Thinking in circles

Katrina DowlingMusicLeave a Comment

I might be the only one. Often when I see a circle, it makes me think of medieval music and then medieval music makes me think of the Trinity. Perhaps I’d better explain…

There’s a long and complex history to Western musical notation and both the practice and the thinking it reflects, but I’ll jump in at the fourteenth century, at a point at which innovations in notation mean that more information is being written down in a piece of music than previously, and then I’ll suggest how this notation reveals something of the practice and understanding of music going back to the early middle ages and even to ancient Greece. And how all of it is related to the Trinity.

Let’s meet the notes that represent the most commonly used musical durations – they are simply called long and short duration:

longa longa (‘long note’)

brevis brevis (‘short note’)

The relationship between the note values (durations) of longa and brevis is called tempus. There could be a ratio of either two or three short notes to a long note:

ratio tempus perfectum


ratio tempus imperfectum

If it’s a complex piece and if the notation is serving to communicate to someone at a distance, who hasn’t been able to learn the music at first hand, then the singer is faced with a page full of longs and shorts and has to count them up to figure out whether two or three shorts go into a long. I remember doing this myself when I was first learning to play medieval music from facsimiles. When you get a group of nine short notes, you know that the relationship is three to one!

The tempus can change many times throughout a piece of music, too. So composers began to include little signs in the music to indicate the tempus. The relationship of three short notes to one long note is signified by a circle, which looks whole and perfect:

tempus perfectum tempus perfectum (‘perfect division’)

The other ratio, two short notes to one long note, is signified by a broken circle:

tempus imperfectum tempus imperfectum (‘not perfect division’)

And the life of the singer is made so much easier by the inclusion of these symbols at the start of the music and wherever the tempus relationship changes. You can see the tempus signs towards the top left of each of these snippets of music:

tempus perfectum

tempus perfectum

tempus imperfectum

tempus imperfectum

Now the colourful terms tempus perfectum and tempus imperfectum reveal a legacy that goes back to classical antiquity. In Aristotelian thought, the number three is suggestive of unity, because it can’t be divided in half the way an even number can. Since unity and wholeness are valued, things having a tripartite quality are thought to be perfect. The early Christians were heirs to the great thinkers of antiquity and saw, in this idea, a reflection of the nature of God as three in one. In fact, throughout the early centuries of the middle ages, the love of three-ness was so great that there was a strong preference for singing in rhythmic relationships of threes.

For both Aristotle and medieval philosophers such as Augustine and Boethius, a tripartite rhythmic relationship in music is not merely a symbol of unity and wholeness, a sort of purely intellectual reference to a concept, but it is a sign or revelation of the nature of things. For them, mathematics speaks of the numerical qualities that are very real qualities of every thing in the cosmos, and music is a type of mathematics – it is the mathematics of numerical qualities made tangible.

So, right there in a little trace of ink on an old page of music, we have what is both a symbol and a sign. The circle is a symbol that represents tempus perfectum. Both the circle and the tempus it refers to are signs of the nature of wholeness and Trinity that, as Boethius would say, resonate throughout the music of the spheres, the music of the body and the music that sounds from instruments.

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