The Sound of the Rainbow

Reflections on Beethoven, Wagner, Ligeti, and Wyschnegradsky

Rainbow, South Uist, Hebrides, © Lodewijk Muns 2018
South Uist, Hebrides, August 2018

Rainbow and Ranz

A “merry gathering of country folk” is interrupted by a rainstorm. When the rain and thunderclaps recede, a brief chorale-like phrase, as a heart-felt Thank God!, makes the transition to the finale of Beethoven’s Pastoral Symphony (nr. 6). The clarinet intones a kind of signal, a ranz des vaches or Kuhreihen, as was used in the Alps to gather the herd for milking. Then the horn takes over, and it feels as if sunshine spreads over the land: the sound of the horn gives a sense of spaciousness. The simple, repeated ranz motif is spun out into a peaceful shepherd’s song (Hirtengesang) by the violins. And a rainbow appears over the landscape.

At least, that’s what I had always imagined, prompted by the programme notes. But the authority for the rainbow’s appearance is obscure. There is no mention of it among Beethoven’s own very summary indications.

A rainbow is maybe the most intrinsically visual phenomenon we could think of: it exists only for the eyes. How can a rainbow be represented in music? And is it true that this occurs in the Pastoral Symphony?

The most distinctive features of the rainbow are its arc form, the colour spectrum, and transparency. It is hard to imagine how this could convincingly be represented with musical means. Maybe an ‘arching’ melody might be part of it. ‘Melodic arc’ (or ‘arch’) is a conventional term for a melody that rises and falls. But this doesn’t fit the Hirtengesang very well. Even less, however, the preceding chorale phrase (which is in fact a transformation of the motif that announced the storm): it just goes down. The often repeated opinion that precisely this phrase represents the rainbow (Knapp 2000: 318) seems to me entirely unconvincing.

And yet, the accompaniment of the ranz melody, with a pendulating figure in the first violins and repeated chords in the winds, produces a sound effect that might be described as ‘glistening’. That is an odd kind of onomatopoeia: it translates a visual phenomenon into the auditory domain of speech (the proper term is ‘phonestheme’). And although a rainbow doesn’t actually glisten, the musical glistening suggests the related phenomena of sparkling light and moisture. Not quite a rainbow, but at least a good occasion to think of one.


Richard Wagner must have had the same idea, because the music that he provided for the appearance of the rainbow near the end of Das Rheingold is (obviously, I think) modelled on Beethoven’s glistening orchestration. Wagner’s stage direction  reads:

Suddenly the cloud clears; […] with dazzling radiance a rainbow bridge stretches across the valley to the castle, which now shines in the evening sun. (My transl.)

Richard Wagner, Das Rheingold (1854)

To a rather dull triadic melody line in the low register Wagner adds, like Beethoven, a pendulating movement and repeated chords in threes. But here the movement is spread over all the violins (divided in eight groups), plus the extravagant ensemble of six harps. In private Wagner confessed that the harp was the only instrument of which he had no technical knowledge. He thought of having the parts altered in this place, because “the effect of the harp is like a cloud of incense” (Wagner 1876: 771, my transl.).

The graphic appearance of this passage on the page is maybe more startling than the sound effect. Mässig bewegt is the tempo indication, but this ‘moderate movement’ of the bass line and sound mass as a whole comprehends a faster micromovement in the individual parts. Ironically, in this case where the rainbow is visible on stage, the base line doubles this symbolically by displaying an arc form, or rather an arched series of arches.

Watercolour Jazz

‘Micromovement’ (or ‘micropolyphony’) and ‘sound mass’ are concepts associated with some of György Ligeti’s best known works. His piano etude Arc-en-ciel (Book 1, nr. 5, 1985) is too slow and thinly textured however to display these features. It may owe its title to its ethereal, floating character, and maybe its ‘shimmering’ chord structures. As we may try in vain to find the borders of the rainbow’s colours, the chords individually sound jazzy (in the manner of Bill Evans), but get blurred in the polyrhythmic groupings. These groupings are hard to follow by ear, particularly given the piece’s slow tempo. (The original manuscript edition gives a metronome tempo which is 1.3 times faster – 56 for the eighth note, instead of 84 for the sixteenth!) The jazz connection is strengthened by the composer’s indication with swing. In none of the recordings I’ve heard the pianist actually performs it this way.

