The Color of Sound, the Sound of Color; Sound and Light, Music and Art

Note to the reader: I have placed references, some with additional comments, in parentheses within the body of the text in order to avoid the need for the reader to constantly scroll down to the end to read footnotes. I recognize that this creates an interruption in the flow of the text, and the reader's train of thought, but think this is the lesser of the two inconveniences, because the reader can more easily re-read a few lines than re-locate where s/he left off. Thanks for tolerating.

What is meant when critics, listeners, or musicians talk about the "color" of a musical instrument or of a musical composition? They produce and emit sound waves, not light waves or colors. The dictionary defines color in music as the "tonal quality," but Michael Kennedy's Oxford Dictionary of Music (Oxford Univ. Press, 1985, 2^nd ed. 1994, rev. 2006, p. 185) says: "It is impossible for music to convey colours, but it is customary to speak of 'colouring' or 'tone-colour' where variations of timbre (defined, p. 890, as: "Tone-colour; that which distinguishes the quality of tone or voice of one instrument or singer from another, e.g., flute from clarinet, soprano from mezzo, etc."),or tone are produced by different intensities of the overtones of sounds. 'Shade' is perhaps a more accurate term, since the differences are often those of 'darker' or 'lighter' sound." ('Shade' seems to me to be a word more associated with color than sound, a synonym of 'hue.' Am I missing something here?) [Julia Simner, in "The Rules of Synesthesia," writes: "Timbre is the aspect of sound unrelated to pitch and loudness, which allows us to distinguish between the same notes on different instruments; e.g., a piano versus a trumpet." (The Oxford Handbook of Synesthesia, p. 151)] But on the other hand, the "color and music" entry in The New Harvard Dictionary of Music (Cambridge, Mass, Belknap Press, 1986, pp. 179-80) states: "there has persisted a class of listeners for whom specific vowels, pitches, timbres, chords and chord progressions, (more recently) keys, entire compositions, and even styles have specific color analogs." Some scientific studies suggest that this constitutes nearly one fifth of the subjects (P.E. Vernon, "Synaesthesia in Music," Psyche 10/4, Apr. 1930); Cytowic & Eagleman (Richard E. Cytowic & David M. Eagleman), Wednesday is indigo blue, Cambridge, MA, & London, UK: MIT Press, 2009 (paperback, 2011) say 1 in 23 (p. 8). I am personally not one of those for whom this is true, but am certainly intrigued by the existence of this phenomenon.

If a work of music can have color, can a work of visual art, painting in particular, have a sound? Can a particular pigment suggest an equivalent musical timbre or tone? There are some artists for whom this is the case. You have certainly heard of the blues in music, but are you aware of the key of blue in painting? Some artists are able to create works that are harmonious because of the interrelationships of the colors as they are spread across the medium to which they are applied, generally oil or acrylic on canvas, but also pastels and watercolors on paper, and which thereby enhance the subject, in some cases rendering beautiful one that might otherwise be quite bland, uninteresting, or even ugly. Even color in photographs can suggest music to some artists, such as Marcia Smilack. The first mention of this phenomenon dates from 1873, by the Austrian doctor Fidelius A. Nussbaumer, who was a synesthete, quoting his clockmaker brother, Johann, then living in Venice, Italy, also a synesthete as writing in a letter: "If I were a painter and musician, then I could make colors exactly for each different tone, and find musical tones for each color, including all possible dissonances, and people would then adjudge that we are gifted by Nature to find and present the relationship between light and sound." (Cited by Jörg Jewanski in "Synesthesia in the Nineteenth Century," in The Oxford Handbook of Synesthesia, p. 379) You can read the details here.

Scientists are learning new things almost daily about these sensorial interconnections by studying and using brain scanning equipment on people who have them as well as by interviewing them. They admit that there are many pitfalls in the research methodology and that there is still much to be learned. They are also able to verify that artists and musicians no longer living likely did, and were not imagining or inventing it to attract attention to themselves or gain notoriety, and that some, like Vincent Van Gogh, who said nothing about it, probably had them, based on specific characteristics of their works. Here is a link to a good recent article on the subject.

Today, artists and musicians are also said to be 'out' of the (synesthesia) closet' or 'in' it, and this terminology is sometimes applied retroactively to those of the past, like Alexander Scriabin, perhaps the most innovative and adventurous composer associating colors with his music (See below) was definitely 'in' it. Islandic pianist, Vikingur Olafsson, avowedly experiences it. In his note in the booklet accompanying his most recent (March 2020) release, "Debussy · Rameau," he writes:

Another shared element of these two giants of French music is what could be called a synesthetic streak. In my view, a certain blending of sensory experience sems natural to how the two approached music. Debussy famously surrounded himself with poets and painters, drawing inspiration for his limitless musical imagination from a wide range of sources, from symbolist poetry to Japanese woodblock prints. Dubbed the "Newton of Harmony," Rameau had a certain scientific interest in the colours in sounds as well as in light, but also a remarkable originality in what we call the colours of orchestration. In addition, his late writings reveal an unusual sense of the tactile, embodied nature of tonal harmony from the standpoint of the performer. As extraordinary innovators of both harmony and form, with a unique ear for colour and a keen sense of the theatrical, both composers wrote music which engages more senses than just that of hearing. And both enjoyed giving their compositions titles that stimulate the imagination – the music itself ranging from the purely programmatic to the entirely abstract. All these things inform the way the music of this album has been selected and arranged. As in previous albums, however, I have let the music itself guide me, rather than any fixed ideology. (pp. 8-9)

I must add that Olafssons's touch and sustain, or lack thereof in the Rameau, who did not have pedals at his disposal on his instruments, are perfect for this music. See my article on the French clavecinistes elsewhere in these pages, making this CD one of the best I've ever heard for this repertoire, especially because of its carefully built program. He seems, however, not to know that Debussy edited some of Rameau's works for (re)-publication when the other editions were not available because of WW I, so he had an intimate knowledge of some of them, although not necessarily those on this program.

[The previous paragraphs were added on July 9, 2020, with the 1^st sentence having been separated from the paragraph that precedes them.]

