Music and Colour ( Color ): a new approach to the relationship

© Copyright Ian C. Firth 2007, 2009, 2010

The idea that there is a link or correspondence between music and colour is a very old and very persistent one. According to McClain’s (1978) analysis, Plato linked the major second and perfect fifth to yellow and the perfect fourth to red, in an extension of the Pythagorean harmony of the spheres to encompass planets, tones and colours. Aristotle (1984) suggested a parallel between the harmony of colours and the harmony of musical intervals. Newton (1730/1952), when investigating the spectrum of light, linked the intervals tone, minor third, fourth, fifth, major sixth, minor seventh and octave to the colours red, orange, yellow, green, blue, indigo and violet.

The two-dimensional nature of musical notes

Table 1

Musical intervals arranged by ascending or descending fifths and ascending or descending major thirds (after Longuet-Higgins, 1962, 1987)

Augmented seventh 50 27	Augmented fourth 25 18	Small halftone 25 24	Augmented fifth 25 16	Augmented second 75 64	Augmented sixth 225 128	Augmented third 675 512
Imperfect fifth 40 27	Minor tone 10 9	Major sixth 5 3	Major third 5 4	Major seventh 15 8	Diatonic tritone 45 32	Small limma 135 128
Imperfect third 32 27	Dominant seventh 16 9	Perfect fourth 4 3	Octave 2 1	Perfect fifth 3 2	Major tone 9 8	Imperfect sixth 27 16
False Octave 256 135	Minor fifth 64 45	Diatonic semitone 16 15	Minor sixth 8 5	Minor third 6 5	Minor seventh 9 5	Imperfect fourth 27 20
Diminished sixth 1024 675	Diminished third 256 225	Diminished seventh 128 75	Diminished fourth 32 25	Diminished octave 48 25	Diminished fifth 36 25	Great limma 27 25

For every interval in Table 1, there is a symmetrically opposite interval which combines with it to make an octave. A perfect fourth and a perfect fifth combine thus to make an octave:

3/2 x 4/3 = 2/1

A major sixth and a minor third combine thus:

5/3 x 6/5 = 2/1

An augmented third and a diminished sixth combine thus:

675/512 x 1024/675 = 2/1

The table below shows these intervals as note names.

Table 2

Notes arranged by ascending or descending fifths and ascending or descending major thirds (from Longuet-Higgins, 1962a, 1987)

D#	A#	E#	B#	Fx	Cx	Gx	Dx
B	F#	C#	G#	D#	A#	E#	B#
G	D	A	E	B	F#	C#	G#
Eb	Bb	F	C	G	D	A	E
Cb	Gb	Db	Ab	Eb	Bb	F	C
Abb	Ebb	Bbb	Fb	Cb	Gb	Db	Ab

The boundary areas of Table 2 are used much less than the central area of the table. There is a repeating pattern and note names are repeated, that is, different notes have the same name. Musical context should make clear which note is being used, and, other things being equal, the note closest to C is to be preferred.

A third (octaves) dimension can be imagined perpendicular to the page, corresponding to pitch height.

The two-dimensional nature of hue

The proposed match is based on the structural similarity of the rules for combining elementary colours and elementary musical intervals.

In additive colour mixing (mixing coloured lights) the primary colours are red, green and blue. They combine according to the following rules: red and green make yellow, and yellow and blue make white (or grey, depending on the brightness). Similarly a major third and a minor third make a fifth, and a fifth and a fourth make an octave. (Other musical intervals can be regarded as compounds of these primaries. For example, a major seventh is a compound of a perfect fifth and a major third, and a minor sixth is a compound of a perfect fourth and a minor third.) These rules can be represented by tree structures.

Figure 1

If we wish to cross match corresponding points in the two structures we have two choices. We can match a major third with red and a minor third with green, or we can match a major third with green and a minor third with red. If we match red to the major third, we can construct Table 3, in which symmetrically opposite notes are assigned colours which cancel each other out to produce white, in the same way that the intervals combine to make an octave.

For each step up from C we add red, for each step down from C we add blue-green, for each step to the left from C we add blue, and for each step to the right from C we add yellow.

Table 3

The assignment of colours to notes which results when yellow, blue, red and green are linked to the perfect fifth, perfect fourth, major third and minor third respectively.
Code: b = blue, y = yellow, r = red, g = green.

