allowing users to sell each other content they create. 
     Music Shaper can impact society by helping transform the internet from a market of advertisers to a more desirable market of content producers, and simultaneously advance the state of the art in distributed computing. 
     Goals of the Music Shaper include one or more of constructing a software system that allows untrained musicians, to compose and play complete works of music, using intuitive 2D and 3D visual, touch, and gesture based interfaces. These interfaces are designed using a geometric and higher dimensional interpretation of the syntax and semantics of music theory. Embodiments enable the user to sculpt music out of geometric shapes with their fingertips, the product being a work that is consistent with the rules of Western music theory, but not unnecessarily limited in content, structure, or genre. 
     In an embodiment the invention provides a method of representing a complete chord catalog, the method comprising the steps of: constructing a parameterized curve encircling an axis multiple times; representing “n” musical octaves with the curve such that for any integral number of octaves the curve origin and end lie in the same plane as the axis; positioning notes on the curve to form a 12 tone equal temperament tuning system for each octave; taking 3 notes at a time selecting the 7 largest triangles that interconnect 3 notes wherein each newly selected triangle is neither of an inversion of or a rotationally symmetric copy of any one of the previously selected triangles [and] wherein each of the selected triangles represents a musical chord; and, from the 7 chords, selecting a set of chords that forms a four layer decision tree; wherein each chord in the set of chords is a composite (more than 3 notes) of 2 to 4 of the 7 chords, the set of chords includes every unique composite chord, and in three adjacent layers successive chords are selected such that the latter chord shares a vertex with the prior chord. 
     In another embodiment the invention provides a method of creating colorations for three note chords, the method comprising the steps of: selecting a first set of CIECAM02 environmental parameters including adaptation, surrounding lighting, background luminance, and white point; after the environmental parameters are selected, selecting a second set of CIECAM02 parameters including lightness and chroma; displaying a CIECAM02 hue wheel parameterized by lightness and chroma; in a default interval color selection, locating six substantially equally spaced roundels on the hue wheel, each roundel identifying a different interval color; providing a roundel or hue wheel adjustor enabling a user to relocate the roundels on the hue wheel for adjusting interval colors; selecting sets of interval colors for mixing to produce chord coloration for symmetric chord pairs, asymmetric chords, and corresponding colors for chord inversions; verifying that the chord colors when mapped from a CIELUV color space to a CIECAM02 color space are in gamut; for “n” octaves defining (n×12) notes, setting a first lightness for the lowest frequency note and a second lightness for the highest frequency note, the intermediate notes being spaced by equal frequency increments; for each represented note, determining a chroma value that assures the note is displayable for all hues; varying hue to represent different inversions of a chord; varying lightness to indicate note frequency; and, from the collection of three note chords inherent in the “n” octaves, selecting and displaying an image of the chord that is colored in accordance with the above steps. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention is described with reference to the accompanying figures. These figures, incorporated herein and forming part of the specification, illustrate embodiments of the present invention and, together with the description, further serve to explain the principles of the invention and to enable a person skilled in the relevant art to make and use the invention. 
         FIG. 1  shows a drawing of an interval lotus of the present invention. 
         FIG. 2  shows a drawing of chord construction of the present invention. 
         FIG. 3  shows a drawing of multiple triad chords within a note circle of the present invention. 
         FIG. 4  shows a drawing of a triad chord and lotus reaches emanating from triad vertices of the present invention. 
         FIGS. 5A-B  show a symmetric lotus and corresponding plume tabulation of the present invention. 
         FIGS. 6A-F  and  FIG. 7  show construction of a starburst of the present invention. 
         FIGS. 8A-C  show interval formation from intersecting starbursts of the present invention. 
         FIGS. 9A-C  show formation of triad and composite chords of the present invention. 
         FIGS. 10A-C  show harmony spirals of the present invention. 
         FIG. 11  and  FIGS. 12A-B  show note grids of the present invention. 
         FIG. 12C  shows exemplary transformations provided by the present invention. 
         FIGS. 13A-H  show a rhythm system of the present invention. 
         FIG. 14  shows a loop selector of the present invention. 
         FIG. 15A-D  show a graph of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The disclosure provided in the following pages, including Attachment I, describes examples of some embodiments of the invention. The designs, figures, and descriptions are non-limiting examples of certain embodiments of the invention. For example, other embodiments of the disclosed device may or may not include the features described herein. Moreover, disclosed advantages and benefits may apply to only certain embodiments of the invention and should not be used to limit the disclosed inventions. 
       FIG. 1  shows an interval lotus  100 . Arranged with a circle  102 , the lotus shows twelve notes (see e.g.,  104  note C) of an octave evenly spaced around the circle. Inside the circle are reaches of the lotus along paths between a root note, here D#, and each of the other notes around the circle. 
     The reaches appear as plumes with varying different hues. As seen, the plumes to either side of a central plume from D# to A ( 116 ) colored in pinkish purple appear as mirror images in both form and hue. As shown, the D# to E ( 106 ), D is colored in olive green, D# to F ( 108 ), C# is colored in blue, D# to F# ( 110 ), C is colored in blue purple, D# to G ( 112 ), B is colored in orange, D# to G# ( 114 ), A# is colored in lime green. These colors may be referred to herein in accordance with the hue table below. 
     