The first comprehensive science-based book about this subject is The Oxford Handbook of Synesthesia, Julia Simner (Univ. of Edinburgh, UK) and Edward M. Hubbard (Univ. of Wisconsin-Madison, USA), eds, Oxford University Press, 2013, Pp. xvii + 1077. It is a collection of 49 essays by 75 different scientists (incl. the eds, the aforementioned Richard E. Cytowic (also a synesthete) and Jörg Jewanski, and a prolific Jamie Ward, in Brighton, UK – no known relation, who authored the excellent concluding/summary chapter: "Synesthesia; Where have we been? Where are we going?"); each chapter ends with its own list of "References," so some seminal works appear in several while others only appear in one. The editors, like me, are not synesthetes, though eager to understand the phenomenon; unlike me, they are scientists. Some contributors are synesthetes, and one of them, Sean A. Day, of Trident Technical College in Charleston, SC, makes and writes music; Chapter 44, pp. 902-923, is his first-person narrative, which is well worth reading: it will open your eyes and mind to some synesthesias that appear/seem totally illogical, irrational, and paradoxical: seeing milk as sky blue, for example. The very first written record of synesthesia was also a first person narrative, by Austrian Georg Tobias Ludwig Sachs (1776-1814), in 3.5 pages (§ 157-160, pp. 80-84) of his doctoral dissertation (in Latin) on albinism (He and his younger sister were albinos; how's that for a paradox?) at Erlangen University in Bavaria in 1812 (Oxford Handbook, p. 370, (See also this article.). I wonder how the examiners on his committee reacted and what they thought. It would have been interesting to have been a fly on the wall of that room.

Both Day and Sachs have/had multiple synesthesias, as do many, but not all synesthetes; and there are two types of synesthetic perception: to wit, Day is a 'projector' (seen outside) rather than an 'associator' ('seen' in the brain, or the 'mind's eye'). More than 150 types have been identified: Day began the Synesthesia List in 1992 and continues to maintain and moderate it; you will not find a complete list there, but his subscribers represent c. 65 different varieties. This shows that one person's reality is not necessarily that of another, throwing our general concept of 'reality' as a, fixed, identifiable, objective thing, out the window; each person's reality appears to be what her/his brain filters from what her/his senses send to it, so we each experience the world in a way that is different from everyone else's and therefore unique, in the same way that our DNA is. This adds a whole new dimension to tolerance of differences, too. While this book is not an easy 'beach read,' it is written for the layman/non-scientist as well as the researcher, and is a huge compendium of information that can be explored, with the help of indexes, and does not need to be read cover to cover. It is expensive, so you will likely not want to purchase it; some libraries catalogue it as a non-circulating reference work, but others do not. You may find yourself wanting to photocopy a particular essay.

Day writes of his synesthesias: "One of my favorite things to do is to take long-distance cross-country driving trips on the highway, listening to music; it is like having a constantly changing tinted windshield; however, I never eat or drink while I am driving, and will pull to the side of the road if I encounter an odor (such as a skunk) which is too powerful to 'see through.'" (p. 908) Concerning his composition of scores, he writes: "When I started composing music in my teens, I immediately thought of incorporating my synesthesia, in terms of choosing my orchestration for pieces by what colors I wanted to see. However, unfortunately, I quickly moved to going wholly overboard with this, moving instead towards trying to "paint pictures" via orchestration." (p. 909) […] "Since about 1997 – that is, since I was about 35 years old – [this] has become my approach to orchestration: either just ignore my synesthesia altogether, or, if the piece calls for a focal instrument, concentrate only on that one color and texture, without trying to combine it with those of other instruments. However, that is just me. 'Colored music' synesthesia does not necessarily have to be based upon timbre. It could also be based upon the musical notes, or the key or tonality of the music, or the genre, or the overall structure. Thus, while famous musicians such as Duke Ellington and Leonard Bernstein had synesthesia based upon the timbres of musical instruments, Gyorgi Ligeti's colored music was also an extrapolation of his grapheme-based synesthesia." (p. 910)

Day and one of his Synesthesia List correspondents, Joseph Long, agreed to an experiment to place before the entire community: to note their synesthetic responses to two works: Alexander Scriabin's Piano Sonata # 5, and Ravel's Bolero, written as an illustration of orchestration and how the timbres of the musical phrase change with the progressive addition of different instruments. For Joseph, the Scriabin "which he himself sometimes performs in concert, is a wild rainbow of colors, as it moves all over the keyboard, with very atypical tonal sequences and chord progressions. [How can he perform this accurately without being distracted, as is Day by odors while driving?] For me, the sonata is monochromatic throughout its entirety, a cyan color like anything else played on the piano. Contrariwise, for Long, Ravel's Bolero is visually tedious, as it presents the same small sequence of colors over and over again; for me, on the other hand, Bolero is a wonderful exploration of colors, as each reiteration of the theme changes orchestration, and more colors are added as more instrumental timbres are added towards the fantastically complex multicolored climax." (pp. 911-12) Most readers are familiar enough with Bolero that they can compare how they perceive it with these two synesthetic perceptions, and perhaps either have a clearer concept of what a synesthete experiences in relation to what they do, or discover that they, too are synesthetes…?

Part VI of the Handbook deals with creativity from several perspectives, but focuses primarily on that of contemporary artists, understood to include architects and film animators and similar related fields, and also includes a chapter on literature. It mentions several artists who "paint sound" in the sense that they listen to music and paint what it inspires as it plays, but doesn't explain their processes or strokes, although there is an interesting chapter on this subject. It also mentions in passing a few composers such as Alexander Scriabin and Olivier Messiaen and some painters such as Wassily Kandinsky and Piet Mondrian who were synesthetes (avowedly or not) without going into much detail, and some other mechanical and visual experiments that associated colored displays of one sort or another with music being performed; many of these are described in greater detail below, since I am more focused on music. [These 6 paragraphs, the last 2 sentences of the preceding one, and the sentence in square brackets in the opening were added on 15 August 2016.]