D# 3b 3r	A# 2b 3r	E# b 3r	B# 3r	Fx y 3r	Cx 2y 3r	Gx 3y 3r	Dx 4y 3r
B 3b 2r	F# 2b 2r	C# b 2r	G# 2r	D# y 2r	A# 2y 2r	E# 3y 2r	B# 4y 2r
G 3b r	D 2b r	A b r	E r	B y r	F# 2y r	C# 3y r	G# 4y r
Eb 3b	Bb 2b	F b	C	G y	D 2y	A 3y	E 4y
Cb 3b bg	Gb 2b bg	Db b bg	Ab bg	Eb y bg	Bb 2y bg	F 3y bg	C 4y bg
Abb 3b 2b2g	Ebb 2b 2b2g	Bbb b 2b2g	Fb 2b2g	Cb y 2b2g	Gb 2y 2b2g	Db 3y 2b2g	Ab 4y 2b2g

The numbers refer to the quantity of colour. Thus "2yr" for F# means 2 parts yellow, one part red.

When opposing blues and yellows assigned to a note are allowed to cancel each other out appropriately, we get Table 4. For example, for Eb the yellow and blue cancel each other out to make white, leaving the colour for Eb as green. Sharp notes are predominantly purple, red and yellow while flat notes are predominantly blue and green.

Table 4

D# 3b3r	A# 2b3r	E# b3r	B# 3r	Fx y3r	Cx 2y3r	Gx 3y3r	Dx 4y3r
B 3b2r	F# 2b2r	C# b2r	G# 2r	D# y2r	A# 2y2r	E# 3y2r	B# 4y2r
G 3br	D 2br	A br	E r	B yr	F# 2yr	C# 3yr	G# 4yr
Eb 3b	Bb 2b	F b	C	G y	D 2y	A 3y	E 4y
Cb 4bg	Gb 3bg	Db 2bg	Ab bg	Eb g	Bb yg	F 2yg	C 3yg
Abb 5b2g	Ebb 4b2g	Bbb 3b2g	Fb 2b2g	Cb b2g	Gb 2g	Db y2g	Ab 2y2g

If green is linked to the major third and red to the minor third and opposing blues and yellows assigned to a note are allowed to cancel each other out appropriately, we get Table 5, in which sharp notes are predominantly yellow and green, and flat notes are predominantly blue and red.

Table 5

D# 3b3g	A# 2b3g	E# b3g	B# 3g	Fx y3g	Cx 2y3g	Gx 3y3g	Dx 4y3g
B 3b2g	F# 2b2g	C# b2g	G# 2g	D# y2g	A# 2y2g	E# 3y2g	B# 4y2g
G 3b g	D 2bg	A bg	E g	B yg	F# 2yg	C# 3yg	G# 4yg
Eb 3b	Bb 2b	F b	C	G y	D 2y	A 3y	E 4y
Cb 4br	Gb 3br	Db 2br	Ab br	Eb r	Bb yr	F 2yr	C 3yr
Abb 5b2r	Ebb 4b2r	Bbb 3b2r	Fb 2b2r	Cb b2r	Gb 2r	Db y2r	Ab 2y2r

In both tables the ring of keys around C (E B G Eb Ab Db F A) corresponds approximately to the colour circle. The difference between colours such as yellow for G and 2 x yellow for D is presumably one of greater saturation. There is evidence that supersaturated yellow is perceived as brown (Boynton, 1979).

Table 4 seems preferable to the writer as it accounts, for example, for Wagner’s choice of the key of Eb major for the Rhinegold prelude to match the green waters of the Rhine, or the intensification of excitement by the modulation from the key of C major to E major at the end of Ravel’s Bolero (white to red), or the minor third which begins Greensleaves, or the move from a cool key (Bb major - blue) to a warmer key (A major - purple) to represent sunrise in Richard Strauss's Alpine Symphony. (Of course, contrary examples can probably be found.) Table 4 also seems intuitively preferable, as to the writer a major third sounds warmer than a minor third.

A third dimension corresponding to brightness can be imagined perpendicular to the page.

Notes an octave apart have the same hue but differ in brightness. Enharmonic equivalents such as C# and Db have different hues but the same brightness.

