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Color-Encoded Music Scores: What Visual Communication Can Do for Music Reading Author(s): Celso Wilmer Source: Leonardo, Vol. 28, No. 2 (1995), pp. 129-136Published by: The MIT PressStable URL: http://www.jstor.org/stable/1576134Accessed: 03-07-2015 05:46 UTC

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GENERAL ARTICLE

Color-Encoded Music Scores: What Visual Communication Can Do for Music Reading

Celso Wilmer

N ot long ago, a group of adventurous young people-three girls and a boy-accepted my invitation to play a Bach chorale together on the piano. Why adventurous? Be- cause none of them could play the piano or read music. Two hours later, the whole piece was played, from start to finish, by these four musical novices.

For this to be possible, the traditional musical score had to be transformed to better communicate the music. Estab- lished early in the present millennium, traditional musical notation was clearly not meant by its creators-Christian monks transcribing sacred music-to be accessible to a wide public. So the system developed, becoming ever more abbre- viated and complex, always aiming at faithfulness to the com- position, but entirely neglecting the other half of the commu- nicative process-namely, the reading, or decoding, of this complex notation. Now, however, as the end of the millennium draws near, two factors make the present time particularly ripe for a critique of the music-reading process: the ad- vent of visual communication as a field of study and Piaget's pedagogical theory.

The purpose of this article is to present the genesis of a new musical notation system geared to expanding the music- literate public-a self-evident musical score. My intention is to encourage readers to try this bold experiment for themselves-that is, to try to play Mozart's Sonata XVI or Satie's "Gymnopedies" while reading scores written with this musical notation system.

THE SPECIFICITY OF MUSIC READING: TIME AGAINST TIME To say that traditional scores do not aim at maximal expansion of the reading public is not to say that it is in anyone's interest that they should remain hermetic. Clearly, the idea of a truly reader-friendly score should appeal to everyone-composers, publishers, musicians, teachers, instrument-makers, students and interested laypersons. But if we were to ask a conductor how he feels about changing the musical notation system, he might answer, with just a hint of irritation: "Well, I learned music from traditional scores. Why should the reading public be any bigger than it is? After all, in music as in anything else,

Celso Wilmer (visual communicator, mathematician, musician, educator), Departamento de Artes, Pontificia Universidade Catolica, Rua Marques de Sao Vicente, 225, 22451-041 Rio deJaneiro, Brazil. Translated by Paulo Henriques Britto.

Received 21 January 1993.

ABSTRACT

Visual communication and Piaget's pedagogical theory can be applied to music reading with interesting results. The purpose of the author's project is to make musical scores easier to read and play and thus facilitate the teaching of music. This article de- ~---:L-- L:-- ---..;.: ...... t.....'J

some people have the knack, and scriues nls soluiorL a music-writ- others do not." ing system based on a Cartesian others

doubt not.

traditionalscrepresentation of sound duration No doubt the traditional score and color-encoded representation has achieved the maximum ex- of pitch. One of the advantages pansion of its public. The point of the system, which he calls is, however, that the potential Rainbow Scores, is that it enables

mre fo mui redn -h one to create videos of musical market for music reading-the scores that move along before number of people who would be the student's eyes at metronome- able to read music written in an controlled speed. improved system aiming at maximum communication-is much larger.

What, then, would be the rationale for self-evident notation? Precisely the specificity of music reading. The reader of a score cannot afford to break off repeatedly in order to figure out the meaning of a new symbol, for this disrupts the flow of the music and destroys the tune. It is the accumula- tion of these frustrating interruptions that often discourages beginners.

Music reading is one context in which visual communica- tors should clearly do all that is possible to save users' time. The communicator's task is to minimize the time span between sighting a symbol and playing the note it stands for on the instrument: hence, the need for self-evidence.