       
         
               
             
               
               
               
             
           
               
                   
               
               
                 Hue Table 
               
             
          
           
               
                   
                 Hue 
                 Designation 
               
               
                   
                   
               
               
                   
                 Dark green or olive green 
                 G1 
               
               
                   
                 Blue 
                 B 
               
               
                   
                 Purple or blue purple 
                 P 
               
               
                   
                 Orange 
                 O 
               
               
                   
                 Light green or lime green 
                 G2 
               
               
                   
                 Pinkish purple 
                 F 
               
               
                   
                   
               
             
          
         
       
     
     The interval lotus may be used in connection with formulating and/or describing, among other things, musical notes, diads, and triads. For example, the interval lotus aids selection of key and chords using a circular context. 
       FIG. 2  shows how a particular musical chord, a three note triad, is fitted into a note circle  200 . At right in the  FIG. 210  are four basic triads, major, minor, diminished, augmented and three additional triads 7 No 5, Mb5, and Sus 2. The triads characterize chord quality and are represented by polygons of different colors or hues. Further, the major and minor chords are structural mirror images as are the 7 No 5 and Mb5 chords. Any one of these triads may be fitted into the interval lotus space and aligned to provide a particular root note. At left in the  FIG. 211 , a minor chord  204  is shown fitted into the interval lotus space. A delta or chevron  206  imposed on the chord points to E, the chord root note  208 . As seen, different or additional triad chords  202 ,  204  may also be fitted into the interval lotus space. 
       FIG. 3  shows a four triad chords in a note circle  300 . As shown, a Sus 2 triad  302  has root note D, a major triad  304  has a root noted F, a diminished chord  306  has a root note F#, and a fourth triad  308  has a root note A. 
       FIG. 4  shows a single triad chord in an interval lotus including lotus reaches emanating from chord vertices  400 . In particular, the chord shown is an augmented chord  408  with vertices  402 ,  404 ,  406  at respective notes C#, A, and F. Starbursts at the chord vertices are discussed below. 
     Chords may be derived from seven (7) base vector triads and may be represented by selected corresponding colors and shapes such as polygons and these may be used to construct individual chords. Alternately a library of chords or keys and chords may be navigated by decision tree, by geometric configuration, and also by chord name. Intervals are represented by the coloration of a lotus, and the interaction of the lotus can be used to show individual interval influences for note choices and the structure of chord support for a given configuration of notes. Embodiments of the present invention enable visualization of these choices. These choices can be visualized in real time for played notes such as midi notes. A library of keys can also be implemented by chord choice in tree format. As is further explained below, embodiments of the present invention may provide a chord navigator allowing for rotation and basic transformations of key objects, along with root/mode setting, and quick play of modes for musical feeling ear training. 
     In an embodiment, a chord selection application allows the user to see the geometric configuration of keys  220  in the note circle, test out notes, and apply composite chords to the note circle  102 . Here, the user may rotate key, set accidental, set mode, apply multiple chords and rotate them through constrained locations. In various embodiments, the twelve (12) notes on the circle are active midi note send regions. Notes not in the key will be prevented from playing, as will notes outside a chord if a chord is selected. The application displays the seven (7) basic triads from which all other notes may be selected. The interface will display the selected key and mode, and will also display the current selected chord components and its root note. In some embodiments the chords will show a delta on the triangle, to indicate their root position, and the system will indicate which mode has been selected by highlighting it. The system may also highlight a point of the key if it has been set with an accidental and the system may allow chords to be locked and unlocked, and also cleared. 
     The above provides an introduction to methods of visualization of various musical elements as disclosed herein. These and other methods useful in tasks including composing, editing, and playing musical works are explained in some detail below. 
       FIGS. 5A-12B  illustrate means for visualizing and/or displaying musical notes, intervals, triad chords, and composite chords. 
