Tropoi Music Theory

Understanding the Tropoi

In Western music, the octave is divided into 12 equal parts called semitones (or half-tones). However, Byzantine (i.e., Eastern Roman) music, which forms the foundation of many contemporary music systems in the Near and Middle East (including Greek, Turkish, and Arabic traditions, as well as Ottoman music), takes a more nuanced approach. Here, the octave is divided into 72 notes called twelfth tones (this small interval isalso known as a comma or a morio). This means each tone is split into 12 parts instead of two, effectively adding five extra microtonal steps between each semitone.

To better understand these divisions, we can use the cent system, where an octave is divided into 1200 cents. In this system:

Semitones occur every 100 cents
Twelfth tones occur every 16.667 cents

To demonstrate these differences, we present variations of the Rast pentachord. The Rast pentachord consists of five degrees:

Root: 0 cents
Second degree: 200 cents
Third degree: variable (400 cents in Western music)
Fourth degree (perfect fourth): 500 cents
Fifth degree (perfect fifth): 700 cents

Let's explore the variations of the Rast pentachord, each with a different tuning of the third degree:

Standard Western Tuning (400 cents)

This is the standard Western tuning with the third degree at 400 cents, which you might be most familiar with from Western classical and popular music. This creates a major third interval.

One Twelfth Tone Lower (383 cents)

Here, we lower the third degree by one twelfth tone to 383 cents, creating a subtle but noticeable difference in the character of the melody. This tuning most closely aligns with the perfect 5/4 ratio of the natural major third.

Two Twelfth Tones Lower (367 cents)

With the third degree lowered by two twelfth tones to 367 cents, we begin to hear a more distinct Eastern character in the melody.

Three Twelfth Tones Lower (350 cents)

This variation lowers the third degree by three twelfth tones to 350 cents, creating what is known as a neutral third. This interval is characteristic of many tropoi and creates a distinctly Eastern sound.

Traditional Greek Birthday Song Example

To hear these microtonal differences in a familiar context, here's the traditional Greek birthday song in the Rast Tropoi. This version is tuned with the traditional Byzantine approach, where the major third is lowered by two commas (367 cents), giving it that characteristic Eastern Mediterranean sound that's distinct from Western major scales.