THE ELEMENTS OF MUSIC SCORES To illustrate the improvements behind a self-evident score, such as the one used by my young friends, let us take the following passage from Mozart's Sonata XVI (1788) [1] and show how this can be done (Fig. 1). Anything that a composer can play on the piano and record on paper is essen- tially, like any common song, a set of musical notes in tempo- ral succession. Each note is characterized by its pitch, which tells us which piano key was pressed, and its duration, which tells us how long (proportionally speaking) the key in question was held.

Fig. 1. Passage from Mozart's Sonata XVI, shown in traditional notation.

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LEONARDO, Vol. 28, No. 2, pp. 1129-136, 1995 ? 1995 ISAST This content downloaded from 148.206.159.132 on Fri, 03 Jul 2015 05:46:31 UTC

All use subject to JSTOR Terms and Conditions

Except for intensity directions, practi- cally all the graphic elements in a musical score relate to the pitch and the duration of notes. Let us begin with pitch.

Self-Evident Representation of Pitch The first question a layperson might ask about Fig. 1 is: "Which key should I press?"

To show clearly the correspondence between the lines and spaces in the staff (where the notes are placed) and the piano keys, the score need only represent a keyboard, with the same lines as those in the staff marked on it [2]. (This correspondence is brought home in Fig. 2, which will be explained in due time. As examination of Fig. 2 shows, the system employs exactly the same staff lines as those used in the traditional system.)

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Thus the F and G clef signs may be omitted, since the correspondence is now evident. The brace linking the left- and right-hand staves should be replaced by a symbol that more transpar- ently represents the possibility of moving the two apart so that additional lines may be placed between them. In the new system a stylized spring will be used instead.

The piano can be seen as the most complete of all instruments-in the sense that its range of pitches from the lowest to the highest contains those of all other instruments. For this reason, I have given the piano the privilege of being pictured in my score. If, on the piano, the lower notes are on the left and the higher ones on the right, of course the score should reflect this fact. The reason the traditional system does not

Fig. 2. The Rain- drop score for the passage from Mozart's Sonata XVI pictured in Fig. 1. (a) The notation is written according to the new system. (b) The keyboard diagram with the same lines as the staff shows the correspondence between notes and keys. (c) The correspondence is the same as that in the traditional system, which allows immediate conversion of a score from the new system to the old, and vice versa.

do so is that it was devised with the intention of recording vocal music, long before the piano had been invented. But, given the pressing need for making readers' response to the score as prompt as possible, the representation of pitch from bottom to top is anachronistic and unjustifiable [3].

The staff should be vertical rather than horizontal, so that pitch variation, which is perpendicular to it, may be represented analogously to its arrangement on the keyboard. This means that the musical text can progress either from top to bottom or from bottom to top, in either case accompanied by the keyboard diagram.

But we will make our choice only after the criteria involved are better un- derstood. Although at first it would seem that just about anyone would fa- vor a top-bottom direction, caution is required before accepting the dictates of common sense unfounded on pedagogical sense.

Self-Evident Duration Symbols Since there is a direct correspondence between notes and keys, the musician knows from the start which keys to press. Now he or she must be told for how long each key must be pressed. The traditional notation of oval symbols with various kinds of stems provides this information, but training is required before one can decode the text fast enough to play as one reads. In fact, these symbols were devised for fast writing-not for fast reading.

Imagine what the result would have been if Mozart's fingers did not touch a keyboard, but rather touched a sort of wax-covered conveyor belt moving to- wards or away from him. Every touch of Mozart's fingers would have left a track in the wax: the pitch of each note would be shown in the location of the corresponding track on the horizontal axis, whereas the note's duration would sim- ply correspond to the track's length.

REQUIEM FOR AN UNWRITEN OPUS The resort to an imaginary conveyor belt should not deceive us as to the real con- venience of this form of representing duration. For if in place of the wax-covered belt we have a paper reel and instead of fingers we have pens activated by keys, we get an automatic way to record music on paper. Since the complexity of such a mechanism surely does not exceed that of a piano, it follows that this method has

130 Wilmer, Color-Encoded Music Scores

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Fig. 3. Levels of abstraction of an idea, according to Piaget.

been technologically feasible since at least the early eighteenth century, when the piano was invented.