     Embodiments of the present invention may utilize one or more display architectures to characterize elements of a musical work. Features of a display architecture may include two and/or three dimensional geometric figures and collections of such geometric figures. Additional information about the musical element may be added by marking geometric figures as through the selection of hue, chroma, and lightness values. 
     Geometric figures include loti, starbursts, intervals, diads, triads, and groups of one or more of these figures. And, as explained below, loti may be used as building blocks to construct a starburst. From two intersecting starbursts an interval between notes may be determined. Three intervals may be used to determine a triad musical chord and multiple triad chords may be used to determine a composite chord. 
     Turning now to the construction of starbursts from loti,  FIG. 5A  shows a symmetric lotus  500 A indicative of an exemplary octave in a 12 tone equal temperament tuning system. The notes of the octave are indicated by evenly spaced marks  504  located along a lotus circle or octave path  501 . Lotus intervals are indicated by plumes that lie along lines between a lotus root note  506  and another note of the octave  504 . Notably, the plumes may emanate from, but avoid contact  508  with either or both of the root note and the notes to which they lead. For example, a maximum lotus interval may be indicated by a plume  502  centrally located in the lotus and lying along a line between a root note  506  and a note opposite the root note  504 . Given there are 12 notes in the octave, five intervals lie to the left of the central interval and five intervals lie to the right of the central interval. 
       FIG. 5B  shows a tabular description of lotus plumes  500 B. At the center of the table is a central or zero plume with a hue “F” which may be equated with pinkish purple or fuchsia. To the right and left of center are first plumes 1(right) and 1(left) with hues “G1” that may be equated with a dark green. To the right and left of the first plumes are second plumes 2(right) and 2(left) with hues “O” that may be equated with orange. To the right and left of the second plumes are third plumes 3(right) and 3(left) with hues “P” that may be equated with purple. To the right and left of the third plumes are fourth plumes 4(right) and 4(left) with hues “B” that may be equated with blue. To the right and left of the second plumes are fifth plumes 5(right) and 5(eft) with hues “G2” that may be equated with a light green. 
     The lotus of  FIG. 5A  is termed a “symmetric lotus” because the plume hues are symmetric about the central plume such that corresponding plume pairs 1(right):1(left), 2(right):2(left), 3(right):3(left), 4(right):−4(left), and 5(right):5(left) have the same hue. In the case of a right asymmetric loti (see e.g.,  FIG. 6D ), the 2 nd  and 3 rd  plume hues on the right are reversed and the 4 th  and 5 th  plume hues on the right are reversed. In the case of a left asymmetric loti (see e.g.,  FIG. 6F ), the 2 nd  and 3 rd  plume hues on the left are reversed and the 4 th  and 5 th  plume hues on the left are reversed. 
     Whether a lotus is symmetric or asymmetric, it may be described as having a lotus root or base note and a corresponding root or maximum interval between notes such that the lotus includes a first or lower range of five intervals to one side of the maximum interval and a second or higher range of five intervals to the other side of the maximum interval. 
     It should be noted that while a lotus may be used to describe intervals in a single octave as seen above, intervals may also extend between a root note and a note in the same or a different octave as is further explained in connection with harmony spirals below. 
       FIGS. 6A-F  show illustrate features of an exemplary starburst harmony spiral  600 A-F. 
     As shown in  FIG. 6A , a starburst harmony spiral  600 A may include a starburst or multi-lotus construct  608  within a harmony or multi-octave spiral  682 . As described below, the starburst may be constructed, in a manner of speaking, by stacking loti in an octave spiral. As shown, there are six plumes  631 - 636  that are the central plumes of six loti and each of the plumes emanates away from a common starburst root note  679  at a starburst midplane  677 . 
       FIG. 6B  shows a portion of the  FIG. 6A  multi-octave spiral  600 B. The portion shown  619  includes an octave of 12 notes, the notes being represented by marks  617  that are equally spaced around the spiral. 
       FIG. 6C  shows the  FIG. 6A  multi-octave spiral  600 C. In the spiral  682 , six lines or plumes indicate starburst root note intervals, each interval spanning between the common starburst root note  679  and a central note of a respective octave. The starburst root note lies in a starburst midplane  677  that is about perpendicular to a spiral axis x-x. As shown, there are three lower intervals  631 - 633  in three lower octaves and three upper intervals  634 - 636  in three upper octaves. 
     Where as here, a common root note  679  is used in connection with each of the intervals  631 - 636 , one note of each octave above and below the starburst root note  679  is unused as it is replaced by the starburst root note. See for example the exemplary unused note  617  in the lowest octave or partial octave of  FIG. 6A . 
