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

© Copyright Ian C. Firth 2007

Related sites:

home.vicnet.net.au/~colmusic/

www.paradise2012.com/visualMusic/musima

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, numerous contrary examples can 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?

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 ranging 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 different levels of brightness. Alternatively, but less satisfactorily, pitch height could 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 much more to the semantics of musical intervals than colour. Green may represent the subdued quality of a minor third but there is no reason to think that it represent its pathos. Blue is the colour more often 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 6 or 7 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, and animation by the Vivid Group.

Musical Keys and Colours

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.

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.

Need for Data

Conclusion

Ian C. Firth, 2007
Unit 9, 52-56 Goderich Street,
East Perth WA 6004
Australia

References

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

Firth, I. C. (1981). On the linkage of musical keys to colours. Speculations in Science and Technology, 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, 244-48.

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, N. Y.: Nicolas Hays Ltd.

Marks, L. E. (1974). On associations of light and sound: the mediation of brightness, pitch and loudness. American Journal of Psychology, 87, 173-88.

Marks, L. E. (1975). On colored hearing synesthesia: cross-modal translations of sensory dimensions. Psychological Bulletin, 82(3), 303-31.

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

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

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.

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