At that time, the theoretical basis for the representation of time through length had recently been established, with epochal consequences for science. It was Ren6 Descartes (1596-1650) who, with the creation of analytic geometry, introduced this novel approach, which opened up a whole new world of possibilities for mathematics, physics and many other fields-but not music. This is an ironic omission, for it is precisely in music that subjection to the inflexible passage of time requires a notation al- lowing fast reading.

If musicians had realized the possibility of representing duration by means of the Cartesian method instead of relying on an abstract convention, automatic recording would have been invented long ago. Rather than interrupting the flow of their ideas to transcribe each passage they conceived, composer-pianists since Mozart might have been able to write much more than they actually did [4].

PIAGET AND MUSIC TEACHING Let us now turn to pedagogy to find a criterion for choosing the most adequate direction-top-bottom or bottom-top-for reading a musical text, as well as to find corroboration for the de- cisions we have already made.

As a result of the in-depth research into cognitive development in children carried out by Jean Piaget (1896-1980), mathematical education has undergone a major revolution in recent years. One consequence of this revolution is the present practice of making abundant use of concrete materials and graphic resources as necessary aids in the process of abstraction of mathematical concepts [5]. The same must be accom- plished for teaching music. Let me sum up Piaget's thesis in a few words: There is a natural order in the abstraction of any new idea by a learner (in this case,

musical ideas such as pitch and duration) from one level to the next, on each of which the idea must be elabo- rated before progress is possible:

concrete -> graphic -, conceptual

It makes sense that a new idea should be more readily understandable on lower levels. On the concrete level, students rely not only on reasoning (an at- tribute of the conceptual level) but also on the judgment of the eye (graphic level) and particularly on touch, changes in perspective and familiarity with objects-which are specific to the concrete level (Fig. 3).

This is why so many people find it dif- ficult to read traditional scores: in them, all the symbols are placed on the most abstract level, the conceptual. All the conventions used in traditional scores are beyond the scope of the visual. For this reason I have decided to bring the representation of pitch and duration down to the graphic level, which is accessible even to the self-taught.

It follows that a pedagogically ideal score would be one that, short of reach- ing the concrete level-which would amount to the composer at the piano showing how to play the piece in question-would remain on the graphic level and, if possible, allude to some equivalent concrete experience of the reader's.

Upon closer examination, I found that the conveyor-belt image suggested the appropriate shapes of the symbols to be used in this ideal score because it is a vivid representation of what the composer plays on the piano. In the conveyor-belt image, each track in the wax starts with a round shape (where the finger touches the wax) that, after a while, narrows and vanishes when the finger is lifted. The result is a drop-shaped figure. So, like the tracks in the wax, I de-

sounds

colors COLOR lf CONCLUSION CODE 1Q ABOUT COLORS J

Fig. 5. Stages in the pedagogic process of representing musical sounds by means of colors.

cided that the symbols should resemble drops-falling drops.

So, applying this criterion to the two possible directions to follow in reading the score-top-bottom or bottom-top- one can conclude that it is much easier to visualize drop-shaped notes falling directly on the keyboard diagram or on the piano keyboard right below them. That is, the logic of the system springs into view when we imagine, in place of the composer's fingers, a sort of cascade made up of drops, each of which presses a given key for a period of time corresponding to the note's duration.

I believe that the advantage of this analogy over the conveyor-belt image is that it demonstrates a rationale for reading music from bottom to top. For, if, according to the Bauhaus school of design, form follows function and the function of the score is above all pedagogical (in my opinion), then the best form is the one following the logic most easily assimilable by the public. The idea of falling drops evokes a vivid mental image that is consistent with Piaget's concrete level (corresponding to the composer playing the piece). The reader needs only to grasp that (1) as they fall, large drops press the piano keys for a long time and short drops for a short time, and (2) the positions of the drops move to the left or to the right, equivalent to the positions of the piano keys themselves. So the reader's responses are ready.