     In the spiral  682  of  FIG. 6A , right asymmetric, and left asymmetric loti are formed. These loti are octaves of the spiral that are collapsed to form a planar figure. For example, in  FIG. 6D , a right asymmetric lotus characteristic of an upper octave (see e.g.  634 )  600 D is shown. As indicated by the corresponding tabulation of lotus plumes, intervals to the left of the root interval  635  have hues matching those of a symmetric lotus while intervals to the right of the root interval swap 2 nd  and 3rd interval hues and swap 4 th  and 5 th  interval hues. 
     In  FIG. 6F , a left asymmetric lotus characteristic of a lower octave  631 - 633  is shown  600 F. As indicated by the corresponding tabulation of lotus plumes, intervals to the right of the root interval  633  have hues matching those of a symmetric lotus while intervals to the left of the root interval swap 2 nd  and 3rd interval hues and swap 4 th  and 5 th  interval hues as compared to the symmetric lotus. 
     In  FIG. 6E , a symmetric lotus is shown  600 E. This lotus is formed by the starburst root note  679  and the six notes to either side of the starburst root note. Notably, unlike asymmetric loti that fill upper and lower octaves, the symmetric lotus includes the adjoining symmetric portions of the first upper right asymmetric lotus and the first lower left asymmetric lotus. Because the symmetric lotus octave includes notes to either side of the starburst root note, all of the notes in this octave are used. And, because octaves other than the symmetric lotus octave do not include the starburst root note, one note of each such octave is not used. 
       FIG. 7  illustrates construction of an exemplary starburst harmony spiral including two octaves  700 . 
     At left is a schematic  702  of upper and lower octaves  706 ,  708  joined at a common spiral root note  679  at a starburst midplane  677 . The upper octave  706  includes a right asymmetric portion  712  and a left symmetric portion  713 . The lower octave  708  includes a right symmetric portion  723  and a left asymmetric portion  722 . About the midplane  677  the left symmetric octave  713  and the right symmetric octave  723  are joined at the common spiral root note  679  to form a symmetric octave  730 . 
     At right is a harmony spiral  704  including the two octaves  706 ,  708  joined at the common spiral root note  679 . 
     The spiral display of the upper octave  706  may be collapsed to form a right asymmetric lotus with a central plume  734 . The octave asymmetric portion  712  has a note color sequence of B-G2-O-P-G1-F. 
     The spiral display of the lower octave  708  may be collapsed to form a left asymmetric lotus with a central plume  733 . The octave asymmetric portion  722  has a note color sequence of G2-B-P-O-G1-F. 
     At the starburst root note  679  the symmetric portions  713 ,  723  of the octaves  706 ,  708  are joined. Together, these symmetric octave portions may be collapsed to form a symmetric lotus, for example a lotus with a central plume that superposes plumes of the upper and lower octaves  733 ,  734 . 
     As used herein, applicant coins the term “normal starburst” to refer to a particular starburst, that is to a starburst including a right asymmetric lotus joined to a left asymmetric starburst at a common root note. 
     Turning now to the construction of triad chords, each such chord may be represented by a triangle where each edge of the triangle is an interval between notes on a harmony spiral. As explained below, these trial intervals result from the intersections of starbursts such as the starbursts described above. 
       FIG. 8A  shows exemplary intersecting starbursts  800 A. Here, two starbursts  802 ,  804  having corresponding root notes  812 ,  814  are located in a harmony spiral  806 . Where the two starbursts intersect may be determined by the starburst location within the harmony spiral  806 . In various embodiments, two intersecting starbursts intersect along but a single line that extends between notes on the harmony spiral. 
       FIG. 8B  shows a first view of the intersection  800 B of the two starbursts of  FIG. 8A . Here, the intersection of first and second starbursts  802 ,  804  occurs along but a single line  822 . In an exemplary intersection, the intersection occurs along a line formed by the intersection of i) a plume  824  of a first note e.g., G2 in the first starburst and ii) a plume  826  of a second note e.g., G2 in the second starburst. 
       FIG. 8C  shows a second view of the intersection  800 C of the two starbursts of  FIG. 8A . Here, only the intersecting plumes  824 ,  826  are shown to better illustrate the corresponding notes  834 ,  836  that the intersecting plumes extend between. As mentioned above and as further described below, these intersecting plumes may be used to determine a side of a triad chord. 
       FIGS. 9A-C  show triads formed from intervals and composite chords formed from triads  900 A-C. 
       FIG. 9A  shows the formation of a first triad chord  900 A. At left is a planar view  902  of three intersecting starbursts  931 - 933  within a collapsed harmony spiral  901 . At right is a perspective view  904  of the harmony spiral  901  showing the intersections of the  922 - 924  of the starbursts  931 - 933 . 
     Here, intersections among the starbursts are i)  931  to  932  resulting in a first interval  922 , ii)  932  to  933  resulting in a second interval  923 , and iii)  933  to  931  resulting in a third interval  924 . 