Color in music relates directly to orchestration, in the instruments chosen by a composer for a piece of orchestral music and how their sounds blend with and complement each other. The progenitor of the modern clan of creative exotic orchestral colorists is Hector Berlioz (1803-1869), although he had his ancestral roots in the French Baroque composers such as Jean-Baptiste Lully (1632-1687, actually Italian) and Jean-Philippe Rameau (1683-1764). This grew out of the figuration and ornamentation of the Italian Baroque string players and composers (Many were violinists themselves.) that focused on brilliant, florid, highly ornamented and virtuosic playing, which contrasted with the German emphasis on counterpoint. As Ian Watson, harpsichordist and organist, and Artistic and Music Director of Arcadia Players, said in his introductory comments to a recent concert of Italian Baroque music by the group that I attended, "You should expect to see bright colors: red, yellow, blue." Lully's and Rameau's direct French lineage includes Camille Saint-Saëns (1835-1921), Emmanuel Chabrier (1841-1894), Gabriel Fauré (1845-1924), Claude Debussy (1862-1918), Paul Dukas (1865-1965), Maurice Ravel (1875-1937), Olivier Messiaen (1908-1992), and Pierre Boulez (b. 1925), among many others, but also has numerous international cousins such as Nikolai Rimsky-Korsakov (1844-1908), Mikhail Ippolitov-Ivanov (1859-1935), Alexander Nikolayevich Scriabin (1872-1915), Ottorino Respighi (1879-1936), Manuel de Falla (1876-1946), and Joaquin Rodrigo (1901-1999), to mention but a few.

None of these, however, created works directly inspired by or based on the 7 colors of the rainbow/spectrum or the 12 of the standard color wheel, nor did they have any concept or organized theory of a close direct relationship between specific colors and sounds or tones, although Rimsky-Korsakov and Scriabin did conceive of some relationships between specific colors and keys (not necessarily the same ones, either with each other or with different ones among their own works!). Scriabin never admitted to perceiving colors when hearing sounds. His color system is a rational one, based on Newton's Opticks (See below.), which corresponds to the circle of fifths that associates specific colors with specific keys, with red at C, and blue at F minor.

The general thrust of his composition, however, was towards a multi-media presentation involving sound and color, as with his c. 25-minute long Prometheus; The Poem of Fire, Op. 60 (1910), in the score of which he includes a 2-note part, written on the uppermost stave (of 30!; Bowers, New Scriabin, p. 94, & Bowers, Biography, v. 2, p. 203; See my separate article: "Scriabin's 5^th, …" elsewhere in these pages) and identified as (Tastiera per) Luce (The first page of the score is reproduced in Cytowic & Eagleman, p. 192; its cover is reproduced on p. 193 and in Mitchell [See below], p. 82), for a keyboard operating a turntable of colored lamps that he devised, the clavier à lumières (a model is found in the museum in his Moscow apartment) to project colors into a hall. It was not adequately developed to function for the Moscow première, conducted by Serge(i) Koussevitzky on 2 (= 15: Russia changed from the Julian to the Gregorian calendar in 1918) March 1911, however, so was withdrawn. The first performance with colored lighting, using a machine designed by the Edison Testing Laboratories that projected the colors onto a gauze screen behind the orchestra, was given in Carnegie Hall in NYC on 21 March 1915 (about a month before Scriabin's death) by the Russian Symphony Society Orchestra, conducted by Modest Altschuler, a 'cellist, Moscow Conservatory classmate of Scriabin, and the orchestra's founder, with Margaret Volavay at the piano. (See my companion article for a more detailed discussion of this work and its history.) Scriabin's unfinished magnum opus, Mysterium, was to have been a week-long performance in the foothills of the Himalayas combining dance, poetry, and perfume/scents, as well as music and colored lighting, a sort of ecstatic apotheosis of the arts, mysticism, and philosophy. You can get a taste of what it might have become, at least in sound, on YouTube.

Another Russian composer, also a scientist (physics), mathematician, musicologist, and a music critic and press editor, contemporary of Scriabin, who wrote the first biography of him, Leonid Sabaneyev/Sabaneev (1881-1968), wrote a brief article about this subject, "O zvuko-tsvetovom sootvetstvii" (On sound-color correspondence) in the journal Muzyka (founded by him and Scriabin in November 1910; No. 1 issued on 27 Nov. [= 10 Dec.]), No. 9 (29 Jan. [= 11 Feb.] 1911), pp. 196-200) in which he lists the colors corresponding to the notes of the scale (Russians use the German naming system) for the major keys for both Rimsky-Korsakov and Scriabin.

For Rimsky-Korsakov:

C = white, benign
G = brownish gold, bright
D = yellow
A = bright pink
E = blue, shining
H (B natural) = gloomy, dark steely blue
Fis (F# ) = greenish
Dis (D#) = darkish, warm
Ais (A#) = violet
Es (Eb) = gloomy, gray-blue
B = darkish, dusky
F = light green

For Scriabin:

C = red
G = orange-pink
D = bright yellow
A = green
E = blue
H (B natural) = like E
Fis (F#) = bright blue
Dis (D#) = purple
Ais (A#) = purple violet
Es (Eb) & B = steel gray, metallic luster
F = red, dark

These are really more associations than equivalences, and some are atmospheres or moods rather than colors, in spite of my use of the = sign to be consistent with other such relationship: the article merely has a space there. There is also a section giving general associations for most people:

C = white
F = red (for R-K = green)
D = yellow
B = gloomy, leaden
E = color of steel, military

In the text, he writes that sharp notes are generally brighter, flat ones, a more complex coloring with metallic tones corresponding to their major ones, while a minor key is often the same color associated with the major, but milder, lighter. They often follow the order of the spectrum, and the circle of fifths. He writes that the associations have a dual relationship: physiological (vision-hearing) and psychological (atmosphere, mood). This may be the earliest such statement in print? The article, sent to me as a pdf file by Rebecca Mitchell, has never been translated into English. (I had help gleaning this information in it from several acquaintances and friends including Camille Blum, an Amherst College undergraduate student of Russian, Nadezda Spivak of the Amherst College Center for Russian Culture, founded by Thomas P. Whitney, Class of 1937, diplomat, journalist, translator, author, and collector of Russian art, manuscripts, rare books, journals, and newspapers, all donated or bequeathed to the college, and Ron Hawkins of Asheville, NC.)

Sabaneyev was a very close friend of Scriabin (Vladimir Derzhanovskii wrote, in a 1913 letter to Igor Stravinsky: "There is only one God, Scriabin, and Sabaneev is his prophet." Mitchell, p. 85, but Sabaneyev had some doubts about the self-proclaimed savior of Russia through transcendent modern music as the new Orpheus, and characterized him in an 1914 letter to fellow composer Alexandr Krein as: "Messiah Absolutovich", p. 97), spending time with him nearly every evening in his apartment where a circle of his followers and supporters, "an eclectic mix [of] artists, old nobility, wealthy merchants, and members of Russia's emerging professional classes mingled freely at evening performances and discussions devoted to Scriabin's music and ideas" (Mitchell, p. 96). He wrote an account of the funeral after Scriabin's death on 16 April [= 29 April] 1915, attended by a throng of thousands, who followed the coffin in a procession to its final resting place (photo in Mitchell, p. 63), for the press instead of the planned introduction to Mysterium, then in progress. He left Russia in 1926 for Paris, and later Nice, where he died and is buried; his unpublished music manuscripts passed to his widow, who donated them, after 1973, to the Library of Congress, to which he had attempted to sell them in 1937. An excellent treatment of them can be found in: Rebeca Mitchell, Nietzsche's Orphans, New Haven & London: Yale University Press, 2015, pp. 61-103.

