While you live, shine,
Have no grief at all;
Life exists only for a short while,
And time demands its toll.

This piece of music, the first complete musical manuscript for which we have a living record today, was carved into a tombstone somewhere between 200 BC and 100 AD. The song, written in honor of a deceased wife, is as rich in what it reflects of the history of our musical thought as it is in what it expresses of its composer’s emotion and sentiment.

We find in its notation three layers of symbolism. The top layer describes the rhythm of the song. The bottom layer gives us the lyrics of the song. It is the second layer where we’ll focus our attention today. The second layer is the series of pitches intended to be played. The system here uses the alphabet used by the Greeks at the time – one recognizable as an ancestor of our own – to indicate the different pitches. ‘C’ is one note, ‘Z’ is another note; a system that seems notably standardized and recognizably similar to how we express notes today.

The musical sophistication manifested in the Song of Seikilos would not have been possible without centuries of thought, innovation, and collaboration. One of the most pivotal figures in this process was Pythagoras of Samos.

Pythagoras formed around himself and his school a body of work in the 6th century BC that enriched and progressed Western thought in almost countless ways – in mathematics, astronomy, philosophy, ethics, and numerous other fields. His work in music theory spanned all the fields above, and illuminates the past to reveal much of our present music.

Though the alphabet of musical notation used on the Seikilos epitaph – the same Pythagoras worked with – seems foreign, it’s translates simply into our modern alphabet:

First notes of the Song of Seikilos in its original Greek alphabet:  C   Z   Z   K    I   Z
First notes of the Song of Seikilos in our modern alphabet:           A   E   E   C#  D  E

For ease of discussion, we’ll consider Pythagoras’s work using our modern musical alphabet, as well as our modern words for musical terms.

One of Pythagoras’s central beliefs was the notion that all of celestial harmony, the beautiful movements of planets and stars, could be explained with the simple numbers 1, 2, 3, and 4. This notion informed the basis of his musical theory as well, and manifested in how Pythagoras experimented with a tool called the ‘monochord.’

The monochord, or ‘single string,’ was a single string stretched out, which one could pluck to create a pitch (not unlike a single guitar string). He would clamp this single string at different lengths, allowing different portions of the string to vibrate, creating a multitude of pitches with a single string. This is the same idea that allows a guitarist to produce different pitches from a single guitar string.

Let’s say the monochord was tuned to ‘A’, meaning that when the open string is plucked, the pitch ‘A’ is created. Recalling that every pitch exists in many different octaves, we can call this particular pitch, ‘A1’, meaning that it is in its lowest octave. Pythagoras would call this initial pitch, that of the full string, the ‘fundamental.’ (This isn’t our first time discussing the fundamental – recall its physical characteristics from .)

The sound of this string being plucked:

Pythagoras would then brace the string at half of its length, and pluck only one half of it, creating a new pitch.

The sound of this new pitch, in relation to the pitch of the full string being plucked:

The pitch created is clearly different from the first, yet somehow sounds the same. Pythagoras would use the same letter to represent this note, and say that it was the same note an ‘octave’ higher. We can call this note A2.

Pythagoras would then brace the monochord at one third of its length, and pluck the two-thirds side of the string.

The sound of two-thirds the total string being plucked, again in relation to the fundamental pitch.

This length of string is longer than that of A2, and so sounds like a lower pitch. Pythagoras would call this pitch the ‘dominant.’ We can also call it E1, an ‘E’ note in the same octave as the full-string fundamental.

Pythagoras would finally brace the monochord string at one quarter of its length, plucking the three-quarters length.

The sound of three-quarters the total string being plucked, in relation to the fundamental.

This string length is just a tad bit longer than the string that created E1, and so the pitch this string length generates is just a bit lower than E1. Pythagoras would call this pitch the ‘subdominant,’ and we would also call it D1.

The fundamental, octave, dominant, and subdominant. So simple a method to reach them, yet such a profound course of history leading up to it. These pitches, and their relationship to the fundamental, created a lattice of musical understanding that we still use today. The octave, dominant, and subdominant will always sound particularly consonant with their fundamental – we call them ‘concords.’ So, as in our example above, E and D are concordant with A. This was the foundation of an understanding of pitch when the Song of Seikilos was written.

Let’s examine the Song of Seikilos again, this time emphasizing the pitch relationships it is built on. The note A is the fundamental, E the dominant, and D the subdominant.

A E E C# D E D C# D E D C# B A B G A C# E D C# D C# A B G A C# B D E C# A A A F# E

The Song of Seikilos contains 37 total notes, and all but 14 of these are concords. These other 14 notes created tension. We call these notes, which are not con cordant, dis cordant. Notice how tension increases in the middle of the song with the use of more discords; the heavy usage of the fundamental particularly serves to resolve the tension for the song’s conclusion.

Listen again to the Song of Seikilos – perhaps you can hear its subtle creation and resolution of melodic tension. For the Greeks, melody was always in service to the lyrics. How does the use of concords and discords illuminate the lyrics in this song? The particular tetrachord structure at use here was traditionally held as one expressing moderation – does the song express moderation to you?

So much care and thought to create such a simple song. And still, we have more to discover. As in the illustration above, we can see the relation that A has to E and D – is there a deeper relationship between D and E? And where do the discordant notes come from? Where did those #’s come from?

Continue our journey with Pythagoras in the next Music Monday – “Plucky Pythagoras, Part 2″