Round Sharp Flat EXAMPLE OF A RAINDROP Drop Drop Drop SCORE

Referring to the Raindrop score of the passage from Mozart's Sonata XVI (see Fig. 2) one can determine the following:

1. The positions of the symbols show which key to play for each note, since Tone Sharped lbne the same lines appear in the keyboard diagram and in the staff.

Fig. 4. Musical notes in the new system. 2. The number of beats to each mea- Each note of the scale in use is represented sure (3) and the duration (length) of by a round drop. Accidental alterations each beat are shown graphically, instead (sharps and flats) that raise or lower the note by a semitone are represented by the indicated by the symbol sharp drop and flat drop. With this redefi- 3. The staff is a Cartesian axis, divided nition of the concepts of sharp and flat, the in numbered measures of equal length. new score is the same for any key. It is also subdivided into beats or other

Wilmer, Color-Encoded Music Scores 131


Dmin FMi, Avm c Mj Z ma Mi BC nM (a)

(b)

Fig. 6. (a) The harmonic neighborhood of C major consists of the chords made up of the notes in the scale of C major (C, D, E, F, G, A, B). (b) When these notes are colored in thirds (C, E, G, etc.), this color method expresses the concept of consonance in terms of relationships of proximity between colors. This is done at first with a base key-in the major mode, C major. (c) The solution is gen- eralized for any key, replacing each chord with the harmonic function it represents. Thus, re- specting the way the chords are structured, the color code is compatible with key transposition.

(c)

fractions, so that the duration of any two notes can be compared visually.

4. Thus, there is no need for ties join- ing two note symbols to show that the duration of a note should be extended. The system also dispenses with any other special duration symbols, such as dotted notes, triplets, appoggiaturas, etc.

5. No rest symbols are needed: silence (no sound) is represented by empty space (no symbol).

EASY-TO-TRANSPOSE SCORES Key transposition is the process by which the key of a musical piece is changed in order to adapt it to a singer's register, to allow more convenient fingering on a different instrument or to otherwise adapt the piece to musicians' needs.

Generally speaking, any given compo- sition will tend to predominantly use the seven notes in the scale of the key in which it is written, other notes being un- derstood as alterations of these seven (accidentals). This is reflected in the design of the piano keyboard: for the key of C major, the full scale is played on the white keys, while the accidentals are played on the black keys. On the piano, fingering is easiest in C major. On the guitar, however, A major is the most convenient key; in it the bass line is played mostly on open strings.

Up to a certain point, the traditional system acknowledges the frequent need to effect key transposition. When the piece uses only the notes in the scale of its key, all that need be done in order to transpose it is to raise or lower all the notes on the staff the same number of lines or spaces.

But when the piece employs accidentals, transposition in the traditional system requires a complete rewriting of the text. This is so because accidentals can be indicated differently in the two keys involved. For example, the seventh step in C major is B, whereas in G major it is F#-hence the sharp sign in the key sig- nature of G major. So this seventh step lowered by one semitone is, in C major, B flat (indicated on the staff by t), and, in G major, natural F (on the staff, #).

It is this use of different symbols (in this case, 1 and #) that prevents sight transposition when the musician must play in a key other than the one in the score he or she is reading.

To overcome this problem, accidentals must be treated as functions, in the mathematical sense of the term. The sharping function raises the note by one semitone and the flatting function lowers



it by one semitone, regardless of whether the original note is # or 6, or whether it refers to a white or a black key.

Thus the seventh step lowered by one semitone will be equally represented in the two keys, and indeed in any other, by a flat drop (Fig. 4) (in a color score, by a red flat drop). This makes it possible to produce an easy-to-transpose score. In it, the notes, represented by drops, are printed on a transparent sheet of paper, while the staff lines are on an opaque sheet behind it. By changing the relative positions of the two, we automatically get a transposition of the piece in any key- something that musicians have always longed for, but that was quite unfeasible in the traditional system.