Sabaneyev also contributed an article: "Scriabin's 'Prometheus'," to the Blaue Reiter Almanac, edited by Franz Marc and Wassily Kandinski, and published in 1912 (pp. 56-68), in which he repeated some of the color-sound correspondences information. A "New Documentary Edition," edited by Klaus Lankhheit, was published in Munich in 1965, and translated into English in 1974, published by Thanes and Hudson in London and by The Viking Press in New York; the article is found on pp. 127-140, with an editorial footnote on p. 131 giving the gist of the 1911 Muzyka article, but the list of colors in incomplete.

[The 2^nd of the 6 preceding paragraphs was expanded and separated from the 1^st and the other 4 were added on March 1, 2018.]

Orchestral color is possible because each instrument family has its own characteristic tonal timbre or color, and each instrument within that family has its own range or voice. Think of the string families: the violin, viola, violoncello, and double bass, or the viol/gamba family, for example, not to exclude the harp; or of the woodwind family, from piccolo, flute, clarinet, oboe, bassoon, to contrabassoon. A composer can therefore deftly combine and isolate these families and instruments to evoke images and atmospheres, even if they are not directly associated with a specific color of the spectrum or the color wheel. The single instrument with the greatest range and potential for tonal color is the organ because its many pipes made of various materials imitate the sounds of all the instruments of the orchestra. "The organ attains its full power not by adding more pressure or volume but by adding different colors that do not have individual dynamics, as orchestral voices do." (Charles A. Riley, II, Color Codes; Modern Theories of color in Philosophy, Painting and Architecture, Literature, Music, and Psychology, Hanover, NH, and London: Univ. Press of New England, 1995, p. 284). Earlier instruments had more color than modern ones, whose technological advances to achieve greater power and reliability in staying in tune have often homogenized and distilled or purified their sounds. This is particularly noticeable in the development of the piano, and is an important aspect of the modern authentic or historically-informed performance movement. I am certainly sensitive to both of these aspects of musical color, and the challenges of describing them.

Scriabin's clavier à lumières was not the first instrument to connect sound and color. Several different people over the years in different countries, beginning with French Jesuit mathematician Louis Bertrand Castel (1688-1757) in the 18^th century, worked on creating one, with varying degrees of completion and success, but some were actually produced and demonstrated. All were keyboard machines that projected colors using colored lights that match those on the keys of the notes played, generally, but not universally, organized chromatically with red on middle C and progressing upward or descending downward from there. The effort is chronicled by Adrian Bernard Klein (1892-1969) in his Colour-Music: The Art of Light (London: The Technical Press, Ltd., 1911, with subsequent editions containing updates in 1930 and 1937, the title changed for this third and later ones to Coloured Light; An Art Medium), which includes numerous drawings and photographs, and detailed descriptions of the major ones in its Chapter V. See also Kenneth Peacock, "Instruments to Perform Color-Music; Two Centuries of Technological Experimentation," Leonardo, Vol. 21/4, (1988), 397-406, for a more succinct synopsis with illustrations. The instrument has various names, depending on its inventor, from Castel's "Clavessin oculaire" [ocular harpsichord] or "Clavessin pour les yeux" [harpsichord for the eyes], about which he wrote two essays in 1725 and 1735, and of which a model was made in 1734, with blue at middle C (Klein, pp. 183-87; Peacock, pp. 399-400) down to his own "Klein Colour Projector" in 1920 (Klein, pp. 204-12; Peacock, p. 404, but he appears to believe that this is a different individual from the author of the book). D.D. Jameson is presumed to have made, although there is no documentation of a demonstration, a device in the mid 19^th century (A 23-page pamphlet was published in 1844.) that he called "Colour-Music" described thus: "A pianoforte having been prepared in the manner described, any air may be slowly played. As each note is struck, its equivalent in Colour – Key, Height – Octave, Length – Time should be placed in a series on a white paper. This will be found to be of more or less pleasing character, according to the varied character of the music." (Klein, p. 3 & 188-89; Peacock, p. 401) Apparently red was at C.

Alexander Wallace Rimington (1854-1918) created a Colour-Organ in 1893, still extant in his studio in London, that was installed in a Hall (in converted public baths; it is over 10 feet tall) in Norwood, UK, and private and public performances were given, followed by a major performance at the old St. James's Hall in London on 6 June 1895 with several others on subsequent dates there and in other locations around England, involving simultaneous performances of music "with coloured light accompaniment according to the analogical scale." (Klein, pp. 7-8 & 190-91 with 2 illus. between; 1893 patent spec., pp. 265-273; Peacock, pp. 401-402, illus. p. 399)

Rimington published a book entitled: Colour-Music; the Art of Mobile Colour (New York: Frederick A. Stokes Co., 1911, & London: Hutchinson & Co., 1912); you can read it here. The 4-ocatve (48 keys) instrument looks like an organ rather than a piano, with swell pedals that can increase or decrease the intensity of the colors projected. "Deep Red" is at middle C and the tones progress/descend chromatically up and down with each octave having a greater or lesser base intensity; playing chords blends the colors projected onto a fabric that hangs like a drapery with folds rather than being stretched taut like a screen, giving them more texture. The 185-page book contains numerous black and white photos of various views and parts of the instrument and its components and mechanisms. Rimington's opening one-sentence paragraph reads: "Hitherto there has been no pure colour art, that is to say, no art dealing solely with colour for its own sake as music deals with sound." (p. 1) Later he writes: "Colour stands in a very similar relation to us to that which music occupies as a means of emotional expression, and the increase in the happiness and interest of life due to music will probably find a parallel in the pleasure and interest derivable from colour." (p. 82) Exploring this concept further, he talks about enjoying a sunset over the Bay of Genoa as an "evening symphony of colour" that unfolds like a series of notes of changing colors (pp. 89-92).