     These intervals are shown in the harmony spiral  901  and form a triad chord  921 , for example a triad chord including the notes F-A#-C# in a first minor chord. As will be appreciated by skilled artisans, any triad chord may be constructed as a particularly colored geometric figure within the harmony spiral  901  such that a musician visualizes the chord from chord geometry, hue, and location within the harmony spiral. 
       FIG. 9B  shows the formation of a second triad chord  900 B. At left is a planar view  952  of three intersecting starbursts  981 - 983  within a collapsed harmony spiral  951 . At right is a perspective view  954  of the harmony spiral  951  showing the intersections of the  972 - 974  of the starbursts  981 - 983 . 
     In the planar view, intersections among the starbursts are i)  981  to  982  resulting in a first interval  972 , ii)  982  to  983  resulting in a second interval  973 , and iii)  983  to  981  resulting in a third interval  974 . 
     These intervals are shown in the harmony spiral  951  and form a triad chord  971 , for example a triad chord including the notes F-A#-C# in a second minor chord. As will be appreciated by skilled artisans, any triad chord may be constructed as a colored geometric figure within the harmony spiral  951  such that a musician visualizes the chord. 
     Hue variations of the intervals  922 - 924  ( 972 - 974 ) and triad chord  921  ( 971 ) are therefore associated with musical sounds such that a musician learns to “hear” the corresponding musical note combinations before the notes are actually played. Among other things, this “intuition” enables a musician to choose a next note to achieve a desired musical effect when note combination is played. 
       FIG. 9C  shows a composite chord  900 C. Here, multiple triad chords  992 - 995  are displayed in a harmony spiral  991 . A first triad chord  992  includes the notes F#-A-C. A second triad chord  993  includes the notes F-C-A. A third triad chord  994  includes the notes E-A-D. A fourth triad chord includes the notes E-A-C. Where the triad chords have triad hues, the intersection of any two or more of these chords may result in a hue derived from the colors combined at the intersection. 
       FIGS. 10A-B  show exemplary harmony spirals  1000 A-B. In  FIG. 10A , a three dimensional harmony spiral is shown  1000 A. Displayed within the spiral  1001  are three exemplary triad chords  1002 - 1004  that illustrate the visual presentation of triad chords within a spiral harmony construct. Any of the harmony constructions mentioned herein may utilize this three dimensional geometric harmony construct. Notably, any parameterized curve might be used in place of a three dimensional spiral to describe a harmony space. 
     In  FIG. 10B , a two dimensional harmony spiral is shown  1000 B. Displayed within the spiral  1011  are two exemplary triad chords  1012 - 1013  that illustrate the visual presentation of triad chords within a spiral harmony construct. Any of the harmony constructions mentioned herein may utilize this two dimensional geometric harmony construct. Notably, any parameterized curve might be used in place of a two dimensional spiral to describe a harmony space or plane. 
     In  FIG. 10C , a three dimension harmony spiral is shown  1000 C. As see, a plume  1054  emanating from a root note  1056  is shown in the spiral  1052 . Here the plume hue and/or lightness varies along its length with the hue being a washed out hue at an upper octave and a deep hue near the root note, for example a washed out fuchsia at an upper octave and a deep fuchsia near the root note. Any of the harmony constructions mentioned herein may utilize this three dimensional geometric harmony construct. Notably, any parameterized curve might be used in place of a three dimensional spiral to describe a harmony space. 
       FIG. 11  shows a note grid  1100 . The note grid displays musical notes in a horizontal dimension and octaves in a vertical dimension against a dark background  1105 . In various embodiments, the note grid is comparable with or conveys information similar to that of a planar representation of the curved outer layer of a harmony spiral. 
     While various shapes, objects, pictures, or the like might be chosen, here the notes of the note grid are indicated by a geometric figure, in this case a circle  1104 . The note being played may, as here, be indicated by a marker such as a circle within the note. Here, the note being played  1102  is a D note in the fourth octave. 
     As seen in the column of the note being played, the notes are shaded with a light to dark gradient that lightens as the octave increase. Starburst interval hues are shown for all of the notes, behind the notes, which suggests to a musician the next sound to be selected. In each column other than the column of the note being played, frequency of the notes is indicated by note greyscale shading, from light at higher octaves to dark at lower octaves. 
       FIGS. 12A-B  show a note grid similar to that of  FIG. 11  and a corresponding triad chord  1200 A-B. As seen in the note grid of  FIG. 12A , three notes are being played including notes A#-C# in the fourth octave and the note F in the third octave. Here, it is a gray inner cloud  1202  that indicates the note being played. 
     In the harmony spiral  1201  of  FIG. 12B , the notes played are root notes of three starbursts  1281 - 1283 . Intersections of these three starbursts result in three intervals  1272 - 1274  that determine a triad chord  1271 . 