COLOR-ENCODED SCORES As a teaching resource, colors make it easier to apprehend Gestalten in music scores, highlighting the relative values of the various features. Of all the different ways colors can be used-to signal repeating passages, the sections of a song, the parts of a choral, etc.-I believe the most interesting is in notes and chords.

On the surface level, the use of color in notes, together with verticalization of the staff, reinforces the positional representation of pitch, making it easy to identify the key corresponding to each note. On a deeper and more original level, color provides a visual model for the teaching of certain relationships between sounds that are far from obvious in the field of harmony. A schema of the three stages in the development of this model is shown in Fig. 5.

The first stage in the model's development establishes the correspondence between notes and colors. Here one must be careful, for if we are to reach conclusions concerning relationships between sounds, it is necessary at this stage to choose colors that are also related to one another [6]. (The second stage refers to the observation of the colors, for instance, in a particular chord, followed by conclusions that can be drawn from them-such as, blue, purple and magenta are neighboring colors. This leads to an initial conjecture and later to a conclusion in terms of music such as "this chord.")

The basic relationship between colors is expressed by their proximity in the rainbow or in Newton's disk (the color spectrum in a circular shape). The following circular sequence of colors should be visually memorized by stu-

1

(a)

(b) X Fig. 7. Two examples of color-encoded scores. (a) The passage from Mozart's Sonata XVI. (b) A passage near the beginning of Satie's "Gymnopedie 1." An examination of the colors shows us that the top example is a classical piece (with the initial chord [here, the tonic] containing the first three colors-blue, purple and magenta-of the system I propose); the bottom example, a modern piece (the initial chord contains four colors-yellow, green, blue and purple; yellow replaces blue [the tonic's color] in the bass).

The chords pictured in Fig. 6a consti- tute the harmonic neighborhood of a piece written in C major. When I applied the colors of the sequence above to the chords in Fig. 6a, I obtained a color en- coding for C major (which is explained in detail in the caption of Fig. 6). The visual result in notation is shown in Fig. 6b. We can see that each note in the scale (horizontal axis) lends the color it is assigned in this key to the whole chord built on it (vertical axis). This

dents learning the system I propose: blue -o purple -> magenta -> red -> orange -> yellow -> green -> (blue).

As for sounds, relationships of "near- ness" are expressed by the notion of consonance-their ability to "sound good" when played simultaneously in a chord. Those chords traditionally held to be definitive of consonance in West- ern music may be either major or minor, and one of each kind is built upon each of the 12 existing tones.



Trois Gymnopedies (1)

Fig. 8. Example of a Raindrop Score of the first 16 bars in the andante of Mozart's Sonata XVI. Even in black and white, the note- key correspondence is made clear by the piano keyboard diagram.

Fig. 9. Example of a Rainbow Score: Satie's "Gymnopedie 1." In this example, the color code was applied not only to notes but also to chords built on notes. Thus, the background color of the left- hand staff repeats the bass color, while the background of the right- hand staff is in the color of the chord as a whole, which is based on the chord's keynote. An examination of these colors and their relationships shows important aspects of chords and their harmonic relationships.

color appears in the spaces of the right- hand staff.

On the basis of this particular example, I devised a color code for any key. Notes were replaced by the steps in the scale, and chords by harmonic functions. We might say that a harmonic function is the place occupied by a chord within a musical piece. Let us consider the tonic, the subdominant and the dominant. For instance, in the

Table 1. Key for adding color to color-encoded scores.

Step 1 (and 8)

3 5 7 2 4 6

Harmonic Function I tonic III mediant V dominant VII subtonic II supertonic IV subdominant VI submediant

key of C major the chord that occupies the place of the tonic is C major (C-E- G), while F major (F-A-C) is the place of the subdominant and G major (G-B-D) is that of the dominant [7] (Figs 6b and 6c). (In mathematical terms, steps and harmonic functions are functions of the key, and for each key they are actualized as notes and chords.)