It has been suggested that the piece has “a general arc-like contour” (Quinnett 2014: 48), but its initial descent and final ascent would at best represent an inverted (reflected?) rainbow. Most convincingly, the music’s final ‘fading away’ in diminishing intervals in the highest register might suggest the rainbow’s untraceable, transparent endpoints. Ligeti’s titles however are known not to have great significance, and I don’t think we should overemphasize the pictorial aspect of this music.

Angelica Kauffman: Colour
Angelica Kauffman, Elements of Art: Colour, ceiling painting in the Royal Academy of Art, London, ca 1779. The art of painting fills her palette with colours from the rainbow. At her feet is a chameleon.

The Omnicoloured Arc

Both the arc and the colour spectrum play a role in Arc-en-ciel (1956) by the Russian-Parisian composer Ivan Wyschnegradsky (1893-1979). It exists in two versions, one with opus nr. 37, and a second, unfinished, op. 56a. Both are written for six pianos which are each tuned a little differently; together they fill out the octave in twelfth tones, instead of the regular semitones.

Wyschnegradsky’s sound world and arcane philosophy (no pun intended) have been strongly influenced by those of the idol of his youth, Skryabin. That includes a fascination with the synesthetic association of colour and pitch, as well as a tendency towards mystical grandiosity.

The colour spectrum is continuous, though perception and linguistic habits divide this continuum in distinctly labelled colours. A painter doesn’t pick selected colours to make a scale, unless she has to work with colour pencils or crayons (and there is no standard for that). The domain of pitch, on the other hand, is not usually approached as a continuum. All over the world musicians use scales of five to twelve pitches. Anything in between is ‘out of tune’.

Wyschnegradsky however felt he had to come closer to a continuous musical ‘space’ by dividing the pitch continuum into smaller intervals than the usual semitones. This way arrived at a tuning that he called ‘ultrachromatic’ (‘chromatic’ referring to the semitone scale; the fact that the Greek ‘chroma’ means ‘colour’ may be considered a quirk of etymology).

The different tunings of the six pianos in Arc-en-ciel II are brought into correspondence with six colours (red, orange, yellow, green, blue, purple). But the composer acknowledges that “No physical or psycho-physiological law has forced me to associate a colour with a specific pitch”, according to the score fragment helpfully reproduced on the handsome website dedicated to the composer.

Also, in these pieces Wyschnegradsky replaced ‘octave equivalence’ with that of the major seventh. That means that the scale is repeated not every octave (as in practically all music) but at a slightly smaller interval. Described with a geometrical analogy, this should present a “curved space” (Barthelmes 2010).

Though the rainbow may have been an inspiration in the creation of the composer’s musical system, these compositions are even less than Ligeti’s etude of the same title a sonorous image of the rainbow. Most listeners will tend to hear this music as weirdly out of tune. But its ultrachromatic sonorities can be heard as an extension of Skryabin’s late-romantic, chromatic sound world, that has almost seamlessly developed out of that of Chopin. As for pictorial associations – I tend to see coloured incense and stained glass, rather than a rainbow.


Barthelmes, Barbara. 2010. Komponieren im Raum-Zeit-Kontinuum: Ivan Wyschnegradskys Komposition “Arc-en-ciel”. SWR.

Knapp, Raymond. 2000. “A Tale of Two Symphonies: Converging Narratives of Divine Reconciliation in Beethoven’s Fifth and Sixth.” Journal of the American Musicological Society 53 (2): 291.

Quinnett, Lawrence. 2014. Harmony and Counterpoint in the Ligeti Etudes, Book I: An Analysis and Performance Guide. Florida State University.

Wagner, Cosima. 1976. Die Tagebücher. Vol. 1. München: Piper.