When Scriabin's Prometheus was presented at Carnegie Hall in NYC on 20 March 1915, it featured a machine called the "Chromola" developed by Preston S. Miller, president of the Illuminating Engineering Society, that projected colors onto 8-by-10-foot strips of gauze suspended in front of the audience, which critics found unrelated to the music (Will South, Color, Myth, and Music: Stanton Macdonald Wright and Synchromism, NC Museum of Art, 2001, p. 82; several reviews are reprinted in Klein, Appendix II, pp. 240-48). Claude Bragdon staged a colored light show entitled "Cathedral Without Walls" in Central Park in 1916 (Ibid.), but there was apparently no music. Danish-born Thomas Wilfred invented the "Clavilux" in Huntington, NY, beginning in 1916, and gave a concert with it in a NYC theater on 10 January 1922, following that with a European tour in 1925, playing in Paris, London, and Copenhagen, after which several instruments were installed in American theaters. It involved various light sources with prisms and colored filters to project geometric shapes onto a screen with a keyboard of five manuals of sliding keys and rheostats to vary intensity for quite spectacular shows ; he called this the new art of "Lumia." (Klein, pp. 16-21 & 194-5, 4 illus. between; Peacock, p. 405) No specific color is associated with a particular musical note or key, however. (For more infomation on Wilfred and his Clavilux, see this Smithsonian article: https://www.smithsonianmag.com/smithsonian-institution/artist-painted-light-admiring-astronomer-helped-make-him-star-180967384/?utm_source=smithsoniandaily&utm_medium=email&utm_campaign=20171201-daily-responsive&spMailingID=31994560&spUserID=NzQwNDU4Mjg5NTQS1&spJobID=1180143970&spReportId=MTE4MDE0Mzk3MAS2.)

American pianist Mary Hallock-Greenewalt patented a "color-organ" using rheostats that she named Sarabet (after her mother) and demonstrated in NYC in 1921, and in her 400+-page book described it and her new art called "Nourathar." She also wrote color indications above the top lines on the staffs of scores such as Beethoven's "Moonlight" Sonata No. 14, Op. 27/2 (Klein. pp. 21-22 & 193-4, illus. facing p. 192; Peacock, p. 404, illus p. 400). There were others who also created instruments including the 7-octave one invented by Alexander Burnett Hector (1865 [Aberdeen, Scotland]-1958?) in 1912 in Australia, and patented in the US in 1929 that used incandescent lamps, each controlled by a key, with intensity controlled by rheostats connected to the bellows of the organ; yellow was at middle C (Klein, pp. 22-23 & 198-204; Peacock, p. 403).

Hungarian composer Alexander László (1895-1970) produced, beginning in 1925 in Munich, concerts using an instrument he called the "Sonchromatoscope" consisting of 4 slide projectors and colored spotlights (Peacock, p. 404, illus. p. 402), accompanying music of his own composition or by others including Scriabin, Rachmaninoff, and Chopin, that he called Farblichtmusik [Color-Light-Music]. (A 71-page book was published: Die Farblichtmusik, Leipzig: Breitkopf & Härtel, 1925; UNC-CH has a copy, but I have not seen it.) He wrote a set of Preludes for piano and colored light that employed a special system of notation (Ibid.). A reproduction of a watercolor depiction of a 1925 color-light-music performance is reproduced in Karin V. Maur, The Sound of Painting; Music in Modern Art (trans. from German by John W. Gabriel, Munich, London, New York, Prestel, 1999), p. 91.

Both American painters Morgan Russell and Stanton Macdonald-Wright (more about them below) worked together on developing a mechanical device to project colors while music was being played at about the same time. Russell sketched a "Kinetic Light Machine" sometime between 1916 and 1923 (reproduced in South, p. 83), although only Macdonald-Wright (who was actually in NYC at the time of the Prometheus and "Cathedral Without Walls" events, but it is not known if he attended either or both) actually did so, in the 1920s, then living in Los Angeles, devising a small light machine that he referred to in correspondence with Russell (still living in Paris) as a "color organ" and that was used in theatrical productions in 1927 when he was director of the Santa Monica Theater Guild. Others of his experiments were related to cinematography; some were precursors to Technicolor films. Nearly all of these machines, however, worked on the basis of analogy between color and music without marrying the two, since no single instrument produced both color and sound.

A related area of music that directly involves color, and which occasionally actually involves famous visual artists, is the world of ballet and opera, where sets and lighting are used as a context and backdrop for the action and singing of costumed performers. Many artists who are not directly associated with the concept of sound-inspired works of visual art designed costumes, sets, and lighting for these types of musical works, always inspired by the music, which invariably came first, and to which they listened for ideas and inspiration, often collaborating or at least co-operating with the composers. One can think, for example, of Léon Bakst (1866-1924) working with Debussy's Prélude à l'après-midi d'un faune (1894), or Pablo Picasso's (1881-1973) collaboration with Erik Satie (1866-1925) for his Parade (1917).

In recent years, British artist and set designer David Hockney (b. 1937) has been inspired by the music of Richard Wagner (1813-1883) to create innovative sets for some of the latter's operas for Los Angeles Opera. He also created sets and lighting for Maurice Ravel's L'Enfant et les sortilèges (1924-25) and Satie's Parade for the Metropolitan Opera in NYC in 1980-81, and for Igor Stravinsky's (1882-1971) Le Rossignol (1914) for the Met in 1981; in all these cases, colored lights are projected onto colored sets. He generally paints the sets (He paints with a 3-foot long brush [Richard E. Cytowic, Synesthesia, A Union of the Senses, New York, Berlin, and Heidelberg: Springer-Verlag, 1989, p. 276, & Cytowic & Eagleman, p. 184]) on site, literally while listening to recordings of the music repeatedly; he cannot read music or play an instrument. He says the music "dictat[es] his arm motions – the lines, curves, blots, and dots, as well as the color and overall dimensions. 'On all operas I've done, the music gives me the set – the color and the shape.'." (Cytowic, p. 276, & Cytowic & Eagleman, p. 184); "'It's the music that attracts me to doing the set designs, rather than the plot.'" (Cytowic, p. 275, & Cytowic & Eagleman, p. 183) Then he plays with the lights until he gets them right (Cytowic, p. 278, & Cytowic & Eagleman, p. 185).