At this point, to understand better the color model adopted in this project (Fig. 6c), the reader is invited to apply colors to Fig. 6 according to the instruc- tions in Table 1. In Fig. 6c, I recommend the use of felt-point pens to color in the small circles, and the use of color pen- cils to color the background rectangles.

For Fig. 6b, after the circles on the horizontal axis are colored, note that the circles on the staff above should be given the same color as the corresponding circle on the horizontal axis below them. (Note that after step 7, the sequence returns to step 2.) Figure 6b is

an application of the color model to the C major key-therefore the colors correspond to those in Fig. 6c. Figure 6a shows how this method of coloring by thirds applies to the piano in the case of C major, therefore the colors for the circles are those of Fig. 6b (whether or not the note has an alteration-thus both F and F# are yellow).

Since this color code respects the way chords are structured, it is compatible with key transposition. This means that, even when colors are used, the score re- mains the same for any key. This is so because colors are not assigned to particular notes or chords, but rather to the steps and harmonic functions they stand for. The notes and chords of a key re- ceive color as a consequence of the steps and harmonic functions that they oc- cupy in each particular score. In any key, the color blue represents the tonic- and also stands for the key. For example, in Fig. 7, we can conclude that the keys


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are G major (Fig. 7a) and D major (Fig. 7b) because the tones in blue are 6 and 0, respectively.

EXAMPLES OF COLOR- ENCODED SCORES The reader is again invited to apply color to the examples of Rainbow Scores and their respective keyboards shown in Fig. 7. The letters that appear in these scores correspond to the colors previ- ously discussed: B stands for blue; 0, orange; P, purple; Y, yellow; M, magenta; G, green; and R, red.

* A passage from Mozart's Sonata XVI is shown in Fig. 7a. (The Raindrop Score of this passage is shown in Fig. 8.) The colors indicate the following: 1. The melody begins on step 3 (purple) of the tonic, resting on step 1 (blue). 2. Background colors (blue-magenta-blue) indicate the tonic-dominant-tonic harmonic movement. 3. The tonic chord is complete (steps 1-3-5; blue-purple-magenta); while in the dominant chord (magenta-red-orange) step 3 (red) is missing and step 7 (yellow) has been added. 4. The tonic is in its root position- from low to high we have steps 1-3-5 (blue-purple-magenta).

* A passage from Satie's "Gymnop6die 1" (1887) [8] is shown in Fig. 7b and in Fig. 9.

The common procedure I have adopted is to give the color of the bass (the lowest note) to the left- hand staff and the color of the chord to the right-hand staff.

It should be observed that this piece begins outside (yellow-green background colors) the tonic, arriv- ing at it only in the second measure (blue-purple background). The chords used here, unlike classical chords (three colors), result from the combination of neighboring chords, with four colors: for instance, G maj + B min (yellow-green- blue-purple in this key).

This example shows that the color code can also be applied to contem- porary harmony, which arose in the late nineteenth century with Debussy, Ravel and others. The concept of consonance was expanded, and a perfect chord was no longer defined as one that is major or mi- nor, but as one that is a combination of two neighbors in the major-minor

Fig. 10. A triad of notes in the G major scale (G-B-D#) is represented in every system discussed in this article, illustrating the five improvements in music reading brought about by the new musical notation system: (1) representation of duration by a Cartesian system; (2) representation of accidental alterations by a functional system; (3) representation of melody and chords by a color-encoded system; (4) teaching of music reading by a Piagetian system; (5) dynamic music reading, introduced by the possibility of a video music score [11].

sequence. The new chords-maj + min, min + maj, maj + min + maj, etc.-came to express new moods, paving the way for the chords used in jazz, bossa nova and contempo- rary music. I believe this color coding is adequate for any musical piece-classical or popular, old or modern.