Table 6 below shows Table 4 as a colour display. No attempt has been made to control colour saturation or brightness.

Table 6

Fifths-thirds space interpreted as a colour display. No attempt has been made to control colour saturation or brightness.

D#	A#	E#	B#	Fx	Cx	Gx	Dx
B	F#	C#	G#	D#	A#	E#	B#
G	D	A	E	B	F#	C#	G#
Eb	Bb	F	C	G	D	A	E
Cb	Gb	Db	Ab	Eb	Bb	F	C
Abb	Ebb	Bbb	Fb	Cb	Gb	Db	Ab

Other Models of Musical Pitch

The theory presented here was worked out before the publication of the musical pitch models of Shepard (1982), Krumhansl (1990) and Lerdahl (2001).

All three models assume the identity of enharmonic equivalents such as F# and Gb and therefore do not lend themselves to a matching of notes and colours. All three models are concerned with relatedness in music but not with musical semantics.

Colour-Music?

The thought will probably occur to some readers that a way of testing the Table 4 and Table 5 theories would be to make animated sequences of colours to represent melodies, thus producing a visual analogue of music.

While rhythm can be represented visually, it is doubtful that the harmonic half of music can. First, since pitch height corresponds to brightness (Marks, 1974,1975) there is the problem of producing a very wide grey scale. A semitone is much more than a just noticeable difference in pitch and it would be very difficult to represent, say, three octaves with 36 obviously difficult levels of brightness.   Alternatively, but less satisfactorily, pitch height cold be represented as physical height in a display, or as size (low notes bigger, high notes smaller), or as both.

Secondly and more importantly, there is almost certainly more to the semantics of musical notes than colour.   Green may represent the subdued quality of a minor third but there is no reason to think that it represents its pathos.   Blue is the colour traditionally associated with melancholy. Colours do not show the stability of musical intervals, or the gravitational pull the tonic exerts on the leading note.
In the writer’s view, musical notes have six or seven qualities:

• Simple pitch height above the tonic
• Hedonic quality (major/neutral/minor)
• Stability
• Primary vs compound
• Resolves up vs resolves down
• Number of semitones between a note and the note it resolves to
• Colour

However, for the curious, here is one attempt to represent musical notes visually. The music is the first prelude from J.S. Bach’s The Well Tempered Clavier, script by Ian Firth, andanimation by the Vivid Group.

Musical Keys and Colours

Many musicians have linked musical keys to colours (Scholes, 1970).  From Table 6 we can read off a colour to match any keynote. The available evidence, which is largely anecdotal, indicates that everyone is different in matching keys to colours. This may be due to erroneous early learning, as key-colour associations are often formed during childhood.  Or it may be due to the association of a colour with a particular composition written in a key, carried over to the key. Or it could be due to linking a change of key to a colour, rather than the new key itself.

The writer agrees with those musicians who think that minor keys have the same hues as major keys but are darker. The darkness may arise from the pitch-brightness parallel (Marks, 1974, 1975) and the fact that a minor scale is constructed by lowering the third, sixth and sometimes seventh notes of the major scale by a semitone.

Key-colour associations are the commonest form of synaesthesia in music. This might be because a change of key has only two properties:  the musical pitch difference between the old and new keys (e.g. up or down a perfect fifth) and a colour change. Note-colour associations appear to be much rarer, and this might be because notes have multiple qualities, some possibly more salient than colour.
Research is needed into how key-colour associations are formed. Vernon (1930) gives a useful description of how he came to link keys to colours.

Enharmonic Modulations

An enharmonic modulation is a change of key which assumes that the enharmonic equivalents are identical. For example, the key of Db is suddenly re-notated  as C#, which then moves to F#.  Acoustically enharmonic equivalents are the same on the piano but differ slightly on stringed instruments (Piston, 1950). The use of enharmonic modulations by great composers, particularly in the 19th century, suggests that colour (if it is linked to music) is not an important aspect of musical structure.

The Incidence of Key-Colour Associations

Cuddy (1985) suggested that the incidence of music-colour associations among musicians may be about 12%.

In one experiment carried out by the writer using 39 music students as subjects (11 of whom had absolute pitch)  seven (18%) had pre-existing key-colour associations. In a second experiment using 21 music students and musicians as subjects, all of whom had absolute pitch, seven (33%) had pre-existing key-colour associations.