Cytowic pointed out in the interview that the set for Le Rossignol is "all blue." Hockney replied: "But there are a lot of different blues in it. It's not just all one blue. […] The [non-synesthete] viewer does not notice the myriad nuances and merely perceives the design as blue." (Cytowic, p. 279, & Cytowic & Eagleman, p. 186) Cytowic conducted a series of tests with him in 1981 in which "Hockney chose from a complete set of color chips. In addition to the effect of single tones on color matching, further experiments examined melody via major and minor arpeggios and triad chords." High ones evoked reds, pinks, and yellows; minor ones evoked blues and purples. "For Hockney, the thing that most predicts a restricted response is melody. Thus the pilot studies confirmed what the artist himself acknowledged – that the music itself, its melody, dictates shape, color, and movement." (Cytowic, p. 276, & Cytowic & Eagleman, p. 184) Hockney says further that he cannot listen to other music, such as a Beethoven quartet, in the background when he is working on other pieces because it makes him "'lose the lines of what [he is] drawing at the moment.'" (Cytowic, p. 279, & Cytowic & Eagleman, p. 187).

Sculptor Dale Chihuly (b. 1941) devised new sets for Debussy's Pelléas et Mélisande. All of these artists use(d) the existing music to determine the colors and forms in their own personal styles, but none has created original works from the base of a musical scale or chord. In these instances, in Riley's words: "color works by analogy as a mimetic double to music." (p. 295) He says further: "As a parallel to the chromaticism of the score or as a separate chromo-argument, the sequence of chromatic ideas has a power of its own and evident box office appeal." (p. 296).

All of these elements are related to people's emotional responses to the products or works of both art forms. Many critics and writers about music have long associated modes with moods – the words are related, after all, major being happy and upbeat, minor, more sad and dark, based on the characteristics of works composed in certain keys, often seeking to justify the characteristics and key choices with mention of events in the composers' lives at the time of their composition. This is not unlike the concept of the effect of warm (such as red or yellow) and cold or cool (such as blue or violet) colors in art.

Biologically, physically, and scientifically, the perception of color by the eye and the brain, however, is completely individual and genetic: no two people actually perceive the same color in precisely the same way. "Color is the psychophysical combination of chroma (hue), saturation (density of chroma), and luminance (brightness). These three dimensions, which can be selectively disassociated, enable us to perceive 10⁶ colors." (Cytowic, p. 163) Hence, a specific color eludes a precise definition, "refuses to conform to schematic and verbal systems. It often will not even conform to itself physically" (Riley, p. 12), because the definer can describe only her/his own perception. If you want to explore the science of light and color, there are some interesting podcasts that you can access here.

The four movements entitled "Purple," "Red," "Blue," and "Green," of Arthur Bliss' (1891-1975) A Colour Symphony, Op. 24 (1921-22, rev. 1932) were inspired by the symbolic meanings of these colors that he considered the primary ones in heraldry as he personally perceived them. Thus, contrary to the suggestion of the titles, they have nothing to do with a system of sound-color correspondences. This adds yet another dimension to the subject, however, because heraldic meanings of colors are completely unrelated to other color associations. There are only 5 (blue, red, purple, black, and green), which join with 2 metals (gold and silver) to make 7, but they are not the ROYGBIV ones of the rainbow, which has no black or white, and orange and indigo are missing, although in more modern times, orange has been added in along with maroon, the latter missing from the rainbow. The heraldic colors/tinctures are also related to planets and gemstones for astrological and mineral associations, and to human virtues, but to my knowledge never had any associations with sounds or musical notes.

Aaron Jay Kernis (b. 1960 near Philadelphia, PA, educated at the San Francisco Conservatory of Music, the Manhattan School of Music, and Yale University, and since 2003 member of the faculty of the Yale School of Music) has written several works with the word "color" or the name of a color in their titles: Color Wheel (2001) for orchestra, Colored Field (1994, winner of the Gravemeyer Award in 2002), a concerto work in two versions, originally for English horn, and then arranged for 'cello, and Trio in Red (2001) for clarinet, violin, and piano. Only the two versions of Colored Field have been recorded, with the soloists for whom they were written in both cases, and it is not a synesthetic work; it was inspired by the composer's visit to the Auchwitz-Birkenau concentration camps and the vision of the fields surrounding them, now covered with grasses but soaked with the red blood of the victims at the time the camps were operating, and is in effect a political, anti-war piece which magnificently exploits orchestral and instrumental color. Color Wheel was commissioned by the Philadelphia Orchestra for the opening of the Kimmel Center; it has been described as an apocalyptic-sounding piece. The Philadelphia Inquirer review described it thus: "The work was really meant to highlight the traditional orchestra, which it did in novel ways. He manages to use color as an emotional tool in and of itself. Kernis formed an emotional arch that was, if unpredictable, still discernible as the stuff of a heroic human journey." It appears that his use of the term 'color' in the titles also has to do with orchestral color as described above, but Trio in Red may be a different situation; since it has not been recorded, I am not in a position to examine and evaluate it.

The world premiére recording of Color Wheel was released in June 2020, paired with yet another work by Kernis with a colorful title: Symphony No. 4, "Chromelodeon," composed in 2018, co-commissioned by the New England Conservatory in Boston (for its 150th anniversary), Hugo Wolff, director of the Nashville Symphony Orchestra, and Giancarlo Guerrero, its music director (who are the performers of the recording: Naxos 8.559838), and The Bellingham (WA) Music Festival, Michael Palmer, Artistic Director. Kernis is the author of the notes in the accompanying booklet; he writes:

Two visual elements have influenced Color Wheel. Color wheels are tools used by artists and designers that teach color relationships by organizing colors in a circle so you can visualize how they relate to each other. Most color wheels show primary colors and myriads of related hues. I feel that this piece concentrates on the bolder contrasts of basic primary colors. (I sometimes see colors when I compose, and the qualities of certain chords do elicit specific sensations in me –for example, I see the A major that ends this work as bright yellow.) I've also been fascinated with Sufi whirling dervishes and their ecstatic spinning. This work may have some ecstatic moments, but it is full of tension, continuous energy[,] and drive.

Harmonically, Color Wheel explores a wide gamut of colors, from huge overtone-derived chords, strongly contrasting levels of consonance and dissonance, and occasional touches of jazz harmony and syncopation. (p. 2)

(The above three paragraphs were added on June 24, 2020.)