     As mentioned above, embodiments of the present invention provide a means for visualizing musical elements including musical notes, intervals, chords, and composite chords through the use of geometric figures with hue and/or greyscale coloration or shading indicative of the musical sound emulated. Musicians may work at composing, “listening to,” and revising musical works utilizing any of, or a combination of any of, the loti, harmony spiral, and note grid geometric constructs. 
     For example, a computer(s) with display device(s) may display on one or on multiple screens any or all of these geometric constructs. In an embodiment, a computer display presents on a single screen at least one of each of a three dimensional harmony spiral, a note grid corresponding to the harmony spiral, and a lotus formed from an octave of the harmony spiral. 
       FIG. 12C  illustrates transformations to and from staff musical notation  1200 -C. In an embodiment, a computer display presents on a single screen a portion of a musical work  1232  in staff notation and one, several, or all of a lotus  1204 , a harmony parameterized curve  1206 , a second lotus  10 , and a chord type chart  1210 . In some embodiments, a note gird corresponding to the harmony parameterized curve  1206  is included in the display. In an embodiment, the display includes staff notation, a lotus, a harmony parameterized curve with one or more chords formed from normal starbursts, and a note grid corresponding to the harmony parameterized curve. Applicant notes that a “harmony parameterized curve” may be any curve, collection of joined line segments, or the like encircling a point or line multiple times and suitable for conveying the information contained by and in applicant&#39;s applicant&#39;s harmony spiral. 
     In the musical work: i) a first bar  1211  includes a half note E and a quarter note E and the first bar may be represented at least in part by a lotus filled with a triad chord  1231  sounding the note E; ii) a second bar  1212  includes a half note B and a quarter note B and the second bar may be represented at least in part by a lotus filled with a triad chord  1232  sounding the note B; iii) a third bar  1213  includes a dotted quarter note F, a ⅛ note G, a quarter note F and the third bar may be represented at least in part by a lotus filled with triad chords  1233  sounding the notes F and G; and, iv) a fourth bar  1214  includes a dotted half note E and the fourth bar may be represented at least in part by a lotus  1234  filled with a triad chord sounding the note E. 
     The first lotus  1204  provides, among other things, a chord visualization or selection tool. Having constructed a chord  1222 , skilled artisans will recognize that the included pentagon in the form of a star  1224  marks out notes that should not be played together with the triad chord  1222 . The harmony parameterized curve  1206  shows several chords including chords that span multiple octaves; as mentioned above, a corresponding note grid may also be displayed. The second lotus  1208  shows the formation of a triad chord from starbursts. These tools provide means for visualizing, composing, and editing the musical work  1212 . 
     Where the musical work  1212  is being composed, the first lotus  1204  and the harmony parameterized curve may be used to visualize the movement from a first note or chord to a different second note or chord as in the movement between the first and second bars  1211 - 1212 . Chord hues indicative of the sounds of chords of the chord library  1210  may aid in this or related selection(s). 
     In an embodiment, a user begins with a particular note or chord and utilizes geometric figures with particular hues such as notes or triad cords of a harmony parameterized curve to select a movement to a second note or chord. In an embodiment, chords within the harmony parameterized curve are formed from normal starbursts. As the user progresses, a transformation and/or decoding of the geometric figures with particular hues may be used i) to fill in the staff musical notation with the corresponding notes or ii) an associated music player may play the note(s) and/or chord(s). As such, there is a transformation of colored figures with particular hues selected using the tools to music in staff notation. 
     As seen above, visualization of a musical work may include transformations and/or decoding of geometric figures with particular hues presented in a harmony parameterized curve to staff musical notation and vice versa. 
       FIGS. 13A-H  show a rhythm system  1300 A- 1300 H. As seen in rhythm system display of  FIG. 13A , the rhythm may include one or more of a time circle  1302  with peripheral time increments  1304 . The time circle encloses geometric figures such as polygons, for example a polygon  1312  having vertices near, touching, or tangent to the time circle. In some embodiments, plural polygons are superimposed. A time marker  1308  marks a radial path between a time circle center  1306  and a time circle increment or increment boundary  1318 . 
     The time circle  1302  may be simulated or replaced by a continuous tape such a tape formed when the time circle is broken and extended to form a linear element with polygon  1312  vertices  1314  located and spaced to indicate timing. 
     Increments of time  1302  may be quantized such that polygon vertices  1314  sit at only particular points on the time circle, for example in the manner of a snap fit or snap to grid. As skilled artisans will understand, digital computers typically operate in a quantized manner and rational number representations of position on the time circle may therefore provide what is nearly but not actually a continuous representation of time or change of time. 