Both experiments were carried out in Sydney. These numbers suggest that in any large city in the developed world,  it would be possible to accrue, over time, enough subjects to make a worthwhile  investigation of how key-colour associations are formed. Subjects with absolute pitch and key-colour associations would be harder to find than those without absolute pitch.  The subjects in the second experiment were young people mostly living in the northern suburbs of Sydney (population four million). Presumably subjects with absolute pitch and key-colour associations could be found in other regions of Sydney and among older musicians. If a subgroup with key-colour associations and absolute pitch is to be studied,  it could be risky as a thesis topic as the anticipated numbers might not eventuate, but other researchers might like to consider trying.  

Need for Data

The theory should not be accepted as true without supporting data, which may be difficult to obtain. Research carried out by the writer was inconclusive, that is, there was a trend in favour of the theory which did not reach statistical significance.  Much more research is needed.

Conclusion

The question remains of how a parallel between colours and keynotes, if it exists, could arise. Most psychologists at present would probably favour an explanation in terms of the evolution of human perceptual systems, and music and evolution is a topic currently receiving attention from music psychologists. Plato might have seen in it a reflection of a non-physical reality. Taoists might see in it a complex manifestation of the cosmic forces of yin and yang (flat notes yin, sharp notes yang, cool colours yin, warm colours yang).  The writer thinks that there may be some substance in the ancient belief that there is something cosmic about music but this would be very much a minority view.

Address for Correspondence

Critical comments are invited and should be sent to:

Ian C. Firth
Unit 9, 52-56 Goderich Street
East Perth WA 6004
Australia

References and Sources

Aristotle (1984). Sense and sensibilia.  In The Complete Works of Aristotle, Volume 1, pp 693-713.  Princeton, NJ: Princeton University Press.

Boynton, R.M. (1979). Human Color Vision.  New York:  Holt, Rinehart & Winston.

Cooke, D. (1959). The Language of Music.  London: Oxford University Press.

Cuddy, L. (1985).  The color of melody.   Music Perception, Vol 2 No 3 pp 345-360.

Firth, I.C. (1981).  On the linkage of musical keys to colours.   Speculations in Science and Technology, Vol 4, 501-508.

Firth, I.C. (2005). Keys and colours in Das Rheingold. (Unpublished paper)

Firth, I.C. (2005) Musical key perception in relation to colour. (Unpublished paper)

Krumhansl, C. (1990). Cognitive Foundations of Musical Pitch.  New York: Oxford University Press.

Lerdahl, F. (2001) Tonal Pitch Space.  New York: Oxford University Press.

Longuet-Higgins, H.C. (1962a) Letter to a musical friend.  Music Review, 23, 271-80.

Longuet-Higgins, H.C. (1962b) Second letter to a musical friend.  Music Review, 23, 271-80.

Longuet-Higgins, H.C. (1987). Mental Processes: Studies in Cognitive Science.   Cambridge, Mass.: MIT Press.

McClain, E.G. (1978). The Pythagorean Plato.   Stony Brook, NY.: Nicolas Hays.

Marks, L.E. (1974) On associations of light and sound: the mediation of brightness, pitch and loudness  American Journal of Psychology, 87, 173-188.

Marks, L.E. (1975). On colored hgearing synesia: cross modal translations of sensory dimensions.  Psychological Bulletin, 82(3), 303-331.

Newton, I.(1730/1952) Opticks. New York: Dover.

Peacock, K. (1985). Synesthetic perception:Alexander Scriabin’s color hearing.  Music Perception, 2, 483-505.

Piston, W. (1950). Harmony. London: Gollancz.

Scholes, P. (1970). Colour and Music, in The Oxford Companion to Music, pp 202-210.  Oxford: Oxford University Press.

Shepard, R.N. (1982). Structural representations of musical pitch.   In Diana Deutsch (ed.) The Psychology of Music, First Edition, pp 344-390. London and New York: Academic Press.

Steblin, R. (1983).  A History of Key Characteristics in the Eighteenth and Early Nineteenth Centuries.  Ann Arbor, Michigan: UMI Research Press.

Vernon, P.E. (1930).  Synaesthesia in music.  Psyche, Vol 10, pp 22-40.