* I have used the example of Stevie Nicks's "Sara" (1979) [9] in lectures to test whether our color code makes sense for untrained ears. The following three combinations of bass (left hand) and chord (right hand) were

played in some order (without men- tioning their names): F-F maj, F-G maj, F-A min (where A min = A + C + E); the audience is invited to ar- range them as to consonance. Most of the people gave the correct answer. Next, I asked which combination should correspond to each of these pairs of colors for bass and chord (which I also presented in random order): blue-purple, blue- orange and blue-blue. Again, the majority of people answered cor- rectly: the most consonant combination (F-F major) was related to the



closest colors (blue-purple), and the most dissonant combination (F-G major) to the most contrasting pair of colors (blue-orange).

ADHESIVE DROPS The use of color allows an additional resource for immediate identification of the key to be played for a given note in the score: colored notes made of adhesive paper. If a student using a score no- tated with this system glues color paper notes onto the piano keys-following the keyboard diagram-his or her eyes can move directly from the score to the instrument, skipping the diagram. (The same can be done on a guitar or other stringed instruments.)

CONCLUSION AND FINAL EXAMPLES This system of music writing is called Raindrop Scores, in its black-and-white version, and Rainbow Scores in its color version. This project originated in my study (as a teacher of mathematics and a student of visual communication at the Pontifical Catholic University of Rio de Janeiro-PUC) entitled "O quadro- negro de Matematica" ("The Mathemat- ics Blackboard"), an analysis of visual or- ganization of the blackboard in terms of how to use text, figures, colors, etc. on the blackboard to communicate mathematical ideas more efficiently.

The judicious use of color proposed in the blackboard study suggested the same treatment for musical scores, which was the subject of a term paper I wrote and presented for the visual communication course I was taking, "Cores no ensino de Musica" ("Color in Music Teaching"), supervised, as was the ear- lier study, by Ana Maria Hirsch at PUC's Art Department.

It was only later that I acquired an

overall view of the specificity of music reading and the urgent need to prompt immediate responses from readers. This led to the project for my notation system. This article is a summary of the project, which I have described at greater length in "Partituras de Arco-Iris-a genese de uma escrita musical auto-evidente" (Rainbow Scores-The Genesis of a Self- Evident Music Writing) [10].

The resulting work, then, stands at the crossroads of music, pedagogy, visual communication and mathematics, and what it boils down to is: anyone should be able to read a score. Anyone can play Satie's "Gymnopedie 1." The final examples, shown in Figs 8 and 9, are offered to all adventurous readers.

Finally, I would like to present the reader a single diagram of the synthesis of the features of the music writing system discussed here. Through this diagram, the reader can gain an idea of other possibilities for systems that com- bine some of these features (Fig. 10).

Acknowledgments Clarice Johnson kindly offered me her home and her friendship when I was living abroad. Both were special, and they made Rainbow Scores not only possible but also a pleasure to work on. Rejane Spitz is a dear friend who iinspires me with her enthusiasm.

The editors of Leonardo were kind to offer me a chance to present this project in their journal, for which I thank them. I also thank Cristiana and Luisa.

References and Notes 1. W.A. Mozart, Piano Sonatas (score) (London: Augener, n.d.).

2. The keyboard diagram that appears on the score does not imply that it is meant only for the piano. The score resembles a traditional score in that it can be used with any melodic or harmonic instrument. A diagram representing the fingerboard of a guitar or violinl, for example, could appear instead. In a generic score, the piano keyboard is only an additional feature, chosen not only because the piano is such an important instrument for composers and audiences but also because it is one of the few instruments orn which the tones are placed in a lin- ear progression from bass to treble.

3. In A Soprano on Her Head (Moab, UT: Real People

Press, 1982), Eloise Ristad, all American therapist who specialized in musicians' difficulties, wrote that some of her students could make sense out of traditional scores only after rotating them so that the notes stood exactly above the keys-that is, verticalizing the staff, precisely as I propose.