Michael Torke (b. 1961 in Milwaukee, WI, studied at the Eastman School of Music with Joseph Schwantner and Christopher Rouse, and at Yale University, currently living and working in NYC), a self-identified synesthete, is the composer of numerous pieces that include colors or words that have color associations in their titles. These include: Color Music (1989), a 53.5-minute 5-movement orchestral suite including "Green" (1986), "Purple" (1987), "Ecstatic Orange" (1985, but originally written while still a student), Ash" (1989), and "Bright Blue Music" (1985), a series of pieces that each explore a single, specific color; and Chrome (1993), Bronze (1990), Rust, and Slate (both 1989), Copper, Charcoal, and Black and White (all 1988). Note that some of these are metals that may be the inspiration rather than the colors thereof. Of these, Color Music and a few of the others have been recorded. The movements of Color Music are also somewhat in the minimalist vein, with recurrent repetition of the melodies and steady pulses and rhythms, often concluding in a climax or sustained tone.

Jennifer Higdon (b. 1962, educated at Bowling Green State University in KY, the Curtis Institute in Philadelphia, PA, where she now teaches, and at the University of Pennsylvania) has compared composing to painting a canvas, but it is not clear whether she sees colors when creating or hearing music. Her Blue Cathedral, which has become quite famous, is the only work that includes the name of a color in its title. Another color-related title is Music Box of Light. All of her works emphasize interesting color combinations, but this emanates from their orchestration.

American composer Phillip Ramey (b. 1939) wrote Color Etudes for piano in 1994, when he was living in Tangiers, Morocco; it is a set of 9 crafted like études have always been, as a character piece to address a particular piano figuration, and that follow in a circle, a spectrum that runs from dark through light and back to dark, from “Purple,” through “Green,” “Maroon,” “Orange,” “Red,” “Gold,” “Blue,” “Silver,” and ends in “Black,” so this is like a re-ordered ROYGBIV with the 2 heraldic metals fitted in, and maroon substituted for Indigo. He says he is attempting to create the textures that he associates with or that are inspired when he sees these colors. Evoking textures on the piano is much more challenging than with a full orchestra’s array of instruments, but it certainly offers a greater range than any other percussive instrument. His style is, in this work, neo-Romantic lyricism and the music is primarily tonal, with melodies and background chords. He created an orchestral version in 2002.  The piano version has been recorded by Stephen Gosling on Toccata Classics in Vol. 1 of what will be the complete music for piano of Ramey; its accompanying booklet has 1.5 pages of detailed descriptive notes by Benjamin Folkman. Vols. 2-4 have also been released. [This paragraph added December 2017.]

Riley, reporting on Swedish composer Daniel Nelson's (b. 1965, educated at Peabody Conservatory in Baltimore, MD, and the University of Chicago, currently living and working in Sweden) Pigmentata (1991), a solo piano work commissioned by Bosnia-born pianist Pedja Muzijevic, says it is "a response to the radiantly chromatic paintings of American artist Ed[ward Francis] Paschke [(1939-2004 ) …] based on a succession of three modal chords that are directly analogous, according to the composer, to the chromatic sensation experienced by a viewer of Paschke's art." (Riley, p. 278) Nelson's program note for its world première says:

This composition is not a study of a specific Paschke painting, nor does it attempt to express specific colors in music. I have attempted, rather, to translate the visual experience in my perception of Paschke's use of color into a sonic event… Presentation of a synaesthetic relationship between color and music, although an inherently important aspect of the composition, is really not the central purpose of Pigmentata. Rather, my subjective attempts at translating color into music to supply an appropriate harmonic foundation with which to transmit the sensation I experienced while attending the Ed Paschke retrospective show [in Chicago]: a sensation, nonetheless, full of vibrant and radiant colors." (Riley, p. 278)

This work appears neither to be published or recorded and is not listed among his works on his web site.

Nelson writes about his 4-minute orchestral fanfare entitled Force of a Rainbow (2006), to which you can listen on his web site: "Likt en regnbåge sprakar musiken med gnistrande färger. Och likt en regnbåge varar upplevelsen bara en kort stund. Men i motsats till naturfenomenet som alltid tynar bort, väller musiken istället fram med ett alltjämnt tilltagande kraft. Som vågor i ett hav av regnbågar." [Like a rainbow, music sparkles with flashing colours. And like a rainbow, the experience lasts only a short while. But in contrast to the natural phenomenon, which always fades away, music surges/streams forward with a steadily increasing power. Like waves in a sea of rainbows. Trans. Kyle Frackman]. Purplelectric (1997) is a work for flute and organ. His own translation of his note about it says:

Purple is a bold, electrifying, and ecstatic color which demands attention, And although I don't believe in synesthetic relationships between music and color, I do think that one[']s perception of dissimilar sensorary [sic.] encounters may lead to emotional responses of comparable qualities. In other words, for me as a listener, the music of Purplelectric gives rise to an emotional response similar to that of being intensely subjugated [sic.] to the color purple. It stands to reason, however, that these responses are articulated to us, and indeed by us, through external association[s]. Where our personal experiences differ, so too do our emotional responses to given items differ. When titling my composition Purplelectric I am thus attempting to underline my own auditory experience of the work, and perhaps trying to steer other listeners to hear the piece the same way I do. I am, however, in no way suggesting that the music sounds purple. After all, how does purple sound?

While I am not aware of any composers who developed a complete system of specific color-sound correspondences, some clearly did associate some colors with specific key signatures, in a manner similar to the way in which the Symbolist poets, such as Arthur Rimbaud, associated a specific color with a particular vowel. For example, Fauré said to pianist Marguerite Long, on 19 January 1908 prior to her performance of his Ballade for piano and orchestra: « Voilà une bien jolie robe en Fa-dièse majeur, tout à fait dans le ton de la Ballade. » [That's a very pretty dress (It was a long white one with golden flowers.) in F-sharp major, precisely the key of the Ballade; Ton also means a shade of a color] (Long, at the piano with Fauré, Paris: René Julliard, 1963, trans. Olive Senior-Ellis, New York: Taplinger, 1981, p. 57; this is also reported in Cecilia Dunoyer, Marguerite Long; A Life in French Music 1874-1966, Bloomington & Indianapolis: Indiana Univ. Press, 1993, pp. 31-32.).