     Tempo is typically measured in Beats Per Minute (“BPM”) and a tempo control  1320  may be varied over time which allows a user to set a particular tempo, for example 125, and subsequently adjust this tempo as the rhythm system  1300 A runs. 
     In various embodiments, a circumference of or indicated on the time circle  1302  will be equal to a certain musical distance, for example a measure of music such a measure of 16 beats. Alternatively, the time circle circumference may indicate a bar of music, for example a bar of 4 beats. Here, a point in the rhythm layers may be chosen for attachment of a rhythm driver to the time circle to relate distance to beats providing a particular ration of distance to beats. 
     An exemplary quantization provides that between any two beats, time may be divided by a quantization factor. This factor will be a product of primes—i.e. 2^n 1 *3^n 2 *5^n 3  . . . where n is 0 . . . m and where m is an integer. 
     Where an embodiment lacks quantization, playback may occur as with an effectively continuous tape where quantization intervals are small enough to mimic continuous playback. 
     In order to support song structure, time circles may be nested as in a tree like structure. For example, a large circle can represent a movement and can contain an integral number of sub-circles. These sub-circles can also contain sub-sub-circles and so on to provide a desired number of levels. This tree structure may be controlled with a layer interface to create sub-layers. At a selected point in the structure of sub-layers, a beat driver is attached to i) connect the BPM setting, ii) distance around the circles, iii) set the speed of time, and iv) determine the point where quantization will be applied. With these features, a rhythm system may represent a single movement of music, for example a movement of music with a single bpm, quantization, and rhythm structure. More complex musical representations may utilize an orchestration system that connects multiple musical movements into more complex systems and may be represented as a graph. 
     Linear representations of time such as a note ribbon are similarly divided by quantization and rhythm structure. In an embodiment a note ribbon represents both continuous positioning, without snap to, and quantized positions with snap to such that a user selects one or the other. 
       FIGS. 13B-H  illustrate methods of constructing a rhythm for a musical work or a portion of a musical work  1300 B-H. 
     In various embodiments, a library of geometric shapes such as planar geometric shapes including one or more of polygons with a plurality of sides such as a triangle, square, pentagon, hexagon and the like is provided. These shapes include ones having vertices such as quantity n vertices where each vertex is associated with a musical voice. 
       FIG. 13B  shows a rhythmic geometric shape in the form of a square  1314  having four vertices  1312 . 
     The rhythm system may be used to compose one or multiple song layers. For example, a first song layer is composed that includes four rhythmic verses wherein each verse includes four phrase sets and is represented by four phrase set circles embedded in a verse circle such that each phrase set includes four phrases and is represented by four phrase circles embedded in a phrase set circle. 
       FIG. 13C  illustrates a musical phrase using a phrase circle. It shows a shape circle  1316  and a geometric shape in the form of a square  1314  within the phrase circle. Vertices of the square  1312  are proximate the shape circle circumference. 
       FIG. 13D  illustrates a musical phrase set using a phrase set circle. It shows a phrase set circle  1330  with four shape circles  1316 ,  1320 ,  1324 ,  1328  within. Respective geometric shapes include a square  1314  within the first shape circle  1316 , a triangle  1318  within the second shape circle  1320 , a square  1322  within the third shape circle  1324 , and a pentagon  1326  within the fourth shape circle  1328 . 
       FIG. 13E  illustrates a musical verse using a verse circle. It shows a verse circle  1340  with four phrase set circles  1331 - 1334  within. 
       FIG. 13  F illustrates a song layer using a song layer circle. It shows a first song layer circle  1350  with four verse circles  1341 - 1344  therein. As indicated, each verse circle includes four phrase set circles  1330  and each phrase set circle includes four shape circles  1316 . 
     Each phrase includes four beats and is represented by a selected library shape (e.g.  1314 ) embedded in a shape circle. In a series of steps (i) verses are ordered in a selected verse sequence v 1 -v 4 , (ii) phrase sets are ordered within each verse in a selected verse-phrase set sequence ps 1 -ps 4 , (iii) phrases within each phrase set are ordered in a selected verse-phrase set-phrase sequence p 1 -p 4 , (iv) vertices within each phrase are ordered in a selected verse-phrase set-phrase-vertex sequence vx 1 -vxn. 
     The song layer rhythm may be played by sounding the voice of each vertex in order, beginning with (v 1 , ps 1 , p 1 , vx 1 ) and ending with (v 4 , ps 4 , p 4 , vxn). 
     As seen in  FIG. 13G , multiple song layers may be used to compose the rhythm for a more complex musical work. In particular, first, second and third song layers  1351 - 1353  may collectively represent a musical work where the song layers are played in an order chosen by the user. 