4. Techniques for recording traditional scores automatically have receintly beern designed. However, because of traditional duration symbols, computer memory is needed: the duration of each symbol can only be indicated after its total relative time has beeni calculated. The mechanical recording system proposed here could have a vastly larger public, because of its much lower cost.

5. See, for instance, "Modelos na aprendizagem da matematica" ("Models in the Learning of Math- ematics"), my master's thesis in mathematics, supervised by Aristides Camargos Barreto at PUC's Math- ematics Department (1976).

6. In mathematical terms, we could say that there should be not only a one-to-one correspondence between notes and colors but also isomorphism between the two sets, so that relationships of proximity in one would correspond to their counterparts in the other.

7. The theory of harmonic functionis describes the chord according to its furnction in a given musical piece arnd not in isolation, as it tends to be treated in traditional music teaching. According to Koellreutter, "The theory of harmonic functions [was] created by Hugo Riemann in the late nineteenth century (1893), developed and perfected by Max Reger and Hermann Grabher, as an extension of step harmony theory [i.e. harmony structured according to the steps of the scale], the only one then in use. ..." Koellreutter observes: "This seems to the author of the present work an excellent resource to use in place of anachronistic or obsolete methods still in use." See H.J. Koellreuter, Harmonia funcional (Sao Paulo: Ricordi Brasileira, 1978).

8. E. Satie, Three Gymnopedies (score) (G. Schirmer, 1969).

9. S. Nicks, "Sara" (score) (Welsh Witch Music, Home Box Office, 1982), from Fleetwood Mac Deluxe Anthology (New York: Warner Bros., n.d.).

10. C. Wilmer, unpublished manuscript written in 1987.

11. A video score is a common videotape that ex- hibits a music score written not in the traditional system, but in a Cartesian system (a necessary con- dition for it). It moves before the student's eyes at one of a few metronome-corntrolled speeds (very slow, slow, regular), so that it may fit the student's current needs. It also includes the possibility of the student's simultaneously listening to the music of that score. A prototype of a Rainbow Scores video score was presented to the public at the 1993 Mostra Atlantic de Realidade Virtual (Atlantic Vir- tual Reality Exhibition).



Article Contentsp. 129p. 130p. 131p. 132p. 133p. 134p. 135p. 136

Issue Table of ContentsLeonardo, Vol. 28, No. 2, 1995Front Matter [pp. 98 - 148]Gateway [pp. 81 - 84]The Leonardo GalleryArt as Signal: Inside the Loop [pp. 85 - 92]

Color PlatesArtists' ArticlesAudio Jackets and Other Electroacoustic Clothes [pp. 93 - 97]"She Loves It, She Loves It Not: Women and Technology", an Interactive CD-ROM [pp. 99 - 104]

Semiotic Variety in Digital Video Imagery: The Case of "Maxwell's Demon" [pp. 105 - 111]Programmed Graphics in Computer Art and Animation [pp. 113 - 121]Intuitive Three-Dimensional Sketching in Digital Space: The Synthesis of the Genetic Code for Buildings/Organisms [pp. 123 - 127]Color-Encoded Music Scores: What Visual Communication Can Do for Music Reading [pp. 129 - 136]Crisscrossing the Interface: The Design, Display and Evaluation of an Interactive Computer Exhibit [pp. 137 - 142]SolArt Global NetworkThe SolArt Global Network '95: Artworks for the Solar Age [pp. 143 - 144]Perspectives and Prejudices about Some Major Issues [pp. 144 - 145]Solar Energy Is the Energy [pp. 145 - 146]"Secrets of the Sun" in Los Angeles [p. 147]

DocumentThe Performing and Visual Arts and New Technologies Seminars [pp. 149 - 154]

Abstracts [pp. 155 - 156]Back Matter

Colores de Acordes,

Documents

Transcript of Colores de Acordes,