Olivier Messiaen said he perceived colors when he heard certain chords, particularly those built from modes, and that when he saw colors, he heard chords; he said combinations of these colors were important in his compositional process. "The phenomenon of natural resonance is analogous to that of complementary colors in the sense that one acts on our ear[s], the other on our eyes. When I hear music, I see in my mind complexes of colors corresponding to complexes of sounds, so it's understandable that color interests me as well as sound." (Olivier Messiaen: Musique et couleur, Paris, Belfond, 1986; Olivier Messiaen: Music and Color; Conversations with Claude Samuel, trans. by E. Thomas Glasow, Portland, OR: Amadeus Press, 1994, p. 62) The title of his 8-volume treatise is: Traité de rhythme, de couleur, et d'ornithologie, and he notated colors in some of his scores to help conductors interpret them. He also said concerning his Des Canyons aux étoiles (1977), inspired by a visit to Bryce Canyon National Park: "'the most beautiful thing in the United States. The piece I composed about Bryce Canyon is red and orange, the color of the cliffs.'" (Cytowic, p. 238; he does not give the source of the quote; it comes from Messiaen, p. 161).

Referring to the central movement, entitled "Bryce Canyon et les rochers rouge-orange" […and the Red-Orange Rocks], Messiaen says: "[…] this movement evolves through all the shades of red, violet, and orange, with the most varied nuances: red-orange, purple-red, hyacinth-violet, etc." (Messiaen, p. 167) When asked by Claude Samuel: "This primordial red of Bryce Canyon – with what type of harmony or instrumentation did you attempt to translate it?" he replied: "That's difficult for me to answer. Nevertheless, I'll point out that the piece is written around the key of E major, which for me represents the color of red; but I don't believe in an exact correspondence between such and such note, key, or color. On the other hand, I think complexes of sound correspond to complexes of color. […] But if the sound complex is transposed by a semitone, one tone, a third, a fourth, or a fifth, the colors change." (Ibid.) The final movement of the work, "Zion Park et la Cité céleste," is in the key of A Major and ends in an A Major chord because that is the key that corresponds to blue for Messiaen (Ibid., p. 168). David Hockney also says that "'Blue has this quality of being spatial, which other colors do not.'" (Cytowic, p. 278, & Cytowic & Eagleman, p. 185) At the NYC première, the public seemed to 'get it,' but not the critics.

The closest examination of Messiaen's very complex experiences of color-sound synesthesia, perhaps the most complex of any of which I am aware, is by Jonathan W. Bernard in the chapter "Colour" in The Messiaen Companion, Peter Hill, ed., Portland, OR, Amadeus Press, 1995, pp. 203-219, which is a summary with further study of his earlier article, "Messiaen's Synaesthesia: The Correspondence between Colour and Sound Structure in His Music," in Music Perception, vol. 4 (1986), pp. 41-68. Messiaen struggled throughout his life to describe and explain his associations, always in his 'mind's eye,' never physically seeing colors when hearing tones, and not hearing tones when seeing physical colors, but also perceiving them when reading musical scores, in the hope that some others might also perceive, or at least comprehend them, but also knowing that every person likely perceives such associations in a unique manner. He indicated above the staves in his scores the colors that he perceived as he composed the various segments of them just as he indicated tempos and expressive notations. His experiences were far more nuanced than just color-note/tone associations like those experienced by many composers and artists, with the experiences being induced by harmonies. For most of us, however, his music is just simply sublimely beautiful.

Des Canyons aux étoiles also contains bird calls, those of the birds he found on the site among them. This returns us, however, to the issue of orchestral color since it does not suggest a relationship between those colors and specific chords, keys, or notes. Another composer to have used bird songs in works (The Hermit Thrush, Op. 92, 1921, for example), several years before Messiaen, is Amy Beach (1867-1944), who is also thought to have perhaps been a synesthete. Coincidentally, the 10^th movement (of 12) of Messiaen's Des Canyons aux étoiles is entitled "La Grive des bois" (The Wood Thrush). Franz Liszt (1881-1886) appears to have been a synesthete; there are recollections by others of his having asked musicians to produce specific colors when he was Kapellmeister in Weimar (Cytowic & Eagleman, p. 93, n. 8 for references). Both Jean Sibelius (1868-1957) and György Ligeti (1923-2006) are also thought to have been synesthetes (Cytowic & Eagleman, p. 93).

The concept of syn(a)esthesia, defined as "a phenomenon in which one type of stimulation evokes the sensation of another, as the hearing of a sound resulting in the sensation of the visualization of a color" (American Heritage Dictionary of the English Language, New College Edition, Boston: Houghton Mifflin Co., 1976, p. 1305), or as "a concomitant sensation, esp[ecially]: a subjective sensation or image of a sense (as of color) other than the one (as of sound) being stimulated" (Merriam Webster's Collegiate Dictionary, 10^th ed., Springfield, Mass.: Merriam Webster, Inc., 1993, p. 1196), and by Cytowic as "an involuntary joining in which the real information of one sense is accompanied by a perception in another sense" (p. 1; Itals in original), is not new, or even recent. Aristotle (384-322 BCE) in Ancient Greece postulated this concept in works known in their Latin translations, De Anima I and II and De sensu et sensibilia, in which he stated that "although the senses come from outside us through different channels of the sense organs, they do not remain separate in our sense experience." (Cytowic, p. 70) Ptolmey (90-168) in Roman Egypt discussed colors in his Optics and the mathematical progressions of scales in his Harmonics. In the Renaissance, Leonardo da Vinci mentioned it in his Notebooks.

In the 18^th century, Isaac Newton (1642-1727) weighed in, in his Opticks, or a Treatise on the Reflexions, Refractions, Inflexions and Colours of Light (1704), in which "he attempted to correlate the energy of sound and color" (Cytowic, p. ix). He created a color wheel that corresponds to the Dorian mode; red is at C. I have not tracked down all of these early mentions or references. All of them laid the groundwork for a more scientific attempt, beginning in the 18^th century, to establish a correlation between color and sound, which is technically called chrom(a)esthesia. But no one was able to truly analyze and scientifically describe the phenomenon. In fact, there are many types of synesthesia, and a single individual may possess more than one type; such a person is said to be "polymodal" (Cytowic & Eagleman, p. 23). Indeed, even within the same type of synesthesia, no two individuals are likely to experience it, just as they do not perceive specific colors, in the exact same way. However, that red is at C for many of the composers and color instruments seems not to be a coincidence; Cytowic cites an unpublished study of a synesthetic boy at different ages from childhood and adolescence in which he consistently placed some shade of red at C; but if a different color is mentioned, it is yellow (Cytowic, pp. 47-48).

For part II of this article, click here.

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