3: A double history of harmony (Pythagoras and late medieval music c.1150-1250)

BBC Radio 3 - Sunday Feature, Harmony of the Spheres

Harmony, Harmonia, harmonious, harmonic, harmonica, harmonium, harmonise – what is harmony, and why do we care? Harmony is often mischaracterised as ‘a harmony’ to mean a melody played over the top of a main melody (especially in popular music), but harmony and melody are quite separate things: melody is the lateral relationship between pitches (i.e. one thing after another), whereas harmony concerns the ‘vertical’ relationship between different pitches played simultaneously.


Like listening whilst you read? You can find today’s listening at the bottom of the page.


A union of opposites

Since Ancient Greece, Europeans have been carving up harmonic relationships into consonance (or concord, notes that sound stable when played together) and dissonance (or discord, notes that sound unstable, as if prompting a resolution to something stable). The Greeks even personified these tendencies in their gods: Harmonia (whom the Romans named Concordia) was the goddess of serene balance, whereas Eris (Discordia to the Romans) was the goddess of strife (one can imagine the dissonant tones ‘disagreeing’). Notice below how Eris (left) appears strangely content whereas Harmonia (right) looks vaguely troubled? Food for thought…

Why this opposition between consonance and dissonance? The Greek philosopher Pythagoras and his followers understood the universe to be structured by patterns and harmonious relationships. He discovered that if the lengths of strings were in simple ratios (say, 10 cm:20 cm, i.e. 1:2) they would make a harmonious, pleasing sound that would resonate clearly. If the lengths were not in simple ratios (say, 99:106) then discord would follow.

Pythagoras on the Purpose of Life and the Meaning of Wisdom ...

It could be argued that the Greeks created the categories of consonance and dissonance as a sort of social construction, determined merely by whim or cultural preference. Pythagoras’ discovery suggested otherwise: we can sense the physical relations between frequencies and universally apprehend the stability (perhaps sweetness) of simple ratios and the instability (perhaps sourness) of complex ratios. Our emotional response to music, therefore, has some basis in objective physical relationships.

In my first post, I highlighted how Greek mythology represented the universe as a dialogue between order and chaos, and that music embodied a pure form of this dialogue. Consonance and dissonance are yet further manifestations of this balance: too much stability and a piece lacks life and dynamism, too much instability and it falls apart entirely (much as the balance of bitter ingredients can either transform or ruin a dish).

Pythagoras’ discovery prompts a similar reflection on the relationship between physics/mathematics (let’s call it rationality) and our emotions (let’s say irrationality): that emotions can be rendered logical through patterned beauty, and that mathematical proportions can be rendered emotional through sound. How mysterious that the reconciliation of these opposites forms the basis for some of our deepest artistic and spiritual experiences.

Music of the Spheres, Harmony of the Spheres - Celestial Spheres ...

The Notre Dame School (12th-13th centuries)

Last post I introduced the flowing beauty of medieval plainchant and discussed how the invention of sheet music cleared a path for composers to produce more complex work. Despite written evidence that the Greeks used harmony in their music, it was only circa 1150 (and even then, almost exclusively around Paris) that composers routinely composed for multiple voices (poly-phony, polyphony), and hence multiple pitches.

An 800-year history of Paris's Notre Dame Cathedral
Notre Dame Cathedral: the home of medieval harmony

Whenever men and women (or children) have sung together, octaves (the simplest ratio, 2:1) have been a part of music. This Notre Dame School was remarkable for taking the first tentative steps into more complex ratios between notes: what we now call fifths (3:2) and fourths (4:3), the first step on a millenium-long journey which would peak in the wild dissonances of the 20th century.

Last post, I referred to music’s first revolution: the invention of notation. In my estimation, the movement from monophony to polyphony, with its infinite expressive potential, was music’s second revolution. It is to music what the development of three-dimensional perspective was to fine art, or what the addition of colour is to a pencil sketch. Suddenly, music had a platform from which to dive into ever-deeper expressive waters.

The Last Supper: The Greatest Masterpiece of the Renaissance
Da Vinci’s The Last Supper (1495-8, enhanced): art in three dimensions

Below is an example of what early polyphony sounded like. You will no doubt hear the flowing qualities that were typical of medieval plainchant, though you may find these early harmonic experiments a little austere. Nevertheless, these chants have a meditative simplicity which is unique to the period.

For contrast, contemporary composer Ola Gjeilo’s Ubi Caritas (2012) refreshingly pairs medieval melody with modern harmony. The version below is recast for male voices only, highlighting the piece’s debt to medieval chant (which was sung almost exclusively by monks, rather than nuns). This performance similarly unifies tradition and modernity, with singers in casual clothes and a modern stairwell. This isn’t a cheap attempt to make classical music relevant, it naturally expresses the timlessness, and hence relevance, of musical beauty and its spiritual undercurrents.


Ubi caritas et amor, Deus ibi est.

Congregavit nos in unum Christi amor.

Exsultemus, et in ipso jucundemur.

Timeamus, et amemus Deum vivum.

Et ex corde diligamus nos sincero.


Where charity and love are, there God is.

The love of Christ has gathered us into one.

Let us exult, and in Him be joyful.

Let us fear and let us love the living God.

And from a sincere heart let us love each other (and Him).


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