     In the above rhythm composition method, the manner of composing a rhythm may further comprise the step of using the distance between adjacent vertices (see e.g., distance  1313  of  FIG. 13B ) to indicate the time between sounding the voices of the adjacent vertices. 
     And, in the above method, the manner of composing a rhythm may further comprise the step of sounding the voice of a vertex for a time period indicated at least in part by an out-of-plane projection extending from the vertex. See for example  FIG. 13  H which includes a planar geometric shape, here a triangle  1380  within a shape circle  1316  and an out-of-plane projection  1382  extending from a vertex  1381  of the triangle. 
       FIG. 14  shows a loop selector  1400  for use with the rhythm system  1300 A-H. The loop selector  1400  may be a rhythm system mode providing a display of one or more rhythm system elements  1300 A-H. A recording interface with the ability to play over the existing rhythm system may be attached thereto. Such recorded audio, or midi may be mapped or transformed and mapped to a loop for creating shapes with a shape selector which may be saved by name, with copy/cut/paste functions, to a time scale in the rhythm system. 
     Loop selection methods provide for visualization of a rhythmic structure of a musical composition on a touch screen device display  1490  such as a computer display, tablet computer display, or the like. In one such method, the steps include i) providing a sound recording of a musical work, the musical work having an underlying rhythm identifiable by events in the recording, ii) transforming the sound recording into an event recording  1402  that chronologically marks the initiation of each event  1404  such that the time span between successive events  1405  may be compared, iii) selecting a portion of the recording  1406  including a sequence of events  1411 - 1417 , iv) displaying a shape circle  1408 , v) mapping the events in the sequence of events  1411 - 1417  to corresponding locations around the perimeter of a shape circle such that the mapped events take the same order around the shape circle perimeter as in the sequence, locations of adjacent mapped events are indicative of the time span between the corresponding events in the sequence of events, and the sum of the time spans between mapped events is indicative of the time span of the selected recording portion, and vi) visualizing the rhythmic structure of the musical composition by fitting one or more polygons  1420 ,  1430  to the mapped events such that polygon vertices coincide with mapped events. 
     The above method may further comprise wherein first and second polygons  1420 ,  1430  are fitted to first and second sets of mapped events and the touch screen  1490  is used to rotate the first polygon  1420  relative to the second polygon  1430  to vary the timing between mapped events. 
     The above method may further comprise wherein timing changes made with the touch screen  1490  result in corresponding timing changes in the event recording  1402 . 
       FIGS. 15A-D  show a graph methods of storing and reassembling musical works and/or portions of musical works  1500 A-D. 
     In particular, a method of mixing multiple musical works into continuous playable streams comprises the steps of: i) providing digital data storage accessible to a network shared by a plurality of users, see e.g., musical works stored in nodes  1 - 8  of network  1501  of  FIG. 15A ; ii) in the data storage, constructing a directed graph having a set of nodes and a set of edges, see e.g., directed graph  1500 A; iii) wherein each node contains a musical work and no two nodes contain the same musical work, iv) wherein each user has access to a user specific group of plural nodes, each pair of nodes e.g. being interconnected by an edge, see e.g. nodes  1500 B of  FIG. 15B  accessible to user  1 , nodes  1500 C of  FIG. 15C  accessible to user  2 , and exemplary edges  1512 - 1526 - 1568  (interconnecting nodes  1 - 2 - 6 - 8 ),  1552 - 1527 - 1578  (interconnecting nodes  5 - 2 - 7 - 8 ) interconnecting nodes of the first and second users v) wherein each edge identifies instructions used to mix the musical works contained by the two nodes the edge interconnects, and vi) wherein musical works are mixed irrespective of user access rights to create a mixed different from the musical work found in any one node. 
     As seen in  FIG. 15D , an exemplary mixed work includes content of nodes  5 - 2 - 6 . Here, Mix  1  includes i) a leading portion of node  5 , ii) a mix of a trailing portion of node  5  and a leading portion of node  2 , iii) a central portion of node  2 , iv) a mix of a trailing portion of node  2  and a leading portion of node  6 , and v) a trailing portion of node  6 . As mentioned above edges provide, among other things, an indication of overlapping node portions and which node portion(s) will be included and/or played in the overlap. 
     While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not limitation. It will be apparent to those skilled in the art that various changes in the form and details can be made without departing from the spirit and scope of the invention. As such, the breadth and scope of the present invention should not be limited by the above-described exemplary embodiments, but should be defined only in accordance with the following claims and equivalents thereof.